Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like kmeans and its wide family of variants are still widely used, all of them require the number of clusters (k) to be supplied as input, and many are notably sensitive to initialization. Convex clustering provides a more stable alternative by formulating the clustering task as a convex optimization problem, ensuring a unique global solution. However, it faces challenges in handling high dimensional data, especially in the presence of noise and outliers. Additionally, strong fusion regularization, controlled by the tuning parameter, can hinder effective cluster formation within a convex clustering framework. To overcome these challenges, we introduce a robust approach that integrates convex clustering with the Median of Means (MoM) estimator, thus developing an outlier resistant and efficient clustering framework that does not necessitate a prior knowledge of the number of clusters. By leveraging the robustness of MoM alongside the stability of convex clustering, our method enhances both performance and efficiency, especially on large scale datasets. Theoretical analysis demonstrates weak consistency under specific conditions, while experiments on synthetic and real world datasets validate the method’s superior performance compared to existing approaches.

Small Language Models (SLMs) offer efficient and practical alternatives to large-scale models in resource-constrained environments. We present a principled framework for constructing SLM ensembles that jointly optimize three competing objectives: prediction accuracy, output diversity, and fairness. Our method combines an interpretable cost-function formulation with a multi-objective evolutionary algorithm to discover Pareto-optimal ensemble configurations. We further introduce a two-stage combiner that produces diverse candidate responses and selects final outputs via embedding-based semantic consensus. Experiments on the MentalChat16k mental-health dialogue dataset show that the best-performing SLM ensemble configurations can match or surpass a fine-tuned Llama 3.1 70B model, achieving improvements of 0.86% in ROUGE-1, 5.84% in ROUGE-2, 4.93% in ROUGE-L, and 7.01% in semantic similarity. These results indicate that strategically orchestrated ensembles of small models can offer competitive or superior performance to significantly larger LLMs, while providing greater flexibility, interpretability, and accessibility for researchers operating under limited resources.

Despite notable progress in domain adaptation for classification, regression-based domain adaptation remains challenging, particularly in terms of handling complex data structures, ensuring cross-domain generalization, and maintaining the precision and mathematical rigor required to validate model effectiveness. Unlike classification tasks, which are more resilient to variations in feature scaling, regression tasks are notably more sensitive, making their performance more vulnerable in domain adaptation scenarios. In this paper, we propose a generalized regularization technique grounded in the Grassmannian manifold to address the feature alignment problem. This approach leverages the underlying manifold structure of the data while preserving mathematical bounds, thereby enhancing the precision and efficiency of problem-solving. To demonstrate the effectiveness of the proposed algorithm, we apply it to estimate multi-output parameters in two distinct domains: 1) the Arabidopsis thaliana plant dataset, collected from a high-throughput phenotyping platform at Palacký University, and 2) the publicly available dSprites shape recognition with six adaptation tasks. These tasks are critical to advance agricultural research and address generalization challenges in multi-output regression. Accurate predictions provide deeper insights into plant growth and health, thereby supporting more effective crop management strategies. We evaluate the effectiveness of our framework by comparing it with state-of-the-art regression alignment techniques that are independent of the underlying backbone and adaptable to transfer learning tasks. Experimental results show that our framework consistently outperforms existing methods,results description. The source code will be made publicly available upon acceptance at https://github.com/lingping-fuzzy.

In the rapidly advancing field of AI-assisted medical diagnosis, the generation of medical reports for Chest X-rays (CXR) has significantly improved with the increased availability of radiographs and their corresponding reports. However, these reports often contain complex medical terminology, making them difficult for patients and non-healthcare professionals to understand. In this study, we introduce a strategy called Chained Prompting for Improved Readability of Medical Reports (CPIR-MR), which translates original medical reports into more comprehensible language. Our primary contribution is the creation of a new extension to the IU X-Ray dataset, providing Simplified Medical Reports (SMRs) generated by CPIR-MR. Additionally, we demonstrate that standard methodologies can effectively produce these simplified reports by proposing a multi-modal text decoder (MTD) that combines BLIP with a classification network to generate simplified medical explanations (SMEs) when fine-tuned on SMRs.

Fairness in machine learning has become increasingly crucial, particularly in graph-based models where biased representations can reinforce societal inequalities. Traditional fairness-aware learning methods on graphs focus on graph rewiring, debiasing node embeddings, adversarial learning, and additional fairness constraints. However, these approaches often struggle to balance fairness and task performance. We propose a novel edge partitioning strategy that creates two distinct subgraphs, maintaining a balance between bias and diversity. We categorize edges as homophilic or heterophilic depending on the sensitive attribute of the corresponding node pairs. An edge is s-homophilic if it joins two nodes with the same sensitivity value, otherwise s-heterophilic. The partition splits the input graph into two subgraphs, both containing all nodes, one with only s-homophilic edges and the other with s-heterophilic ones. Using a Graph Neural Network (GNN), we obtain independent node representations from both graphs, which are then aggregated into a unified node embedding. To enforce fairness, we jointly optimize a primary task loss and a fairness loss, ensuring predictive accuracy and bias mitigation. We evaluate our approach on three benchmark datasets and find that it achieves improved fairness metrics while maintaining accuracy comparable to that of existing state-of-the-art methods.

Spectral clustering has proven effective in grouping speech representations for speaker diarization tasks, although post-processing the affinity matrix remains difficult due to the need for careful tuning before constructing the Laplacian. In this study, we present a novel pruning algorithm to create a sparse affinity matrix called spectral clustering on p-neighborhood retained affinity matrix (SC-pNA). Our method improves on node-specific fixed neighbor selection by allowing a variable number of neighbors, eliminating the need for external tuning data as the pruning parameters are derived directly from the affinity matrix. SC-pNA does so by identifying two clusters in every row of the initial affinity matrix, and retains only the top p% similarity scores from the cluster containing larger similarities. Spectral clustering is performed subsequently, with the number of clusters determined as the maximum eigengap. Experimental results on the challenging DIHARD-III dataset highlight the superiority of SC-pNA, which is also computationally more efficient than existing auto-tuning approaches. Our implementations are available at https://github.com/nikhilraghav29/SC-pNA.

Clustering stands as one of the most prominent challenges in unsupervised machine learning. Among centroid-based methods, the classic $k$-means algorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a well-known fact that $k$-means and its variants face several challenges, including heavy reliance on initial cluster centroids, susceptibility to converging into local minima of the objective function, and sensitivity to outliers and noise in the data. When data contains noise or outliers, the Median-of-Means (MoM) estimator offers a robust alternative for stabilizing centroid-based methods. On a different note, another limitation in many commonly used clustering methods is the need to specify the number of clusters beforehand. Model-based approaches, such as Bayesian nonparametric models, address this issue by incorporating infinite mixture models, eliminating the predefined cluster count requirement. Motivated by these facts, we propose an efficient and automatic clustering technique in this article by integrating the strengths of model-based and centroid-based methodologies. Our method mitigates the effect of noise on the quality of clustering while simultaneously estimating the number of clusters. Statistical guarantees on an upper bound of clustering error and rigorous assessment through simulated and real datasets suggest the advantages of our proposed method over existing state-of-the-art clustering algorithms.

Large Language Models (LLMs) have recently garnered widespread attention due to their adeptness at generating innovative responses to the given prompts across a multitude of domains. However, LLMs often suffer from the inherent limitation of hallucinations and generate incorrect information while maintaining well-structured and coherent responses. In this work, we hypothesize that hallucinations stem from the internal dynamics of LLMs. Our observations indicate that, during passage generation, LLMs tend to deviate from factual accuracy in subtle parts of responses, eventually shifting toward misinformation. This phenomenon bears a resemblance to human cognition, where individuals may hallucinate while maintaining logical coherence, embedding uncertainty within minor segments of their speech. To investigate this further, we introduce an innovative approach, HALLUSHIFT, designed to analyze the distribution shifts in the internal state space and token probabilities of the LLM-generated responses. Our method attains superior performances compared to existing baselines across various benchmark datasets. Our codebase is available at https://github.com/sharanya-dasgupta001/hallushift.

Imbalanced image datasets pose significant challenges for developing robust classifiers, particularly when certain classes are heavily underrepresented. To tackle this issue, we propose Density-Driven Attraction (DDA) Oversampling, a novel technique designed to improve class representation in the latent space. Our approach begins by projecting images into disentangled latent representations, ensuring clear separation between classes and precise identification of subclasses. At the core of this method is the Density-Driven Attraction Force (DDAF), a mechanism inspired by gravitational forces. DDAF quantifies the attraction between components of well-represented and underrepresented classes, adjusting the attraction based on the density of each component. This process recalibrates the distributions of underrepresented classes by leveraging their strongest attractions, effectively simulating the natural principles of mass attraction. Extensive classification experiments on six multiclass imbalanced datasets demonstrate that DDA Oversampling outperforms existing state-of-the-art methods, resulting in more accurate and balanced class distributions. Our code is made available at https://github.com/priyomondal/DDAO.

In the past there have been studies in kernelized versions of sparse recovery algorithms; most notably for l1-norm minimization and orthogonal matching pursuit. However, there has been no work on a kernel version of a related problem – low-rank matrix recovery via nuclear norm minimization. In this paper, we address this hitherto unsolved problem. The ensuing formulation is solved using the Majorisation Minimization (MM) approach. The reason for using MM is to ensure there are no additional hyper-parameters to tune. We apply this technique for Collaborative Representation based Classification (CRC). Experiments have been carried forth on video based face recognition on the VidTIMIT and iSAFE databases. Comparison has been done with other CRC approaches along with two dictionary learning based and two deep learning based techniques. Results show that our method improves over all of the aforesaid.

Graph neural networks (GNNs) witness impressive performances on homophilic graphs characterized by a higher number of edges connecting nodes of similar class labels. A decline in the performance of GNNs can be experienced when applied to heterophilic graphs where most of the edges connect nodes with different class labels. This study presents a novel and versatile preprocessing framework comprising three fundamental stages. This framework can be seamlessly integrated with various GNN architectures to address heterophily within graphs effectively. In the initial stage, we predict class probabilities for nodes through a dense network. It is widely acknowledged that conventional feature-based similarity measures, such as cosine similarity, might not always accurately capture the correspondence between node pairs. Moving to the second stage, we introduce a reweighting strategy guided by class embeddings generated from autoencoders to counter this limitation. In the final stage, we utilize the reweighted similarity coefficients in a two-stage graph rewiring process. This process involves node deletion and subsequent insertion to generate a more homophily-oriented neighborhood. We reuse class embeddings by fusing them with the original node features to enrich the node features with class-level information. The updated node features and the rewired graph structure are ultimately fed into the GNN model. This facilitates effective message passing (MP) across neighborhoods. We extensively evaluate our approach on various standard graph datasets encompassing homophilic and heterophilic characteristics. Across these datasets, our framework consistently improves the performance of the established baseline methods.

Many-to-many voice conversion (VC) is a technique aimed at mapping speech features between multiple speakers during training and transferring the vocal characteristics of one source speaker to another target speaker, all while maintaining the content of the source speech unchanged. Existing research highlights a notable gap between the original and generated speech samples in terms of naturalness within many-to-many VC. Therefore, there is substantial room for improvement in achieving more natural-sounding speech samples for both parallel and nonparallel VC scenarios. In this study, we introduce a generative adversarial network (GAN) system with a guided loss (GLGAN-VC) designed to enhance many-to-many VC by focusing on architectural improvements and the integration of alternative loss functions. Our approach includes a pair-wise downsampling and upsampling (PDU) generator network for effective speech feature mapping (FM) in multidomain VC. In addition, we incorporate an FM loss to preserve content information and a residual connection (RC)-based discriminator network to improve learning. A guided loss (GL) function is introduced to efficiently capture differences in latent feature representations between source and target speakers, and an enhanced reconstruction loss is proposed for better contextual information preservation. We evaluate our model on various datasets, including VCC 2016, VCC 2018, VCC 2020, and an emotional speech dataset (ESD). Our results, based on both subjective and objective evaluation metrics, demonstrate that our model outperforms state-of-the-art (SOTA) many-to-many GAN-based VC models in terms of speech quality and speaker similarity in the generated speech samples.

Capsule networks (CapsNets) aim to parse images into a hierarchy of objects, parts, and their relationships using a two-step process involving part-whole transformation and hierarchical component routing. However, this hierarchical relationship modeling is computationally expensive, which has limited the wider use of CapsNet despite its potential advantages. The current state of CapsNet models primarily focuses on comparing their performance with capsule baselines, falling short of achieving the same level of proficiency as deep convolutional neural network (CNN) variants in intricate tasks. To address this limitation, we present an efficient approach for learning capsules that surpasses canonical baseline models and even demonstrates superior performance compared with high-performing convolution models. Our contribution can be outlined in two aspects: first, we introduce a group of subcapsules onto which an input vector is projected. Subsequently, we present the hybrid Gromov-Wasserstein (HGW) framework, which initially quantifies the dissimilarity between the input and the components modeled by the subcapsules, followed by determining their alignment degree through optimal transport (OT). This innovative mechanism capitalizes on new insights into defining alignment between the input and subcapsules, based on the similarity of their respective component distributions. This approach enhances CapsNets' capacity to learn from intricate, high-dimensional data while retaining their interpretability and hierarchical structure. Our proposed model offers two distinct advantages: 1) its lightweight nature facilitates the application of capsules to more intricate vision tasks, including object detection; and 2) it outperforms baseline approaches in these demanding tasks. Our empirical findings illustrate that HGW capsules (HGWCapsules) exhibit enhanced robustness against affine transformations, scale effectively to larger datasets, and surpass CNN and CapsNet models across various vision tasks.

Alzheimer’s disease (AD), characterized by progressive cognitive decline and memory loss, presents a formidable global health challenge, underscoring the critical importance of early and precise diagnosis for timely interventions and enhanced patient outcomes. While MRI scans provide valuable insights into brain structures, traditional analysis methods often struggle to discern intricate 3D patterns crucial for AD identification. Addressing this challenge, we introduce an alternative end-to-end deep learning model, the 3D Hybrid Compact Convolutional Transformers 3D (HCCT). By synergistically combining convolutional neural networks (CNNs) and vision transformers (ViTs), the 3D HCCT adeptly captures both local features and long-range relationships within 3D MRI scans. Extensive evaluations on prominent AD benchmark dataset, ADNI, demonstrate the 3D HCCT’s superior performance, surpassing state of the art CNN and transformer based methods in classification accuracy. Its robust generalization capability and interpretability marks a significant stride in AD classification from 3D MRI scans, promising more accurate and reliable diagnoses for improved patient care and superior clinical outcomes.

