Detecting the integer parameter vector in a box-constrained linear model with additive Gaussian noise arises from many applications. The maximum likelihood (ML) detector detects the integer parameter vector by solving a Box-constrained Integer Least Squares (BILS) problem and achieves the highest success probability (i.e., the probability that the detected integer vector equals the original integer vector). However, due to the high complexity of the ML detector, the Babai detector is frequently used to approximate solutions to the BILS problem, especially in time-constrained applications. Considering the success probability achieved by existing Babai detector frameworks is not always satisfying, this paper focuses on proposing a fast block-based Babai detector framework within polynomial complexity to narrow the gap to the ML detector. Unlike element-wise Babai detectors, the proposed method partitions the model matrix into blocks and applies the appropriately sized ML detector to each block. Theoretical analysis shows that the success probability of the block-based Babai detector increases with the block size and therefore is better than the Babai detector. To further improve the success probability, an extended block-based Babai detector is proposed with a reasonable increase in complexity. Simulation results illustrate the theoretical findings and indicate that the proposed detectors achieve a better trade-off between the success probability and complexity compared with conventional Zero-Forcing (ZF), Successive Interference Cancellation (SIC)/Babai detectors, as well as the generalized Babai detector proposed by Chang et al.. For example, in a 16 × 16 MIMO system with 16-QAM modulation, the (extedned) block-based Babai detector can improve the success probability by 5.3% (8.7%) at SNR = 15dB and achieve a gain of approximately 1.5 dB (2 dB) at a BER of 10−3, compared with Chang et al.’s generalized Babai detector, while requiring only 45.1% (57.9%) of the computational complexity on average over the tested SNR range.

Recent developments in the detection of epilepsy and classification of seizures using electroencephalogram (EEG) signals have shown notable progress, yet they still face some challenges. For example, tensor decomposition techniques struggle with high computational demands, and deep learning methods often do not fully utilize the spatial structure of EEG data. This paper presents MavenNet, a Multichannel Wavelet Convolutional Network aimed at improving automated detection of epilepsy and seizure classification. MavenNet begins by applying the continuous wavelet transform to represent the multichannel temporal spectrum as a third-order tensor, which is then processed through multichannel convolution operations. To enhance the interpretability of the model, Class Activation Mapping (CAM) is used to visualize the spectrogram features that are essential for making classification decisions. Experimental results from three widely used datasets and one private dataset indicate that MavenNet outperforms leading algorithms. The proposed model maintains the spatial structure of EEG signals and increases the transparency and reliability of classification outcomes, positioning it as a valuable tool for clinical diagnosis of epilepsy.

Multi-objective Bayesian optimization (MOBO) aims to optimize multiple competing objective functions in the expensive-to-evaluate scenario. The Expected Hypervolume Improvement (EHVI) is a commonly used acquisition function for MOBO and shows a good performance. However, the computation of EHVI becomes challenging as the number of objective functions grows. In this paper, we revisit the formulation of EHVI, as well as its multi-point counterpart qEHVI, and derive much simpler analytic expressions for them. The main contributions of this paper include: (1) first formulating EHVI as a particular hypervolume improvement, and thus immediately obtaining a formal proof of its NP-hardness, faster algorithms in both theory and practice, and more results on its derivatives; (2) first obtaining the analytic expressions of qEHVI for any q > 1 and m ≥ 2 where m is the number of objectives; and (3) demonstrating the advantages of our formulation over existing exact and approximation methods for computing EHVI and qEHVI through a large number of numerical experiments.

Deep Reinforcement Learning (DRL) has gained significant attention for its ability to solve combinatorial optimization problems, including the Traveling Salesman Problem (TSP). While traditional approaches assume known and deterministic cost coefficients, real-world scenarios often involve uncertainty, such as traffic conditions or varying travel times. To address this, we introduce a Multiobjective Robust Combinatorial Optimization (MO-RCO) model that incorporates robustness as an additional objective. By transforming a classical robust combinatorial optimization (RCO) problem into a multiobjective framework, MO-RCO allows decision-makers to explore optimal solutions via a Pareto front, while utilizing pre-trained multiobjective models to estimate robust solutions for new uncertain instances. This enables our method to balance optimality and robustness and provide a scalable solution for new RCO problems. Our results demonstrate the efficiency of MO-RCO in solving the min-max TSP with budget uncertainty, showcasing its potential for real-world applications in robust decision-making.

The discovery of the mathematical form of partial differential equations (PDEs) from data has broad applications and significant implications in many fields. Existing data-driven methods such as the well-known SINDy method, however, struggle to identify arbitrary forms of PDEs with minimal prior knowledge. In this paper, we propose a data-driven method for PDE identification, named Evo-SINDy, which leverages a multi-population co-evolutionary algorithm to address the limitations of SINDy. This method is able to efficiently identify PDEs from a sufficiently large search space that best match data characteristics, ensuring minimal reliance on prior knowledge. Experimental results demonstrate that Evo-SINDy can identify more numbers of one-dimensional PDEs within a unified framework than the other known methods, and outperforms two recently-proposed methods that use open libraries in terms of computational efficiency.

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of the insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes. The code is available at [https://github.com/CIAM-Group/L2C\_Insert](https://github.com/CIAM-Group/L2C\_Insert).

Surrogate models are widely employed to address optimization problems with high computational complexity. However, interpretable surrogate models for Combinatorial Optimization Problems (COPs) remain underexplored. In this paper, a novel surrogate model, termed the Controllable Multimodal Landscape (CML), is proposed for the k-order Traveling Salesman Problem (k-order TSP). The proposed method is inspired by the observation that a Traveling Salesman Problem (TSP) with cities arranged on a convex hull exhibits a unimodal landscape. For the k-order TSP, multiple local optima (or high-quality solutions) are collected, and convex hull TSPs are constructed based on them to generate multiple unimodal landscapes sharing the same search space. These unimodal landscapes are then combined to form a multimodal landscape that approximates the original landscape of the k-order TSP. Particle Swarm Optimization (PSO) is used to optimize the parameters of the CML. Experimental results demonstrate that the proposed CML surrogate model achieves higher accuracy than Random Forest (RF) in most test cases involving k-order TSP instances.

Abstract. The multimodal variational autoencoder (VAE) is a probabilistic latent variable model for modeling the generative process of multiple modalities. Existing multimodal VAEs typically divide the latent variable into two types of variables, aiming to represent shared information across modalities and specific information for each modality. However, previous models lack a mechanism to ensure the disentanglement of these two latent variables, causing degraded generation coherence and quality. Failing in disentanglement hampers their performances, particularly concerning the unconditional coherence metric. Further, since these models are derived from VAE, they inherently struggle to generate high-quality samples. In this work, a new probabilistic latent variable model, named multimodal VAE with mixture-of-distributions prior (MVP), is proposed to address these issues. A mixture of conditional distributions is used as priors for the two latent variables separately, while each mixture component is conditioned on learnable pseudoinputs. These pseudoinputs function as prototypes for modal-specific information, which are parameters of the prior for modal-specific latent variables. Experiments conducted on the PolyMNIST and Tri-modal Fashion-MNIST datasets show that MVP outperforms all previous models in terms of generation coherence and quality. Furthermore, experiments confirm that MVP achieves better disentanglement between the two latent variables than that of other existing methods. An implementation of the MVP model is available at https://github.com/fan222/MVP_multimodal-vae-with-mixture-of-prior .

