Search

Many real-world optimization problems involve uncertainties, and in such situations it is often desirable to identify robust solutions that perform well over the possible future scenarios. In this paper, we focus on input uncertainty, such as in manufacturing, where the actual manufactured product may differ from the specified design but should still function well. Estimating a solution’s expected fitness in such a case is challenging, especially if the fitness function is expensive to evaluate, and its analytic form is unknown. One option is to average over a number of scenarios, but this is computationally expensive. The archive sample approximation method reduces the required number of fitness evaluations by reusing previous evaluations stored in an archive. The main challenge in the application of this method lies in determining the locations of additional samples drawn in each generation to enrich the information in the archive and reduce the estimation error. In this paper, we use the Wasserstein distance metric to approximate the possible benefit of a potential sample location on the estimation error, and propose new sampling strategies based on this metric. Contrary to previous studies, we consider a sample’s contribution for the entire population, rather than inspecting each individual separately. This also allows us to dynamically adjust the number of samples to be collected in each generation. An empirical comparison with several previously proposed archive-based sample approximation methods demonstrates the superiority of our approaches. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a method for generating new individuals such that their mean vector and the covariance matrix are defined by formulas analogous to the covariance matrix adaptation evolution strategy (CMA-ES). In contrast to CMA-ES, which generates new individuals using multivariate Gaussian distribution with an explicitly defined covariance matrix, the introduced method uses combinations of difference vectors between archived individuals and univariate Gaussian random vectors along directions of past shifts of the population midpoints. We use this method to formulate the differential evolution strategy (DES)—an algorithm that is a crossover between differential evolution (DE) and CMA-ES. The numerical results presented in this paper indicate that DES is competitive against CMA-ES in performing both local and global optimization. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) has two salient components: 1) a dynamical rule governing particle motion and 2) an interparticle communication topology. Recent practice has focused on the fully connected topology (Gbest) despite earlier indications on the superiority of local particle neighborhoods. This paper seeks to address the controversy with empirical trials with canonical PSO on a large benchmark of functions, categorized into 14 properties. This paper confirms the early lore that Gbest is the overall better algorithm for unimodal and separable problems and that a ring neighborhood of connectivity two (Lbest) is the preferred choice for multimodal, nonseparable and composition functions. Topologies of intermediate particle connectivity were also tested and the difference in global/local performance was found to be even more marked. A measure of significant improvement is introduced in order to distinguish major improvements from refinements. Lbest, according to the experiments on the 84 test functions and a bi-modal problem of adjustable severity, is found to have significant improvements later in the run, and to be more diverse at termination. A mobility study shows that Lbest is better able to jump between optimum basins. Indeed Gbest was unable to switch basins in the bi-modal trial. The implication is that Lbest’s larger terminal diversity, its better ability to basin hop and its later significant improvement account for the performance enhancement. In several cases where Lbest was not the better algorithm, the trials show that Lbest was not stuck but would have continued to improve with an extended evaluation budget. Canonical PSO is a baseline algorithm and the ancestor of all contemporary PSO variants. These variants build on the basic structure of baseline PSO and the broad conclusions of this paper are expected to follow through. In particular, research that fails to consider local topologies risks underplaying the success of the promoted algorithm. [ABSTRACT FROM AUTHOR]

In the last two decades, a variety of different types of multiobjective optimization problems (MOPs) have been extensively investigated in the evolutionary computation community. However, most existing evolutionary algorithms encounter difficulties in dealing with MOPs whose Pareto optimal solutions are sparse (i.e., most decision variables of the optimal solutions are zero), especially when the number of decision variables is large. Such large-scale sparse MOPs exist in a wide range of applications, for example, feature selection that aims to find a small subset of features from a large number of candidate features, or structure optimization of neural networks whose connections are sparse to alleviate overfitting. This paper proposes an evolutionary algorithm for solving large-scale sparse MOPs. The proposed algorithm suggests a new population initialization strategy and genetic operators by taking the sparse nature of the Pareto optimal solutions into consideration, to ensure the sparsity of the generated solutions. Moreover, this paper also designs a test suite to assess the performance of the proposed algorithm for large-scale sparse MOPs. The experimental results on the proposed test suite and four application examples demonstrate the superiority of the proposed algorithm over seven existing algorithms in solving large-scale sparse MOPs. [ABSTRACT FROM AUTHOR]