Cooperative co-evolution (CC) is a practical and efficient evolutionary framework for solving large-scale global optimization problems (LSGOPs). The performance of CC depends on how variables are being grouped and can be improved through guided variable decomposition for various optimization problems. However, achieving a proper variable decomposition is computationally expensive. This article proposes an effective yet efficient differential grouping (EDG) method to reduce the associated computational cost. Our method exploits the historical interrelationship information of previous variable groups to examine interactions between the remnant variable groups. This allows us to spend less computing resources without compromising the accuracy of the final grouping result. Our proposal utilizes the covariance matrix adaptation evolution strategy (CMA-ES) algorithm, in conjunction with EDG, to solve LSGOPs. Further, to reduce time complexity and improve the stability of CMA-ES, we substitute the complex matrix decomposition step with simpler matrix operations to compute the square root of the covariance matrix. Results from our experiments and analysis indicate that EDG is a competitive method to solve LSGOPs and improve the performance of CC. The proposed schemes significantly enhance the searchability of CMA-ES compared to the other large-scale variants of CMA-ES and state-of-the-art large-scale optimizers. Moreover, our EDG could be integrated with evolutionary optimizers of different flavors like differential evolution (DE).

Principal component analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in statistics, machine learning, computer vision, and related fields. However, PCA is well-known to fall prey to outliers and often fails to detect the true underlying low-dimensional structure within the dataset. Following the Median of Means (MoM) philosophy, recent supervised learning methods have shown great success in dealing with outlying observations without much compromise to their large sample theoretical properties. This article proposes a PCA procedure based on the MoM principle. Called the MoMPCA, the proposed method is not only computationally appealing but also achieves optimal convergence rates under minimal assumptions. In particular, we explore the nonasymptotic error bounds of the obtained solution via the aid of the Rademacher complexities while granting absolutely no assumption on the outlying observations. The derived concentration results are not dependent on the dimension because the analysis is conducted in a separable Hilbert space, and the results only depend on the fourth moment of the underlying distribution in the corresponding norm. The proposal's efficacy is also thoroughly showcased through simulations and real data applications.

The mean shift algorithm is a simple yet very effective clustering method widely used for image and video segmentation as well as other exploratory data analysis applications. Recently, a new algorithm called MeanShift++ (MS++) for low-dimensional clustering was proposed with a speedup of 4000 times over the vanilla mean shift. In this work, starting with a first-of-its-kind theoretical analysis of MS++, we extend its reach to high-dimensional data clustering by integrating the Uniform Manifold Approximation and Projection (UMAP) based dimensionality reduction in the same framework. Analytically, we show that MS++ can indeed converge to a non-critical point. Subsequently, we suggest modifications to MS++ to improve its convergence characteristics. In addition, we propose a way to further speed up MS++ by avoiding the execution of the MS++ iterations for every data point. By incorporating UMAP with modified MS++, we design a faster algorithm, named UMAP embedded quick mean shift (UEQMS), for partitioning data with a relatively large number of recorded features. Through extensive experiments, we showcase the efficacy of UEQMS over other state-of-the-art algorithms in terms of accuracy and runtime.

Voice conversion (VC) is the process of converting the vocal texture of a source speaker similar to that of a target speaker without altering the content of the source speaker’s speech. With the ongoing developments of deep generative models, generative adversarial networks (GANs) appeared as a better alternative to the conventional statistical models for VC. However, the existing VC model-generated speech samples possess substantial dissimilarity from their corresponding natural human speech. Therefore, in this work a GAN-based VC model is proposed which is incorporated with a self-attention (SA) mechanism based generator network to obtain the formant distribution of the target mel-spectrogram efficiently. Moreover, the modulation spectra distance (MSD) is also incorporated in this work as a feature-specific loss in terms of getting high speaker similarity. The proposed model has been tested with CMU Arctic and VCC 2018 datasets. Based on the objective and subjective evaluations, we observe the proposed feature-specific loss-based self-attentive GAN (FLSGAN-VC) model significantly performed better than the state-of-the-art (SOTA) MelGAN-VC model.

Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution, with a limited amount of labeled data. The underlying requirement for effective few-shot generalization is to learn a good representation of the task manifold. This becomes more difficult when only a limited number of tasks are available for training. In such a few-task few-shot setting, it is beneficial to explicitly preserve the local neighborhoods from the task manifold and exploit this to generate artificial tasks for training. To this end, we introduce the notion of interval bounds from the provably robust training literature to few-shot learning. The interval bounds are used to characterize neighborhoods around the training tasks. These neighborhoods can then be preserved by minimizing the distance between a task and its respective bounds. We then use a novel strategy to artificially form new tasks for training by interpolating between the available tasks and their respective interval bounds. We apply our framework to both model-agnostic meta-learning as well as prototype-based metric-learning paradigms. The efficacy of our proposed approach is evident from the improved performance on several datasets from diverse domains in comparison to recent methods.

The problem of class imbalance arises in machine learning due to the unequal class-specific distribution of data, where most samples belong to one class, and only a few represent the others. To tackle this issue, one paradigm is to use oversampling techniques that synthesize artificial samples of the minority class using the convex combination of the minority class samples taken in some specialized way for different methods. Existing methods do not take into account any information regarding the actual distribution of the minority class, which leads to inconsistencies between the generated distribution and the actual distribution that the minority class might have. In this paper, we propose a parametrization-based method that tries to estimate the statistics of the minority class samples using the statistics of the nearby classes. Using the different hyperparameters, we can control the distribution such that it may approximate the original distribution. Experiments using synthetic and real-world benchmark datasets demonstrate the usefulness of our techniques across multiple metrics.

Kernel k-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Its merits are thoroughly validated on a suite of simulated datasets and real data benchmarks that feature nonlinear and multi-view separation. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from the non-convexity of the underlying objective function. In this paper, we generalize recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings. Called Kernel Power k-Means, our algorithm uses majorization-minimization (MM) to better solve this non-convex problem. We show that the method implicitly performs annealing in kernel feature space while retaining efficient, closed-form updates. We rigorously characterize its convergence properties both from computational and statistical points of view. In particular, we characterize the large sample behavior of the proposed method by establishing strong consistency guarantees as well as finite-sample bounds on the excess risk of the estimates through modern tools in learning theory. The proposal's efficacy is demonstrated through an array of simulated and real data experiments.

Since the last three decades, numerous search strategies have been introduced within the framework of different evolutionary algorithms (EAs). Most of the popular search strategies operate on the hypercube (HC) search model, and search models based on other hypershapes, such as hyper-spherical (HS), are not investigated well yet. The recently developed spherical search (SS) algorithm utilizing the HS search model has been shown to perform very well for the bound-constrained and constrained optimization problems compared to several state-of-the-art algorithms. Nevertheless, the computational burdens for generating an HS locus are higher than that for an HC locus. We propose an efficient technique to construct an HS locus by approximating the orthogonal projection matrix to resolve this issue. As per our empirical experiments, this technique significantly improves the performance of the original SS with less computational effort. Moreover, to enhance SS's search capability, we put forth a self-adaptation technique for choosing the effective values of the control parameters dynamically during the optimization process. We validate the proposed algorithm's performance on a plethora of real-world and benchmark optimization problems with and without constraints. Experimental results suggest that the proposed algorithm remains better than or at least comparable to the best-known state-of-the-art algorithms on a wide spectrum of problems.

Clusters in real data are often restricted to low-dimensional subspaces rather than the entire feature space. Recent approaches to circumvent this difficulty are often computationally inefficient and lack theoretical justification in terms of their large-sample behavior. This article deals with the problem by introducing an entropy incentive term to efficiently learn the feature importance within the framework of center-based clustering. A scalable block-coordinate descent algorithm, with closed-form updates, is incorporated to minimize the proposed objective function. We establish theoretical guarantees on our method by Vapnik-Chervonenkis (VC) theory to establish strong consistency along with uniform concentration bounds. The merits of our method are showcased through detailed experimental analysis on toy examples as well as real data clustering benchmarks.

Image-to-image (I2I) translation has become a key asset for generative adversarial networks. Convolutional neural networks (CNNs), despite having a significant performance, are not able to capture the spatial relationships among different parts of an object and, thus, do not qualify as the ideal representative model for image translation tasks. As a remedy to this problem, capsule networks have been proposed to represent patterns for a visual object in such a way that preserves hierarchical spatial relationships. The training of capsules is constrained by learning all pairwise relationships between capsules of consecutive layers. This design would be prohibitively expensive both in time and memory. In this article, we present a new framework for capsule networks to provide a full description of the input components at various levels of semantics, which can successfully be applied to the generator-discriminator architectures without incurring computational overhead compared to the CNNs. To successfully apply the proposed capsules in the generative adversarial network, we put forth a novel Gromov-Wasserstein (GW) distance as a differentiable loss function that compares the dissimilarity between two distributions and then guides the learned distribution toward target properties, using optimal transport (OT) discrepancy. The proposed method-which is called generative equivariant network (GEN)-is an alternative architecture for GANs with equivariance capsule layers. The proposed model is evaluated through a comprehensive set of experiments on I2I translation and image generation tasks and compared with several state-of-the-art models. Results indicate that there is a principled connection between generative and capsule models that allows extracting discriminant and invariant information from image data.

In machine learning and computer vision, mean shift (MS) qualifies as one of the most popular mode-seeking algorithms used for clustering and image segmentation. It iteratively moves each data point to the weighted mean of its neighborhood data points. The computational cost required to find the neighbors of each data point is quadratic to the number of data points. Consequently, the vanilla MS appears to be very slow for large-scale datasets. To address this issue, we propose a mode-seeking algorithm called GridShift, with significant speedup and principally based on MS. To accelerate, GridShift employs a grid-based approach for neighbor search, which is linear in the number of data points. In addition, GridShift moves the active grid cells (grid cells associated with at least one data point) in place of data points towards the higher density, a step that provides more speedup. The runtime of Grid Shift is linear in the number of active grid cells and exponential in the number of features. Therefore, it is ideal for large-scale low-dimensional applications such as object tracking and image segmentation. Through extensive experiments, we showcase the superior performance of GridShift compared to other MS-based as well as state-of-the-art algorithms in terms of accuracy and runtime on benchmark datasets for image segmentation. Finally, we provide a new object-tracking al-gorithm based on GridShift and show promising results for object tracking compared to CamShift and meanshift++.

The task of unpaired image-to-image translation has witnessed a revolution with the introduction of the cycle-consistency loss to Generative Adversarial Networks (GANs). Numerous variants, with Cycle-Consistent Adversarial Network (CycleGAN) at their forefront, have shown remarkable empirical performance. The involvement of two unalike data spaces and the existence of multiple solution maps between them are some of the facets that make such architectures unique. In this study, we investigate the statistical properties of such unpaired data translator networks between distinct spaces, bearing the additional responsibility of cycle-consistency. In a density estimation setup, we derive sharp non-asymptotic bounds on the translation errors under suitably characterized models. This, in turn, points out sufficient regularity conditions that maps must obey to carry out successful translations. We further show that cycle-consistency is achieved as a consequence of the data being successfully generated in each space based on observations from the other. In a first-of-its-kind attempt, we also provide deterministic bounds on the cumulative reconstruction error. In the process, we establish tolerable upper bounds on the discrepancy responsible for ill-posedness in such networks.

Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin’s theory of evolution as well as Mendel’s theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a random process, can be suitably used instead. Specifically, we compare the performance of 10 evolutionary algorithms driven by chaotic dynamics and pseudo-random number generators using chaotic processes as a comparative study. In this study, the logistic equation is employed for generating periodical sequences of different lengths, which are used in evolutionary algorithms instead of randomness. We suggest that, instead of pseudo-random number generators, a specific class of deterministic processes (based on deterministic chaos) can be used to improve the performance of evolutionary algorithms. Finally, based on our findings, we propose new research questions.

In context to high-dimensional clustering, the concept offeature weightinghas gained considerable importance over the years to capture the relative degrees of importance of different features in revealing the cluster structure of the dataset. However, the popular techniques in this area either fail to perform feature selection or do not preserve the simplicity of Lloyd’s heuristic to solve the$k$-means problem and the like. In this paper, we propose a Lasso Weighted$k$-means ($LW$-$k$-means) algorithm, as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features ($p$) can be much higher than the number of observations ($n$). The$LW$-$k$-means method imposes an$\ell _1$regularization term involving the feature weights directly to induce feature selection in a sparse clustering framework. We develop a simple block-coordinate descent type algorithm with time-complexity resembling that of Lloyd’s method, to optimize the proposed objective. In addition, we establish the strong consistency of the$LW$-$k$-means procedure. Such an analysis of the large sample properties is not available for the conventional sparse$k$-means algorithms, in general.$LW$-$k$-means is tested on a number of synthetic and real-life datasets and through a detailed experimental analysis, we find that the performance of the method is highly competitive against the baselines as well as the state-of-the-art procedures for center-based high-dimensional clustering, not only in terms of clustering accuracy but also with respect to computational time.

During the last two decades, the notion of multiobjective optimization (MOO) has been successfully adopted to solve the nonconvex constrained optimization problems (COPs) in their most general forms. However, such works mainly utilized the Pareto dominance-based MOO framework while the other successful MOO frameworks, such as the reference vector (RV) and the decomposition-based ones, have not drawn sufficient attention from the COP researchers. In this article, we utilize the concepts of the RV-based MOO to design a ranking strategy for the solutions of a COP. We first transform the COP into a biobjective optimization problem (BOP) and then solve it by using the covariance matrix adaptation evolution strategy (CMA-ES), which is arguably one of the most competitive evolutionary algorithms of current interest. We propose an RV-based ranking strategy to calculate the mean and update the covariance matrix in CMA-ES. Besides, the RV is explicitly tuned during the optimization process based on the characteristics of COPs in a RV-based MOO framework. We also propose a repair mechanism for the infeasible solutions and a restart strategy to facilitate the population to escape from the infeasible region. We test the proposal extensively on two well-known benchmark suites comprised of 36 and 112 test problems (at different scales) from the IEEE CEC (Congress on Evolutionary Computation) 2010 and 2017 competitions along with a real-world problem related to power flow. Our experimental results suggest that the proposed algorithm can meet or beat several other state-of-the-art constrained optimizers in terms of the performance on a wide variety of problems.

