The emergence of bias in deep neural models represents a significant reliability concern, which may lead to overoptimistic results on seen data while compromising the model's ability to generalize effectively on unseen datasets. Recent studies conducted on The Cancer Genome Atlas (TCGA), which is a publicly available repository of histopathology images, reveal that the TCGA cancerous features extracted by deep neural networks surprisingly are able to discriminate slides based on their origin sites. This finding undoubtedly indicates the existence of site-specific patterns embedded in the extracted features learned by deep networks rather than focusing on histomorphologic patterns. Consequently, this biased behavior raises concerns about the reliability of these networks. This observation motivates us to conduct a series of experiments in which we present two distinct evolutionary feature selection strategies, each differentiated by its objective function evaluation. The primary goal is to select the features with a minimized foot-print of data source signatures, thereby ensuring a more accurate and site-independent cancer classification. We have conducted nine comprehensive independent experiments across nine cancer types, employing each evolutionary strategy. The comparison between results obtained through evolutionary strategies and the original feature sets highlights the substantial impact of feature selection methods on bias reduction while maintaining accuracy in cancer-type discrimination. Furthermore, the comparison of the two strategies with each other demonstrates the intricate nature of bias and its integration with cancerous features during the training process.

Feature selection plays a pivotal role in the data preprocessing and model-building pipeline, significantly en-hancing model performance, interpretability, and resource efficiency across diverse domains. In population-based optimization methods, the generation of diverse individuals holds utmost importance for adequately exploring the problem landscape, particularly in highly multi-modal multi-objective optimization problems. Our study reveals that, in line with findings from sev-eral prior research papers, commonly employed crossover and mutation operations lack the capability to generate high-quality diverse individuals and tend to become confined to limited areas around various local optima. This paper introduces an augmen-tation to the diversity of the population in the well-established multi-objective scheme of the genetic algorithm, NSGA-II. This enhancement is achieved through two key components: the genuine initialization method and the substitution of the worst individuals with new randomly generated individuals as a re-initialization approach in each generation. The proposed multi-objective feature selection method undergoes testing on twelve real-world classification problems, with the number of features ranging from 2,400 to nearly 50,000. The results demonstrate that replacing the last front of the population with an equivalent number of new random individuals generated using the genuine initialization method and featuring a limited number of features substantially improves the population's quality and, consequently, enhances the performance of the multi-objective algorithm.

Multi-loss functions are present in various aspects of deep learning. In multi-modal, cross-modal, and multi-task learning contexts, multi-loss functions are essential elements for handling complex data with diverse information sources. Different tasks or modalities may have conflicting objectives. By combining them into a single loss function, the model might struggle to strike the right balance between these objectives, leading to suboptimal performance. The Multi-objective Adam optimizer, also referred to as MAdam, is an extension of Adam optimizer that is applied for optimizing several competing loss functions in deep learning. The MAdam algorithm exhibits sensitivity to its initialization, necessitating the injection of ex-treme points into the initial population. Additionally, this scheme encounters difficulties in effectively capturing the disconnected and non-convex Pareto fronts. In this paper, an opposition-based scheme was introduced into MAdam framework as global search is necessary for escaping local optima in gradient-based multi-objective optimization approaches. The Opposition-based MAdam, explores multiple directions over the landscape, that leads to independence from specific initialization. In a series of experiments, we demonstrate the scalability of our method by capturing the entire Pareto front using the MNIST dataset for binary classification of digit images 2 and 3. This was achieved with a fully connected network, employing multi-objective mean absolute error and binary cross-entropy as losses. OMAdam matches Adam's Fl-score in the early generations, a result to its high exploratory capacity which enhances its performance in initial stages of classification tasks. This results in a reduction of computational costs compared to both Adam and MAdam. The variation in Fl-score values along the Pareto front trajectory enables practitioners to select a post hoc solution based on the trade-offs achieved among conflicting loss functions as multiple objectives. This contrasts with Adam, which offers limited options due to its single-solution approach.

Feature selection is a crucial step in the model-building pipeline in machine learning (ML) applications such as Electroencephalogram (EEG) signal processing, providing benefits on model performance and computational efficiency. EEG signals play a pivotal role in elucidating human nature through promising ML mechanisms. However, extracting a large number of features from the EEG signals can be a challenge of efficient EEG processing. A multi-objective feature selection strategy applied to the extracted features from EEG signals can simultaneously improve the accuracy of the process and reduce the number of features. However, the high dimensionality of the EEG feature vectors actually diminishes the exploration capabilities of multi-objective algorithms, impeding their real-world applicability. Hence, we propose a novel correlation-based multi-objective feature selection (COR-MFS) method, that aims to reduce dimensionality before applying the multi-objective algorithm. In the initial phase, a correlation-based dimension re-duction method is applied to filter the most relevant features with highest correlation with the class label. Subsequently, a multi-objective feature selection algorithm is applied to the shrunk search space enhancing optimization efficiency and facilitating the search process. We evaluated the proposed COR-MFS method using six large-scale EEG datasets and observed significant improvements compared to the stand-alone multi-objective feature selection. This underscores the effectiveness of our innovative framework in providing more accurate solutions with fewer number of features for extensive EEG-based classification tasks.

Feature selection is a demanding and costly endeavor within the realms of machine learning and data mining, targeting the elimination of irrelevant and redundant features. This endeavor significantly bolsters classification accuracy or other post processing components, such as search or clustering. In this context, the feature selection can be as a single-objective optimization task, with the primary objective of maximizing classification accuracy or multi-objective one while minimizing the number of selected features as well which can be tackled using population-based metaheuristic algorithms. Considering that feature selection (FS) inherently poses a binary problem, given that most metaheuristic algorithms operate in continuous domains (such as Real-coded GA, DE, PSO, and CMA-ES), transitioning them to binary search spaces necessitates substantial operator modifications. One of the crucial steps of the population-based algorithms is initialization of the population which significantly impacts both the convergence speed and the quality of the final solution. However, in most cases, especially with continuous algorithms, random initialization emerges as the predominant method for generating candidate solutions (initial population) which lacks diversity in the large-scale feature selection search spaces. In this paper, two novel population initialization methods within the continuous search space are introduced, followed by a comparative analysis against the traditional random initialization method. Experimental results conducted on ten datasets with 300 to 11,000 features demonstrate the effectiveness of population-level uniform initialization, surpassing the widely recognized individual-level uniform initialization method. The experiments are conducted using Differential Evolution as the single-objective algorithm and Generalized Differential Evolution3 as a multi-objective algorithm as our case studies. This study demonstrates the crucial role of initialization in the population-based optimization algorithms when they tackle binary problems.

Feature selection is a pivotal component of machine learning and data analysis, to optimize model performance by eliminating irrelevant and redundant features, to address the challenges associated with the “curse of dimensionality” and interpretability. In this context, we present feature selection as a multi-objective binary optimization task with the dual aim of maximizing classification accuracy while minimizing the number of selected features. In order to address this optimization challenge, we introduce the Multi-objective Binary Differential Evolution algorithm (MOBDE). It's worth noting that DE originally is an extremely powerful real-value coded algorithm, and to make it binary, set-based operators must replace vector-based operations. Optimization in binary space is deemed more suitable than real-value optimization because a many-to-one mapping can waste the efforts of the optimizer when solving a binary problem like feature selection. The algorithm leverages a partial opposition-based binary operator to generate diverse solutions to enhance its exploration within the search space. Additionally, it incorporates a majority voting mechanism as a local search strategy to bolster the algorithm's exploitation capabilities. Results from experimentation on eleven datasets underscore the efficiency of MOBDE, outperforming the widely recognized NSGA-II method in terms of the hypervolume (HV) performance metric and minimizing the number of selected features. The proposed algorithm and its experimental outcomes are comprehensively detailed and analyzed, offering valuable insights into its efficacy for feature selection tasks.

Deep neural networks (DNNs) have shown ex-ceptional performance in various domains, leading to their widespread adoption. However, the necessity to deploy DNNs on resource-constrained devices calls for improved model efficiency. Accordingly, DNN pruning has emerged as a critical technique in the field of machine learning, offering significant improve-ments in computational efficiency and model simplicity. This paper introduces an innovative post-training pruning approach for DNNs without any retraining, that utilizes multi-objective optimization to achieve substantial sparsity rates while preserving significant accuracy levels. The proposed method transforms the post-training weight pruning challenge into a two-variable, bi-objective optimization problem. The optimizer finds the optimal minimum and maximum threshold values through optimization, effectively converting the real-valued weights between these two thresholds to zero. The task and model-independency of the proposed framework make it applicable across various models, tasks, and datasets without constraints on the number of weights. The approach provides a decision-maker, where users can select the best strategy within resource constraints to achieve their desired accuracy. In order to assess our method, we evaluated the pruning of RESNET50 model on CIFAR10 and CIFAR100 benchmark datasets. In CIFAR10, by reducing 70% of the weights within the optimal threshold values, the network's accuracy only decreases by 0.1. Similarly, in CIFAR100, an appropriate weight range was selected, resulting in a 65 % reduction in weights while maintaining a negligible 0.1 decrease in network accuracy. This demonstrates the effectiveness of the optimization in achieving significant model size reduction without compromising performance on large DNNs.

The utilization of binary representation of the embeddings over real valued features represents a promising avenue, in terms of memory savings and faster operations for various machine learning models. In this research paper, we delve into the exploration of barcode representation for text embeddings derived from BERT, which is optimized using Co-ordinate Search algorithm. These binary embeddings present a compact representation of text, thereby mitigating memory and computational demands, which is especially advantageous in the context of resource-intensive large-scale text processing tasks. In our study, we introduce a novel optimal threshold technique, coupled with the Coordinate Search algorithm to transform continuous BERT embeddings into binary barcodes thereby enabling effective Natural Language Processing while sustaining computational efficiency. The optimal barcode representations have been applied in Natural Language Processing applications, showcasing its innovative potential in revolutionizing text representation. Through an extensive series of experiments on various NLP task encompassing diverse datasets, we comprehensively evaluate our approach, comparing it against a spectrum of thresholding techniques. The binary embeddings achieved by optimal thresholds outperform traditional binarization methods in terms of accuracy. The proposed method for generating a binary representations is versatile, being independent of the model, data and task, making it applicable across various machine learning applications.