As a well-known engineering practice, concurrent engineering (CE) considers all elements involved in a product’s life cycle from the early stages of product development, and emphasizes executing all design tasks simultaneously. As a result, there exist various complex design problems in CE, which usually have many design parameters or require different disciplinary knowledge to solve them. To address these problems and enable concurrent design, different methods have been developed. The original problem is usually divided into small subproblems so that each subproblem can be solved individually and simultaneously. However, good decomposition, optimization, and communication strategies among subproblems are still needed in the field of CE. This paper attempts to study and analyze cooperative co-evolution (CC) based design optimization in CE by employing a parallel CC framework. Furthermore, it aims to develop new concurrent design methods based on parallel CC to solve different kinds of CE problems. To achieve this goal, a new novelty-driven CC is developed for design problems with complex structures and a novel concurrent design method is presented for quasi-separable multidisciplinary design optimization (MDO) problems. The efficacy of the new methods is studied on universal electric motor design problems and a general MDO problem, and compared to that of some existing methods. Additionally, this paper studies how the communication frequency among subpopulations affects the performance of the proposed methods. The optimal communication frequencies under different communication costs are reported as experimental results for both proposed methods on the test problems. Based on this paper, an effective self-adaptive method is proposed to be used in both optimization schemes, which is able to adapt the communication frequency during the optimization process. [ABSTRACT FROM PUBLISHER]

This paper examines evolutionary nonlinear projection (NLP), a form of multidimensional scaling (MDS) performed with an evolutionary algorithm. MDS is a family of techniques for producing a low dimensional data set whose points have a one-to-one correspondence with the points of a higher dimensional data set with the added property that distances or dissimilarities in the higher dimensional space are preserved as much as possible in the lower dimensional space. The goal is typically visualization but may also be clustering or other forms of analysis. In this paper, we review current methods of NLP and go on to characterize NLP as an evolutionary computation problem, gaining insight into MDS as an optimization problem. Two different mutation operators, one introduced in this paper, are compared and parameter studies are performed on mutation rate and population size. The new mutation operator is found to be superior. NLP is found to be a problem where small population sizes exhibit superior performance. It is demonstrated experimentally that NLP is a multimodal optimization problem. Two broad classes of projection problems are identified, one of which yields consistent high-quality results and the other of which has many optima, all of low quality. A number of applications of the technique are presented, including projections of feature vectors for polyominos, of vectors that are members of an error correcting code, of behavioral assessments of a collection of agents, and of features derived from DNA sequences. [ABSTRACT FROM AUTHOR]

Evolutionary multitasking is a recently proposed paradigm to simultaneously solve multiple tasks using a single population. Most of the existing evolutionary multitasking algorithms treat all tasks equally and then assign the same amount of resources to each task. However, when the resources are limited, it is difficult for some tasks to converge to acceptable solutions. This paper aims at investigating the resource allocation in the multitasking environment to efficiently utilize the restrictive resources. In this paper, we design a novel multitask evolutionary algorithm with an online dynamic resource allocation strategy. Specifically, the proposed dynamic resource allocation strategy allocates resources to each task adaptively according to the requirements of tasks. We also design an adaptive method to control the resources invested into cross-domain searching. The proposed algorithm is able to allocate the computational resources dynamically according to the computational complexities of tasks. The experimental results demonstrate the superiority of the proposed method in comparison with the state-of-the-art algorithms on benchmark problems of multitask optimization. [ABSTRACT FROM AUTHOR]