To solve the nonconvex constrained optimization problems (COPs) over continuous search spaces by using a population-based optimization algorithm, balancing between the feasible and infeasible solutions in the population plays an important role over different stages of the optimization process. To keep this balance, we propose a constraint handling technique, called the υ -level penalty function, which works by transforming a COP into an unconstrained one. Also, to improve the ability of the algorithm in handling several complex constraints, especially nonlinear inequality and equality constraints, we suggest a Broyden-based mutation that finds a feasible solution to replace an infeasible solution. By incorporating these techniques with the matrix adaptation evolution strategy (MA-ES), we develop a new constrained optimization algorithm. An extensive comparative analysis undertaken using a broad range of benchmark problems indicates that the proposed algorithm can outperform several state-of-the-art constrained evolutionary optimizers.

Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode seeking, and finding the number of clusters in a dataset in an automated fashion. However, the merits of mean shift quickly fade away as the data dimensions increase and only a handful of features contain useful information about the cluster structure of the data. We propose a simple yet elegant feature-weighted variant of mean shift to efficiently learn the feature importance and thus, extending the merits of mean shift to high-dimensional data. The resulting algorithm not only outperforms the conventional mean shift clustering procedure but also preserves its computational simplicity. In addition, the proposed method comes with rigorous theoretical convergence guarantees and a convergence rate of at least a cubic order. The efficacy of our proposal is thoroughly assessed through experimental comparison against baseline and state-of-the-art clustering methods on synthetic as well as real-world datasets.

We propose a novel Evolutionary Algorithm (EA) based on the Differential Evolution algorithm for solving global numerical optimization problem in real-valued continuous parameter space. The proposed MadDE algorithm leverages the power of the multiple adaptation strategy with respect to the control parameters and search mechanisms, and is tested on the benchmark functions taken from the CEC 2021 special session & competition on single-objective bound-constrained optimization. Experimental results indicate that MadDE is able to achieve superior performance on global numerical optimization problems when compared against state-of-the-art real-parameter optimizers. We also provide a hyperparameter optimization algorithm SUBHO for improving the search performance of any EA by finding an optimal set of control parameters, and demonstrate its efficacy in enhancing MadDE's performance on the same benchmark. The source code of our implementation is publicly available at https://github.com/subhodipbiswas/MadDE.

The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning. This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically show that the proposed$t$-entropy satisfies the prominent axiomatic properties of an entropy measure. We demonstrate an application of the proposed entropy measure for multi-level thresholding of images. We also propose the entropic-loss as a measure of the divergence between two probability distributions, which leads to robust estimators in the context of parametric statistical inference. The consistency and asymptotic breakdown point of the proposed estimator are mathematically analysed. Finally, we also show an application of the$t$-entropy to feature weighted data clustering.

The introduction of Variational Autoencoders (VAE) has been marked as a breakthrough in the history of representation learning models. Besides having several accolades of its own, VAE has successfully flagged off a series of inventions in the form of its immediate successors. Wasserstein Autoencoder (WAE), being an heir to that realm carries with it all of the goodness and heightened generative promises, matching even the generative adversarial networks (GANs). Needless to say, recent years have witnessed a remarkable resurgence in statistical analyses of the GANs. Similar examinations for Autoencoders however, despite their diverse applicability and notable empirical performance, remain largely absent. To close this gap, in this paper, we investigate the statistical properties of WAE. Firstly, we provide statistical guarantees that WAE achieves the target distribution in the latent space, utilizing the Vapnik–Chervonenkis (VC) theory. The main result, consequently ensures the regeneration of the input distribution, harnessing the potential offered by Optimal Transport of measures under the Wasserstein metric. This study, in turn, hints at the class of distributions WAE can reconstruct after suffering a compression in the form of a latent law.

Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated $k$-means algorithm over $60$ years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers, and data that are not well-suited to Euclidean measures of fit, but many are supported largely empirically. Moreover, combining such approaches in a piecemeal manner can result in ad hoc methods, and the limited theoretical results supporting each individual contribution may no longer hold. Toward addressing these issues in a principled way, this paper proposes a cohesive robust framework for center-based clustering under a general class of dissimilarity measures. In particular, we present a rigorous theoretical treatment within a Median-of-Means (MoM) estimation framework, showing that it subsumes several popular $k$-means variants. In addition to unifying existing methods, we derive uniform concentration bounds that complete their analyses, and bridge these results to the MoM framework via Dudley's chaining arguments. Importantly, we neither require any assumptions on the distribution of the outlying observations nor on the relative number of observations $n$ to features $p$. We establish strong consistency and an error rate of $O(n^{-1/2})$ under mild conditions, surpassing the best-known results in the literature. The methods are empirically validated thoroughly on real and synthetic datasets.

Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents an entropy c -means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multiobjective optimization methods, nondominated sorting genetic algorithm II (NSGA-II) and multiobjective evolutionary algorithm based on decomposition (MOEA/D). We also propose a method to select a suitable tradeoff clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multiobjective methods for fuzzy clustering.

Despite its well-known shortcomings, k-means remains one of the most widely used approaches to data clustering. Current research continues to tackle its flaws while attempting to preserve its simplicity. Recently, the power k-means algorithm was proposed to avoid poor local minima by annealing through a family of smoother surfaces. However, the approach lacks statistical guarantees and fails in high dimensions when many features are irrelevant. This paper addresses these issues by introducing entropy regularization to learn feature relevance while annealing. We prove consistency of the proposed approach and derive a scalable majorization-minimization algorithm that enjoys closed-form updates and convergence guarantees. In particular, our method retains the same computational complexity of k-means and power k-means, but yields significant improvements over both. Its merits are thoroughly assessed on a suite of real and synthetic data.

Classical clustering methods usually face tough challenges when we have a larger set of features compared to the number of items to be partitioned. We propose a Sparse MinMax k-Means Clustering approach by reformulating the objective of the MinMax k-Means algorithm (a variation of classical k-Means that minimizes the maximum intra-cluster variance instead of the sum of intra-cluster variances), into a new weighted between-cluster sum of squares (BCSS) form. We impose sparse regularization on these weights to make it suitable for high-dimensional clustering. We seek to use the advantages of the MinMax k-Means algorithm in the high-dimensional space to generate good quality clusters. The efficacy of the proposal is showcased through comparison against a few representative clustering methods over several real world datasets.

Activation functions in the neural networks play an important role by introducing non-linear properties to the neural networks. Thus it is considered as one of the essential ingredients among other building blocks of a neural network. But the selection of the appropriate activation function for the enhancement of model accuracy is strenuous in a sense; the performance of the NN-model is influenced by a proper selection of activation function for a dataset. Proper activation function selection is still a trial and error method for which the model accuracy improves for classification. As a solution to this problem, we have proposed an activation function ensembling by majority voting that has significantly improved the model accuracy in a classification context. The proposed model is tested on four benchmark datasets such as MNIST, Fashion MNIST, Semeion, and ARDIS IV datasets. The result shows that the performance of the proposed model is appreciably better than other traditional methods such as Convolutional Neural Network (CNN), Support Vector Machine (SVM), Recurrent Neural Network (RNN).

Differential evolution (DE) has established itself as a simple but efficient population-based, nonconvex optimization algorithm for continuous search spaces. Unlike the conventional real-coded genetic algorithms (GAs) and evolution strategies (ESs), DE uses a mandatory self-referential mutation for its population members, each of which are perturbed with the scaled difference(s) of the individuals from the current generation (iteration). These difference vectors determine the direction of the search moves for the individuals. However, unlike the better individuals, they are not retained in the elitist evolution cycle of DE. In this paper, we show that by archiving the most promising difference vectors from past generations and then by reusing them for generating offspring in the subsequent generations, we can strikingly improve the performance of DE. This strategy can be integrated with any classical or advanced DE variant with no serious overhead in time or space complexity. We demonstrate that when combined with the DE-based winners of the IEEE Congress on Evolutionary Computation (CEC) 2013, 2014, and 2017 competitions on real parameter optimization, the simple reuse strategy leads to a statistically significant performance improvement in the majority of test cases. We further showcase the efficacy of our proposal on a practical optimization problem concerning the design of circular antenna arrays with a prespecified radiation pattern.

A large amount of research effort has been dedicated to adapting boosting for imbalanced classification. However, boosting methods are yet to be satisfactorily immune to class imbalance, especially for multi-class problems. This is because most of the existing solutions for handling class imbalance rely on expensive cost set tuning for determining the proper level of compensation. We show that the assignment of weights to the component classifiers of a boosted ensemble can be thought of as a game ofTug of Warbetween the classes in the margin space. We then demonstrate how this insight can be used to attain a good compromise between the rare and abundant classes without having to resort to cost set tuning, which has long been the norm for imbalanced classification. The solution is based on a lexicographic linear programming framework which requires two stages. Initially, class-specific component weight combinations are found so as to minimize a hinge loss individually for each of the classes. Subsequently, the final component weights are assigned so that the maximum deviation from the class-specific minimum loss values (obtained in the previous stage) is minimized. Hence, the proposal is not only restricted to two-class situations, but is also readily applicable to multi-class problems. Additionally, we also derive the dual formulation corresponding to the proposed framework. Experiments conducted on artificial and real-world imbalanced datasets as well as on challenging applications such as hyperspectral image classification and ImageNet classification establish the efficacy of the proposal.

Although over the past one decades, several variants of Differential Evolution (DE) have been introduced for solving the global optimization functions, no single variant of DE shows better performance on a variety of optimization problems. During the last five years, to lighten this deficiency, many variants of DE which employ multiple mutation and crossover strategies in a single structure of algorithm, called as multi-operators variant of DE (MODE), have been proposed. In this work, ESHADE, an enhanced version of a MODE, is introduced including various mutation strategies and an exponential population size reduction (EPSR) technique is utilized to reduce size of the population for the next iteration. Additionally, a version of uni-variate sampling method is employed in later iterations to provide a balance between exploitative and explorative search. To perform the comparative analysis, the proposed algorithm is benchmarked on the problem suite of the 100-digit challenge on single objective numerical optimization at CEC-2019. Comparative analysis reveals that the ESHADE can provide high-quality solutions as compared to state-of-the-art algorithms.

Class imbalance is a long-standing problem relevant to a number of real-world applications of deep learning. Oversampling techniques, which are effective for handling class imbalance in classical learning systems, can not be directly applied to end-to-end deep learning systems. We propose a three-player adversarial game between a convex generator, a multi-class classifier network, and a real/fake discriminator to perform oversampling in deep learning systems. The convex generator generates new samples from the minority classes as convex combinations of existing instances, aiming to fool both the discriminator as well as the classifier into misclassifying the generated samples. Consequently, the artificial samples are generated at critical locations near the peripheries of the classes. This, in turn, adjusts the classifier induced boundaries in a way which is more likely to reduce misclassification from the minority classes. Extensive experiments on multiple class imbalanced image datasets establish the efficacy of our proposal.

We present a novel alternative convergence theory of the fuzzy C -means (FCM) clustering algorithm with a super-class of the so-called "distance like functions" which emerged from the earlier attempts of unifying the theories of center-based clustering methods. This super-class does not assume the existence of double derivative of the distance measure with respect to the coordinate of the cluster representative (first coordinate in this formulation). The convergence result does not require the separability of the distance measures. Moreover, it provides us with a stronger convergence property comparable (same to be precise, but in terms of the generalized distance measure) to that of the classical FCM with squared Euclidean distance. The crux of the convergence analysis lies in the development of a fundamentally novel mathematical proof of the continuity of the clustering operator even in absence of the closed form upgrading rule, without necessitating the separability and double differentiability of the distance function and still providing us with a convergence result comparable to that of the classical FCM. The implication of our novel proof technique goes way beyond the realm of FCM and provides a general setup for convergence analysis of the similar iterative algorithms.

The fuzzy$k$-nearest neighbor classifier (F$k$NN) improves upon the flexibility of the$k$-nearest neighbor classifier by considering each class as a fuzzy set and estimating the membership of an unlabeled data instance for each of the classes. However, the question of validating the quality of the class memberships estimated by F$k$NN for a regular multiclass classification problem still remains mostly unanswered. In this paper, we attempt to address this issue by first proposing a novel direction of evaluating a fuzzy classifier by highlighting the importance of focusing on the class memberships estimated by F$k$NN instead of its misclassification error. This leads us to finding novel theoretical upper bounds, respectively, on the bias and the mean squared error of the class memberships estimated by F$k$NN. Additionally the proposed upper bounds are shown to converge toward zero with increasing availability of the labeled data points, under some elementary assumptions on the class distribution and membership function. The major advantages of this analysis are its simplicity, capability of a direct extension for multiclass problems, parameter independence, and practical implication in explaining the behavior of F$k$NN in diverse situations (such as in presence of class imbalance). Furthermore, we provide a detailed simulation study on artificial and real data sets to empirically support our claims.

Support vector machines (SVMs) seek to optimize three distinct objectives: maximization of margin, minimization of regularization from the positive class, and minimization of regularization from the negative class. The right choice of weightage for each of these objectives is critical to the quality of the classifier learned, especially in case of the class imbalanced data sets. Therefore, costly parameter tuning has to be undertaken to find a set of suitable relative weights. In this brief, we propose to train SVMs, on two-class as well as multiclass data sets, in a multiobjective optimization framework called radial boundary intersection to overcome this shortcoming. The experimental results suggest that the radial boundary intersection-based scheme is indeed effective in finding the best tradeoff among the objectives compared with parameter-tuning schemes.