In order to solve huge-scale optimization problems, many evolutionary algorithms have been proposed. In this paper, we introduce Block Differential Evolution (BDE) algorithm. The BDE can be categorized into the class of memory-efficient optimization algorithms. The main contribution is to solve large and huge-scale problems effectively and efficiently by reducing the problem dimension by utilizing a dimension-blocking scheme. With respect to the block size times reduced memory usage, furthermore, the proposed algorithm is computationally more efficient because DE operations (i.e., mutation, crossover, and selection) are performed on much smaller vector sizes. In fact, the employed blocking approach helps us to map the higher-dimensional problems into a lower-dimensional one which is more convenient to process during the optimization steps. There is a great demanding potential for the proposed approach to be utilized in embedded systems with low computational resources as a compressed optimization algorithm. This strategy is instantiated and evaluated on some well-known benchmark problems and compared with the baseline classic DE algorithm; the reported results are promising and encouraging for conducting further investigations. To the best of our knowledge, that is the first time a variable blocking scheme has been used in any meta-heuristic algorithm. A detailed explanation of the geometrical behavior of the proposed blocking approach is provided which explains how in a higher search space, a blocking approach is meaningful and applicable to accelerate convergence rate while the memory saving is huge. The reported results in this paper show the experiments on Large-Scale Global Optimization Problems proposed in CEC-2013 benchmark suite with 1,000, 10,000, and 100,000 dimensions and clearly are evidence of the possibility of satisfying two conflicting objectives, namely, efficiency and effectiveness, simultaneously. In order to utilize CEC-2013 benchmark problems for the huge dimensions 10,000D and 100,000D, some modifications and expansions have been done. The proposed approach can be utilized in another population-based optimization algorithm (swarm or evolutionary), and it is not restricted to the DE algorithm. In this paper, DE has been used as a parent algorithm for our conducted case study.

Many real-world optimization problems can be modelled with several competing objectives. Most of the time, such optimization problems fall under the category of expensive problems. These are problems in which each fitness evaluation is time-consuming, for example, one fitness call could take hours or even days to compute. The time-consuming process of evaluating the function values or gradient of the objective functions may degrade the running speed of many optimization algorithms. The coordinate search (CS) approach is introduced as a single-objective gradient-free method for addressing large-scale, non-convex, and costly optimization problems. Due to the low computation and memory requirements of the CS algorithm, it can also be efficiently extended to address multi-objective optimization problems. The subject of this study is to develop a CS-based algorithm aimed at computationally expensive multi-objective optimization problems. In order to generate a set of non-dominated solutions, a population is created to apply the CS algorithm on each individual and finally reach an optimized interval. We demonstrate the efficacy of the proposed multi-objective CS method by comparing it with NSGA-II and MOEA/D as one of the well-known multi-objective algorithms on ZDT benchmark functions. Promising results are reported with the assumption of a limited number of fitness evaluations (NFF) which is desired during tackling complex and expensive optimization problems. Another major advantage of the proposed algorithm is that it provides regions of the Pareto front, that using sampling can generate as many Pareto front solutions as needed unlike other common optimization algorithms including NSGA-II.

Optimization problems widely arise in various science and engineering fields and can be computationally expensive in many real-world applications. Evaluation of the fitness function to assess a candidate solution is the main operation in all optimization procedures which can be heavily compute-intensive. Machine learning-based surrogate models can contribute to learning the specific pattern among the decision variables and objective values to consequently reduce the computation time of fitness evaluation. In this study, we have proposed a novel pairwise surrogate model to identify the superiority between candidate solutions in a pairwise comparison despite the fact that most of the surrogate models try to predict the exact fitness value. The proposed idea can significantly help the optimizer to reach better results in a shorter period of time. It seems comparing two candidate solutions for a greedy selection is much easier than approximating fitness values for both. We demonstrated Graph Neural Network (GNN) for this purpose to be trained on a limited number of pairwise ranks and then utilized to compare a pair of candidate solutions. In order to examine the efficacy of our model, we utilized different well-known single-objective optimization benchmarks in dimensions 10,20, and 30. Moreover, the results of the learning-based evaluation are compared with the results from the real fitness evaluation. The results, assessed in terms of the number of fitness calls and the best-found solution, showed that the proposed method is able to decrease the computing cost of fitness evaluation significantly while we achieve a comparable solution. Our model can be tested with any optimization algorithm which employs a comparison-based mechanism among its candidate solutions.

Generally speaking, labeled data is difficult and expensive to provide for applications in machine learning and data mining. One of the earliest approaches to tackle this problem is semi-supervised self-training to take advantages of labeled and unlabeled data to create pseudo-labeled data. However, reaching a high level of confidence to predict the unseen data by a classifier with a limited number of labeled samples is a challenging task. Generating pseudo-labeled data can collaboratively improve the self-training to increase its confidence for further predictions. This paper proposes a collaborative framework between augmentation and self-training to accurately train a model with very limited labeled data. Our framework includes two components where the first component is an unsupervised technique to augment labeled data and feed to the second component which is self-training. The first component uses a custom variational autoencoder architecture (VAE) to generate new samples by adding randomly generated noise to encoded latent representation. As a result, the augmentation component can generate the unique and unexplored images with respect to limited input data distribution. We evaluated the proposed framework on handwritten MNIST image dataset. The conducted experiment shows that the generative component can be helpful in overcoming the problem of inaccurate self-training prediction when sufficient labeled data is not accessible.

Multi-objective optimization is a branch of computation to solve mathematical optimization problems when conflicting multiple objective functions must be simultaneously optimized. Many population-based algorithms, such as NSGA-II are used to find an optimal Pareto set of solutions in a short time. However, previous research works showed the performance of classic NSGA-II is degraded when solving problems with many objectives (M ≥ 5). In this work, we aim to take advantage of center-based sampling scheme to increase the exploration and exploitation capability of NSGA-II algorithm. This sampling strategy has demonstrated promising results on several single-objective evolutionary algorithms such as GA, DE, and PSO. Recently, a novel clustering center-based strategy has been proposed, which motivated us to utilize center-based sampling scheme in NSGA-II to solve multi-objective optimization problems. The outcomes confirm that the proposed clustering center-based NSGA-II is able to effectively solve CEC-2017 multi-objective benchmark problems with 2, 3, 5, 10, and 15 objectives.

Feature selection is an expensive challenging task in machine learning and data mining aimed at removing irrelevant and redundant features. This contributes to an improvement in classification accuracy, as well as the budget and memory requirements for classification, or any other post-processing task conducted after feature selection. In this regard, we define feature selection as a multi-objective binary optimization task with the objectives of maximizing classification accuracy and minimizing the number of selected features. In order to select optimal features, we have proposed a binary Compact NSGA-II (CNSGA-II) algorithm. Compactness represents the population as a probability distribution to enhance evolutionary algorithms not only to be more memory-efficient but also to reduce the number of fitness evaluations. Instead of holding two populations during the optimization process, our proposed method uses several Probability Vectors (PVs) to generate new individuals. Each PV efficiently explores a region of the search space to find non-dominated solutions instead of generating candidate solutions from a small population as is the common approach in most evolutionary algorithms. To the best of our knowledge, this is the first compact multi-objective algorithm proposed for feature selection. The reported results for expensive optimization cases with a limited budget on five datasets show that the CNSGA-II performs more efficiently than the well-known NSGA-II method in terms of the hypervolume (HV) performance metric requiring less memory. The proposed method and experimental results are explained and analyzed in detail.

A supervised feature selection method selects an appropriate but concise set of features to differentiate classes, which is highly expensive for large-scale datasets. Therefore, feature selection should aim at both minimizing the number of selected features and maximizing the accuracy of classification, or any other task. However, this crucial task is computationally highly demanding on many real-world datasets and requires a very efficient algorithm to reach a set of optimal features with a limited number of fitness evaluations. For this purpose, we have proposed the binary multi-objective coordinate search (MOCS) algorithm to solve large-scale feature selection problems. To the best of our knowledge, the proposed algorithm in this paper is the first multi-objective coordinate search algorithm. In this method, we generate new individuals by flipping a variable of the candidate solutions on the Pareto front. This enables us to investigate the effectiveness of each feature in the corresponding subset. In fact, this strategy can play the role of crossover and mutation operators to generate distinct subsets of features. The reported results indicate the significant superiority of our method over NSGA-II, on five real-world large-scale datasets, particularly when the computing budget is limited. Moreover, this simple hyper-parameter-free algorithm can solve feature selection much faster and more efficiently than NSGA-II.

Multi-objective optimization is a prevalent challenge in the area of deep learning. There is a lack of robust multi-objective optimization methods applicable in deep learning capable of training networks by simultaneously optimizing conflicting multiple loss functions. Its applications include a wide range of deep neural network branches such as multi-loss, multi-task, multi-modal, and cross-modal learning. In this paper, we develop MAdam as a multi-objective extension of the well-known Adam optimization algorithm. MAdam is a classical population-based approach that uses the gradient information of multiple objectives to accelerate population convergence toward an optimal minimum. The method applied a non-dominated sorting algorithm to keep selective population members and improve the diversity across the landscape. The performance of MAdam is evaluated on the standard ZDT test functions as the proof of concept. Promising results show the capability of this approach to converge towards an estimated Pareto front and to generate a well-distributed set of non-dominated solutions.