In cells, various proteins interact to form protein-protein interaction networks. Protein complexes serve as the fundamental units that enable essential functions in biological organisms. Directly detecting protein complexes in protein-protein interaction networks using biology-based methods is costly and time-consuming. In recent years, different computational methods have emerged for identifying or predicting protein complexes within these networks. Following a comprehensive analysis of the issue, the optimization algorithm based on meta-heuristic methods has been completely executed for this specific type of challenge, which started in 2004. This paper provides a systematic survey of such meta-heuristic algorithms. Specifically, 34 related methods published between 2004 and 2024 are collected and summarized, focusing on how to model problems and design optimization algorithms, which are the key components of this survey. Our observations and analyses have revealed several limitations in existing studies and suggested potential avenues for future research.

In the realm of evolutionary multiobjective optimization, the hypervolume indicator serves as a crucial metric for assessing the quality of solution sets. Due to the high costs in hypervolume computation, hypervolume-based optimization algorithms always meet the challenge of finding a certain number of points in a given point set to maximize the hypervolume indicator, especially when there are many objectives. In response, the greedy decremental algorithm for hypervolume subset selection problem (gHSSD) has emerged as a noteworthy alternative. This paper introduces a general algorithm for gHSSD, applicable in any dimensionality above two. The proposed algorithm leverages a space partition tree and incorporates a once-build-multiple-use strategy, effectively reducing time complexity. We prove that the proposed algorithm has a time complexity of O((n-k+n)nd-12logn) where n is the number of points, k is the number of points to be reserved, and d the dimensionality. Theoretically, this complexity is competitive with the current best algorithms for d=3,4 and better than them for all 5≤d≤7. To validate our algorithm, we have conducted extensive tests on various random point sets and multiobjective optimization benchmarks. Experimental results suggest that our implementation is more efficient than or competitive with state-of-the-art algorithms on many instances as n increases for d=3,4.

To release the full potentials of massive multi-user multiple-input multiple-output (MU-MIMO) for wireless communication, beamforming design is a must. In this paper, three algorithms are progressively developed for the maximization of the weighted sum-rate (WSR) problem. First, an effective beamforming algorithm is developed by applying the majorization-minimization (MM) procedure in two stages, by which the WSR problem is transformed into a series of quadratic convex problems. We prove that the proposed algorithm converges to a stationary point of the WSR. Second, to improve the efficiency of the two-stage beamforming algorithm, the inherent low-dimensional structure within the beamforming update is exploited aiming to reduce the computational complexity of the matrix inversion. Third, to further reduce the complexity, a deep unfolding beamforming network is developed, which unfolds the improved beamforming algorithm into a layer-wise structure and employs a trainable module structured on the dynamics developed to approximate the matrix inversion. Experimental results demonstrate that the proposed algorithms perform significantly better than the classical weighted minimum mean square error (WMMSE) beamforming and state-of-the-art deep unfolding beamformers in terms of sum-rate and require significantly less CPU time.

For the signal detection problem in a multiple-input multiple-output (MIMO) system, it has been demonstrated that deep learning can improve the detection accuracy and/or reduce the complexity of traditional detection algorithms under the assumption that the channel scenario remains the same in training and test. However, this assumption is not appropriate since the communication environment in practice is constantly changing. As a result, the performance of deep-learning-based detection methods will degrade significantly due to their lack of generalization ability. To address this problem, we model the channel scenario adaptation problem as a multi-scenario learning task and propose two schemes to improve the adaptability of model-driven detection network to cross-channel scenarios. For the case where the test channel scenario has been seen in the training stage, a hypernetwork is introduced to the deep-learning-based iterative soft thresholding algorithm (DISTA) to generate a personalized set of network parameters for each channel scenario, which is named hyperDISTA. Experimental results show that hyperDISTA trained in multiple channel scenarios can not only adapt to each seen channel scenario but also outperform existing deep-learning-based detectors trained in the single channel scenario at high signal-to-noise ratio (SNR) regimes. For the case where the test channel scenario is unseen in the training stage, we propose to retrain the hyperDISTA in a semi-supervised manner. Experimental results show that the retrained hyperDISTA achieves a performance that is comparable to that of the maximum likelihood detection algorithm (MLD).

Many multiobjective evolutionary algorithms (MOEAs) have been proposed for dealing with various problem difficulties in multiobjective optimization over the past three decades. However, none of them can perform best for all problem difficulties. When solving a certain multiobjective optimization problem (MOP), a good multiobjective optimizer should take its problem features into account. When the problem features are unknown in advance, it is difficult to choose an appropriate algorithm as the prior solver. In this paper, we propose a Q-learning evolutionary multiobjective framework, denoted by QL-MOEA, to solve the MOPs with both separable variables and interacting variables. In QL-MOEA, either NSGA-II or MOEA/D is adaptively selected by intelligent agent in different stages of the evolution of population. Our experimental results show that QL-MOEA outperforms the baseline NSGA-II or MOEA/D in convergence speed.

The hardness of the Unconstrained Binary Quadratic Program (UBQP) problem is due its rugged landscape. Various algorithms have been proposed for UBQP, including the Landscape Smoothing Iterated Local Search (LSILS). Different from other UBQP algorithms, LSILS tries to smooth the rugged landscape by building a convex combination of the original UBQP and a toy UBQP. In this paper, our study further investigates the impact of smoothing rugged landscapes using different toy UBQP problems, including a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{1}$(construct by “$+/-1$‘), a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{2}$(construct by “$+/-\mathrm{i}$’) and a toy UBQP with matrix$\hat{\boldsymbol{Q}}^{3}$(construct randomly). We first assess the landscape flatness of the three toy UBQPs. Subsequently, we test the efficiency of LSILS with different toy UBQPs. Results reveal that the toy UBQP with$\hat{\boldsymbol{Q}}^{1}$(construct by “$+/-1$”) exhibits the flattest landscape among the three, while the toy UBQP with$\hat{Q}^{3}$(construct randomly) presents the most non-flat landscape. Notably, LSILS using the toy UBQP with$\hat{\boldsymbol{Q}}^{2}$(construct by “$+/\cdot \mathbf{i})$emerges as the most effective, while$\hat{\boldsymbol{Q}}^{3}$(construct randomly) has the poorest result. These findings contribute to a detailed understanding of landscape smoothing techniques in optimizing UBQP.