Main objective of this work is to analyze the ability of the Differential Evolution (DE) framework equipped with a multi-donor mutation strategy and annealing-based local search technique to find the global minimum of the potential energy functions, which are used for molecular cluster modeling. Finding such stable molecular clusters is a significant and well-established optimization problem arising from the area of molecular distance geometry and has important implications in artificial drug design as well. Results for moderate (3, 5, 10, 15, 20, 25, and 30 atomic molecules) scale problems are presented here for the Lennard-Jones potential function based atomic clusters. Our experiments reveal that the proposed DE variant is able to yield better results than the competing state-of-art DE based optimizers and the results are with par to the best results listed in the Cambridge energy landscape database (http://doye.chem.ox.ac.uk/jon/structures/LJ.html).

The classification accuracy of a -nearest neighbor ( NN) classifier is largely dependent on the choice of the number of nearest neighbors denoted by . However, given a data set, it is a tedious task to optimize the performance of NN by tuning . Moreover, the performance of NN degrades in the presence of class imbalance, a situation characterized by disparate representation from different classes. We aim to address both the issues in this paper and propose a variant of NN called the Adaptive NN (Ada- NN). The Ada- NN classifier uses the density and distribution of the neighborhood of a test point and learns a suitable point-specific for it with the help of artificial neural networks. We further improve our proposal by replacing the neural network with a heuristic learning method guided by an indicator of the local density of a test point and using information about its neighboring training points. The proposed heuristic learning algorithm preserves the simplicity of NN without incurring serious computational burden. We call this method Ada- NN2. Ada- NN and Ada- NN2 perform very competitive when compared with NN, five of NN's state-of-the-art variants, and other popular classifiers. Furthermore, we propose a class-based global weighting scheme (Global Imbalance Handling Scheme or GIHS) to compensate for the effect of class imbalance. We perform extensive experiments on a wide variety of data sets to establish the improvement shown by Ada- NN and Ada- NN2 using the proposed GIHS, when compared with NN, and its 12 variants specifically tailored for imbalanced classification.

A switched-parameter Differential Evolution (DE) enforced with equiprobable switching between two alternative mutation strategies, an optional blending crossover, and a threshold-based selection mechanism is proposed for optimization of complex functions corrupted with additive noise. In order to handle the noisy optimization problems, the DE framework is coupled with three new algorithmic components. Each individual is subjected to one of the two well known mutation strategies namely DE/best/1 and DE/rand/1 with equal chances. In the recombination stage, binomial and blending crossovers are opted in the same switchable strategy as done for mutation. A novel threshold-based selection mechanism is used to allow less fit offspring to survive occasionally, thus countering the noisy function behavior. Additive Gaussian noise is used to simulate the noisy behavior of functions defined over continuous search spaces. A benchmark suite comprising of 21 well-known numerical functions is considered to compare and contrast the proposed method with other state-of-the-art evolutionary algorithms specifically tailored for noisy optimization scenario. The proposed method shows very competitive performance indicating highly robust behavior against the noisy functional landscapes.

This paper proposes a novel fuzzy rule-based penalty function approach for solving single-objective nonlinearly constrained optimization problems. Of all the existing state-of-the-art constraint handling techniques, the conventional method of penalty can be easily implemented because of its simplicity but suffers from the lack of robustness. To mitigate the problem of parameter dependency, several forms of adaptive penalties have been suggested in literature. Instead of identifying a complex mathematical function to compute the penalty for constraint violation, we propose a Mamdani type IF-THEN rule-based fuzzy inference system that incorporates all the required criteria of self-adaptive penalty without formulating an explicit mapping. Effectiveness of the proposed constrained optimization algorithm has been empirically validated on the basis of the standard optimality theorems from the literature on mathematical programming. Simulation results show that fuzzy penalty not only surpasses its existing counterpart i.e., self adaptive penalty, but also remain competitive against several other standard as well as currently developed complex constraint handling strategies.

In practical situations, it is very often desirable to detect multiple optimally sustainable solutions of an optimization problem. The population-based evolutionary multimodal optimization algorithms can be very helpful in such cases. They detect and maintain multiple optimal solutions during the run by incorporating specialized niching operations to aid the parallel localized convergence of population members around different basins of attraction. This paper presents an improved information-sharing mechanism among the individuals of an evolutionary algorithm for inducing efficient niching behavior. The mechanism can be integrated with stochastic real-parameter optimizers relying on differential perturbation of the individuals (candidate solutions) based on the population distribution. Various real-coded genetic algorithms (GAs), particle swarm optimization (PSO), and differential evolution (DE) fit the example of such algorithms. The main problem arising from differential perturbation is the unequal attraction toward the different basins of attraction that is detrimental to the objective of parallel convergence to multiple basins of attraction. We present our study through DE algorithm owing to its highly random nature of mutation and show how population diversity is preserved by modifying the basic perturbation (mutation) scheme through the use of random individuals selected probabilistically. By integrating the proposed technique with DE framework, we present three improved versions of well-known DE-based niching methods. Through an extensive experimental analysis, a statistically significant improvement in the overall performance has been observed upon integrating of our technique with the DE-based niching methods.

Time varying nature of the constraints, objectives and parameters that characterize several practical optimization problems have led to the field of dynamic optimization with Evolutionary Algorithms. In recent past, very few researchers have concentrated their efforts on the study of Dynamic multi-objective Optimization Problems (DMOPs) where the dynam-icity is attributed to multiple objectives of conflicting nature. Considering the lack of a somewhat diverse and challenging set of benchmark functions, in this article, we discuss some ways of designing DMOPs and propose some general techniques for introducing dynamicity in the Pareto Set and in the Pareto Front through shifting, shape variation, slope variation, phase variation, and several other types. We introduce 9 benchmark functions derived from the benchmark suite used for the 2009 IEEE Congress on Evolutionary Computation competition on bound-constrained and static MO optimization algorithms. Additionally a variant of multiobjective EA based on decomposition (MOEA/D) have been put forward and tested along with peer algorithms to evaluate the newly proposed benchmarks.

Group Counseling Optimizer (GCO) is a recently proposed population-based metaheuristics that simulates the ability of human beings to solve problems through counseling within a group. It is motivated by the fact that the human thinking ability is often predicted to be the most rational. This research article examines the performance of GCO on the benchmark test suite designed for the CEC 2014 Competition for Computational Expensive Optimization. Experimental results on 24 black-box optimization problems (8 test problems with 10, 20 and 30 dimensions) have been tabulated along with the algorithm complexity metrics. Additionally we investigate the parametric behavior of GCO based on these test instances.

We present a novel human society inspired algorithm for solving single-objective bound constrained optimization problems. The proposed Monarchy Driven Optimization (MDO) algorithm is a population-based iterative global optimization technique for multi-dimensional and multi-modal problems. At its core, this technique introduces a monarchial society where the outlook of its population is fashioned by the thoughts of individuals and the monarch. A detailed study including the tuning of MDO parameters is presented along with the theory. It is applied to standard benchmark functions comprising unimodal and multi-modal as well as rotated functions. The results section suggests that, in most instances, MDO outperforms other well-known techniques such as Particle Swarm Optimization (PSO), Differential Evolution (DE), Gravitational Search Algorithm (GSA), Comprehensive Learning Particle Swarm Optimization (CLPSO) and Artificial Bee Colony (ABC) optimization in terms of final convergence value and mean convergence value, thus proves to be a robust optimization technique.

The Particle Swarm Optimization (PSO) algorithm is a novel population based swarm algorithm has shown good performance on well-known numerical test problems. However, PSO tends to suffer from premature convergence on multimodal test problems. This is due to lack of diversity of population in search space and leads to stuck at local optima and ultimately fitness stagnation of the population. To enhance the performance of PSO algorithms, in this paper, we propose a method of population adaptation (PA). The proposed method can identify the moment when the population diversity is poor or the population stagnates by measuring the Euclidean distance between particle position and particles average position of a population. When stagnation in the population is identified, the population will be regenerated by normal distribution to increase diversity in the population. The population adaptation is incorporated into the PSO algorithm and is tested on a set of 13 scalable CEC05 benchmark functions. The results show that the proposed population adaptation algorithm can significantly improve the performance of the PSO algorithm with standard PSO, ATREPSO and ARPSO.

The paper proposes a novel non-homogeneity measure based kernelized image segmentation algorithm for noisy images. Every 3×3 neighbourhood of every single pixel is considered for generating localized spatial domain non-homogeneity measures for every individual window. Then these spatial domain non-homogeneity measures are converted into fuzzy domain non-homogeneity coefficients by aggregating the localized measures into a single distribution and then deriving fuzzy domain values from a Gaussian membership function. Quantitative analyses have been rendered with respect to state-of-the-art noisy-image segmentation techniques and results show improved performance. Speckle-noise ridden SAR images and Rician noise ridden medical images are finally considered to show real-life applications of our algorithm.

In real life, we often need to find multiple optimally sustainable solutions of an optimization problem. Evolutionary multimodal optimization algorithms can be very helpful in such cases. They detect and maintain multiple optimal solutions during the run by incorporating specialized niching operations in their actual framework. Differential evolution (DE) is a powerful evolutionary algorithm (EA) well-known for its ability and efficiency as a single peak global optimizer for continuous spaces. This article suggests a niching scheme integrated with DE for achieving a stable and efficient niching behavior by combining the newly proposed parent-centric mutation operator with synchronous crowding replacement rule. The proposed approach is designed by considering the difficulties associated with the problem dependent niching parameters (like niche radius) and does not make use of such control parameter. The mutation operator helps to maintain the population diversity at an optimum level by using well-defined local neighborhoods. Based on a comparative study involving 13 well-known state-of-the-art niching EAs tested on an extensive collection of benchmarks, we observe a consistent statistical superiority enjoyed by our proposed niching algorithm.

This paper presents a novel search metaheuristic inspired from the physical interpretation of the optic flow of information in honeybees about the spatial surroundings that help them orient themselves and navigate through search space while foraging. The interpreted behavior combined with the minimal foraging is simulated by the artificial bee colony algorithm to develop a robust search technique that exhibits elevated performance in multidimensional objective space. Through detailed experimental study and rigorous analysis, we highlight the statistical superiority enjoyed by our algorithm over a wide variety of functions as compared to some highly competitive state-of-the-art methods.

This article proposes a multipopulation-based adaptive differential evolution (DE) algorithm to solve dynamic optimization problems (DOPs) in an efficient way. The algorithm uses Brownian and adaptive quantum individuals in conjunction with the DE individuals to maintain the diversity and exploration ability of the population. This algorithm, denoted as dynamic DE with Brownian and quantum individuals (DDEBQ), uses a neighborhood-driven double mutation strategy to control the perturbation and thereby prevents the algorithm from converging too quickly. In addition, an exclusion rule is used to spread the subpopulations over a larger portion of the search space as this enhances the optima tracking ability of the algorithm. Furthermore, an aging mechanism is incorporated to prevent the algorithm from stagnating at any local optimum. The performance of DDEBQ is compared with several state-of-the-art evolutionary algorithms using a suite of benchmarks from the generalized dynamic benchmark generator (GDBG) system used in the competition on evolutionary computation in dynamic and uncertain environments, held under the 2009 IEEE Congress on Evolutionary Computation (CEC). The simulation results indicate that DDEBQ outperforms other algorithms for most of the tested DOP instances in a statistically meaningful way.

Suppression of impulse noise in images is an important problem in image processing. In this paper, we propose a novel adaptive iterative fuzzy filter for denoising images corrupted by impulse noise. It operates in two stages-detection of noisy pixels with an adaptive fuzzy detector followed by denoising using a weighted mean filter on the “good” pixels in the filter window. Experimental results demonstrate the algorithm to be superior to state-of-the-art filters. The filter is also shown to be robust to very high levels of noise, retrieving meaningful detail at noise levels as high as 97%.

This paper aims to design new strategies to extend traditional multiobjective optimization algorithms to efficiently obtain Pareto-optimal solutions in presence of noise on the objective surfaces. The first strategy, referred to as adaptive selection of sample size, is employed to balance the tradeoff between quality measure of fitness and run-time complexity. The second strategy is concerned with determining statistical expectation, instead of conventional averaging, of fitness samples as the measure of fitness of the trial solutions. The third strategy attempts to extend Goldberg's method to compare slightly worse trial solutions with its competitor by a more statistically viable comparator to examine possible placement of the former solution in the Pareto optimal front. The traditional differential evolution for multiobjective optimization algorithm has been modified by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the extended algorithm reveal that the extended algorithm outperforms its competitors with respect to three performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions. The extended algorithm has been applied on the well known box-pushing problem, where the forces and torques required to shift the box by two robots are evaluated to jointly satisfy the conflicting objectives on task-execution time and energy consumption in presence of noise on range estimates from the sidewalls of the workspace. The application justifies the importance of the proposed noise-handling strategies in practical systems.

Differential Evolution (DE), a rather new members of the evolutionary computing paradigm, has rose to widespread popularity in a short time interval owing to its simple design and robust performance in a wide variety of problems. Inspired from the effect of the teacher on the knowledge gained by the learners in a class, we propose a teaching and learning based self-adaptive DE (TLBSaDE) for solving real parameter optimization problems. A benchmark suite consisting of 28 test problems, proposed for the CEC 2013 Special Session and Competition on Real Parameter Optimization, is used. The results are obtained on 10, 30 and 50 dimensional problems.

Estimation of Distribution algorithms (EDAs) are probabilistic-model based optimization techniques that exploit promising solution candidates by developing particles around them in accordance to a pre-specified distribution. This paper attempts to approach constrained optimization problems by an interdependent parallel functioning of a modified Gaussian distribution based EDA with differential mutation on the lines of rand/1 perturbation scheme. A modified penalty function free from scaling parameters has been proposed to deal with the constraints associated. The results have been collected from functional landscapes defined by the CEC 2010 benchmark and have been compared with existing state-of-the-art methods for constrained optimization.