One of the main obstacles of adopting digital pathology is the challenge of efficient processing of hyperdimensional digitized biopsy samples, called whole slide images (WSIs). Exploiting deep learning and introducing compact WSI representations are urgently needed to accelerate image analysis and facilitate the visualization and interpretability of pathology results in a postpandemic world. In this article, we introduce a new evolutionary approach for WSI representation based on large-scale multiobjective optimization (LSMOP) of deep embeddings. We start with patch-based sampling to feed KimiaNet, a histopathology-specialized deep network, and to extract a multitude of feature vectors. Coarse multiobjective feature selection uses the reduced search space strategy guided by the classification accuracy and the number of features. In the second stage, the frequent features histogram (FFH), a novel WSI representation, is constructed by multiple runs of coarse LSMOP. Fine evolutionary feature selection is then applied to find a compact (short-length) feature vector based on the FFH and contributes to a more robust deep-learning approach to digital pathology supported by the stochastic power of evolutionary algorithms. We validate the proposed schemes using The Cancer Genome Atlas (TCGA) images in terms of WSI representation, classification accuracy, and feature quality. Furthermore, a novel decision space for multicriteria decision making in the LSMOP field is introduced. Finally, a patch-level visualization approach is proposed to increase the interpretability of deep features. The proposed evolutionary algorithm finds a very compact feature vector to represent a WSI (almost 14000 times smaller than the original feature vectors) with 8% higher accuracy compared to the codes provided by the state-of-the-art methods

In recent years, center-based sampling has demonstrated impressive results to enhance the efficiency and effectiveness of meta-heuristic algorithms. The strategy of the center-based sampling can be utilized at either or both the operation and/or population level. Despite the overall efficiency of the center-based sampling in population-based algorithms, utilization at operation level requires customizing the strategy for a specific algorithm which degrades the scheme's generalization. In this paper, we have proposed a population-level center-based sampling method which is operation independent and correspondingly can be embedded in any population-based optimization algorithm. In this study, we applied the proposed scheme for Differential Evolution (DE) algorithm to enhance the exploration and exploitation capabilities of the algorithm. We cluster candidate solutions and inject the centroid-based samples into the population to increase the overall quality of the population and thus decrease the risk of premature convergence and stagnation. By a high chance, the center-based samples are effectively generated in the promising regions of the search space. The proposed method has been benchmarked by employing CEC-2017 benchmark test suite on dimensions 30, 50, and 100. The results clearly indicate the superiority of the proposed scheme, and a detailed results analysis is provided.

Deep neural networks (DNNs) show impressive performance for hyperspectral image (HSI) classification when abundant labeled samples are available. The problem is that HSI sample annotation is extremely costly and the budget for this task is usually limited. To reduce the reliance on labeled samples, deep semi-supervised learning (SSL), which jointly learns from labeled and unlabeled samples, has been introduced in the literature. However, learning robust and discriminative features from unlabeled data is a challenging task due to various noise effects and ambiguity of unlabeled samples. As a result, recent advances are constrained, mainly in the pre-training or warm-up stage. In this paper, we propose a deep probabilistic framework to generate reliable pseudo labels to explicitly learn discriminative features from unlabeled samples. The generated pseudo labels of our proposed framework can be fed to various DNNs to improve their generalization capacity. Our proposed framework takes only 10 labeled samples per class to represent the label set as an uncertainty-aware distribution in the latent space. The pseudo labels are then generated for those unlabeled samples whose feature values match the distribution with high probability. By performing extensive experiments on four publicly available datasets, we show that our framework can generate reliable pseudo labels to significantly improve the generalization capacity of several state-of-the-art DNNs. In addition, we introduce a new DNN for HSI classification that demonstrates outstanding accuracy results in comparison with its rivals.

Differential Evolution (DE) is one of the well-established population-based optimization algorithms which has received a lot of attention regarding its potential to solve complex optimization problems. However, DE is capable to explore a huge search space in its early run phase, called exploration phase, its weakness in exploitation avoids local refinement of the promising shrunk region. Therefore, employing a local search can be an efficient strategy to improve the search performance of DE via accelerating of fine tuning phase. This paper purposes an effective Memetic DE algorithm using a well-known single-solution-based optimization method, i.e., Coordinate Descent (CD) algorithm. Local coordinate search is applied on the promising region resulted by top ranked individuals selected from the final population of DE. The proposed method updates the value of each coordinate iteratively by evaluating the sampled points from the local region to improve the resulted candidate solution. Since coordinate search algorithm shrinks the region rapidly, it requires a very small portion of the computational budget to find the optimal coordinates' value. In order to evaluate the proposed Memetic DE, several experiment series are conducted on functions of CEC-2017 benchmark for different number of dimensions (i.e., D=30, 50, and 100). Results clearly indicate that the utilized local coordinate search improves the quality of resulted solution by DE significantly using a very low computational budget, i.e., 20×D.

This paper presents 3D-RadViz, a visualization method for high dimensional data using a three dimensional radial visualization technique. The proposed technique extends the capabilities of the classical two dimensional radial visualization (RadViz) in order to reduce overlapping data points. For evaluation purposes, the paper applies the proposed 3D-RadViz alongside with t-SNE and a recently published 3-dimensional radial visualization technique to the same real-world datasets from the UCI machine learning repository. The contribution of the work is an interactive, deterministic, and high-performance library, implemented in Python, that can be utilized to realize better high dimensional data visualization using the proposed 3D-RadViz technique. The paper also suggests some directions for future enhancements to the proposed visualization approach.

Population-based algorithms are a well-established category of metaheuristic optimization algorithms in which individuals collaborate with each other to find the optimal solution in a search space. During the search process, each individual provides a partial intelligence which can assist the population movement toward promising regions. In this paper, a dimension-wise strategy is proposed to collect the intelligence of whole population to generate a new trial candidate solution. For new individual, the value of each variable is calculated using the votes of a more-crowded cluster of individuals obtained on each dimension (one-dimensional clustering). Accordingly, a group of candidate solutions in the population collaborate to determine a variable value of new individual. Utilizing this strategy, collective intelligence (CI) aims the algorithm to find better candidate solutions. Since the proposed method keeps untouched all other parts of the algorithm, it can be used with any population-based algorithm. This paper presents the modification of two well-known population-based algorithms based on the proposed strategy in utilizing Collective Intelligence (CI), Differential Evolution (CIDE) and Particle Swarm optimization (CIPSO). In conducted experiments, two proposed algorithms are compared with classical version of DE and PSO on 30 functions of CEC2017 benchmark. The results indicate that the proposed method generates an individual with better objective function value than many of the individuals in the population which leads totally better results in overall.

Solving real-world complex optimization problems using simple metaheuristic algorithms is a challenging but attractive task. Making matrix multiplication efficient is one of the interesting problems. This time-consuming algebric operation is required in many applications in science and engineering, thus reducing its complexity targets more efficient computation. In fact, many of practical and theatrical complicated calculations can be modeled efficiently as matrix-based operations, therefore matrix multiplication is computationally expansive operator among all others. In this paper, a simple metaheuristic method based on Micro Genetic Algorithm is proposed to find Strassen's equivalent solutions which is an algebraic method to compute the product of two matrices with minimal number of multiplications. Since there are numerous optimal solutions, the modeled problem is a large-scale and highly multi-modal optimization problem. The proposed method could find more than 160, 000 valid solutions with same complexity as Strassen's in a large-scale search space. Among all discovered solutions found using the proposed method, there are 701 distinct solutions which is the maximum number of discovered Strassen's equivalent solutions to the best of our knowledge. The proposed algorithm is simple but very efficient to find more and more solutions, in fact, that is a great demonstration of “evolution in action” to tackle real-world complex problems like the current one, which just one set of its equations has been discovered by the Germen mathematicians and has remained mysterious for more than 50 years.

One of the widely used models for studying economics of climate change is the Dynamic Integrated model of Climate and Economy (DICE), which has been developed by Professor William Nordhaus, one of the laureates of the 2018 Nobel Memorial Prize in Economic Sciences. Originally a single-objective optimal control problem has been defined on DICE dynamics, which is aimed to maximize the social welfare. In this paper, a bi-objective optimal control problem defined on DICE model, objectives of which are maximizing social welfare and minimizing the temperature deviation of atmosphere. This multi-objective optimal control problem solved using NonDominated Sorting Genetic Algorithm II (NSGA-II) also it is compared to previous works on single-objective version of the problem. The resulting Pareto front rediscovers the previous results and generalizes to a wide range of non-dominant solutions to minimize the global temperature deviation while optimizing the economic welfare. The previously used single-objective approach is unable to create such a variety of possibilities, hence, its offered solution is limited in vision and reachable performance. Beside this, resulting Pareto-optimal set reveals the fact that temperature deviation cannot go below a certain lower limit, unless we have significant technology advancement or positive change in global conditions.

Differential Evolution (DE) algorithm has been shown notable performance in solving complex optimization problems. In recent years, some variants of the DE algorithm have been proposed based on the concept of center-based sampling strategy. To the best of our knowledge, the related papers employed center-based sampling for population initialization or as the base vector in mutation operator. In fact, they were operation-level approaches applied during the optimization process, and none of them was about proposing a population-level approach to utilize center-based sampling to accelerate convergence rate of algorithms. This paper proposes a novel center-based sampling scheme for the DE algorithm that utilizes center-based sampling as a member of the population. In our scheme, one candidate solution is the center of the best candidate solutions, while other individuals in the population behave similarly to the standard DE algorithm. The center-based candidate solution is not updated using standard operators and is set to the center in each iteration. To validate our scheme, we benchmark our algorithm on CEC-2017 benchmark functions with three dimensions of 30, 50, and 100. Also, we design some experiments to analyze the behavior of the proposed center-based scheme. Our experiments demonstrate a significant improvement of the proposed algorithm on the majority of benchmark functions.

Image thresholding is a crucial image processing task. Most of the time, it plays a pivotal role in an image processing chain, therefore, any error in image thresholding can propagate to other steps such as edge detection, area/volume estimation, or object recognition. Multi-level image thresholding is a popular method for image segmentation, dividing an image into homogeneous regions. Conventional algorithms are timeconsuming due to utilising an exhaustive search, especially when the number of threshold levels increases. On the other hand, population-based metaheuristic algorithms have been successfully applied to this problem. In this paper, we propose a center-based differential evolution (DE) algorithm for high-dimensional multilevel image thresholding (many-level image thresholding). While DE has been shown to yield satisfactory performance for various real-world optimisation problems, in our algorithm, DE is further boosted with a center-based sampling strategy. We evaluate our algorithm on a set of benchmark images on high-dimensional search spaces and with regards to an entropy-based objective function and peak signal-to-noise ratio (PSNR). The obtained results demonstrate that the proposed algorithm can improve upon the performance of other metaheuristic image thresholding techniques.