Matrix factorization (MF) methods decompose a data matrix into a product of two-factor matrices (denoted as U and V ) which are with low ranks. In this article, we propose a generative latent variable model for the data matrix, in which each entry is assumed to be a Gaussian with mean to be the inner product of the corresponding columns of U and V . The prior of each column of U and V is assumed to be as a finite mixture of Gaussians. Further, we propose to model the attribute matrix with the data matrix jointly by considering them as conditional independence with respect to the factor matrix U , building upon previously defined model for the data matrix. Due to the intractability of the proposed models, we employ variational Bayes to infer the posteriors of the factor matrices and the clustering relationships, and to optimize for the model parameters. In our development, the posteriors and model parameters can be readily computed in closed forms, which is much more computationally efficient than existing sampling-based probabilistic MF models. Comprehensive experimental studies of the proposed methods on collaborative filtering and community detection tasks demonstrate that the proposed methods achieve the state-of-the-art performance against a great number of MF-based and non-MF-based algorithms.

Pareto local search (PLS) is a natural extension of local search for multiobjective combinatorial optimization problems (MCOPs). In our previous work, we improved the anytime performance of PLS using parallel computing techniques and proposed a parallel PLS based on decomposition (PPLS/D). In PPLS/D, the solution space is searched by multiple independent parallel processes simultaneously. This article further improves PPLS/D by introducing two new cooperative process techniques, namely, a cooperative search mechanism and a cooperative subregion-adjusting strategy. In the cooperative search mechanism, the parallel processes share high-quality solutions with each other during the search according to a distributed topology. In the proposed subregion-adjusting strategy, a master process collects useful information from all processes during the search to approximate the Pareto front (PF) and redivide the subregions evenly. In the experimental studies, three well-known NP-hard MCOPs with up to six objectives were selected as test problems. The experimental results on the Tianhe-2 supercomputer verified the effectiveness of the proposed techniques.

The hypervolume contribution is widely used in indicator-based multiobjective algorithms. We propose an algorithm to compute exact 4-D hypervolume contributions for a set of n points in O(n32logn) time. Our algorithm improves the currently best time complexity O(n2) by O(nlogn), and it is the first algorithm of subquadratic time for this problem. Our algorithm is built upon a space partition method in computational geometry and a geometric structure called the anchored gradient. We also propose a new space partition strategy to reduce the practical running time and the space overhead of this algorithm. Experimental results on a variety of test instances show that our proposed algorithm performs better than the existing state-of-the-art algorithm especially on point sets with cliff or other irregular properties.

The research on expensive multiobjective optimization has attracted particular attention in the area of multiobjective evolutionary computation. Many existing multiobjective evolutionary algorithms (MOEAs) are only suited for small-scale expensive multiobjective optimization problems (MOPs) with less than ten decision variables. The main reason lies in the fact that some optimization techniques used in expensive MOEAs, such as Gaussian Process (GP), are not applicable for exploring high-dimensional search space. The naive way to overcome this difficulty is to convert a high-dimensional expensive MOP into a low-dimensional MOP, which can be solved by existing expensive MOEAs efficiently. In this paper, we investigate the combination of MOEA/D with a weighted optimization framework (WOF) and GP, denoted by MOEA/D-WOFGP, for solving high-dimensional expensive MOPs, where the WOF converts a high-dimensional MOP into a low-dimensional search space of weight variables, and the GP-based learning method is used to predict high-quality solutions within a limited number of function evaluations. Some experiments are conducted to compare the performance of MOEA/D-WOFGP with other expensive MOEAs assisted by variable grouping. Our experimental results show that MOEA/D-WOFGP is advantageous when dealing with high-dimensional expensive MOPs.

Approximating the Pareto fronts of large-scale multiobjective optimization problems (LSMOPs) is a very changeling task due to their huge search spaces caused by the large number of decision variables. It is a commonly-used idea that large scale optimization problems are often transformed into small scale optimization problems that can be solved by existing optimization methods. In this paper, we investigate an improved version of MOEA/D with dimensionality reduction for large-scale multiobjective optimization, denoted by LS-MOEA/D-GSD. The major ideas in our proposed method focus on two aspects. On the one hand, the original search space of LSMOPs is transformed into a small-scale MOP on weight variables of several guided search directions via the genetic operators in differential evolution. On the other hand, the computational resources are allocated to both the original search space and reduced search space. Some experiments are conducted to test the performance of our proposed algorithm on the well-known large scale multiobjective test suites, i.e., LSMOP1-9 with up to 1000 variables. Our experimental results show that our algorithm outperforms several state-of-the-art multiobjective evolutionary algorithms for large scale multiobjective optimization.

As an extension of local search for multiobjective case, the basic version of Pareto Local Search (PLS) suffers from a poor anytime behavior. Researches have been carried out to overcome this drawback from different aspects. In this paper, we focus on the mechanism of neighborhood exploration in bi-objective Travelling Salesman Problems (bTSPs). Inspired by existing fast local search strategies for single objective TSP, we propose two speed-up strategies to help PLS quickly find promising neighboring solutions in bTSPs. In the experimental studies, we investigate the sensitivity of parameters and test the performance of several PLS variants with different combinations of the two strategies. The experimental results verify the effectiveness of the two strategies and their combination.

Signal detection plays a significant role at the receiver of current multiple-input multiple-output (MIMO) communication systems. In this paper, we propose a deep learning aided Douglas-Rachford network (DRNet) for MIMO signal detection. Specifically, DRNet is developed based on Douglas-Rachford splitting approach, which is a classic method for non-smooth convex signal recovery. It is known that the transmitted signal in MIMO systems is drawn from a discrete quadrature amplitude modulation (QAM) constellation and ordinary least square (OLS), namely zero-forcing (ZF), performs poorly in small size MIMO systems. In order to obtain better performance, we design an implicit penalty for the unknown transmitted signal and use a deep neural network (DNN) to learn the corresponding proximal gradient of the penalty. Meanwhile, we vectorize the hyper-parameters in the Douglas-Rachford splitting approach and make them learnable. Simulation results show that the proposed DRNet outperforms the original Douglas-Rachford splitting approach and is robust to varying signal-to-noise ratio (SNR). Moreover, compared with existing model-driven deep MIMO detectors, DRNet also has lower bit-error-rate (BER).

In this paper, we investigate the transmit beamforming design for weighted sum-rate maximization in massive multiple-input multiple-output (MIMO) downlink systems. Currently, the most popular algorithm for this scenario is the weighted minimum mean square error (WMMSE) algorithm. We propose a two-stage majorization-minimization (MM) based beamforming (dubbed TMMBF) which transforms the weighted sum-rate maximization problem into a quadratic convex problem by utilizing the MM method twice. The proposed algorithm converges to a stationary point of the weighted sum-rate maximization problem. Interestingly, we find that the WMMSE algorithm is a special case of the TMMBF algorithm, thus unifying the WMMSE algorithm into the MM framework for the first time. In addition, the surrogate function of TMMBF is tighter than that of WMMSE, resulting in faster convergence of the TMMBF algorithm. The simulation results on 3GPP channel models generated from Quadriga show that the TMMBF algorithm has better performance and faster numerical convergence compared to the WMMSE algorithm.