Covariance Matrix Adaptation and Evolution Strategy (CMA-ES) is an efficient method of optimization that iteratively generates new individuals around an ever-adaptive recombination point. Although it ensures speed and high rate of exploitation, CMA-ES suffers a major drawback as the scheme of generating new members scattered around an influential mean may often lead to members drawn to local minima. The result is that while precision of better solutions increases, the ability to reform is lost. In this paper we incorporate a directional feature to the generation wise perturbation of individuals in standard version of CMA-ES that utilizes potentially useful information from previous generation to retain the influence of old recombination point. Coupled with a modified population size we attempt to form an algorithm that amalgamates the effectiveness of CMA-ES along with the ability to explore. The performance is tested on IEEE CEC (Congress on Evolutionary Computation) 2013 Special Session on Real-Parameter Optimization in 10, 30 and 50 dimensions. The results obtained clearly indicates that the proposed algorithm addressed as CMA-ES with Memory based Directed Individual Generation (CMA-ES-DIG) is able to perform excessively well on majority of the test cases in a statistically meaningful way.

Real life problems which deal with time varying landscape dynamics often pose serious challenge to the mettle of researchers in the domain of Evolutionary Computation. Classified as Dynamic Optimization problems (DOPs), these deal with candidate solutions which vary their dominance over dynamic change instances. The challenge is to efficiently recapture the dominant solution or the global optimum in each varying landscape. Differential Evolution (DE) algorithm with modifications of adaptability have been widely used to deal with the complexities of a dynamic landscape, yet problems persist unless dedicated structuring is done to exclusively deal with DOPs. In Adaptive Differential Evolution with Locality based Crossover (ADE-LbX) the mutation operation has been entrusted to a locality based scheme that retains traits of Euclidean distance based closest individuals around a potential solution. Diversity maintenance is further enhanced by incorporation of local best crossover scheme that renders the landscape independent of direction and empowers the algorithm with an explorative ability. An even distribution of solutions in different regions of landscape calls for a solution retention technique that adapts this algorithm to dynamism by using its previous information in diverse search domains. To evaluate the performance of ADE-LbX, it has been tested over Dynamic Problem instance proposed as in CEC 09 and compared with State-of-the-arts. The algorithm enjoys superior performance in varied problem configurations of the problem.

Dynamic Constrained Optimization Problems (DCOP) are a unique class of optimization problems where the objective function as well as the constraint functions change with respect to time. Conventional DCO algorithms involve Genetic Algorithms (GAs) accompanied by a separate constraint-handling technique e.g., a repair method, or a penalty function. However, ordinary repair methods with elitism significantly decrease the diversity of the population during the exploitation stage and penalty functions cannot properly deal with disconnected feasible regions. In this paper, we propose a new approach based on the Gravitational Search Algorithm as well as a modified version of a repair method that produces improved results. The proposed approach incorporates knowledge-reusing and knowledge-restarting in order to produce a quick recovery and faster convergence.

This paper presents a fuzzy partition and Tsallis entropy based thresholding approach for multi-level image segmentation. Image segmentation is considered as one of the most critical tasks in image processing and pattern recognition area. However, discriminating many objects present in an image automatically is the most challenging one. As a result, multilevel thresholding based methods gain importance in recent times, because of its ability to split the image into more than one segments. Efficiency of these algorithms still remains a matter of concern. Over the years, fuzzy partition of 1-D histogram has been employed successfully in bi-level image segmentation to improve the separation between object and the background. Here a fuzzy based technique is adopted in multi-level image segmentation scenario using Tsallis entropy based thresholding. Differential Evolution, a widely used meta-heuristic in recent times, is used for lesser computation time of the proposed algorithm. Both visual and statistical comparison of outcomes between Tsallis and Fuzzy - Tsallis entropy based methods are given in this paper to establish the superiority of the technique.

Multi-Carrier Code Division Multiple Access (MC-CDMA) is an emerging wireless communication technology that incorporates the advantages of Orthogonal Frequency Division Multiplexing (OFDM) into the original Code Division Multiple Access (CDMA) technique. But it suffers from the inherent defect called Multiple Access Interference (MAI) due to inappropriate cross-correlation possessed by the different user codes. To reduce MAI, the multi-user detection (MUD) technique has already been proposed in which MAI is treated as noise. Due to high computational cost incorporated by the optimal MUD detector with increasing number of users, researchers are looking for sub-optimal MUD solutions. This paper proposes a binary adaptive Differential Evolution algorithm with a novel crossover strategy (MBDE_pBX) for multi-user detection in a synchronous MC-CDMA system. Since MUD detection in MC-CDMA systems is a problem in binary domain, a binary encoding rule is introduced which converts a binary domain problem of any number of dimensions into a 4-dimensional continuous domain problem. The simulation results show that this new binary Differential Evolution variant can achieve superior bit error rate (BER) performance within much lower optimum solution detection time outperforming its competitors as well as achieving 99.62% reduction in computational complexity as compared to the MUD scheme using exhaustive search.

In the real world, many problems are multimodal as well as dynamic. Such problems require optimizers which not only locate multiple optima in a single run but also track the changing optima positions in the dynamic environments. In this paper a niching parameter free algorithm is designed which can locate multiple optima in changing environments. The proposed algorithm integrates the crowding concept with a competent Evolutionary Algorithm (EA) called Differential Evolution (DE) for maintaining the multiple peaks in a single run. To avoid the use of niching parameter that requires prior knowledge about the fitness landscape, the authors have used local mutation for searching the solution space. A speciation-based memory archive is integrated for regeneration of population after an environmental change is detected. Experimental analysis is conducted on the Moving Peaks Benchmark problem and the performance of the proposed algorithm is compared with other peer algorithms to highlight the overall effectiveness of our work.

Swarm Intelligent algorithms focus on imbibing the collective intelligence of a group of simple agents that can work together as a unit. This research article focus on a recently proposed swarm-based metaheuristic called the Artificial Bee Colony (ABC) algorithm and suggests modifications to the algorithmic framework in order to enhance its performance. The proposed ABC variant shall be referred to as MsABC_Fm (Multi swarm Artificial Bee Colony with Forager migration). MsABC_Fm maintains multiple swarm populations that apply different perturbation strategies and gradually migration of the population from worse performing strategy to the better mode of perturbation is promoted. To evaluate the performance of the algorithm, we conduct comparative study involving 8 algorithms and test the problems on 25 benchmark problems proposed in the Special Session on IEEE Congress on Evolutionary Competition 2005. The superiority of the MsABC_Fm approach is also highlighted statistically.

In this paper an optimally designed PID controller equipped with Power System Stabilizer (PSS) for a Single Machine Infinite Bus (SMIB) system using linearized Modified Philip-Heffron's model is presented. The PSS design based on this model utilizes signals available within the generating station and doesn't require the knowledge about external system parameters like line impedance and infinite bus voltage. A new swarm intelligent Artificial Bee Colony (ABC) algorithm has been used to tune the PSS-PID parameters to enhance the small signal stability due to small variations in generation and loads. Various simulation results and comparisons over different loading conditions on a single machine infinite bus power system using ABC tuned PID-PSS show the superiority of ABC in designing the power system stabilizer for the model considered.

This paper presents a Cluster-based Dynamic Differential Evolution with external Archive (CDDE_Ar) for global optimization in dynamic fitness landscape. The algorithm uses a multipopulation method where the entire population is partitioned into several clusters according to the spatial locations of the trial solutions. The clusters are evolved separately using a standard differential evolution algorithm. The number of clusters is an adaptive parameter, and its value is updated after a certain number of iterations. Accordingly, the total population is redistributed into a new number of clusters. In this way, a certain sharing of information occurs periodically during the optimization process. The performance of CDDE_Ar is compared with six state-of-the-art dynamic optimizers over the moving peaks benchmark problems and dynamic optimization problem (DOP) benchmarks generated with the generalized-dynamic-benchmark-generator system for the competition and special session on dynamic optimization held under the 2009 IEEE Congress on Evolutionary Computation. Experimental results indicate that CDDE_Ar can enjoy a statistically superior performance on a wide range of DOPs in comparison to some of the best known dynamic evolutionary optimizers.

In contrast to the numerous research works that integrate a niching scheme with an existing single-objective evolutionary algorithm to perform multimodal optimization, a few approaches have recently been taken to recast multimodal optimization as a multiobjective optimization problem to be solved by modified multiobjective evolutionary algorithms. Following this promising avenue of research, we propose a novel biobjective formulation of the multimodal optimization problem and use differential evolution (DE) with nondominated sorting followed by hypervolume measure-based sorting to finally detect a set of solutions corresponding to multiple global and local optima of the function under test. Unlike the two earlier multiobjective approaches (biobjective multipopulation genetic algorithm and niching-based nondominated sorting genetic algorithm II), the proposed multimodal optimization with biobjective DE (MOBiDE) algorithm does not require the actual or estimated gradient of the multimodal function to form its second objective. Performance of MOBiDE is compared with eight state-of-the-art single-objective niching algorithms and two recently developed biobjective niching algorithms using a test suite of 14 basic and 15 composite multimodal problems. Experimental results supported by nonparametric statistical tests suggest that MOBiDE is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.

Multimodal optimization amounts to finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and when needed, the current solution may be switched to a more suitable one while still maintaining the optimal system performance. Niching particle swarm optimizers (PSOs) have been widely used by the evolutionary computation community for solving real-parameter multimodal optimization problems. However, most of the existing PSO-based niching algorithms are difficult to use in practice because of their poor local search ability and requirement of prior knowledge to specify certain niching parameters. This paper has addressed these issues by proposing a distance-based locally informed particle swarm (LIPS) optimizer, which eliminates the need to specify any niching parameter and enhance the fine search ability of PSO. Instead of using the global best particle, LIPS uses several local bests to guide the search of each particle. LIPS can operate as a stable niching algorithm by using the information provided by its neighborhoods. The neighborhoods are estimated in terms of Euclidean distance. The algorithm is compared with a number of state-of-the-art evolutionary multimodal optimizers on 30 commonly used multimodal benchmark functions. The experimental results suggest that the proposed technique is able to provide statistically superior and more consistent performance over the existing niching algorithms on the test functions, without incurring any severe computational burdens.

Multilevel thresholding amounts to segmenting a gray-level image into several distinct regions. This paper presents a 2D histogram based multilevel thresholding approach to improve the separation between objects. Recent studies indicate that the results obtained with 2D histogram oriented approaches are superior to those obtained with 1D histogram based techniques in the context of bi-level thresholding. Here, a method to incorporate 2D histogram related information for generalized multilevel thresholding is proposed using the maximum Tsallis entropy. Differential evolution (DE), a simple yet efficient evolutionary algorithm of current interest, is employed to improve the computational efficiency of the proposed method. The performance of DE is investigated extensively through comparison with other well-known nature inspired global optimization techniques such as genetic algorithm, particle swarm optimization, artificial bee colony, and simulated annealing. In addition, the outcome of the proposed method is evaluated using a well known benchmark--the Berkley segmentation data set (BSDS300) with 300 distinct images.

Memetic algorithms (MAs) are population-based meta-heuristic search algorithms that combine the composite benefits of natural and cultural evolutions. An adaptive MA (AMA) incorporates an adaptive selection of memes (units of cultural transmission) from a meme pool to improve the cultural characteristics of the individual member of a population-based search algorithm. This paper presents a novel approach to design an AMA by utilizing the composite benefits of differential evolution (DE) for global search and Q-learning for local refinement. Four variants of DE, including the currently best self-adaptive DE algorithm, have been used here to study the relative performance of the proposed AMA with respect to runtime, cost function evaluation, and accuracy (offset in cost function from the theoretical optimum after termination of the algorithm). Computer simulations performed on a well-known set of 25 benchmark functions reveal that incorporation of Q-learning in one popular and one outstanding variants of DE makes the corresponding algorithm more efficient in both runtime and accuracy. The performance of the proposed AMA has been studied on a real-time multirobot path-planning problem. Experimental results obtained for both simulation and real frameworks indicate that the proposed algorithm-based path-planning scheme outperforms the real-coded genetic algorithm, particle swarm optimization, and DE, particularly its currently best version with respect two standard metrics defined in the literature.

This article presents a novel optimization technique hybridizing the concepts of Genetic Algorithm (GA) and Lbest Particle Swarm Optimization (Lbest PSO). A new topology, namely ‘Dynamically Varying Sub-swarm’ has been incorporated in the search process and some selected crossover and mutation techniques have been used for generation updating. This novel hybridized approach simultaneously ensures a robust search process, a quick convergence and a wide variety of real life applications. Simulations performed over various benchmark functions with the proposed method have been compared with other existing strong algorithms. Experimental results support the claim of proficiency of our algorithm over other existing techniques in terms of robustness, fast convergence and, most importantly its optimal search behavior.

Biometric system is very important for recognition in several security areas. In this paper we deal in designing biometric sensor manager by optimizing the risk. Risk is modeled as a multi-objective optimization with Global False Acceptance Rate and Global False Rejection Rate as two objectives. In practice, multiple biometric sensors are used and the decision is taken locally at each sensor and the data is passed to the sensor manager. At the sensor manager the data is fused using a fusion rule and the final decision is taken. The optimization involves designing the data fusion rule and setting the sensor thresholds. We have implemented a recent fuzzy dominance based decomposition technique for multi-objective optimization called MOEA/DFD and have compared its performance on other contemporary state-of-arts in multi-objective optimization field like MOEA/D, NSGAII. The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. We have simulated the algorithms on different number of sensor setups consisting of 3, 6, 8 sensors respectively. We have also varied the apriori probability of imposter from 0.1 to 0.9 to verify the performance of the system with varying threat. One of the most significant advantages of using multi-objective optimization is that with a single run just by changing the decision making logic applied to the obtained Pareto front one can find the required threshold and decision strategies for varying threat of imposter. But with single objective optimization one need to run the algorithms each time with change in threat of imposter. Thus multi-objective representation appears to be more useful and better than single objective one. In all the test instances MOEA/DFD performs better than all other algorithms.

This paper deals with an interesting application of designing a Fractional Order Controller for a Servo hydraulic positioning system, to compensate the negative effects of fluid leakage across a faulty actuator piston seal. A novel micro artificial bee colony algorithm (μABC) has been proposed for designing this Fractional order Controller based on minimizing Integral Time Absolute Error (ITAE) criterion. As μABC requires a less number of bees, the solution is obtained much faster than that of basic Artificial Bee Colony (ABC) method. Simulations and comparisons of proposed method along with that of GA and an adaptive variant of ABC in terms of time domain indices indicate the superiority of μABC in designing the fractional controller for a much complex plant.