In this modern era, the financial market, more specifically, the stock markets all over the world, deal with an enormous amount of real-time data that facilitates the data analytics and prediction in the field of finance. The main objective of this paper is to propose a novel model of neural network based on Long-Short Term Memory (LSTM) and utilizing one of the most powerful evolutionary algorithms, namely the Differential Evolution (DE), to forecast the next day's stock price of a company. This study focuses on optimizing the ten network hyperparameters related to the detection of temporal patterns of a given dataset, namely, the size of the time window, batch size, the number of LSTM units in hidden layers, the number of hidden layers (LSTM and dense), dropout coefficient for each layer, and the network training optimization algorithm. To the best of our knowledge, this is the first time that all this set of parameters have been optimized simultaneously. Then, the LSTM has been optimized by DE to gain the lower root mean squared error (RMSE) for prediction. The proposed model achieved 8.092 RMSE as its objective value, which is better in comparison with the best statistical forecasting models such as NAIVE, ETS, and SARIMA, which are the-state-of-the-art methods in this filed. Moreover, for shortening the training time as the main source of computational expensiveness, the proposed method works with a lower number of epochs. By this way, DE tries to find a shallower and faster network even with higher accuracy, which is a remarkable approach.

Visualization techniques have received a lot of attention regarding their potential to interpret and analyze the data.One of the marked visualization methods is the Parallel Coordinates Plot (PCP) utilized to high-dimensional datasets (more than three dimensions). Due to that, in visualizing large-scale datasets, the method suffers from high clutters produced from numerous intersection lines between neigh-boring axes, numbers of researchers have conducted techniques to boost PCPs. For instance, reducing the number of crossing lines by utilizing the re-ordering the neighboring axes in the PCP technique is a useful procedure to reduce the clutter. Motivated by this goal, the acquisition of the optimal coordinate's order can be classified as a combinatorial optimization problem. However, in high-dimensional datasets, the optimization algorithm may face difficulty to deal with this issue. In this paper, we propose a smart mutation operator to enhance the performance of Genetic Algorithm (GA) in finding the optimal order of PCP based on diminishing the numerous intersection lines. However, any other user-desired metric can be utilized as an objective function. To assess the introduced method, we conducted a Monte Carlo simulation and several experiments to find an optimal coordinates' order in PCP to visualize the datasets with various numbers of samples and dimensions. In the experimental results, utilizing the smart mutation represents an improvement in PCP visualization in terms of reducing the intersection lines between the neighboring coordinates compared to the original GA.

As many real-world optimization problems are large-scale and expensive, the large search space and expensive gradient computation may lead to failure of metaheuristic and classical algorithms. The problem even gets more crucial as we move from continuous domain to the discrete or mixed type one, because most of the discrete optimization problems are NP-hard and cannot be treated as convex or linear optimization, therefore there exists no cost-effective algorithm to cope with large-scale discrete global optimization (LSDGO) problems. However, due to the low memory demand and computational cost of coordinate descent (CD) search methods they are appropriate algorithms for optimizing large-scale expensive problems. In this paper, we propose a discrete version of CD algorithm called Discrete Coordinate Descent (DCD) as an effective method for solving LSDGO problems. Our proposed algorithm makes the most of two essential phases referred to as finding the region of interest and folding the search space, which shrinks it into two halves per variable and results in ${\left( {\frac{1}{2}} \right)^D}$ shrinking of the whole search space at each iteration (D indicates the problem's dimension). Since the proposed algorithm shrinks the search space rapidly, it requires a low computational budget to find the optimal value for each coordinate. In order to investigate the efficiency of our algorithm precisely, we tested it on 20 well-known large-scale problems with dimensions of 30, 50, 100, and 1000. The results demonstrate the potency of DCD not only in low-scale discrete problems, but in large-scale discrete optimization problems as well.

Crossover is the main genetic operator which influences the power of evolutionary algorithms. Among a variety of crossover operators, there has been a growing interest in multi-parent crossover operators in evolutionary computation. The main motivation of those schemes is establishing comprehensive collective collaboration of more than two chromosomes in the population to generate a new offspring. In this paper, a novel all-parent crossover operator called collective crossover for genetic algorithm is proposed. In this method, all individuals in the current population are involved in recombination part and one offspring is generated. The contribution of each individuals is defined based on its quality in terms of fitness value. The performance of the collective crossover operator is tested on CEC2017 benchmark functions. The results revealed that the proposed crossover operator performs better when compared to well-known two-parent crossover operators including one-point and two-point crossovers. In addition, the differences between collective crossover and the other crossover operators are statistically significant for the most cases.

Particle swarm optimization (PSO) has demonstrated a promising performance for solving challenging optimization problems, but its performance in solving large-scale optimization problems (LSGO) has drastically decreased. In the canonical PSO, velocity has a significant effect on the performance of PSO, which is updated based on cognitive and social factors. It can help particles to share information effectively. In this paper, a center-based velocity is proposed in which a new component, named opening "center of gravity factor", is added to velocity update rule to propose the center-based PSO (CenPSO). Center of gravity factor benefits from center-based sampling strategy, a new direction in population-based metaheuristics, especially to tackle LSGOs. The proposed method is evaluated on two benchmark functions, namely, CEC2010 and CEC2017, with dimensions 100 and 1000. The experimental results verify that CenPSO is significantly better than PSO over the majority of benchmark functions.

Differential Evolution (DE) algorithm is an efficient metaheuristic algorithm in solving complex real-world optimization problems. DE algorithm benefits from two populations for updating individuals, while it might cause memory problems in practice during solving large-scale optimization problems; especially when they are used in an embedded system. One strategy to tackle this problem is utilizing a one-array scheme which benefits from only one population, leading to a half-space memory. This paper proposes a novel DE algorithm based on one-array DE and a random replacement strategy; it adds an additional competition to the selection operator to make better use of the new individual that it might be potentially noteworthy. The positive feature of the introduced replacement strategy is that it does not need any extra computational budget. Also, due to employing one-array strategy, the proposed scheme has a lower memory complexity. Our experiments on CEC-2017 benchmark function with dimensions 30, 50, and 100 clearly illustrate the effectiveness of the proposed DE algorithm.

Interest in visual data analytics related to many-objective optimization has recently risen. This paper introduces a novel visualization scheme based on the Radial Coordinate Visualization (RadVis) for analysis of Pareto fronts during the optimization process. This method illustrates the ranks of the Pareto front, the relative location, and the distribution of candidate solutions. The results show that the proposed method is capable of showing different ranks of Pareto fronts simultaneously. The simplicity of the P-RadVis visualization and its compatibility to work with many-objective algorithms could be beneficial in terms of visual analytics for real-time monitoring of optimization process.

Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their convergence, which is not affordable for practical applications since the most of them are computationally expensive. In other words, these problems are not only large-scale but also computationally expensive, that makes them very difficult to solve. There is no efficient surrogate model to support large-scale expensive global optimization (LSEGO) problems. As a result, the algorithms should address LSEGO problems using a limited computational budget to be applicable in real-world applications. Coordinate Descent (CD) algorithm is an optimization strategy based on the decomposition of a n-dimensional problem into n one-dimensional problem. To the best our knowledge, there is no significant study to assess benchmark functions with various dimensions and landscape properties to investigate CD algorithm and compare with other metaheuristic algorithms. In this paper, we propose a modified Coordinate Descent algorithm (MCD) to tackle LSEGO problems with a limited computational budget. Our proposed algorithm benefits from two leading steps, namely, finding the region of interest and then shrinkage of the search space by folding it into the half with exponential speed. One of the main advantages of the proposed algorithm is being free of any control parameters, which makes it far from the intricacies of the tuning process. The proposed algorithm is compared with cooperative co-evolution with delta grouping on 20 benchmark functions with dimension 1000. Also, we conducted some experiments on CEC-2017, D = 10,30,50, and 100, to investigate the behavior of MCD algorithm in lower dimensions. The results show that MCD is beneficial not only in large-scale problems, but also in low-scale optimization problems.

Driven by the recent technological advancements within the machine learning field, multi-label classification has been introduced as one of the challenging tasks to assign more than one label to each instance in a dataset. Feature selection is one of the predominant feature engineering methodologies which being extensively used as a vital step in predictive model construction to enhance the multi-label classification performance. Many metaheuristic algorithms have been tailored to choose the optimal subset of features in datasets but as a challenging problem, such algorithms suffer from a slow process during fine-tuning. Objective of this paper is to propose a hybrid mechanism by which an obtained feature subset from a Binary Differential Evolution (BDE) algorithm will be further enhanced to minimize the classification error using a local search methodology. Key motivation behind the proposed model is to address the weakness in exploitation of metaheuristic feature selection algorithms with the help of classical feature selection method such as Sequential Backward Selection (SBS) as a local search strategy. The classical feature selection method eliminates more redundant and irrelevant features of obtained subset using the BDE to decrease the classification error. The empirical results obtained on eight various multi-label datasets show that the proposed hybrid approach, which is a fusion of both evolutionary and classical feature selection methods, can minimize the classification error on the obtained feature subset using the BDE.

In machine learning, multi-label classification aims to assign labels of instances in a dataset which are associated to more than one class label. Feature selection as an important task in predictive model construction improves the performance of multi-label classification. Since feature selection task can be interpreted as optimizing multiple objectives in a massive search space, multi-objective evolutionary techniques can be applied to tackle this family of problems. In this paper, a binary multi-objective feature selection is proposed for multi-label data with considering number of features and classification accuracy as objectives. A binary differential evolution is proposed based on opposition-based learning concept and partially voting between two candidate solutions to decide about absence or presence of a feature in third randomly selected solution. Because feature selection is basically a binary optimization problem, proposing a binary operator improves the effectiveness of search process in evolutionary algorithms. The proposed operator is utilized in third version of Generalized Differential Evolution (GDE3) which is a multi-objective optimization algorithm to select best subset of multi-label features with minimum number of features. A benchmarking is conducted on eight multi-label datasets in terms of several multi-objective assessment metrics including the Hypervolume indicator, Pure Diversity, and Set-coverage. Experimental results show significant improvements for proposed method in comparison with the state-of-the-art multi-objective feature selection methods for multi-label classification, which are namely NSGA-II and PSO based approaches.