Detecting overlapping communities of an attribute network is a ubiquitous yet very difficult task, which can be modeled as a discrete optimization problem. Besides the topological structure of the network, node attributes and node overlapping aggravate the difficulty of community detection significantly. In this article, we propose a novel continuous encoding method to convert the discrete-natured detection problem to a continuous one by associating each edge and node attribute in the network with a continuous variable. Based on the encoding, we propose to solve the converted continuous problem by a multiobjective evolutionary algorithm (MOEA) based on decomposition. To find the overlapping nodes, a heuristic based on double-decoding is proposed, which is only with linear complexity. Furthermore, a postprocess community merging method in consideration of node attributes is developed to enhance the homogeneity of nodes in the detected communities. Various synthetic and real-world networks are used to verify the effectiveness of the proposed approach. The experimental results show that the proposed approach performs significantly better than a variety of evolutionary and nonevolutionary methods on most of the benchmark networks.

The objective reduction has been regarded as a basic issue in many-objective optimization. Existing objective reduction methods identify one set of essential objectives using an approximate nondominated front. However, if the Pareto front (PF) of a many-objective optimization problem (MaOP) is irregular, one single set of essential objectives may not be efficient for objective reduction. This article proposes to produce several different sets of essential objectives in objective reduction. More specifically, we use the Gaussian mixture model clustering to classify the obtained nondominated front into different subsets and perform objective reduction on each subset. Both an offline objective reduction method and an online objective reduction method are developed. The experimental results indicate that our proposed methods work well for MaOPs with degenerate or nondegenerate PFs.

This article proposes a novel landscape smoothing method for the symmetric traveling salesman problem (TSP). We first define the homotopic convex (HC) transformation of a TSP as a convex combination of a well-constructed simple TSP and the original TSP. The simple TSP, called the convex-hull TSP, is constructed by transforming a known local or global optimum. We observe that controlled by the coefficient of the convex combination, with local or global optimum: 1) the landscape of the HC transformed TSP is smoothed in terms that its number of local optima is reduced compared to the original TSP and 2) the fitness distance correlation of the HC transformed TSP is increased. Furthermore, we observe that the smoothing effect of the HC transformation depends highly on the quality of the used optimum. A high-quality optimum leads to a better smoothing effect than a low-quality optimum. We then propose an iterative algorithmic framework in which the proposed HC transformation is combined within a heuristic TSP solver. It works as an escaping scheme from local optima aiming to improve the global searchability of the combined heuristic. Case studies using the 3-Opt and the Lin-Kernighan local search as the heuristic solver show that the resultant algorithms significantly outperform their counterparts and two other smoothing-based TSP heuristic solvers on most of the test instances with up to 20 000 cities.

In this article, we first propose a graph neural network encoding method for the multiobjective evolutionary algorithm (MOEA) to handle the community detection problem in complex attribute networks. In the graph neural network encoding method, each edge in an attribute network is associated with a continuous variable. Through nonlinear transformation, a continuous valued vector (i.e., a concatenation of the continuous variables associated with the edges) is transferred to a discrete valued community grouping solution. Further, two objective functions for the single-attribute and multiattribute network are proposed to evaluate the attribute homogeneity of the nodes in communities, respectively. Based on the new encoding method and the two objectives, a MOEA based upon NSGA-II, called continuous encoding MOEA, is developed for the transformed community detection problem with continuous decision variables. Experimental results on single-attribute and multiattribute networks with different types show that the developed algorithm performs significantly better than some well-known evolutionary- and nonevolutionary-based algorithms. The fitness landscape analysis verifies that the transformed community detection problems have smoother landscapes than those of the original problems, which justifies the effectiveness of the proposed graph neural network encoding method.

Adaptive parameter control and mutation operator selection are two important research avenues in differential evolution (DE). Existing works consider the two avenues independently. In this paper, we propose to unify the two modules and develop a unified parameterized mutation operator. With different settings of the parameters, different mutation operators can be retrieved. Further, the settings of the parameters closely relate to the control parameters of the DE. By determining the parameters we can achieve adaptive parameter control and mutation operator selection simultaneously. We propose to use a neural network to output the parameters and learn the network parameter by the natural evolution strategies algorithm under the consideration of modeling the evolution process as a Markov Decision Process. Experimental results on the CEC 2018 test suite show that the proposed method performs significantly better than traditional DEs with different operators and an advanced adaptive DE. We further analyze the time complexity and population diversity of the proposed method. The analysis shows that our method can achieve a balanced exploration and exploitation with a properly learned network.

Community detection in complex attribute network is an indispensable but difficult task in data mining. Recently, using multiobjective evolutionary algorithm (MOEA) to address this task has become popular since it can be naturally modeled as a discrete multiobjective optimization problem (MOP). In this paper, we develop a continuous MOEA, in which a continuous encoding is proposed to convert the discrete MOP into a continuous one by introducing a set of auxiliary continuous variables. Further, we construct a similarity matrix to replace the adjacency matrix by making use of the network node degree information in the encoding. The new similarity matrix not only reserves the property of the adjacency matrix but includes the degree information of all the network nodes. In our experiments, various benchmark networks with or without ground truths are used to compare with some state-of-the-art MOEA-based and non-MOEA-based methods. The experimental results show that the proposed algorithm performs favorably against the compared methods.

Differential evolution is one of the most prestigious population-based stochastic optimization algorithm for black-box problems. The performance of a differential evolution algorithm depends highly on its mutation and crossover strategy and associated control parameters. However, the determination process for the most suitable parameter setting is troublesome and time consuming. Adaptive control parameter methods that can adapt to problem landscape and optimization environment are more preferable than fixed parameter settings. This article proposes a novel adaptive parameter control approach based on learning from the optimization experiences over a set of problems. In the approach, the parameter control is modeled as a finite-horizon Markov decision process. A reinforcement learning algorithm, named policy gradient, is applied to learn an agent (i.e., parameter controller) that can provide the control parameters of a proposed differential evolution adaptively during the search procedure. The differential evolution algorithm based on the learned agent is compared against nine well-known evolutionary algorithms on the CEC'13 and CEC'17 test suites. Experimental results show that the proposed algorithm performs competitively against these compared algorithms on the test suites.

Tuning hyper-parameters for evolutionary algorithms is an important issue in computational intelligence. Performance of an evolutionary algorithm depends not only on its operation strategy design, but also on its hyper-parameters. Hyper-parameters can be categorized in two dimensions as structural/numerical and time-invariant/time-variant. Particularly, structural hyper-parameters in existing studies are usually tuned in advance for time-invariant parameters, or with hand-crafted scheduling for time-invariant parameters. In this paper, we make the first attempt to model the tuning of structural hyper-parameters as a reinforcement learning problem, and present to tune the structural hyper-parameter which controls computational resource allocation in the CEC 2018 winner algorithm by Q-learning. Experimental results show favorably against the winner algorithm on the CEC 2018 test functions.