This paper proposes a method for visualizing combinatorial search spaces named low-dimensional Euclidean embedding (LDEE). The proposed method transforms the original search space, such as a set of permutations or binary vectors, to $\pmb {\mathbb {R}}^{k}$ (with ${k} {=} {2}$ or 3 in practice) while aiming to preserve spatial relationships existing in the original space. The LDEE method uses the t-distributed stochastic neighbor embedding (t-SNE) to transform solutions from the original search space to the Euclidean one. In this paper, it is mathematically shown that the assumptions underlying the t-SNE method are valid in the case of permutation spaces with the Mallows distribution. The same is true for other metric spaces provided that the distribution of points is assumed to be normal with respect to the adopted metric. The embedding obtained using t-SNE is further refined to ensure visual separation of individual solutions. The visualization obtained using the LDEE method can be used for analyzing the behavior of the population in a population-based metaheuristic, the working of the genetic operators, etc. Examples of visualizations obtained using this method for the four peaks problem, the firefighter problem, the knapsack problem, the quadratic assignment problem, and the traveling salesman problem are presented in this paper. [ABSTRACT FROM AUTHOR]

Conventional evolutionary algorithms (EAs) are not well suited for solving expensive optimization problems due to the fact that they often require a large number of fitness evaluations to obtain acceptable solutions. To alleviate the difficulty, this paper presents a multitasking evolutionary optimization framework for solving computationally expensive problems. In the framework, knowledge is transferred from a number of computationally cheap optimization problems to help the solution of the expensive problem on the basis of the recently proposed multifactorial EA (MFEA), leading to a faster convergence of the expensive problem. However, existing MFEAs do not work well in solving multitasking problems whose optimums do not lie in the same location or when the dimensions of the decision space are not the same. To address the above issues, the existing MFEA is generalized by proposing two strategies, one for decision variable translation and the other for decision variable shuffling, to facilitate knowledge transfer between optimization problems having different locations of the optimums and different numbers of decision variables. To assess the effectiveness of the generalized MFEA (G-MFEA), empirical studies have been conducted on eight multitasking instances and eight test problems for expensive optimization. The experimental results demonstrate that the proposed G-MFEA works more efficiently for multitasking optimization and successfully accelerates the convergence of expensive optimization problems compared to single-task optimization. [ABSTRACT FROM AUTHOR]

In offline data-driven optimization, only historical data is available for optimization, making it impossible to validate the obtained solutions during the optimization. To address these difficulties, this paper proposes an evolutionary algorithm assisted by two surrogates, one coarse model and one fine model. The coarse surrogate (CS) aims to guide the algorithm to quickly find a promising subregion in the search space, whereas the fine one focuses on leveraging good solutions according to the knowledge transferred from the CS. Since the obtained Pareto optimal solutions have not been validated using the real fitness function, a technique for generating the final optimal solutions is suggested. All achieved solutions during the whole optimization process are grouped into a number of clusters according to a set of reference vectors. Then, the solutions in each cluster are averaged and outputted as the final solution of that cluster. The proposed algorithm is compared with its three variants and two state-of-the-art offline data-driven multiobjective algorithms on eight benchmark problems to demonstrate its effectiveness. Finally, the proposed algorithm is successfully applied to an operational indices optimization problem in beneficiation processes. [ABSTRACT FROM AUTHOR]