We present an energy efficient sensor manager for differentiated coverage of dynamic object group changing their positions with time. The information about the location of the object group is provided to the sensor manager. The manager invokes optimization algorithm whenever the obtained coverage falls below a threshold to sleep schedule the sensor network. Multi-objective Optimization (MO) algorithms help in finding a better trade-off among energy consumption, lifetime, and coverage. Here the motion of the particle is modeled to follow a polynomial variation and with a constant acceleration. We formulate the scheduling problem as a combinatorial, constrained and multi-objective optimization problem with energy and non-coverage as the two objectives to be minimized. The proposed scheme uses a recent variant of a powerful MO algorithm known as Decomposition based Multi-Objective Evolutionary Algorithm (MOEA/D). Systematic comparison with the original MOEA/D and another well-known MO algorithm, NSGA-II (Non-dominated Sorting Genetic Algorithm) quantifies the superiority of the proposed approach.

This paper investigates the chaotic characteristics in the dynamics of an aggregating swarm model. The range of the parameters of the swarm model is determined for which chaos exists in the dynamics. The trajectories of the individuals are simulated, and the stable, limit cyclic, and chaotic behaviors are demonstrated. The existence of chaos in the swarm is determined by the maximum Lyapunov exponent. The computer simulation supports the results obtained by theoretical analysis.

The seven full papers and one technical correspondence in this special issue focus on the engineering applications of memetic computing.

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

This paper proposes an improved and adaptive variant of the differential evolution algorithm for the design of two-channel quadrature mirror filters with linear phase characteristics. To match the ideal system response characteristics, the algorithm is employed to optimize the values of the filter bank coefficients. The filter response is optimized in both passband and stopband. The overall filter bank response aims at minimizing objectives like reconstruction error, mean square error in passband, and mean square error in stopband. Effective designing can be achieved by efficiently minimizing the objective function. The proposed algorithm is able to perform better than the other existing design methods. Five different design examples are presented to validate the effectiveness of the proposed approach over other conventional design techniques, as well as state-of-the-art evolutionary algorithms found in the literature.

Differential evolution (DE) is one of the most powerful stochastic real parameter optimizers of current interest. In this paper, we propose a new mutation strategy, a fitness-induced parent selection scheme for the binomial crossover of DE, and a simple but effective scheme of adapting two of its most important control parameters with an objective of achieving improved performance. The new mutation operator, which we call DE/current-to-gr_best/1, is a variant of the classical DE/current-to-best/1 scheme. It uses the best of a group (whose size is q% of the population size) of randomly selected solutions from current generation to perturb the parent (target) vector, unlike DE/current-to-best/1 that always picks the best vector of the entire population to perturb the target vector. In our modified framework of recombination, a biased parent selection scheme has been incorporated by letting each mutant undergo the usual binomial crossover with one of the p top-ranked individuals from the current population and not with the target vector with the same index as used in all variants of DE. A DE variant obtained by integrating the proposed mutation, crossover, and parameter adaptation strategies with the classical DE framework (developed in 1995) is compared with two classical and four state-of-the-art adaptive DE variants over 25 standard numerical benchmarks taken from the IEEE Congress on Evolutionary Computation 2005 competition and special session on real parameter optimization. Our comparative study indicates that the proposed schemes improve the performance of DE by a large magnitude such that it becomes capable of enjoying statistical superiority over the state-of-the-art DE variants for a wide variety of test problems. Finally, we experimentally demonstrate that, if one or more of our proposed strategies are integrated with existing powerful DE variants such as jDE and JADE, their performances can also be enhanced.

We propose an online, multiobjective optimization (MO) algorithm to efficiently schedule the nodes of a wireless sensor network (WSN) and to achieve maximum lifetime. Instead of dealing with traditional grid or uniform coverage, we focus on the differentiated or probabilistic coverage where different regions require different levels of sensing. The MO algorithm helps to attain a better tradeoff among energy consumption, lifetime, and coverage. The algorithm can be run every time a node failure occurs due to power failure of the node battery so that it may reschedule the network. This scheduling is modeled as a combinatorial, multiobjective, and constrained optimization problem with energy and noncoverage as the two objectives. The basic evolutionary multiobjective optimizer used is known as decomposition-based multiobjective evolutionary algorithm (MOEA/D) which is modified by integrating the concept of fuzzy Pareto dominance. The performance of the resulting algorithm, which is called MOEA/DFD, is compared with the performance of the original MOEA/D, which is another very well known MO algorithm called nondominated sorting genetic algorithm (NSGA-II), and an IBM optimization software package called CPLEX. In all the tests, MOEA/DFD is observed to outperform all other algorithms.

This paper presents a new, differential-evolution based method for solving the problem of optimal selection of cluster-heads and cluster-members in mobile ad hoc networks. A novel encoding scheme is used to represent nodes in the network graph, and randomly-generated networks of different sizes are solved. The present method handles problems of much larger sizes than do the best-known methods in the literature. Empirical results show the superiority of this method over state-of-the-art approaches on two counts: quality of the solution and time to find the solution.

Orthogonal Frequency Division Multiplexing (OFDM) has emerged as very popular wireless transmission technique in which digital data bits are transmitted at a high speed in a radio environment. But the high peak-to-average power ratio (PAPR) is the major setback for OFDM systems demanding expensive linear amplifiers with wide dynamic range. In this article, we introduce a low-complexity partial transmit sequence (PTS) technique for diminishing the PAPR of OFDM systems. The computational complexity of the exhaustive search technique for PTS increases exponentially with the number of sub-blocks present in an OFDM system. So we propose a modified Differential Evolution (DE) algorithm with novel mutation, crossover as well as parameter adaptation strategies (MDE_pBX) for a sub-optimal PTS for PAPR reduction of OFDM systems. MDE_pBX is utilized to search for the optimum phase weighting factors and extensive simulation studies have been conducted to show that MDE_pBX can achieve lower PAPR as compared to other significant DE and PSO variants like JADE, SaDE and CLPSO.

Particle Swarm Optimization (PSO) is arguably one of the most popular nature-inspired algorithms for real parameter optimization at present. In this article, we introduce a new variant of PSO referred to as Hierarchical D-LPSO (Dynamic Local Neighborhood based Particle Swarm Optimization). In this new variant of PSO the particles are arranged following a dynamic hierarchy. Within each hierarchy the particles search for better solution using dynamically varying sub-swarms i.e. these sub-swarms are regrouped frequently and information is exchanged among them. Whether a particle will move up or down the hierarchy depends on the quality of its so-far best found result. The swarm is largely influenced by the good particles that move up in the hierarchy. The performance of Hierarchical D-LPSO is tested on the set of 25 numerical benchmark functions taken from the competition and special session on real parameter optimization held under IEEE Congress on Evolutionary Computation (CEC) 2005. The results have been compared to those obtained with a few best-known variants of PSO as well as a few significant existing evolutionary algorithms.

In this paper we propose a Self Adaptive Cluster based and Weed Inspired Differential Evolution algorithm (SACWIDE), the total population is divided into several clusters based on the positions of the individuals and the cluster number is dynamically changed by the suitable learning strategy during evolution. Here we incorporate a modified version of the Invasive Weed Optimization (IWO) algorithm as a local search technique. The algorithm strategically determines whether a particular cluster will perform Differential Evolution (DE) or the IWO algorithm (modified). The number of clusters in a particular iteration is set by the algorithm itself self-adaptively. The performance of SACWIDE is reported on the set of 22 benchmark problems of CEC-2011.

Time Division Multiple Access (TDMA) plays an important role in MAC (Medium Access Control) for wireless sensor networks providing real-time guarantees and potentially reducing the delay and also it saves power by eliminating collisions. In TDMA based MAC, the sensor are not allowed to radiate signals when they are not engaged. On the other hand, if there are too many switching between active and sleep modes it will also unnecessary waste energy. In this paper, we have presented a multi-objective TDMA scheduling problem that has been demonstrated to prevent the wasting of energy discussed above and also further improve the time performance. A Modified Discrete Differential Evolution (MDDE) algorithm has been proposed to enhance the converging process in the proposed effective optimization framework. Simulation results are given with different network sizes. The results are compared with the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) and the original Discrete DE algorithm (DDE). The proposed MDDE algorithm has successfully outperformed these three algorithms on the objective specified, which is the total time or energy for data collection.

Real world optimization problems are used to judge the performance of any Evolutionary Algorithm (EA) over real world applications. This is why the performance of any EA over the real world optimization problems is very important for judging its efficiency. In this work, we represent a multi population based memetic algorithm CDELS. It is hybridization of a competitive variant of Differential Evolution (DE) and a Local Search method. As the number of optima is large in this case, we have also incorporated a distant search method to hop from one optima to other optima. However, it is well known that DE has fast but less reliable convergence property. To overcome this limitation, a hybrid mutation strategy is developed to balance between exploration and thorough search. In addition, a proximity checking method is applied to distribute the subpopulations over a larger portion of the search space as this further enhances the searching ability of the algorithm. The performance of CDELS algorithm is evaluated on the test suite provided for the Competition on Testing Evolutionary Algorithms on Real-world Numerical Optimization Problems in the 2011 IEEE Congress on Evolutionary Computation and the simulation results are shown in this paper.

This paper presents a new Multiobjective Evolutionary Algorithm (MOEA) based on decomposition, with fuzzy dominance (MOEA/DFD). The algorithm introduces a fuzzy Pareto dominance concept to compare two solutions and uses the scalar decomposition method only when one of the solutions fails to dominate the other in terms of a fuzzy dominance level. The diversity is maintained through the uniformly distributed weight vectors. In addition, Dynamic Resource Allocation (DRA) is used to distribute the computational effort based on the utilities of the individuals. To assess the performance of the proposed algorithm, experiments were conducted on two general benchmarks and ten unconstrained benchmark problems taken from the competition on real parameter MOEAs held under the 2009 IEEE Congress on Evolutionary Computation (CEC). As per the IGD metric, MOEA/DFD outperforms other major MOEAs in most cases.

The objective of condition based maintenance (CBM) is typically to determine an optimal maintenance policy to minimize the overall maintenance cost based on condition monitoring information. In Aircraft operator and the maintenance people starving to reduce the cost of aircraft maintenance. So the condition based monitoring for electromechanical control valve is very popular recently. This paper has been proposed an optimized Fractional order Proportional-integral-derivative (FOPID) controller for electromechanical actuated worm gear operated fuel shut off valve.

Work load optimization in power generation plants is of practical importance in carbon constrained power industry. The main objective of the coal-fired power generation workload optimization is to minimize fuel consumption while maintaining the desired output and to maintain NOxemission within the environmental license limit. In this article, we represent an efficient Memetic Algorithm (MA) with a constraint handling method for the power generation loading optimization. This MA is developed by combining a competitive variant of Deferential Evolution (DE) and Simplex method. The proposed approach incorporates the constraint handling method to modify the selection rule which guides the search process in better direction. The simulation results based on a coal-fired power plant clearly indicate that our proposed method is very effective and it shows great computational efficiency in power generation workload optimization.

In recent years, there has been a growing interest in real world application of heuristic methods. Memetic Algorithm (MA) is one of such effective heuristics. In this paper, we represent an efficient MA for determining optimal proportional-integral-derivative (PID) controller parameters of an AVR system. This MA is developed by combining a competitive variant of Deferential Evolution (DE) and a Local Search method. The proposed method has excellent features, such as easy implementation, stable convergence characteristic and good computational efficiency. Fast tuning of PID controller parameters results in far better performance of the controller. Performance of our proposed algorithm is compared with other famous heuristics and the simulation results clearly indicate that our proposed approach is indeed more efficient and robust in improving the step response of an AVR system.

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

The six papers in this special issue are representative of the current research trends in differential evolution.

The theoretical analysis of evolutionary algorithms is believed to be very important for understanding their internal search mechanism and thus to develop more efficient algorithms. This paper presents a simple mathematical analysis of the explorative search behavior of a recently developed metaheuristic algorithm called harmony search (HS). HS is a derivative-free real parameter optimization algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. This paper analyzes the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. A simple but very useful modification to the classical HS has been proposed in light of the mathematical analysis undertaken here. A comparison with the most recently published variants of HS and four other state-of-the-art optimization algorithms over 15 unconstrained and five constrained benchmark functions reflects the efficiency of the modified HS in terms of final accuracy, convergence speed, and robustness.

Biogeography deals with the study of the distribution of biodiversity over space and time and has been well studied by naturists and biologists for over the last five decades. Recently, the theory of biogeography has been applied to solve difficult engineering optimization problems in the form of a nature-inspired metaheuristic, known as biogeography-based optimization (BBO) algorithm. In this correspondence paper, we present an in-depth analysis of the linear time-invariant (LTI) system model of immigration and emigration of organisms in an island biogeography system that forms the basis of BBO. We find the bound of the eigenvalues of the general LTI system matrix using the Perron-Frobenius theorem from linear algebra. Based on the bounds of the eigenvalues, we further investigate four important properties of the LTI biogeography system, including the system reasonability with probability distribution vectors, stability, convergence, and nature of the equilibrium state. Our analysis gives a better insight into the dynamics of migration in actual biogeography systems and also helps in the understanding of the search mechanism of BBO on multimodal fitness landscapes.

Time modulated antenna arrays attracted the attention of researchers for the synthesis of low/ultra-low side lobes in recent past. In this article we propose an improved variant of a recently developed ecologically inspired metaheuristic, well-known as Invasive Weed Optimization (IWO), to solve the real parameter optimization problem related to the design of time-modulated linear antenna arrays with ultra low Side Lobe Level (SLL), Side Band Level (SBL) and Main Lobe Beam Width (BWFN). We improvise the classical IWO by introducing two parallel populations and a more explorative routine of changing the mutation step-size with iterations. Experimental results indicate that the proposed algorithm achieves better performance over the design problem as compared to the conventional Taylor Series based method and the only known metaheuristic approach based on the Differential Evolution (DE) algorithm.