Pareto local search (PLS) is a basic building block in many metaheuristics for a multiobjective combinatorial optimization problem. In this paper, an enhanced PLS variant called parallel PLS based on decomposition (PPLS/D) is proposed. PPLS/D improves the efficiency of PLS using the techniques of parallel computation and problem decomposition. It decomposes the original search space into L subregions and executes L parallel processes searching in these subregions simultaneously. Inside each subregion, the PPLS/D process is guided by a unique scalar objective function. PPLS/D differs from the well-known two phase PLS in that it uses the scalar objective function to guide every move of the PLS procedure in a fine-grained manner. In the experimental studies, PPLS/D is compared against the basic PLS and a recently proposed PLS variant on the multiobjective unconstrained binary quadratic programming problems and the multiobjective traveling salesman problems with, at most, four objectives. The experimental results show that regardless of whether the initial solutions are randomly generated or generated by heuristic methods, PPLS/D always performs significantly better than the other two PLS variants.

This paper proposes a novel learning to learn method, called learning to learn iterative search algorithm (LISA), for signal detection in a multi-input multi-output (MIMO) system. The idea is to regard the signal detection problem as a decision making problem over tree. The goal is to learn the optimal decision policy. In LISA, deep neural networks are used as parameterized policy function. Through training, optimal parameters of the neural networks are learned and thus optimal policy can be approximated. Different neural network-based architectures are used for fixed and varying channel models, respectively. LISA provides soft decisions and does not require any information about the additive white Gaussian noise. Simulation results show that LISA 1) obtains near maximum likelihood detection performance in both fixed and varying channel models under QPSK modulation; 2) achieves significantly better bit error rate (BER) performance than classical detectors and recently proposed deep/machine learning based detectors at various modulations and signal to noise (SNR) ratios both under i.i.d and correlated Rayleigh fading channels in the simulation experiments; 3) is robust to MIMO detection problems with imperfect channel state information; and 4) generalizes very well against channel correlation and SNRs.

In evolutionary optimization, the preselection is an efficient operator to improve the search efficiency, which aims to filter unpromising candidate solutions before fitness evaluation. Most existing preselection operators rely on fitness values, surrogate models, or classification models. Basically, the classification based preselection regards the preselection as a classification procedure, i.e., differentiating promising and unpromising candidate solutions. However, the difference between promising and unpromising classes becomes fuzzy as the running process goes on, as all the left solutions are likely to be promising ones. Facing this challenge, this paper proposes a fuzzy classification based preselection (FCPS) scheme, which utilizes the membership function to measure the quality of candidate solutions. The proposed FCPS scheme is applied to two state-of-the-art evolutionary algorithms on a test suite. The experimental results show the potential of FCPS on improving algorithm performance.

The surrogate-assisted optimization algorithms (SAOAs) are very promising for solving computationally expensive optimization problems (EOPs). Generally, the performance of a SAOA is determined by the quality of its surrogate model and the infill sampling criterion. In this paper, we propose a radial basis function (RBF) assisted optimization algorithm with batch infill sampling criterion for solving EOPs (short for RBFBS). In RBFBS, the quality of RBF model is adjusted by choosing a good shape parameter via solving a sub-expensive hyperparameter optimization problem. Moreover, a batch infill sampling criterion that includes a bi-objective-based sampling approach and a single-objective-based sampling approach is proposed to get a batch of samples for expensive evaluation. The experimental results on various benchmark problems show that RBFBS is very promising for expensive optimization.

Decomposition-based multi-objective evolutionary algorithm has been acknowledged as a promising paradigm for multi-objective optimization problems. Nevertheless, its performance deteriorates seriously when the number of objectives increases. To improve its performance, generating high-quality solution is vital. Acknowledging the success of hybridizing different recombination operators, a selection strategy to choose from a set of differential evolution (DE) operators is adopted in this paper. The selection strategy could combine the advantages of these DE operators. Yet, the performance of DE operators depends highly on their control parameters, which should be tuned adaptively along the search process to fully explore their search abilities. An adaptive parameter tuning strategy is hereby proposed by estimating a Cauchy and a normal distribution from history information for the control parameters, respectively. Experimental comparison using DTLZ1-DTLZ4, with the number of objectives ranging from three to ten, is carried out between six state-of-the-art algorithms and the developed algorithm. Empirical results justify the outperformance of the developed algorithm against the compared algorithms in terms of some commonly-used performance metrics.

Decomposition-based constrained multiobjective evolutionary algorithms decompose a constrained multiobjective problem into a set of constrained single-objective subproblems. For each subproblem, the aggregation function and the overall constraint violation need to be minimized simultaneously, which however may conflict with each other during the evolutionary process. To solve this issue, this paper proposes a novel decomposition-based constrained multiobjective evolutionary algorithm with two types of weight vectors, respectively emphasizing convergence and diversity. The solutions associated to the convergence weight vectors are updated only considering the aggregation function in order to search the whole search space freely, while the ones associated to the diversity weight vectors are renewed by considering both the aggregation function and the overall constraint violation, which encourages to search around the feasible region found so far. Once the replacement of solutions does not happen for the diversity weight vectors in a period, the corresponding diversity weight vectors will be transferred to convergence one. Thereafter, all solutions will finally search around the feasible region, which helps to find more feasible or superior solutions. The proposed constraint handling technique can have a good balance to search the feasible and infeasible regions and show the promising performance, which is validated when tackling several constrained multi-objective problems.

Combining machine learning techniques has shown great potentials in evolutionary optimization since the domain knowledge of an optimization problem, if well learned, can be a great help for creating high-quality solutions. However, existing learning-based multiobjective evolutionary algorithms (MOEAs) spend too much computational overhead on learning. To address this problem, we propose a learning-based MOEA where an online learning algorithm is embedded within the evolutionary search procedure. The online learning algorithm takes the stream of sequentially generated solutions along the evolution as its training data. It is noted that the stream of solutions are temporal, dependent, nonstationary, and nonstatic. These data characteristics make existing online learning algorithm not suitable for the evolution data. We hence modify an existing online agglomerative clustering algorithm to accommodate these characteristics. The modified online clustering algorithm is applied to adaptively discover the structure of the Pareto optimal set; and the learned structure is used to guide new solution creation. Experimental results have shown significant improvement over four state-of-the-art MOEAs on a variety of benchmark problems.

In some real-world applications, it has been found that the performance of multiobjective optimization evolutionary algorithms (MOEAs) may deteriorate when boundary solutions in the Pareto front (PF) are more difficult to approximate than others. Such a problem feature, referred to as difficult-to-approximate (DtA) PF boundaries, is seldom considered in existing multiobjective optimization test problems. To fill this gap and facilitate possible systematic studies, we introduce a new test problem generator. The proposed generator enables the design of test problems with controllable difficulties regarding the feature of DtA PF boundaries. Three representative MOEAs, NSGA-II, SMS-EMOA, and MOEA/D-DRA, are performed on a series of test problems created using the proposed generator. Experimental results indicate that all the three algorithms perform poorly on the new test problems. Meanwhile, a modified variant of MOEA/D-DRA, denoted as MOEA/D-DRA-UT, is validated to be more effective in dealing with these problems. Subsequently, it is concluded that the rational allocation of computational resources between different PF parts is crucial for MOEAs to handle the problems with DtA PF boundaries.