This paper introduces sparse representation into spectral clustering and provides a sparse spectral clustering framework via a multiobjective evolutionary algorithm. In contrast to conventional spectral clustering, the main contribution of this paper is to construct the similarity matrix using a sparse representation approach by modeling spectral clustering as a constrained multiobjective optimization problem. Specific operators are designed to obtain a set of high quality solutions in the optimization process. Furthermore, we design a method to select a tradeoff solution from the Pareto front using a measurement called ratio cut based on an adjacency matrix constructed by all the nondominated solutions. We also extend the framework to the semi-supervised clustering field by using the semi-supervised information brought by the labeled samples to set some constraints or to guide the searching process. Experiments on commonly used datasets show that our approach outperforms four well-known similarity matrix construction methods in spectral clustering, and one multiobjective clustering algorithm. A practical application in image segmentation also demonstrates the efficiency of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the application of an automated hybrid approach in addressing the university timetabling problem. The approach described is based on the nature-inspired artificial bee colony (ABC) algorithm. An ABC algorithm is a biologically-inspired optimization approach, which has been widely implemented in solving a range of optimization problems in recent years such as job shop scheduling and machine timetabling problems. Although the approach has proven to be robust across a range of problems, it is acknowledged within the literature that there currently exist a number of inefficiencies regarding the exploration and exploitation abilities. These inefficiencies can often lead to a slow convergence speed within the search process. Hence, this paper introduces a variant of the algorithm which utilizes a global best model inspired from particle swarm optimization to enhance the global exploration ability while hybridizing with the great deluge (GD) algorithm in order to improve the local exploitation ability. Using this approach, an effective balance between exploration and exploitation is attained. In addition, a traditional local search approach is incorporated within the GD algorithm with the aim of further enhancing the performance of the overall hybrid method. To evaluate the performance of the proposed approach, two diverse university timetabling datasets are investigated, i.e., Carter’s examination timetabling and Socha course timetabling datasets. It should be noted that both problems have differing complexity and different solution landscapes. Experimental results demonstrate that the proposed method is capable of producing high quality solutions across both these benchmark problems, showing a good degree of generality in the approach. Moreover, the proposed method produces best results on some instances as compared with other approaches presented in the literature. [ABSTRACT FROM AUTHOR]

The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named quality-diversity (QD) optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, QD algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. First, we present a unifying framework of QD optimization algorithms that covers the two main algorithms of this family (multidimensional archive of phenotypic elites and the novelty search with local competition), and that highlights the large variety of variants that can be investigated within this family. Second, we propose algorithms with a new selection mechanism for QD algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of QD algorithms on three different experimental scenarios. [ABSTRACT FROM PUBLISHER]

Classification algorithms can suffer from performance degradation when the class distribution is unbalanced. This paper develops a two-step approach to evolving ensembles using genetic programming (GP) for unbalanced data. The first step uses multiobjective (MO) GP to evolve a Pareto-approximated front of GP classifiers to form the ensemble by trading-off the minority and the majority class against each other during learning. The MO component alleviates the reliance on sampling to artificially rebalance the data. The second step, which is the focus this paper, proposes a novel ensemble selection approach using GP to automatically find/choose the best individuals for the ensemble. This new GP approach combines multiple Pareto-approximated front members into a single composite genetic program solution to represent the (optimized) ensemble. This ensemble representation has two main advantages/novelties over traditional genetic algorithm (GA) approaches. First, by limiting the depth of the composite solution trees, we use selection pressure during evolution to find small highly-cooperative groups of individuals for the ensemble. This means that ensemble sizes are not fixed a priori (as in GA), but vary depending on the strength of the base learners. Second, we compare different function set operators in the composite solution trees to explore new ways to aggregate the member outputs and thus, control how the ensemble computes its output. We show that the proposed GP approach evolves smaller more diverse ensembles compared to an established ensemble selection algorithm, while still performing as well as, or better than the established approach. The evolved GP ensembles also perform well compared to other bagging and boosting approaches, particularly on tasks with high levels of class imbalance. [ABSTRACT FROM AUTHOR]