Scientists' publication impacts ranking is an important topic in scientometrics which is performed based on various proposed criteria. One of the well-known indicators is h-index which evaluates researchers achievements based on number of citations. The h-index has utilized in many research data sources because of its appropriate properties, but similar to other assessment indicators, it has own disadvantages. hindex cannot give a fair comparison between junior and senior researches. There are two reasons for this unfair comparison: (1) h-index depends on the research period of scholars and (2) the number of received citations can be increased by time, even if researcher doesn't publish new papers, the h-index increases. Consequently, in addition to h-index, the number of the years of academic research (called the research period) is preferable to be considered as an independent indicator, which makes us able to have a more fair evaluation. So these two objectives, maximizing h-index and minimizing research period, can be considered as a multi-criteria comparison task to assess researchers. In this paper, we propose a strategy based on Pareto dominance ranking which uses dominance concept to obtain an order for researchers. In order to complete ranking between scientists in the same rank, a multi-criteria decision making measure called VIKOR is utilized. Therefore, a total ranking measure (P-V index) is obtained using Perto front concept and VIKOR measure. The proposed method is applied on 235 researchers who are conducting research on Evolutionary Computation (EC) topic. The h-index value and the research period of scholars are collected via Google Scholar service. P-V index obtains 26 Pareto ranks for all researchers and places six EC scientists on the first Pareto front.

For several years, the Differential Evolution (DE) algorithm has been an effective method for solving complex real-world optimization problems. Due to its success and popularity, there are several multi-objective optimization algorithms proposed based on DE. However, when DE comes to solving large-scale problems its performance deteriorates. Several recent studies clearly confirm that utilizing center-based sampling method can increase the probability of the closeness of initialized population individuals to the solutions in black-box problems. In this paper, we propose center-based mutation for Third Generalized Differential Evolution (CGDE3) algorithm in order to solve large-scale multi-objective optimization problems; in fact, this time center-based sampling scheme is employed during the optimization process not just during the population initialization phase. For its mutation scheme, the CGDE3 algorithm utilizes five randomly selected candidate solutions from its current population to generate a new trial vector. The proposed method enhances the GDE3 algorithm by improving its exploration ability using extra center-based sampling during the evolution process. This algorithm is tested on benchmarks of CEC 2017 competition on evolutionary multi-objective optimization with dimensions of 100, 500 and 1000. Experimental results confirm that CGDE3 outperforms GDE3 over all three studied large-scale dimensions.

Differential Evolution is a powerful and efficient approach for numerical optimization. A Success-History Based Parameter Adaptation (SHADE) is the recent variant of the adaptive DE that utilizes a historical performance of the successful control parameter. In this paper, we propose a center-based mutation for SHADE algorithm (CSHADE). In this mutation scheme, the base vector for SHADE's mutation is replaced with center-based sampled candidate solution using the normal distribution. The proposed method is evaluated on CEC-2010 and CEC-2013 LSGO benchmark functions with dimension 1000. The experimental results show that CSHADE outperforms SHADE algorithm over the majority of benchmark functions in terms of solution accuracy.

For several years the Differential Evolution (DE) algorithm has been an effective method for solving complex real-world optimization problems. However, when it comes to solving large-scale problems its performance deteriorates. In this paper, we propose five different dynamic center-based DE mutation schemes (DCDE) to solve large-scale optimization problems. In each generation, the proposed dynamic centerbased mutation strategies linearly divide the population into two different groups. Then, the first sub-population group utilizes center-based mutation scheme and the second sub-population employs the classical DE mutation. The proposed dynamic schemes are benchmarked on CEC 2013 large-scale optimization problems. The experimental results show that the overall performance of the proposed dynamic center-based mutation schemes better than the compared algorithms in solving LSGO problems.

In recent years, discovering relationships among entities and their features in a dataset has been received a great attention in data analytics. This study aims to reveal the relationships among entities in a dataset according to a specific sequence of features which are guided according to the accuracy of the hierarchical clustering made up by the features. In this paper, a new metric, called Discriminating Features based Cohesion (DFC) factor, is defined as pair-wise stickiness measure among entities which indicates their degree of attachment (i.e., cohesive force). In this direction, a new framework is proposed; which utilizes an evolutionary algorithm (i.e., DE) for the optimal discriminating feature selection and also a hierarchical clustering method for computing DFC factors. DE algorithm is employed to identify features which their clustering hierarchical tree has the maximum accuracy, then the intermediate and final DFC factors' matrices are computed by using a hierarchical clustering of the most discriminating features. The intermediate and final DFC factors' matrices have been utilized to discovery the knowledge among Dataset Entities including answering crucial data mining queries which cannot be answered by using a standalone clustering method. In order to conduct a case study, a real-world dataset is utilized; which contains 17 entities (i.e., countries) presented by corresponding 24 continuous features. The DE algorithm finds the most discriminating features in each step, which are eliminated for the next step to calculate a matrix of DFC factors. In the final step, the proposed method ranks the entities in terms of their DFC factor and features based on their elimination order (i.e., discrimination power).

Control algorithms are essential in the modern world to tackle with ever-changing environmental disturbances while meeting adequate safety standards. Control systems must be appropriately tuned for each application to ensure reliability and safety. This paper applies a multi-objective optimization method, Generalized Differential Evolution (GDE3), to tune a Linear Quadratic Regulator (LQR) while enabling posteriori decision-making. The utilized case study is the aircraft pitch control. We compare the results of GDE3 with Non-Dominated Sorting Genetic Algorithm (NSGA-II) and conventional tuning. The current findings show that the GDE3 performs better than the other methods. This paper sheds light on how trade-off and condition-specific based optimization can enhance real-time control systems.

The proposed multi-objective optimized hybrid renewable energy system consists of solar panels, wind turbines, a proton exchange membrane (PEM) electrolyzer for hydrogen production, and an absorption cooling system for the summer season. This study is conducted in two locations in Egypt and Saudi Arabia as the case studies. The study presents a thermodynamic analysis to investigate the system performance. In addition, an optimization-based analysis is conducted using NSGA-II algorithm to determine optimal values of the decision variables. The hybrid renewable system can operate in a significant performance with water mass flow rate of 1.8 kg/s to produce hydrogen with a mass flow rate of 0.2 kg/s, and ammonia mass flow rate of about 0.2 kg/s to produce cooling load between 40 and 120 kW with energy and exergy efficiency of more than 65%.

Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms are two commonly employed techniques in designing maximum power point tracking systems in photovoltaic (PV) farms. A mathematical formulation of the objective function is derived by implementing the maximum power theorem for load matching using the relationship between input and output impedances. This paper also proposes a novel Center-based Latin Hypercube (CLHS) initialization scheme for population-based algorithms; it is shown that for population initialization, the newly proposed technique of CLHS gives better results with a small population size. A comprehensive comparative study is conducted on DE and PSO algorithms in terms of control parameters, search components, and population initialization methods to determine the best algorithm with its corresponding optimal parameters settings and population initialization to solve a family of maximum power point tracking problems. The work shows that both algorithms are capable of tracking the maximum power point although the PSO is more effective over a small population size. In this study, in overall, 15,876 and 96,228 settings possibilities for DE and PSO respectively are investigated.

In the last three decades there have been a number of efficient multi-objective optimization algorithms capable of solving real-world problems. However, due to the complexity of most real-world problems (high-dimensionality of problems, computationally expensive, and unknown function properties) researchers and decision-makers are increasingly facing the challenge of selecting an optimization algorithm capable of solving their hard problems. In this paper, we propose a simple yet efficient hybridization of multi- and many-objective optimization algorithms framework called hybrid many-objective optimization algorithm using fusion of solutions obtained by several many-objective algorithms (fusion) to gain the combined benefits of several algorithms and reducing the challenge of choosing one optimization algorithm to solve complex problems. During the optimization process, the Fusion framework (1) executes all optimization algorithms in parallel, (2) it combines solutions of these algorithms and extracts well-distributed solutions using predefined structured reference points or user-defined reference points, and (3) adaptively selects best-performing algorithm to tackle the problem at different stages of the search process. A case study of the fusion framework by considering GDE3, SMPSO, and SPEA2 as multi-objective optimization algorithms is presented. Experimental results on five unconstrained and four constrained benchmark test problems with three to ten objectives show that the Fusion framework significantly outperforms all algorithms involved in the hybridization process as well as the NSGA-III algorithm in terms of diversity and convergence of obtained solutions. Furthermore, the proposed framework is consistently able to find accurate solutions for all test problems which can be interpreted as its high robustness characteristic.

The interest in multi-modal optimization methods is increasing in the recent years since many of real-world optimization problems have multiple/many optima and decision makers prefer to find all of them. Multiple global/local peaks create difficulties for optimization algorithms. In this context, niching is well-known and widely used technique for finding multiple solutions in multi-modal optimization. One commonly used niching technique in evolutionary algorithms is the Clearing method. However, canonical clearing scheme reduces the exploration capacity of the evolutionary algorithms. In this paper, Delaunay Triangulation based Clearing (DT-Clearing) procedure is proposed to handle multi-modal optimizations more efficiently while preserving simplicity of canonical clearing approach. In DT-Clearing, cleared individuals are reallocated in the biggest empty spaces formed within the search space which are determined through Delaunay Triangulation. The reallocation of cleared individuals discourages wasting of the resources and allows better exploration of the landscape. The algorithm also uses an external memory, an archive of the explored niches, thus preventing the redundant visiting of the individuals, henceforth finding more solutions in lesser number of generations. The method is tested using multi-modal benchmark problems proposed for the IEEE CEC 2013, Special Session on Niching Methods for Multimodal Optimization. Our method obtains promising results in comparison with the canonical clearing and demonstrates to be a competitive niching algorithm.

In the recent years, Large-Scale Global Optimization (LSGO) algorithms attempt to solve real-world problems efficiently. The imbalance in the contribution of variables and the interaction among variables pose major challenges for LSGO algorithms. This paper proposes mapping schemes based on the interaction among variables and the imbalance in the contribution of variables. The proposed mapping schemes present the different relations between the constructed class of variables according to the interaction feature and the constructed class of variables according to the imbalance feature. Covering a wide range of real-world problems is considered in the mapping schemes; therefore it can provide some insights to design LSGO benchmark suites. By developing LSGO benchmark suites with the ability of representing many-real world problems, researchers will be motivated to realize the success or failure level of LSGO algorithms for tackling various types of LSGO problems. Also, a preliminary set of experiments is conducted to present the importance of considered features in each scheme.