Pareto Local Search (PLS) is a simple, yet effective optimization approach dedicated to multi-objective combinatorial optimization. It can however suffer from a high computational cost, especially when the size of the Pareto optimal set is relatively large. Recently, incorporating decomposition in PLS had revealed a high potential, not only in providing high-quality approximation sets, but also in speeding-up the search process. Using the bi-objective Unconstrained Binary Quadratic Programming (bUBQP) problem as an illustrative benchmark, we demonstrate some shortcomings in the resulting decomposition-guided Parallel Pareto Local Search (PPLS), and we propose to revisit the PPLS design accordingly. For instances with a priori unknown Pareto front shape, we show that a simple pre-processing technique to estimate the scale of the Pareto front can help PPLS to better balance the workload. Furthermore, we propose a simple technique to deal with the critically-important scalability issue raised by PPLS when deployed over a large number of computing nodes. Our investigations show that the revisited version of PPLS provides a consistent performance, suggesting that decomposition-guided PPLS can be further generalized in order to improve both parallel efficiency and approximation quality.

This work builds upon the kernel regression framework for solving the general image processing problem of denoising, deblurring and interpolating from scattered image samples. A competitive expectation-maximization method estimates globally all parameters of a generative image model, accounting for missing samples. One 2D footprint kernel and a local linear regression plane are estimated per data sample. Kernels can shift and their prior probabilities are estimated as well, unlike in nonparametric models. Missing data yields an underdetermined problem that is regularized by smoothing the marginal mixture density. At each iteration, a balloon estimator computes numerically the spatial “territory” associated to each data samples. Results of these numerical diffusion operations are used to convolve adaptively each kernel in the forward model. Finally, the complete image is reconstructed by smoothing regression for combining conditional means of local linear regressors. Experiments apply this iterative Bayesian technique in image restoration.

Keeping balance between convergence and diversity for many-objective optimisation problems (having four or more objectives) is a very difficult task as revealed in existing research in multiobjective evolutionary optimisation. In this paper, we propose a reference-inspired multiobjective evolutionary algorithm for many-objective optimisation. The main idea is (1) to summarise information inspired by a set of randomly generated reference points in the objective space to strengthen the selection pressure towards the Pareto front; and (2) to decompose the objective space into subregions for diversity management and recombination. We showed that the mutual relationship between a population of solution and the reference points provides not only a new dominance relation to producing fine selection pressure but also a balanced convergence-diversity information that is able to adapt search dynamics. The partition of the objective space into several subregions is able to preserve the Pareto front’s diversity. Moreover, a restricted stable match strategy is proposed to choose appropriate parent solutions from solution sets constructed at the subregions for high-quality offspring generation. Controlled experiments conducted on commonly used benchmark test suites have shown the effectiveness and competitiveness of the proposed algorithm compared with several state-of-the-art many-objective evolutionary algorithms.

Objective: an innovative concept and method is introduced to use a 3-D anatomical graphic pattern called visual patient (VP) visually to index, represent, and render the medical diagnostic records (MDRs) of a patient, so that a doctor can quickly learn the current and historical medical status of the patient by manipulating VP. The MDRs can be imaging diagnostic reports and DICOM images, laboratory reports and clinical summaries which can have clinical information relating to medical status of human organs or body parts. Methods: the concept and method included three steps. First, a VP data model called visual index object (VIO) and a VP graphic model called visual anatomic object (VAO) were introduced. Second, a series of processing methods of parsing and extracting key information from MDRs were used to fill the attributes of the VIO model of a patient. Third, a VP system (VPS) was designed to map VIO to VAO, to create a VP instance for each patient. Results: a prototype VPS has been implemented in a simulated hospital PACS/RIS integrated environment. Two evaluation results showed that more than 70% participating radiologists would like to use the VPS in their radiological imaging tasks, and the efficiency of using VPS to review the tested patients' MDRs was 2.24 times higher than that of using PACS/RIS, while the average accuracyac> by using PACS/RIS was better than that by using VPS; however, this difference was only about 4%. Conclusion: the developed VPS can show the medical status of patient organs/sub-organs with 3-D anatomical graphic pattern and will be welcomed by radiologists with better efficiency in reviewing the patients' MDRs and with acceptable accuracy. Significance: the VP introduces a new way for medical professionals to access and interact with a huge amount of patient records with better efficiency in the big data era.

In this paper, we proposed a generative model for feature selection under the unsupervised learning context. The model assumes that data are independently and identically sampled from a finite mixture of Student's distributions, which can reduce the sensitiveness to outliers. Latent random variables that represent the features' salience are included in the model for the indication of the relevance of features. As a result, the model is expected to simultaneously realize clustering, feature selection, and outlier detection. Inference is carried out by a tree-structured variational Bayes algorithm. Full Bayesian treatment is adopted in the model to realize automatic model selection. Controlled experimental studies showed that the developed model is capable of modeling the data set with outliers accurately. Furthermore, experiment results showed that the developed algorithm compares favorably against existing unsupervised probability model-based Bayesian feature selection algorithms on artificial and real data sets. Moreover, the application of the developed algorithm on real leukemia gene expression data indicated that it is able to identify the discriminating genes successfully.

Solving dynamic multi-objective optimisation problem means to search adaptively for the Pareto optimal solutions when the environment changes. It is important to find out the changing pattern for the efficiency of the evolutionary search. Learning techniques are thus widely used to explore the dependence structure of the changing for population re-initialisation in the evolutionary search paradigm. The learning techniques are expected to discover some useful knowledge from history information, while the learned knowledge can help improve the search speed through good initialisation when change occurs. In this paper, we propose a new learning strategy based on the incorporation of mutual information, stable matching strategy and Newton's laws of motion. Mutual information is used to identify the relationship between previously found solutions; the stable matching strategy is used to associate previous found solutions bijectively and Newton's Laws of motion is applied to re-initialise the new population. Controlled experiments were carried out systematically on some widely used test problems. Comparison against several state-of-the-art dynamic multi-objective evolutionary algorithms showed comparable performance in favour of the developed algorithm.

In an estimation of distribution algorithm (EDA), global population distribution is modeled by a probabilistic model, from which new trial solutions are sampled, whereas individual location information is not directly and fully exploited. In this paper, we suggest to combine an EDA with cheap and expensive local search (LS) methods for making use of both global statistical information and individual location information. In our approach, part of a new solution is sampled from a modified univariate histogram probabilistic model and the rest is generated by refining a parent solution through a cheap LS method that does not need any function evaluation. When the population has converged, an expensive LS method is applied to improve a promising solution found so far. Controlled experiments have been carried out to investigate the effects of the algorithm components and the control parameters, the scalability on the number of variables, and the running time. The proposed algorithm has been compared with two state-of-the-art algorithms on two test suites of 27 test instances. Experimental results have shown that, for simple test instances, our algorithm can produce better or similar solutions but with faster convergence speed than the compared methods and for some complicated test instances it can find better solutions.