Niching techniques have recently been incorporated into evolutionary algorithms (EAs) for multisolution optimization in multimodal landscape. However, existing niching techniques inevitably increase the time complexity of basic EAs due to the computation of the distance matrix of individuals. In this paper, we propose a fast niching technique. The technique avoids pairwise distance calculations by introducing the locality sensitive hashing, an efficient algorithm for approximately retrieving nearest neighbors. Individuals are projected to a number of buckets by hash functions. The similar individuals possess a higher probability of being hashed into the same bucket than the dissimilar ones. Then, interactions between individuals are limited to the candidates that fall in the same bucket to achieve local evolution. It is proved that the complexity of the proposed fast niching is linear to the population size. In addition, this mechanism induces stable niching behavior and it inherently keeps a balance between the exploration and exploitation of multiple optima. The theoretical analysis conducted in this paper suggests that the proposed technique is able to provide bounds for the exploration and exploitation probabilities. Experimental results show that the fast niching versions of the multimodal algorithms can exhibit similar or even better performance than their original ones. More importantly, the execution time of the algorithms is significantly reduced. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for solving high-dimensional expensive problems. The basic idea of SAEAs is the integration of nature-inspired searching ability of evolutionary algorithms and prediction ability of surrogate models. This paper proposes a novel evolutionary sampling assisted optimization (ESAO) method which combines the two abilities to consider global exploration and local exploitation. Differential evolution is employed to generate offspring using mutation and crossover operators. A global radial basis functions surrogate model is built for prescreening of the offspring’s objective function values and identifying the best one, which will be evaluated with the true function. The best offspring will replace its parent’s position in the population if its function value is smaller than that of its parent. A local surrogate model is then built with selected current best solutions. An optimizer is applied to find the optimum of the local model. The optimal solution is then evaluated with the true function. Besides, a better point found in the local search will be added into the population in the global search. Global and local searches will alternate if one search cannot lead to a better solution. Comprehensive analysis is conducted to study the mechanism of ESAO and insights are gained on different local surrogates. The proposed algorithm is compared with two state-of-the-art SAEAs on a series of high-dimensional problems and results show that ESAO behaves better both in effectiveness and robustness on most of the test problems. Besides, ESAO is applied to an airfoil optimization problem to show its effectiveness. [ABSTRACT FROM AUTHOR]

Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-the-art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points. [ABSTRACT FROM AUTHOR]

A comprehensive learning particle swarm optimizer (CLPSO) embedded with local search (LS) is proposed to pursue higher optimization performance by taking the advantages of CLPSO’s strong global search capability and LS’s fast convergence ability. This paper proposes an adaptive LS starting strategy by utilizing our proposed quasi-entropy index to address its key issue, i.e., when to start LS. The changes of the index as the optimization proceeds are analyzed in theory and via numerical tests. The proposed algorithm is tested on multimodal benchmark functions. Parameter sensitivity analysis is performed to demonstrate its robustness. The comparison results reveal overall higher convergence rate and accuracy than those of CLPSO, state-of-the-art particle swarm optimization variants. [ABSTRACT FROM AUTHOR]

There have been few researches on solving multimodal multiobjective optimization problems, whereas they are commonly seen in real-world applications but difficult for the existing evolutionary optimizers. In this paper, we propose a novel multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies. In the proposed algorithm, the properties of decision variables and the relationships among them are analyzed at first to guide the evolutionary search. Then, a general framework using two archives, i.e., the convergence and the diversity archives, is adopted to cooperatively solve these problems. Moreover, the diversity archive simultaneously employs a clustering strategy to guarantee diversity in the objective space and a niche-based clearing strategy to promote the same in the decision space. At the end of evolution process, solutions in the convergence and the diversity archives are recombined to obtain a large number of multiple Pareto optimal solutions. In addition, a set of benchmark test functions and a performance metric are designed for multimodal multiobjective optimization. The proposed algorithm is empirically compared with two state-of-the-art evolutionary algorithms on these test functions. The comparative results demonstrate that the overall performance of the proposed algorithm is significantly superior to the competing algorithms. [ABSTRACT FROM AUTHOR]