Differential Evolution (DE) is a simple powerful evolutionary algorithm for solving global continuous optimization problems. The especial characteristic of DE algorithm is calculating a weighted difference vector of two random candidate solutions in the population to generate the new promising candidate solutions. A major operation of the DE algorithm is the mutation which can affect its performance. The main goal of this study is investigating the influence of ordering vectors on various mutation schemes. We design some Monte-Carlo based simulations to analyze several mutation schemes by calculating the probability of closeness of a new trial solutions to a random optimal solution. These simulations indicate that mutation schemes can enhance the performance of the DE algorithm which they consider right ordering of the vectors in their mutation operators. Also, we introduce a new mutation scheme which considers in ordering vectors in the mutation scheme. We benchmark the modified DE algorithm with the ordered mutation scheme (DE/order) on CEC-2014 test functions with three dimensions 30, 50, and 100. Simulation results confirm that DE/order obtains a promising performance on the majority of the test functions on all mentioned dimensions.

Vibration control of flexible structures has always been one of the most important issues and Among variant available control methods, active vibration control using piezoelectric sensors and actuators has become popular due to its high efficiency and flexibility for designing a control system. The main concern in designing a control system with piezoelectric patches is finding best position for patches. On the other hand, number of used sensors and actuators is another important issue which affects the costs of the project as well as the performance. The main goal of the present study is to control oscillation of a rectangular plate using minimum number of piezoelectric sensors and actuators (i.e., objective one) and finding their optimum placement to get the maximum possible performance (i.e., objective two); the mentioned two objectives are in conflict. The plate have been mathematically modeled using the Kirchhoff-Love theory. By considering the piezoelectric sensor-actuators effects, the control equation of the cantilever plate has been obtained. In order to find the optimum number and placement of the sensors and actuators, the multi-objective genetic algorithm (GA) has been used and the objective functions have been defined based on maximization of observability and countability indexes of the cantilever plate. After conducting the optimization process, a few thumb rules have been extracted using the innovization technique. The results have been verified by implementing the designed controller using the optimum solution found by optimization method. The importance of the rules found by innovization technique have been illustrated in the numerical discussion.

In many-objective optimization, visualization of true Pareto front or obtained non-dominated solutions is difficult. A proper visualization tool must be able to show the location, range, shape, and distribution of obtained non-dominated solutions. However, existing commonly used visualization tools in many-objective optimization (e.g., parallel coordinates) fail to show the shape of the Pareto front. In this paper, we propose a simple yet powerful visualization method, called 3-dimensional radial coordinate visualization (3D-RadVis). This method is capable of mapping M-dimensional objective space to a 3-dimensional radial coordinate plot while preserving the relative location of solutions, shape of the Pareto front, distribution of solutions, and convergence trend of an optimization process. Furthermore, 3D-RadVis can be used by decision-makers to visually navigate large many-objective solution sets, observe the evolution process, visualize the relative location of a solution, evaluate trade-off among objectives, and select preferred solutions. The visual effectiveness of the proposed method is demonstrated on widely used many-objective benchmark problems containing variety of Pareto fronts (linear, concave, convex, mixed, and disconnected). In addition, we demonstrated the capability of 3D-RadVis for visual progress tracking of the NSGA-III algorithm through generations. It is worthwhile to mention that a suitable visualization is a crucial prerequisite for an effective interactive optimization.

Evolutionary algorithms are the most studied and successful population-based algorithms for solving single- and multi-objective optimization problems. However, many studies have shown that these algorithms fail to perform well when handling many-objective (more than three objectives) problems due to the loss of selection pressure to pull the population towards the Pareto front. As a result, there has been a number of efforts towards developing evolutionary algorithms that can successfully handle many-objective optimization problems without deteriorating the effect of evolutionary operators. A reference-point based NSGA-II (NSGA-III) is one such algorithm designed to deal with many-objective problems, where the diversity of the solution is guided by a number of well-spread reference points. However, NSGA-III still has difficulty preserving elite population as new solutions are generated. In this paper, we propose an improved NSGA-III algorithm, called EliteNSGA-III to improve the diversity and accuracy of the NSGA-III algorithm. EliteNSGA-III algorithm maintains an elite population archive to preserve previously generated elite solutions that would probably be eliminated by NSGA-III's selection procedure. The proposed EliteNSGA-III algorithm is applied to II many-objective test problems with three to I5 objectives. Experimental results show that the proposed EliteNSGA-III algorithm outperforms the NSGA-III algorithm in terms of diversity and accuracy of the obtained solutions, especially for test problems with higher objectives.

Cooperative Coevolution (CC) framework has become a powerful approach to solve large-scale global optimization problems effectively. Although a number of significant modifications of CC algorithms have been introduced in recent years, the theoretical studies of population initialization strategies in the CC framework are quite limited so far. The population initialization strategies can help a population-based algorithm to start with better candidate solutions for achieving better results. In this paper, we propose a CC algorithm with population initialization strategies based on the center region to improve its performance. Three population initialization strategies, namely, center-based normal distribution sampling, central golden region, and hybrid random-center normal distribution sampling are utilized in the CC framework. These population initialization strategies attempt to generate points around center-point with different schemes. The performance of the proposed algorithm is evaluated on CEC-2013 LSGO benchmark functions. Simulation results confirm that the proposed algorithm obtains a promising performance on the majority of the nonseparable high dimension benchmark functions.

Differential evolution (DE) is a high performance and easy to implement evolutionary algorithm. The DE algorithm with small population size (i.e., micro-DE) can further increase the efficiency of the algorithm. However, it also decreases its exploration capability, causing stagnation and pre-mature convergence. In this paper, the idea of exploration enhancement at the mutation level is proposed. The proposed algorithm randomly generates the mutation scale factor for each individual and each dimension of the problem using a uniform distribution. Each individual can select a mutation scheme uniformly and randomly from a pool of mutation schemes in each generation, instead of using a fixed mutation scheme for all individuals during generations. The proposed idea is simple and easy to implement, without changing the algorithm complexity or adding overhead running time. This approach relaxes setting of mutation scheme control parameter. In this paper, we provide a detail analysis about the exploration capability of four variants of micro-DE versions, namely classical micro-DE, micro-DE with vectorized random mutation factor, micro-DE with ensemble mutation scheme, and micro-DE with vectorized random mutation factor and ensemble mutation scheme. Experimental results for various dimensions between 30 to 1000 on the CEC BlackBox Optimization Benchmarking 2015 (CEC-BBOB 2015) show superior performance of the proposed approach compared to the micro-DE and micro-DE with randomized mutation factor algorithms.

Recently, Radon transformation has been used to generate barcodes for tagging medical images. The under-sampled image is projected in certain directions, and each projection is binarized using a local threshold. The concatenation of the thresholded projections creates a barcode that can be used for tagging or annotating medical images. A small number of equidistant projections, e.g., 4 or 8, is generally used to generate short barcodes. However, due to the diverse nature of digital images, and since we are only working with a small number of projections (to keep the barcode short), taking equidistant projections may not be the best course of action. In this paper, we proposed to find n optimal projections, whereas n<; 180, in order to increase the expressiveness of Radon barcodes. We show examples for the exhaustive search for the simple case when we attempt to find 4 best projections out of 16 equidistant projections and compare it with the evolutionary approach in order to establish the benefit of the latter when operating on a small population size as in the case of micro-DE. We randomly selected 10 different classes from IRMA dataset (14,400 x-ray images in 58 classes) and further randomly selected 5 images per class for our tests.

Opposition-based learning (OBL) is a recently proposed method, which is successfully used to accelerate the search process of some well-known techniques in soft computing, such as swarm and evolutionary algorithms, artificial neural networks, reinforcement learning, and fuzzy logic systems. Among these opposition-based algorithms, opposition-based differential evolution (ODE) is one of the most popular algorithm. In the past several years, several variants of OBL scheme have been proposed. This paper presents a comparative study conducted on various OBL schemes, all utilized in differential evolution (DE) in order to enhance its accuracy or convergence rate. In the experiments, eight different OBL versions, namely the original OBL, quasi opposition, quasi reflection opposition, current optimum opposition, generalized opposition, centroid opposition, extended opposition, and reflected extended opposition, are embedded in DE algorithm and studied. Results on the CEC-2014 benchmark set for dimensions 10, 30, and 50 are reported.

Many research works have successfully extended algorithms such as evolutionary algorithms, reinforcement agents and neural networks using “opposition-based learning” (OBL). Two types of the “opposites” have been defined in the literature, namely type-I and type-II. The former are linear in nature and applicable to the variable space, hence easy to calculate. On the other hand, type-II opposites capture the “oppositeness” in the output space. In fact, type-I opposites are considered a special case of type-II opposites where inputs and outputs have a linear relationship. However, in many real-world problems, inputs and outputs do in fact exhibit a nonlinear relationship. Therefore, type-II opposites are expected to be better in capturing the sense of “opposition” in terms of the input-output relation. In the absence of any knowledge about the problem at hand, there seems to be no intuitive way to calculate the type-II opposites. In this paper, we introduce an approach to learn type-II opposites from the given inputs and their outputs using the artificial neural networks (ANNs). We first perform opposition mining on the sample data, and then use the mined data to learn the relationship between input x and its opposite x̌. We have validated our algorithm using various benchmark functions to compare it against an evolving fuzzy inference approach that has been recently introduced. The results show the better performance of a neural approach to learn the opposites. This will create new possibilities for integrating oppositional schemes within existing algorithms promising a potential increase in convergence speed and/or accuracy.

This paper presents a Modified Cuckoo Search (MCS) algorithm for solving flow shop scheduling problem with blocking to minimize the makespan. To handle the discrete variables of the job scheduling problem, the smallest position value (SPV) rule is used to convert continuous solutions into discrete job permutations. The Nawaz-Enscore-Ham (NEH) heuristic method is utilized for generating high quality initial solutions. Moreover, two frequently used swap and insert operators are employed for enhancing the local search. To verify the performance of the proposed MCS algorithm, experiments are conducted on Taillard's benchmark set. Results show that MCS performs better than the standard CS and some previous algorithms proposed in the literature.