In this paper, we proposed a generative graphical model for unsupervised robust feature selection. The model assumes that the data are independent and identically sampled from a finite mixture of Student-t distribution for dealing with outliers. The Student t-distribution works as the building block for robust clustering and outlier detection. Random variables that represent the features' saliency are included in the model for feature selection. As a result, the model is expected to simultaneously realise unsupervised clustering, feature selection and outlier detection. The inference is carried out by a tree-structured variational Bayes (VB) algorithm. The feature selection capability is realised by estimating the feature saliencies associated with the features. The adoption of full Bayesian treatment in the model realises automatic model selection. Experimental studies showed that the developed algorithm compares favourably against existing unsupervised Bayesian feature selection algorithm in terms of commonly-used internal and external cluster validity indices on controlled experimental settings and benchmark data sets. The controlled experimental study also showed that the developed algorithm is capable of exposing the outliers and finding the optimal number of components (model selection) accurately.

Recently, MOEA/D (multi-objective evolutionary algorithm based on decomposition) has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem (MOP) into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front (PF; i.e., discontinuous PF or PF with sharp peak or low tail). To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment (MOEA/D-AWA). According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, [Formula: see text]-MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex.

The construction of promising solutions for NP-hard combinatorial optimization problems (COPs) in meta-heuristics is usually based on three types of information, namely a priori information, a posteriori information learned from visited solutions during the search procedure, and online information collected in the solution construction process. Prior information reflects our domain knowledge about the COPs. Extensive domain knowledge can surely make the search effective, yet it is not always available. Posterior information could guide the meta-heuristics to globally explore promising search areas, but it lacks local guidance capability. On the contrary, online information can capture local structures, and its application can help exploit the search space. In this paper, we studied the effects of using this information on metaheuristic's algorithmic performances for the COPs. The study was illustrated by a set of heuristic algorithms developed for the quadratic assignment problem. We first proposed an improved scheme to extract online local information, then developed a unified framework under which all types of information can be combined readily. Finally, we studied the benefits of the three types of information to meta-heuristics. Conclusions were drawn from the comprehensive study, which can be used as principles to guide the design of effective meta-heuristic in the future.

In this paper, we propose a multi-restart memetic algorithm framework for box constrained global continuous optimisation. In this framework, an evolutionary algorithm (EA) and a local optimizer are employed as separated building blocks. The EA is used to explore the search space for very promising solutions (e.g., solutions in the attraction basin of the global optimum) through its exploration capability and previous EA search history, and local search is used to improve these promising solutions to local optima. An estimation of distribution algorithm (EDA) combined with a derivative free local optimizer, called NEWUOA (M. Powell, Developments of NEWUOA for minimization without derivatives. Journal of Numerical Analysis, 28:649-664, 2008), is developed based on this framework and empirically compared with several well-known EAs on a set of 40 commonly used test functions. The main components of the specific algorithm include: (1) an adaptive multivariate probability model, (2) a multiple sampling strategy, (3) decoupling of the hybridisation strategy, and (4) a restart mechanism. The adaptive multivariate probability model and multiple sampling strategy are designed to enhance the exploration capability. The restart mechanism attempts to make the search escape from local optima, resorting to previous search history. Comparison results show that the algorithm is comparable with the best known EAs, including the winner of the 2005 IEEE Congress on Evolutionary Computation (CEC2005), and significantly better than the others in terms of both the solution quality and computational cost.

We developed a probabilistic model for canonical correlation analysis in the case when the associated datasets are incomplete. This case can arise where data entries either contain measurement errors or are censored (i.e., nonignorable missing) due to uncertainties in instrument calibration and physical limitations of devices and experimental conditions. The aim of our model is to estimate the true correlation coefficients, through eliminating the effects of measurement errors and abstracting helpful information from censored data. As exact inference is not possible for the proposed model, a modified variational Expectation-Maximization (EM) algorithm was developed. In the algorithm developed, we approximated the posteriors of the latent variables as normal distributions. In the experiment, the modified E-step approximation accuracy is first empirically demonstrated by being compared to hybrid Monte Carlo (HMC) sampling. The following experiments were carried out on synthetic datasets with different numbers of censored data and different correlation coefficient settings to compare the proposed algorithm with a maximum a posteriori (MAP) solution and a Markov Chain-EM solution. Experimental results showed that the variational EM solution compares favorably against the MAP solution, approaching the accuracy of the Markov Chain-EM, while maintaining computational simplicity. We finally applied the proposed algorithm to finding the mostly correlated properties of galaxy group with the X-ray luminosity.

Both parametric Bayesian mixture and non-parametric Dirichlet process mixture modelling (DPM) approaches for density estimation and clustering allow for automatic model selection. It is interesting to study which approach can better fit the data. In

This paper gives a comprehensive review of the application of meta-heuristics to optimization problems in systems biology, mainly focussing on the parameter estimation problem (also called the inverse problem or model calibration). It is intended for either the system biologist who wishes to learn more about the various optimization techniques available and/or the meta-heuristic optimizer who is interested in applying such techniques to problems in systems biology. First, the parameter estimation problems emerging from different areas of systems biology are described from the point of view of machine learning. Brief descriptions of various meta-heuristics developed for these problems follow, along with outlines of their advantages and disadvantages. Several important issues in applying meta-heuristics to the systems biology modelling problem are addressed, including the reliability and identifiability of model parameters, optimal design of experiments, and so on. Finally, we highlight some possible future research directions in this field.

Experimental scientific data sets, especially biology data, usually contain replicated measurements. The replicated measurements for the same object are correlated, and this correlation must be carefully dealt with in scientific analysis. In this paper, we propose a robust Bayesian mixture model for clustering data sets with replicated measurements. The model aims not only to accurately cluster the data points taking the replicated measurements into consideration, but also to find the outliers (i.e., scattered objects) which are possibly required to be studied further. A tree-structured variational Bayes (VB) algorithm is developed to carry out model fitting. Experimental studies showed that our model compares favorably with the infinite Gaussian mixture model, while maintaining computational simplicity. We demonstrate the benefits of including the replicated measurements in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. Finally, we apply the approach to clustering biological transcriptomics mRNA expression data sets with replicated measurements.

In this paper, we present a memetic algorithm with novel local optimizer hybridization strategy for constrained optimization. The developed MA consists of multiple cycles. In each cycle, an estimation of distribution algorithm (EDA) with an adaptive univariate probability model is applied to search for promising search regions. A classical local optimizer, called DONLP2, is applied to improve the best solution found by the EDA to a high quality solution. New cycles are employed when the computational budget has not been reached. The new cycles are expected to learn from the search history to make the further search efficient and to enable escape from local optima. The developed algorithm is experimentally compared with ε-DE, which was the winner of the 2006 IEEE Congress on Evolutionary Computation (CEC'06) competition on constrained optimization. The results favour our algorithm against the best-known algorithm in terms of the number of fitness evaluations used to reach the global optimum.