The paper employs Lagrange's mean value theorem of differential Calculus to design a new strategy for the selection of parameter vectors in the Differential Evolution (DE) algorithm. Classical differential evolution selects parameter vectors randomly to obtain the donor vectors. These donor vectors thus cannot be directly used as trial solution to the optimization problem. The recombination step indeed is very useful to generate potential trial solutions. The proposed algorithm eliminates the recombination step as the trial solutions can be directly generated by the extended mutation step only. Performance analysis of the proposed algorithm with respect to standard benchmark functions reveals that both in expected convergence time and accuracy in solutions, the proposed algorithm outperforms classical DE/rand/1. Besides extension in mutation strategy, an adaptive selection strategy in the scaling factor F also improves the performance of the proposed algorithm. In addition, the proposed algorithm outperforms classical DE in noisy optimization problem. Further, the number of function evaluation with scaled up dimensions of the optimization problem adds insignificantly small complexity in comparison to that in classical differential evolution to meet up a prescribed level of accuracy in solution quality.

Several variants of the Particle Swarm Optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that control the convergence behavior of the algorithm to the Pareto front in the objective function space. Limited simulation supports have also been provided to substantiate the theoretical derivations.

Design of non-uniform linear antenna arrays is one of the most important electromagnetic optimization problems of current interest. In this article, an adaptive Differential Evolution (DE) algorithm has been used to optimize the spacing between the elements of the linear array to produce a radiation pattern with minimum side lobe level and null placement control. DE is arguably one of the best real parameter optimizers of current interest takes very few control parameters and is easy to implement in any programming language. In this study two very simple adaptation schemes are used to regulate the control parameters F and Cr, upon which the performance of DE is critically dependent. The adaptation schemes are based on the objective function values of the target vectors and donor vectors. The adaptive DE-variant has been used to solve three difficult instances of the design problem and the optimization goal in each example is easily achieved. The results of the proposed algorithm have been shown to meet or beat the recently published results obtained using other state-of-the-art metaheuristics like the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Memetic Algorithms (MA), and Tabu Search (TS) in a statistically meaningful way.

Invasive Weed Optimization (IWO) is a recently developed derivative-free metaheuristic algorithm that mimics the robust process of weeds colonization and distribution in an ecosystem. On the other hand central to an ecosystem is the foraging behavior that pertains to the act of searching for food and forms an integral part of the daily life of most of the living creatures. For over past two decades, a few significant optimization algorithms were developed by emulating the foraging behavior of creatures like ants, bacteria, fish, bees etc. This article presents a hybrid real-parameter optimizer developed by incorporating the principles of Optimal Foraging Theory (OFT) in IWO, with a view to improving the search mechanism of the latter over discontinuous and multi-modal fitness landscapes, riddled with local optima. The hybridization does not impose any serious computational burden on IWO in terms of increasing number of Function Evaluations (FEs). The performance of the resulting hybrid algorithm has been compared with eleven other state-of-the-art metaheuristic algorithms over a test-suite of 16 numerical benchmarks taken from the CEC (Congress on Evolutionary Computation) 2005 competition and special session on real parameter optimization. Our simulation experiments indicate that the proposed algorithm is able to attain comparable results against the nine other optimizers. Owing to its promising performance on benchmarks and ease of implementation (without requiring much programming overhead), the proposed algorithm may serve as an attractive alternative for a plethora of practical optimization problems.

In this paper, the dynamic multi-swarm particle swarm optimizer (DMS-PSO) and a sub-regional harmony search (SHS) are hybridized to obtain DMS-PSO-SHS. A Modified multi-trajectory search (MTS) algorithm is also applied frequently on several selected solutions. Effective diversity maintaining properties of the dynamic multiple swarms in the DMS-PSO without crossover operation and strong exploitative properties of the HS with multi-parent crossover operation strengthen the overall search behavior of the proposed DMS-PSO-SHS. The whole PSO population is divided into a large number sub-swarms which is also the individual HS population. These sub-swarms are regrouped frequently by using various regrouping schedules and information is exchanged among the particles in the whole swarm. Therefore, different from the existing multi-swarm PSOs or local versions of PSO, our sub-swarms are dynamic and its size is small which is also appropriate to be the population of the harmony search. In addition, an external memory of selected past solutions is used to enhance the diversity of the swarm. The DMS-PSO-SHS is employed to solve the 20 numerical optimization problems for the CEC'2010 Special Session and Competition on Large Scale Global Optimization and competitive results are presented.

In this paper, we describe a multi-objective approach to determine an effective mitigation strategy during an outbreak of foot and mouth disease in cattle. The goal of the approach is to minimize the total number of infections. In addition, the direct costs must also be minimized as a secondary objective. The animals culled and vaccinations may also be minimized, as long as the number of infections is not compromised. Thus a three-tier hierarchy of objectives exists. A framework that considers objective hierarchies during a multi-objective optimization algorithm is suggested. Results show that this produces better results than a conventional multi-objective optimization approach.

In this article we describe an optimization-based design method for non-uniform, planar, and circular antenna arrays with the objective of achieving minimum side lobe levels for a specific first null beamwidth and also a minimum size of the circumference. Central to our design is a hybridization of two prominent metaheuristics of current interest namely the Invasive Weed Optimization (IWO) and the Differential Evolution (DE). IWO is a derivative-free real parameter optimization technique that mimics the ecological behavior of colonizing weeds. Owing to its superior performance in comparison with many other existing metaheuristics, recently IWO is being used in several engineering design problems from diverse domains. For the present application, we have modified classical IWO by incorporating the difference vector based mutation schemes from the realm of DE. Three difficult instances of the circular array design problem have been presented to illustrate the effectiveness of the hybrid Differential IWO (DIWO) algorithm. The design results obtained with modified IWO have been shown to comfortably outperform the results obtained with other state-of-the-art metaheuristics like Particle Swarm Optimization (PSO), and Differential Evolution (DE) in a statistically significant fashion.

An Optimal Control is a set of differential equations describing the path of the control variables that minimize the cost functional (function of both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: perform a global search for the control function that optimizes the required objective. Invasive Weed Optimization (IWO) technique is used here for optimal control. However, the direct solution method operates on discrete n-dimensional vectors, not on continuous functions, and becomes computationally unmanageable for large values of n. Thus, a parameterization technique is required, which can represent control functions using a small number of real-valued parameters. Typically, direct methods using evolutionary techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations, both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced, using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with Invasive Weed Optimization into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide range of optimal control problems.

Invasive Weed Optimization Algorithm IWO) is an ecologically inspired metaheuristic that mimics the process of weeds colonization and distribution and is capable of solving multi-dimensional, linear and nonlinear optimization problems with appreciable efficiency. In this article a modified version of IWO has been used for training the feed-forward Artificial Neural Networks (ANNs) by adjusting the weights and biases of the neural network. It has been found that modified IWO performs better than another very competitive real parameter optimizer called Differential Evolution (DE) and a few classical gradient-based optimization algorithms in context to the weight training of feed-forward ANNs in terms of learning rate and solution quality. Moreover, IWO can also be used in validation of reached optima and in the development of regularization terms and non-conventional transfer functions that do not necessarily provide gradient information

This paper proposes a simple, metaheuristic clustering technique, inspired by the mountain clustering method of Yager and Filev, for detecting general quadric shell type clusters. The algorithm employs an ecologically inspired metaheurisitc algorithm, called Invasive Weed Optimization (IWO) to evolve a set of cluster prototypes in the shape of curves/hyper-surfaces. The objective function is modeled using the concept of the mountain function from Yager and Filev's work. The metaheuristic approach can be extended to solid clusters and various shell clusters like circular, elliptical, rectangular etc. The proposed method is tested on several synthetic datasets as well as real images to detect circular and elliptical shell clusters and the results obtained are found to be very promising.

The paper proposes a novel formulation of the classical box-pushing problem by mobile robots as a multi-objective optimization problem, and presents Pareto optimal solution to the problem using non-dominated sorting genetic algorithm-II (NSGA-II). The proposed method adopts local planning scheme, and allows both turning and translation of the box in the robots' workspace in order to minimize the consumption of both energy and time. The planning scheme introduced here determines the magnitude of the forces applied by two mobile robots at specific location on the box in order to align and translate it along the time- and energy- optimal trajectory in each distinct step of motion of the box. The merit of the proposed work lies in autonomous selection of translation distance and other important parameters of the robot motion model using NSGA-II. The suggested scheme, to the best of the authors' knowledge, is a first successful realization of a communication-free, centralized cooperation between two robots used in box shifting problem satisfying both time and energy minimization objectives simultaneously, presuming no additional user-defined constraint on the selection of linear distance traversal.

This paper describes an evolutionary clustering algorithm, which can partition a given dataset automatically into the optimal number of groups through one shot of optimization. The proposed method is based on an evolutionary computing technique known as the Bacterial Evolutionary Algorithm (BEA). The BEA draws inspiration from a biological phenomenon of microbial evolution. Unlike the conventional mutation, crossover and selection operaions in a GA (Genetic Algorithm), BEA incorporates two special operations for evolving its population, namely the bacterial mutation and the gene transfer operation. In the present context, these operations have been modified so as to handle the variable lengths of the chromosomes that encode different cluster groupings. Experiments were done with several synthetic as well as real life data sets including a remote sensing satellite image data. The results estabish the superiority of the proposed approach in terms of final accuracy.

Very recently bacterial foraging has emerged as a powerful technique for solving optimization problems. In this paper, we introduce a micro-bacterial foraging optimization algorithm, which evolves with a very small population compared to its classical version. In this modified bacterial foraging algorithm, the best bacterium is kept unaltered, whereas the other population members are reinitialized. This new small population mu-BFOA is tested over a number of numerical benchmark problems for high dimensions and we find this to outperform the normal bacterial foraging with a larger population as well as with a smaller population.

A gene regulatory network describes the influence of genes over others. This paper attempts to model gene regulatory network by a recurrent neural net with fuzzy membership distribution of weights. A cost function is designed to match the response of neurons in the network with the gene expression data, and a differential evolution algorithm is used to minimize the cost function. The minimization yields fuzzy membership distribution of weights, which on de-fuzzification provides the desired signed weights of the gene regulatory network. Computer simulation reveals that the proposed method outperforms existing techniques in detecting sign, and magnitude of weights of the regulatory network.

This paper applies the differential evolution (DE) algorithm to the task of automatic fuzzy clustering in a Multi-objective optimization (MO) framework. It compares the performances of four recently developed multi-objective variants of DE over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation of the search variables, accommodating variable number of cluster centers, is used for DE. The performances of four DE variants have also been contrasted to that of two most well-known schemes of MO clustering namely the Non Dominated Sorting Genetic Algorithm (NSGA II) and Multi-Objective Clustering with an unknown number of Clusters K (MOCK). Experimental results over six artificial and four real life datasets of varying range of complexities indicates that DE holds immense promise as a candidate algorithm for devising MO clustering schemes.

In fuzzy abduction, one needs to evaluate the membership distribution of the premise (antecedent clause), when the membership distribution of the consequent clause, and the fuzzy implication relations between the antecedent and the consequent clauses are provided. The paper formulates and solves the problem of fuzzy abduction by using type-2 fuzzy sets. It presumes background knowledge about the primary and the secondary antecedent to consequent implication relations to uniquely determine the type-2 fuzzy set corresponding to the antecedent clause, when the same for the consequent clause is provided. The proposed methodology of abduction would serve many interesting applications on predictions, forecasting, and diagnosis, where the environmental factor can be modeled with type-2 secondary distributions.

Determining correlation between aroused emotion and its manifestation on facial expression, voice, gesture and posture have interesting applications in psychotherapy. A set of audiovisual stimulus, selected by a group of experts, is used to excite emotion of the subjects. EEG and facial expression of the subjects excited by the selected audio-visual stimulus are collected, and the nonlinear-correlation from EEG to facial expression, and vice-versa is obtained by employing feed-forward neural network trained with back-propagation algorithm. Experiments undertaken reveals that the trained network can reproduce the correlated EEG-facial expression trained instances with 100 % accuracy, and is also able to predict facial expression (EEG) from unknown EEG (facial expression) of the same subject with an accuracy of around 95.2%.

Harmony Search (HS) is a recently developed stochastic algorithm which imitates the music improvisation process. In this process, the musicians improvise their instrument pitches searching for the perfect state of harmony. Practical experiences, however, suggest that the algorithm suffers from the problems of slow and/or premature convergence over multimodal and rough fitness landscapes. This paper presents an attempt to improve the search performance of HS by hybridizing it with Differential Evolution (DE) algorithm. The performance of the resulting hybrid algorithm has been compared with classical HS, the global best HS, and a very popular variant of DE over a test-suite of six well known benchmark functions and one interesting practical optimization problem. The comparison is based on the following performance indices - (i) accuracy of final result, (ii) computational speed, and (iii) frequency of hitting the optima.

The article considers the task of fuzzy clustering in a multi-objective optimization (MO) framework. It compares the relative performance of four recently developedmulti-objective variants of Differential Evolution (DE) on over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation for the candidates is used for DE. A comparative study of four DE variants with two most well-known MO clustering techniques, namely the NSGA II (Non Dominated Sorting GA) and MOCK (Multi- Objective Clustering with an unknown number of clusters K) is also undertaken. Experimental results reported for six artificial and four real life datasets (including a microarray dataset of budding yeast) of varying range of complexities indicates that DE can serve as a promising algorithm for devising MO clustering techniques.

Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms (EAs) and other search heuristics like the particle swarm optimization (PSO) when tested over both benchmark and real-world problems. DE, however, is not completely free from the problems of slow and/or premature convergence. This paper describes a family of improved variants of the DE/target-to-best/1/bin scheme, which utilizes the concept of the neighborhood of each population member. The idea of small neighborhoods, defined over the index-graph of parameter vectors, draws inspiration from the community of the PSO algorithms. The proposed schemes balance the exploration and exploitation abilities of DE without imposing serious additional burdens in terms of function evaluations. They are shown to be statistically significantly better than or at least comparable to several existing DE variants as well as a few other significant evolutionary computing techniques over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two real-life problems concerning parameter estimation for frequency modulated sound waves and spread spectrum radar poly-phase code design.