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their “opposition-based” version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type-I) opposition, that for each x ∈ [a; b] assigns its opposite as x̆I= a + b - x. This, of course, is a very naive estimate of the actual or true (non-linear) opposite x̆II, which has been called type-II opposite in literature. In absence of any knowledge about a function y = f(x) that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate x̆Iaccording to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform “opposition mining”. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate x̆II= f(x; y).

Differential Evolution (DE) has been successfully used to solve various complex optimization problems; however, it can suffer depending of the complexity of the problem from slow convergence due to its iterative process. The use of the leadership concept was efficiently utilized for the acceleration of Particle Swarm Optimization (PSO) in a single-objective space. The generalization of the leadership concept in multi-objective space is not trivial. Furthermore, despite the efficiency of using the leadership concept, a limited number of multi-objective metaheuristics utilize it. To address these challenges, this paper incorporates the concept of leadership in a multi-objective variant of DE by introducing it into the mutation scheme. The preliminary results are promising as MODEL outperformed the parent algorithm GDE3 and showed the highest accuracy when compared with seven other algorithms.

Generalized opposition-based differential evolution (GODE) is an effective algorithm for global optimization over continuous search space. However, the performance of GODE highly depends on its control parameters. To improve the performance of GODE, this paper proposes an enhanced GODE algorithm called AGODE, which employs an adaptive generalized opposition-based learning (GOBL) mechanism to automatically adjust the probability of opposition during the evolution. Experimental study is conducted on a set of 19 well-known benchmark functions. Computational results show that the proposed approach AGODE outperforms some state-of-the-art DE variants on the majority of test problems.

Cooperative Co-evolutionary algorithms are effective approaches to solve large-scale optimization problems. The crucial challenge in these methods is the design of a decomposition method which is able to detect interactions among variables. In this paper, we proposed a decomposition method based on High Dimensional Model Representation (HDMR) which extracts separable and nonseparable subcomponents for Cooperative Co-evolutionary algorithms. The entire decomposition procedure is conducted before applying the optimization. The experimental results for D=1000 on twenty CEC-2010 benchmark functions show that the proposed method is promisingly efficient to solve large-scale optimization problems. The proposed approach is compared with two other methods and discussed in details.

The capabilities of evolutionary algorithms (EAs) in solving nonlinear and non-convex optimization problems are significant. Among the many types of methods, differential evolution (DE) is an effective population-based stochastic algorithm, which has emerged as very competitive. Since its inception in 1995, many variants of DE to improve the performance of its predecessor have been introduced. In this context, opposition-based differential evolution (ODE) established a novel concept in which, each individual must compete with its opposite in terms of the fitness value in order to make an entry in the next generation. The generation of opposite points is based on the population's current extreme points (i.e., maximum and minimum) in the search space; these extreme points are not proper representatives for whole population, compared to centroid point which is inclusive regarding all individuals in the population. This paper develops a new scheme that utilizes the centroid point of a population to calculate opposite individuals. Therefore, the classical scheme of an opposite point is modified accordingly. Incorporating this new scheme into ODE leads to an enhanced ODE that is identified as centroid opposition-based differential evolution (CODE). The performance of the CODE algorithm is comprehensively evaluated on well-known complex benchmark functions and compared with the performance of conventional DE, ODE, and some other state-of-the-art algorithms (such as SaDE, ADE, SDE, and jDE) in terms of solution accuracy. The results for CODE are promising.

The concept of opposition-based learning (OBL) can be categorized into Type-I and Type-II OBL methodologies. The Type-I OBL is based on the opposite points in the variable space while the Type-II OBL considers the opposite of function value on the landscape. In the past few years, many research works have been conducted on development of Type-I OBL-based approaches with application in science and engineering, such as opposition-based differential evolution (ODE). However, compared to Type-I OBL, which cannot address a real sense of opposition in term of objective value, the Type-II OBL is capable to discover more meaningful knowledge about problem's landscape. Due to natural difficulty of proposing a Type-II-based approach, very limited research has been reported in that direction. In this paper, for the first time, the concept of Type-II OBL has been investigated in detail in optimization; also it is applied on the DE algorithm as a case study. The proposed algorithm is called opposition-based differential evolution Type-II (ODE-II) algorithm; it is validated on the testbed proposed for the IEEE Congress on Evolutionary Computation 2013 (IEEE CEC-2013) contest with 28 benchmark functions. Simulation results on the benchmark functions demonstrate the effectiveness of the proposed method as the first step for further developments in Type-II OBL-based schemes.

One of the main disadvantages of population-based evolutionary algorithms (EAs) is their high computational cost due to the nature of evaluation, specially when the population size is large. The micro-algorithms employ a very small number of individuals, which can accelerate the convergence speed of algorithms dramatically, while it highly increases the stagnation risk. One approach to overcome the stagnation problem can be increasing the diversity of the population. To do so, a micro-differential evolution with vectorized random mutation factor (MDEVM) algorithm is proposed in this paper, which utilizes the small size population benefit while preventing stagnation through diversification of the population. The proposed algorithm is tested on the 28 benchmark functions provided at the IEEE congress on evolutionary computation 2013 (CEC-2013). Simulation results on the benchmark functions demonstrate that the proposed algorithm improves the convergence speed of its parent algorithm.

This paper proposes a novel algorithm for solving combinatorial optimization problems using genetic algorithms (GA) with self-adaptive mutation. We selected the N-Queens problem (8 ≤ N ≤ 32) as our benchmarking test suite, as they are highly multi-modal with huge numbers of global optima. Optimal static mutation probabilities for the traditional GA approach are determined for each N to use as a best-case scenario benchmark in our conducted comparative analysis. Despite an unfair advantage with traditional GA using optimized fixed mutation probabilities, in large problem sizes (where N > 15) multi-objective analysis showed the self-adaptive approach yielded a 65% to 584% improvement in the number of distinct solutions generated; the self-adaptive approach also produced the first distinct solution faster than traditional GA with a 1.90% to 70.0% speed improvement. Self-adaptive mutation control is valuable because it adjusts the mutation rate based on the problem characteristics and search process stages accordingly. This is not achievable with an optimal constant mutation probability which remains unchanged during the search process.

In this paper, Genetic Programming (GP) is employed to obtain an optimum transformation function for bi-level image thresholding. The GP utilizes a user-prepared gold sample to learn from. A magnificent feature of this method is that it does not require neither a prior knowledge about the modality of the image nor a large training set to learn from. The performance of the proposed approach has been examined on 147 X-ray lung images. The transformed images are thresholded using Otsu's method and the results are highly promising. It performs successfully on 99% of the tested images. The proposed method can be utilized for other image processing tasks, such as, image enhancement or segmentation.

Advanced Driver Assistance System (ADAS) is one of latest innovations in the auto-mobile industry and has become a premium feature in many luxury vehicles. ADAS assists drivers by integrating multiple safety and convenience features into a single system. Current ADAS technology usually comprises of an Adaptive Cruise Control (ACC) system in combination with one or more warning/prevention systems. Such as lane departure, collision avoidance, and parking assist systems. This paper outlines a fuzzy logic based ADAS with integrated speed sign detection (SSD) capability. The described system improves safety of the vehicle by dynamically adjusting the speed of the ACC in accordance with the speed limit of the road. The proposed ADAS system will be helpful in reducing speeding violations and enhancing smoother cruise control in heavy traffic conditions. All system design, implementation and testing was done using the MATLAB development environment, and TORCS virtual car simulator.

Most of the recent proposed approaches for sen-sor(mote) localization are focused on 2-D environments with limited functionalities. This is mostly due to the nature of problem which is non-linear, large-scale, and has limited hardware resources. The micro-evolutionary algorithms (MEAs) utilize a small-size population to solve optimization problems. Therefore, such algorithms require much less processing time and memory than standard evolutionary algorithms (EA), suitable for implementation on embedded systems. In this paper, a novel protocol for localization of motes in 3-D environments is proposed, simulated, and discussed. The localization problem is modeled as an optimization problem. The proposed model is based on a realistic approach to the localization problem, where possible errors and noises in the localization procedure such as signal strength detection are addressed. To present a suitable approach to solve the proposed optimization model, a comparative study on performance of the micro-differential evolution (MDE) algorithms is performed and the results are discussed.

Artificial bee colony (ABC) is a new optimization technique which has shown to be competitive with some wellknown evolutionary algorithms. However, ABC is good at exploration but poor at exploitation. Inspired by JADE (adaptive differential evolution with optional external archive), this paper proposes an improved ABC (IABC) algorithm with an external archive, which stores some best solutions during the search process to guide the search of ABC. Experiments are conducted on several benchmark functions. Computational results show that our approach achieves promising performance in terms of solution accuracy and convergence speed.

The particle swarm optimization (PSO) algorithm has been very successful in single objective optimization as well as in multi-objective (MO) optimization. However, the selection of representative leaders in MO space is a challenging task. Most previous MO-based PSOs used exclusively the concept of non-dominance to select leaders which might slow down the search process if the selected leaders are concentrated in a specific region of the objective space. In this paper, a new restriction mechanism is added to non-dominance in order to select leaders in more representative (distributed) way. The proposed algorithm is named leaders and speed constrained multi-objective PSO (LSMPSO) which is an extended version of SMPSO. The convergence speed of LSMPSO is compared to state-of-the-art metaheuristics, namely, NSGA-II, SPEA2, GDE3, SMPSO, AbYSS, MOCell, and MOEA/D. The ZDT and DTLZ family problems are utilized for the comparisons. The proposed LSMPSO algorithm outperformed the other algorithms in terms of convergence speed.

Differential evolution (DE) is a well-known algorithm for global optimization over continuous search spaces. However, choosing the optimal control parameters is a challenging task because they are problem oriented. In order to minimize the effects of the control parameters, a Gaussian bare-bones DE (GBDE) and its modified version (MGBDE) are proposed which are almost parameter free. To verify the performance of our approaches, 30 benchmark functions and two real-world problems are utilized. Conducted experiments indicate that the MGBDE performs significantly better than, or at least comparable to, several state-of-the-art DE variants and some existing bare-bones algorithms.