A mixture of Student t-distributions (MoT) has been widely used to model multivariate data sets with atypical observations, or outliers for robust clustering. In this paper, we developed a novel robust clustering approach by modeling the data sets using mixture of Pearson type VII distributions (MoP). An EM algorithm is developed for the maximum likelihood estimation of the model parameters. An outlier detection criterion is derived from the EM solution. Controlled experimental results on the synthetic datasets show that the MoP is more viable than the MoT. The MoP performs comparably if not better, on average, in terms of outlier detection accuracy and out-of-sample log-likelihood with the MoT. Furthermore, we compared the performances of the Pearson type VII and the student t mixtures on the classification of several benchmark pattern recognition data sets. The comparison favours the developed Pearson type VII mixtures.

In experimental and observational sciences, detecting atypical, peculiar data from large sets of measurements has the potential of highlighting candidates of interesting new types of objects that deserve more detailed domain-specific followup study. However, measurement data is nearly never free of measurement errors. These errors can generate false outliers that are not truly interesting. Although many approaches exist for finding outliers, they have no means to tell to what extent the peculiarity is not simply due to measurement errors. To address this issue, we have developed a model-based approach to infer genuine outliers from multivariate data sets when measurement error information is available. This is based on a probabilistic mixture of hierarchical density models, in which parameter estimation is made feasible by a tree-structured variational expectation-maximization algorithm. Here, we further develop an algorithmic enhancement to address the scalability of this approach, in order to make it applicable to large data sets, via a K-dimensional-tree based partitioning of the variational posterior assignments. This creates a non-trivial tradeoff between a more detailed noise model to enhance the detection accuracy, and the coarsened posterior representation to obtain computational speedup. Hence, we conduct extensive experimental validation to study the accuracy/speed tradeoffs achievable in a variety of data conditions. We find that, at low-to-moderate error levels, a speedup factor that is at least linear in the number of data points can be achieved without significantly sacrificing the detection accuracy. The benefits of including measurement error information into the modeling is evident in all situations, and the gain roughly recovers the loss incurred by the speedup procedure in large error conditions. We analyze and discuss in detail the characteristics of our algorithm based on results obtained on appropriately designed synthetic data experiments, and we also demonstrate its working in a real application example.

This paper proposes a hybrid estimation of distribution algorithm (HyEDA) to address the design problem of code division multiple access cellular system configuration. Given a service area, the problem is to find a set of optimal locations of base stations, associated with their corresponding powers and antenna heights in the area, in order to maximize call quality and service coverage, at the same time, to minimize the total cost of the system configuration. HyEDA is a two-stage hybrid approach which integrates an estimation of distribution algorithm, a K-means clustering method, and a simple local search algorithm. We have compared HyEDA with a simulated annealing method on a number of instances. Our simulation results have demonstrated that HyEDA outperforms the simulated annealing method in terms of the solution quality and computational cost.

We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to errors, aiming to retrieve potentially interesting peculiar objects. Since exact inference is not possible in this model, we develop a tree-structured variational EM solution. This compares favorably against a fully factorial approximation scheme, approaching the accuracy of a Markov-Chain-EM, while maintaining computational simplicity. We demonstrate the benefits of including measurement errors in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. We then use this approach for detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.

Image-data transmission from one site to another through public network is usually characterized in term of privacy, authenticity, and integrity. In this paper, we first describe a general scenario about how image is delivered from one site to another through a wide-area network (WAN) with security features of data privacy, integrity, and authenticity. Second, we give the common implementation method of the digital imaging and communication in medicine (DICOM) image communication software library with IPv6/IPv4 for high-speed broadband Internet by using open-source software. Third, we discuss two major security-transmission methods, the IP security (IPSec) and the secure-socket layer (SSL) or transport-layer security (TLS), being used currently in medical-image-data communication with privacy support. Fourth, we describe a test schema of multiple-modality DICOM-image communications through TCP/IPv4 and TCP/IPv6 with different security methods, different security algorithms, and operating systems, and evaluate the test results. We found that there are tradeoff factors between choosing the IPsec and the SSL/TLS-based security implementation of IPv6/IPv4 protocols. If the WAN networks only use IPv6 such as in high-speed broadband Internet, the choice is IPsec-based security. If the networks are IPv4 or the combination of IPv6 and IPv4, it is better to use SSL/TLS security. The Linux platform has more security algorithms implemented than the Windows (XP) platform, and can achieve better performance in most experiments of IPv6 and IPv4-based DICOM-image communications. In teleradiology or enterprise-PACS applications, the Linux operating system may be the better choice as peer security gateways for both the IPsec and the SSL/TLS-based secure DICOM communications cross public networks.

An evolutionary algorithm (EA) can be used to tune the control parameters of a construction heuristic to an optimization problem and generate a nearly optimal solution. This approach is in the spirit of indirect encoding EAs. Its performance relies on both the heuristic and the EA. This paper proposes a three-phase parameterized construction heuristic for the shared-path protection problem in wavelength division multiplexing networks with shared-risk link group constraints and applies an EA for optimizing the control parameters of the proposed heuristics. The experimental results show that the proposed approach is effective on all the tested network instances. It was also demonstrated that an EA with guided mutation performs better than a conventional genetic algorithm for tuning the control parameters, which indicates that a combination of global statistical information extracted from the previous search and location information of the best solutions found so far could improve the performance of an algorithm.

Guided mutation uses the idea of estimation of distribution algorithms to improve conventional mutation operators. It combines global statistical information and the location information of good individual solutions for generating new trial solutions. This paper suggests using guided mutation in iterative local search. An experimental comparison between a conventional iterated local search (CILS) and an iterated local search with guided mutation has been conducted on four classes of the test instances of the quadratic assignment problem.

Estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutions in the search space) is not directly used for generating offspring in most existing estimation of distribution algorithms. This paper introduces a new operator, called guided mutation. Guided mutation generates offspring through combination of global statistical information and the location information of solutions found so far. An evolutionary algorithm with guided mutation (EA/G) for the maximum clique problem is proposed in this paper. Besides guided mutation, EA/G adopts a strategy for searching different search areas in different search phases. Marchiori's heuristic is applied to each new solution to produce a maximal clique in EA/G. Experimental results show that EA/G outperforms the heuristic genetic algorithm of Marchiori (the best evolutionary algorithm reported so far) and a MIMIC algorithm on DIMACS benchmark graphs.

A novel and fast shape classification and regularization algorithm for on-line sketchy graphics recognition is proposed. We divided the on-line graphics recognition process into four stages: preprocessing, shape classification, shape fitting, and regularization. The attraction force model is proposed to combine progressively the vertices on the input sketchy stroke and reduce the total number of vertices before the type of shape can be determined After that, the shape is fitted and gradually rectified to a regular one, thus the regularized shape fits the user-intended one precisely. Experimental results show that this algorithm can rapidly yield good recognition precision (averagely above 90%) and a fine regularization effect. Consequently, it is especially suitable for weak computation environments such as PDAs, which solely depend on a pen-based user interface.