In his seminal paper published in 2002, Passino pointed out how individual and groups of bacteria forage for nutrients and how to model it as a distributed optimization process, which he called the bacterial foraging optimization algorithm (BFOA). One of the major driving forces of BFOA is the chemotactic movement of a virtual bacterium that models a trial solution of the optimization problem. This paper presents a mathematical analysis of the chemotactic step in BFOA from the viewpoint of the classical gradient descent search. The analysis points out that the chemotaxis employed by classical BFOA usually results in sustained oscillation, especially on flat fitness landscapes, when a bacterium cell is close to the optima. To accelerate the convergence speed of the group of bacteria near the global optima, two simple schemes for adapting the chemotactic step height have been proposed. Computer simulations over several numerical benchmarks indicate that BFOA with the adaptive chemotactic operators shows better convergence behavior, as compared to the classical BFOA. The paper finally investigates an interesting application of the proposed adaptive variants of BFOA to the frequency-modulated sound wave synthesis problem, appearing in the field of communication engineering.

Bacterial-foraging optimization algorithm (BFOA) attempts to model the individual and group behavior of E.Coli bacteria as a distributed optimization process. Since its inception, BFOA has been finding many important applications in real-world optimization problems from diverse domains of science and engineering. One key step in BFOA is the computational chemotaxis, where a bacterium (which models a candidate solution of the optimization problem) takes steps over the foraging landscape in order to reach regions with high-nutrient content (corresponding to higher fitness). The simulated chemotactic movement of a bacterium may be viewed as a guided random walk or a kind of stochastic hill climbing from the viewpoint of optimization theory. In this paper, we first derive a mathematical model for the chemotactic movements of an artificial bacterium living in continuous time. The stability and convergence-behavior of the said dynamics is then analyzed in the light of Lyapunov stability theorems. The analysis indicates the necessary bounds on the chemotactic step-height parameter that avoids limit cycles and guarantees convergence of the bacterial dynamics into an isolated optimum. Illustrative examples as well as simulation results have been provided in order to support the analytical treatments.

One of the major driving forces of bacterial foraging optimization algorithm (BFOA) is the reproduction phenomenon of virtual bacteria each of which models one trial solution of the optimization problem. During reproduction, the least healthier bacteria (with a lower accumulated value of the objective function in one chemotactic lifetime) die and the other healthier bacteria each split into two, which then starts exploring the search place from the same location. This keeps the population size constant in BFOA. The phenomenon has a direct analogy with the selection mechanism of classical evolutionary algorithms. In this article, we provide a simple mathematical analysis of the effect of reproduction on bacterial dynamics. Our analysis reveals that the reproduction event contributes to the quick convergence of the bacterial population near optima.

A modified differential evolution (DE) algorithm is presented for clustering the pixels of an image in its intensity space. The algorithm requires no prior information about the number of naturally occurring clusters in the image. It employs a kernel-induced similarity measure instead of the conventional sum-of-squares distance. Use of the kernel function makes it possible to partition data that is linearly non-separable and non hyper-spherical in the original input space, into homogeneous groups in a transformed high-dimensional feature space. A novel chromosome representation scheme is adopted for selecting the optimal number of clusters from several possible choices. Extensive performance comparison over a test-suit of five gray scale images (with ground truth) indicates that the proposed algorithm has an edge over a few state-of-the-art algorithms for automatic multi-class image segmentation.

Differential evolution (DE) is well known as a simple and efficient algorithm for global optimization over continuous spaces. This article provides a simple mathematical model of the underlying evolutionary dynamics of a one-dimensional DE. The model relates the search process of DE with the classical gradient descent search and also analyzes the convergence behavior of a DE population, very near to optima.

Hardware/software partitioning is a crucial problem in embedded system design. In this paper, we provide an alternative approach to solve this problem using particle swarm optimization (PSO) algorithm. Performance analysis of the proposed scheme with integer linear programming, genetic algorithm and ant colony optimization technique has been compared using standard benchmark datasets, and the computer simulations reveal that the proposed approach outperforms all the meta-heuristic based existing techniques with respect to cumulative runtimes for several runs of the same program. The integer linear programming has been found to yield the optimal solutions, and the proposed swarm scheme yields sub-optimal solution, sufficiently close to the reported results obtained for integer programming.

Some researchers have illustrated how individual and groups of bacteria forage for nutrients and to model it as a distributed optimization process, which is called the bacterial foraging optimization (BFOA). One of the major driving forces of BFOA is the chemotactic movement of a virtual bacterium, which models a trial solution of the optimization problem. In this article, we analyze the chemotactic step of a one dimensional BFOA in the light of the classical gradient descent algorithm (GDA). Our analysis points out that chemotaxis employed in BFOA may result in sustained oscillation, especially for a flat fitness landscape, when a bacterium cell is very near to the optima. To accelerate the convergence speed near optima we have made the chemotactic step size C adaptive. Computer simulations over several numerical benchmarks indicate that BFOA with the new chemotactic operation shows better convergence behavior as compared to the classical BFOA.

Differential Evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE for the design of Fractional-Order Proportional-Integral-Derivative (FOPID) Controllers involving fractional order integrator and fractional order differentiator. FOPID controllers' parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer order PID controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional order closed loop transfer function of the designed plant, Tustin operator-based CFE (continued fraction expansion) scheme was used in this work. Simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and Bacterial Foraging Optimization Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional order plants.

This article presents an algorithm for the automatic detection of circular shapes from complicated and noisy images. The algorithm is based on a recently developed swarm-intelligence technique, well known as the Bacterial Foraging Optimization (BFO). A new fuzzy objective function has been derived for the edge map of a given image. Minimization of this function with an adaptive version of the BFO algorithm leads to the automatic detection of circles on the image.

This article presents an algorithm for the automatic detection of circular shapes from complicated and noisy images. The algorithm is based on a hybrid technique composed of simulated annealing and differential evolution. A new fuzzy objective function has been derived for the edge map of a given image. Minimization of this function with a hybrid annealed differential evolution algorithm leads to the automatic detection of circles on the image. Simulation results over several synthetic as well as natural images with varying range of complexity validate the efficacy of the proposed technique in terms of its final accuracy, speed and robustness.

Differential evolution (DE) has emerged as one of the fast, robust, and efficient global search heuristics of current interest. This paper describes an application of DE to the automatic clustering of large unlabeled data sets. In contrast to most of the existing clustering techniques, the proposed algorithm requires no prior knowledge of the data to be classified. Rather, it determines the optimal number of partitions of the data “on the run.” Superiority of the new method is demonstrated by comparing it with two recently developed partitional clustering techniques and one popular hierarchical clustering algorithm. The partitional clustering algorithms are based on two powerful well-known optimization algorithms, namely the genetic algorithm and the particle swarm optimization. An interesting real-world application of the proposed method to automatic segmentation of images is also reported.

The paper extends the classical Ant Systems by considering non-uniform deposition by the ants, while constructing pheromone trails. A deterministic solution to the ant system dynamics for both uniform and non-uniform pheromone deposition rules has been obtained to determine the parameters of the dynamics that ensure stability in pheromone trails. Computer simulation confirmed the results of stability analysis. Performance of the extended ant system (with nonuniform pheromone deposition rule) is compared with the classical ant system using the well known Traveling Salesperson Problem. Simulation results reveal that the extended ant system outperforms the classical ant system by a large margin with respect to convergence speed without sacrificing the quality of solution.

Differential evolution (DE) has recently emerged as a leading methodology for global search and optimization over continuous, high-dimensional spaces. It has been successfully applied to a wide variety of nearly intractable engineering problems. However, the DE and its variants usually employ a deterministic selection mechanism that always allows the better solution to survive to the next generation. This often prevents DE from escaping local optima at the early stages of search over a multi-modal fitness landscape and leads to a premature convergence. The present work proposes to improve the accuracy and convergence speed of DE by introducing a stochastic selection mechanism. The idea of a conditional acceptance function (that allows accepting inferior solutions with a gradually decaying probability) is borrowed from the realm of the simulated annealing (SA). In addition, the work proposes a center of mass based mutation operator and a decreasing crossover rate in DE. Performance of the resulting hybrid algorithm has been compared with three state-of-the-art adaptive DE schemes. The method is shown to be statistically significantly better on a six-function test-bed and one difficult engineering optimization problem with respect to the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.

This paper presents an alternative formulation of the PSO dynamics by a closed loop control system, and analyzes the stability behavior of the system by using Jury's test and root locus technique. Previous stability analysis of the PSO dynamics was restricted because of no explicit modeling of the non-linear element in the feedback path. In the present analysis, the nonlinear element model of the non-linear element is considered for closed loop stability analysis. Unlike the previous works on stability analysis, where the acceleration coefficients have been combined into a single term, this paper considered their separate existence for determining their suitable range to ensure stability of the dynamics. The range of parameters of the PSO dynamics, obtained by Jury's test and root locus technique were also confirmed by computer simulation of the PSO algorithm.

This paper introduces a method for clustering complex and linearly non-separable datasets, without any prior knowledge of the number of naturally occurring clusters. The proposed method is based on an improved variant of the Particle Swarm Optimization (PSO) algorithm. In addition, it employs a kernel-induced similarity measure instead of the conventional sum-of-squares distance. Use of the kernel function makes it possible to cluster data that is linearly non-separable in the original input space into homogeneous groups in a transformed high-dimensional feature space. Computer simulations have been undertaken with a test bench of five synthetic and three real life datasets, in order to compare the performance of the proposed method with a few state-of-the-art clustering algorithms. The results reflect the superiority of the proposed algorithm in terms of accuracy, convergence speed and robustness.

This paper investigates a novel approach for partitional clustering of a large collection of text documents by using an improved version of the classical Differential Algorithm (DE). Fast and accurate clustering of documents plays an important role in the field of text mining and automatic information retrieval systems. The k-means has served as the most widely used partitional clustering algorithm for text documents. However, in most cases it provides only locally optimal solutions. In this work, the clustering problem has been formulated as an optimization task and is solved using a modified DE algorithm. To reduce the computational time, a hybrid k-means with DE method has also been proposed. The new algorithms were tested on a number of document datasets. Comparison with k-means, a state of the art PSO and one recently proposed real coded GA based text clustering methods reflects the superiority of the proposed techniques in terms of speed and quality of clustering.

Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. It is, however, not free from the problem of slow and premature convergence. In this paper we present an improved variant of the classical DE2 scheme, by utilizing the concept of the local neighborhood of each vector. This scheme attempts to balance the exploration and exploitation abilities of DE without requiring additional function evaluations. The new scheme is shown to be statistically significantly better than three other popular DE variants on a six-function test-bed and also on two real-world optimization problems with respect to the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.

In this paper we propose a novel fuzzy clustering algorithm for automatically grouping the pixels of an image into different homogeneous regions when the number of clusters is not known a-priori. A soft clustering task in the intensity space of an image is formulated as an optimization problem. We use an improved differential evolution (DE) algorithm to automatically determine the number of naturally occurring clusters in the image as well as to refine the cluster centers. We report extensive performance comparisons among the new method, a recently developed genetic-fuzzy clustering technique and the classical fuzzy c-means algorithm over a test suite comprising ordinary gray scale images and remote sensing satellite images. Such comparisons show, in a statistically meaningful way, the superiority of the proposed technique in terms of speed, accuracy and robustness.

In the past few years, there has been a massive growth in the field of biologically inspired global search heuristics. Computational cost having been reduced almost dramatically, researchers from all corners are taking more interset in following the underlying principles of nature to solve nearly intractable search problems. In this paper, we attempt to solve one very important optimization problem arising in the field of two-dimensional IIR (infinite impulse response) filter design, with three naturally inspired global search algorithms. We have used a state-of-the-art real coded genetic algorithm (GA), one very recent and modified version of the particle swarm opimization (PSO) and finally an improved version of the differential evolution (DE) algorithm. The DE algorithm has been modified by us to prevent its premature convergence to some suboptimal region of the search space. The design task is formulated as a constrained minimization problem and solved by the three metaheuristics. Numerical results are presented over three difficult instances of the design problem. The study also compares the results with two recently published filter design methods. Our experiments reveal that the DE family of algorithms should receive primary attention in solving the constrained multidimensional filter design tasks.

Differential evolution (DE) is a simple and efficient algorithm for function optimization over continuous spaces. It has reportedly outperformed many types of evolutionary algorithms and other search heuristics when tested over both benchmark and real-world problems. However, the performance of DE deteriorates severely if the fitness function is noisy and continuously changing. In this paper two improved DE algorithms have been proposed that can efficiently find the global optima of noisy functions. This is achieved firstly by weighing the difference vector by a random scale factor and secondly by employing two novel selection strategies as opposed to the conventional one used in the original versions of DE. An extensive performance comparison of the newly proposed scheme, the original DE (DE/Rand/1/Exp), the canonical PSO and the standard real-coded EA has been presented using well-known benchmarks corrupted by zero-mean Gaussian noise. It has been found that the proposed method outperforms the others in a statistically significant way.

This paper introduces a novel scheme of improving the performance of particle swarm optimization (PSO) by a vector differential operator borrowed from differential evolution (DE). Performance comparisons of the proposed method are provided against (a) the original DE, (b) the canonical PSO, and (c) three recent, high-performance PSO-variants. The new algorithm is shown to be statistically significantly better on a seven-function test suite for the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.

Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. In this paper we present two new, improved variants of DE. Performance comparisons of the two proposed methods are provided against (a) the original DE, (b) the canonical particle swarm optimization (PSO), and (c) two PSO-variants. The new DE-variants are shown to be statistically significantly better on a seven-function test bed for the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.

This paper presents an efficient technique of designing two-dimensional IIR digital filters using a new algorithm involving the tightly coupled synergism of particle swarm optimization and differential evolution. The design task is reformulated as a constrained minimization problem and is solved by our newly developed PSO-DV (Particle Swarm Optimizer with Differentially perturbed Velocity) algorithm. Numerical results are presented. The paper also demonstrates the superiority of the proposed design method by comparing it with two recently published filter design methods.