The classical Differential Evolution (DE) has showed to perform efficiently in solving both benchmark functions and real-world problems. However, DE, similar to other evolutionary algorithms deteriorate in performance during solving high-dimensional problems. Opposition-based Differential Evolution (ODE) was introduced and, in general, has shown better performance comparing to classical DE for solving large-scale problems. In this paper, we propose an enhancement to ODE in order to improve its ability to solve large-scale problems more effectively. The proposed modified version of ODE is called Center-Based Differential Evolution (CDE) which utilizes the exact algorithm of ODE except replacing of opposite points with center-based individuals. This paper compares DE and ODE with the proposed algorithm, CDE. Furthermore, CDE with dynamic range (CDEd) will be compared to CDE with fixed range (CDEf). Experimental verifications are conducted on seven well-known shifted large-scale benchmark functions for dimensions of 100 and 500, including detailed parameter analysis for CDE. The shifted version of the functions ensures there is no bias towards the center of search space, in favor of CDE algorithm. The results clearly show that the CDE outperforms DE and ODE during solving large-scale problems, and also clarifies the superiority of CDEdto CDEf.

This paper examines and optimizes parameters that affect the air cooling of a Lithium-Ion (Li-Ion) battery, used in Electric Vehicles (EVs). A battery pack containing 150 cylindrical type Li-Ion battery cells in a PVC casing is investigated. An equal number of tubes are used in the pack as a medium to cool the battery by using a fan when the vehicle is stationary or with ambient air when in motion. The parameters affecting the air cooling of battery are studied and optimized by considering their practical constraints. The objective function and Number of Transfer Unit (NTU) are developed Finally, a genetic algorithm method is employed to optimize the decision variables. Analysing the results shows that NTU can be maximized by increasing the diameter of tubes on the battery and keeping the air velocity in a certain range.

In this paper, we present a novel Differential Evolution (DE) algorithm to solve high-dimensional global optimization problems effectively. The proposed approach, called DEVP, employs a variable population size mechanism, which adjusts population size adaptively. Experiments are conducted to verify the performance of DEVP on 19 high-dimensional global optimization problems with dimensions 50, 100, 200, 500 and 1000. The simulation results show that DEVP out performs classical DE, CHC (Crossgenerational elitist selection, Heterogeneous recombination, and Cataclysmic mutation), G CMA-ES (Restart Covariant Matrix Evolutionary Strategy) and GODE (Generalized Opposition-Based DE) on the majority of test problems.

Level set methods have been used for image segmentation. Because partial deferential equations are solved to propagate a curve, level-set image segmentation has a slow convergence speed. The objective of this paper is to propose a method that increases the convergence speed. The proposed approach exploits the benefit of multi-resolutional analysis. Wavelet transform is used to decompose the image into different resolutions. The obtained results show a great improvement in terms of speed and accuracy.

The idea of fighting noise with noise is introduced in this paper and it has been utilized to enhance Differential Evolution algorithm to solve noisy problems efficiently. The Monte-Carlo method is employed to investigate applicability of the proposed concept on a simple real-life problem. Based on the current concept, DE with population shaking (DEPS) and with individuals shaking (DEIS) are developed. Furthermore, the parent algorithm, DE, is experimentally compared with DEPS and DEIS on a benchmark test suite with nine well-known noisy functions. Detailed experimental verifications and corresponding analysis are presented for the 2D to 500D problems, for various noise levels and shaking rates.

This paper presents a novel Differential Evolution (DE) algorithm, called DE enhanced by neighborhood search (DENS), which differs from pervious works of utilizing the neighborhood search in DE, such as DE with neighborhood search (NSDE) and self-adaptive DE with neighborhood search (SaNSDE). In DENS, we focus on searching the neighbors of individuals, while the latter two algorithms (NSDE and SaNSDE) work on the adaption of the control parameters F and CR. The proposed algorithm consists of two following main steps. First, for each individual, we create two trial individuals by local and global neighborhood search strategies. Second, we select the fittest one among the current individual and the two created trial individuals as a new current individual. Experimental studies on a comprehensive set of benchmark functions show that DENS achieves better results for a majority of test cases, when comparing with some other similar evolutionary algorithms.

In this paper, the performance of a sequential Differential Evolution (DE) enhanced by neighborhood search (SDENS) is reported on the set of benchmark functions provided for the CEC2010 Special Session on Large Scale Global Optimization. The original DENS was proposed in our previous work, which differs from existing works which are utilizing the neighborhood search in DE, such as DE with neighborhood search (NSDE) and self-adaptive DE with neighborhood search (SaNSDE). In SDENS, we focus on searching the neighbors of individuals, while the latter two algorithms (NSDE and SaNSDE) work on the adaption of the control parameters F and CR. The proposed algorithm consists of two following main steps. First, for each individual, we create two trial individuals by local and global neighborhood search strategies. Second, we select the fittest one among the current individual and the two created trial individuals as a new current individual. Additionally, sequential DE (DE with one-array) is used as a parent algorithm to accelerate the convergence speed in large scale search spaces. The simulation results for twenty benchmark functions with dimensionality of one thousand are reported.

In many image processing applications, image thresholding is considered to be an important task. Opposition-Based Learning (OBL) was recently introduced and used to enhance different computation algorithms. In this paper, a new thresholding algorithm is proposed by utilizing the concept of opposite fuzzy sets. The algorithm is applied on general set of images and compared with the previous opposition-based thresholding algorithm [1] and a commonly used thresholding method, namely the Otsu method. The most reliable results on the test data are achieved using the proposed algorithm.

In algorithms design, one of the important aspects is to consider efficiency. Many algorithm design paradigms are existed and used in order to enhance algorithms' efficiency. Opposition-based Learning (OBL) paradigm was recently introduced as a new way of thinking during the design of algorithms. The concepts of opposition have already been used and applied in several applications. These applications are from different fields, such as optimization algorithms, learning algorithms and fuzzy logic. The reported results confirm that OBL paradigm was promising to accelerate or to enhance accuracy of soft computing algorithms. In this paper, a survey of existing applications of opposition-based computing is presented.

Population-based algorithms, such as Differential Evolution (DE), Particle Swarm Optimization (PSO), Genetic Algorithms (GAs), and Evolutionary Strategies (ES), are commonly used approaches to solve complex problems from science and engineering. They work with a population of candidate solutions. In this paper, a novel center-based sampling is proposed for these algorithms. Reducing the number of function evaluations to tackle with high-dimensional problems is a worthwhile attempt; the center-based sampling can open a new research area in this direction. Our simulation results confirm that this sampling, which can be utilized during population initialization and/or generating successive generations, could be valuable in solving large-scale problems efficiently. Quasi- Oppositional Differential Evolution is briefly discussed as an evidence to support the proposed sampling theory. Furthermore, opposition-based sampling and center-based sampling are compared in this paper. Black-box optimization is considered in this paper and all details about the conducted simulations are provided.

In this paper a scalability test over eleven scalable benchmark functions, provided by the current workshop (Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems-A Scalability Test), are conducted for accelerated DE using generalized opposition-based learning (GODE). The average error of the best individual in the population has been reported for dimensions 50, 100, 200, and 500 in order to compare with the results of other algorithms which are participating in this workshop. Current work is based on opposition-based differential evolution (ODE) and our previous work, accelerated PSO by generalized OBL.

Image thresholding is a challenging task in image processing field. Many efforts have already been made to propose universal, robust methods to handle a wide range of images. Previously by the same authors, an optimization-based thresholding approach was introduced. According to the proposed approach, differential evolution (DE) algorithm, minimizes dissimilarity between the input grey-level image and the bi-level (thresholded) image. In the current paper, micro opposition-based differential evolution (micro-ODE), DE with very small population size and opposition-based population initialization, has been proposed. Then, it is compared with a well-known thresholding method, Kittler algorithm and also with its non-opposition-based version (micro-DE). In overall, the proposed approach outperforms Kittler method over 16 challenging test images. Furthermore, the results confirm that the micro-ODE is faster than micro-DE because of embedding the opposition-based population initialization.

Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.

In this paper, an enhanced version of the opposition-based differential evolution (ODE) is proposed. ODE utilizes opposite numbers in the population initialization and generation jumping to accelerate differential evolution (DE). Instead of opposite numbers, in this work, quasi opposite points are used. So, we call the new extension quasi- oppositional DE (QODE). The proposed mathematical proof shows that in a black-box optimization problem quasi- opposite points have a higher chance to be closer to the solution than opposite points. A test suite with 15 benchmark functions has been employed to compare performance of DE, ODE, and QODE experimentally. Results confirm that QODE performs better than ODE and DE in overall. Details for the proposed approach and the conducted experiments are provided.

Differential evolution (DE) is a simple, reliable, and efficient optimization algorithm. However, it suffers from a weakness, losing the efficiency over optimization of noisy problems. In many real-world optimization problems we are faced with noisy environments. This paper presents a new algorithm to improve the efficiency of DE to cope with noisy optimization problems. It employs opposition-based learning for population initialization, generation jumping, and also improving population's best member. A set of commonly used benchmark functions is employed for experimental verification. The details of proposed algorithm and also conducted experiments are given. The new algorithm outperforms DE in terms of convergence speed.

Evolutionary Algorithms (EAs) are well-known optimization approaches to cope with non-linear, complex problems. These population-based algorithms, however, suffer from a general weakness; they are computationally expensive due to slow nature of the evolutionary process. This paper presents some novel schemes to accelerate convergence of evolutionary algorithms. The proposed schemes employ opposition-based learning for population initialization and also for generation jumping. In order to investigate the performance of the proposed schemes, Differential Evolution (DE), an efficient and robust optimization method, has been used. The main idea is general and applicable to other population-based algorithms such as Genetic algorithms, Swarm Intelligence, and Ant Colonies. A set of test functions including unimodal and multimodal benchmark functions is employed for experimental verification. The details of proposed schemes and also conducted experiments are given. The results are highly promising.

A new robust image thresholding technique is introduced in this paper. Comprehensive experiments show that a single thresholding method can not be successful for all kind of images. The proposed approach uses fusion of some well-known thresholding methods by applying weighted voting at the decision level. The main objective is improving robustness of thresholding approach by participating several methods. Although, the proposed approach can not guaranty the best result for all kind of images but it shows higher performance and consistent/smoother behavior in overall. The performance of the new approach and nine well-established thresholding methods are compared by applying to an image set with high image diversity. The comparison results show that the proposed approach outperforms other nine well-established thresholding approaches. The proposed approach has been explained in details and experimental results are provided.