The performance of traditional multiobjective evolutionary algorithms (MOEAs) often deteriorates rapidly as the number of decision variables increases. While some efforts were made to design new algorithms by adapting existing techniques to large-scale single-objective optimization to the MOEA context, the specific difficulties that may arise from large-scale multiobjective optimization have rarely been studied. In this paper, the exclusive challenges along with the increase of the number of variables of a multiobjective optimization problem (MOP) are examined empirically, and the popular benchmarks are categorized into three groups accordingly. Problems in the first category only require MOEAs to have stronger convergence, and can thus be mitigated using techniques employed in large-scale single-objective optimization. Problems that require MOEAs to have stronger diversification but ignore a correlation between position and distance functions are grouped as the second. The rest of the problems that pose a great challenge to the balance between diversification and convergence by considering a correlation between position and distance functions are grouped as the third. While existing large-scale MOEAs perform well on the problems in the first two categories, they suffer a significant loss when applied to those in the third category. To solve large-scale MOPs in this category, we have developed a novel indicator-based algorithm with an enhanced diversification mechanism. The proposed algorithm incorporates a new solution generator with an external archive, thus forcing the search toward different subregions of the Pareto front using a dual local search mechanism. The results obtained by applying the proposed algorithm to a wide variety of problems (108 instances in total) with up to 8192 variables demonstrate that it outperforms eight state-of-the-art approaches on the examined problems in the third category and show its advantage in the balance between diversification and convergence. [ABSTRACT FROM AUTHOR]

The decomposition-based evolutionary multiobjective optimization (EMO) algorithm has become an increasingly popular choice for a posteriori multiobjective optimization. However, recent studies have shown that their performance strongly depends on the Pareto front (PF) shapes. This can be attributed to the decomposition method, of which the reference points and subproblem formulation settings are not well adaptable to various problem characteristics. In this paper, we develop a learning-to-decompose (LTD) paradigm that adaptively sets the decomposition method by learning the characteristics of the estimated PF. Specifically, it consists of two interdependent parts, i.e., a learning module and an optimization module. Given the current nondominated solutions from the optimization module, the learning module periodically learns an analytical model of the estimated PF. Thereafter, useful information is extracted from the learned model to set the decomposition method for the optimization module: 1) reference points compliant with the PF shape and 2) subproblem formulations whose contours and search directions are appropriate for the current status. Accordingly, the optimization module, which can be any decomposition-based EMO algorithm in principle, decomposes the multiobjective optimization problem into a number of subproblems and optimizes them simultaneously. To validate our proposed LTD paradigm, we integrate it with two decomposition-based EMO algorithms, and compare them with four state-of-the-art algorithms on a series of benchmark problems with various PF shapes. [ABSTRACT FROM AUTHOR]

Decomposition-based many-objective evolutionary algorithms generally decompose the objective space into multiple subregions with the help of a set of reference vectors. The resulting subregions are fixed since the reference vectors are usually predefined. When the optimization problem has a complicated Pareto front (PF), this decomposition may decrease the algorithm performance. To deal with this problem, this paper proposes a dynamical decomposition strategy. Instead of using predefined reference vectors, solution themselves are used as reference vectors. Thus, they are adapted to the shape of PF automatically. Besides, the subregions are produced one by one through successively bipartitioning the objective space. The resulting subregions are not fixed but dynamically determined by the population solutions as well as the subregions produced previously. Based on this strategy, a solution ranking method, named dynamical-decomposition-based ranking method (DDR), is proposed which can be employed in the mating selection and environmental selection in commonly used algorithm frameworks. Compared with those in the other decomposition-based algorithms, DDR has the following properties: 1) no predefined reference vectors are required; 2) less parameters are involved; and 3) the ranking results can not only be utilized directly to select solutions but also serve as a secondary criterion in traditional Pareto-based algorithms. In this paper, DDR is equipped in two algorithm frameworks for handling many-objective optimization problems. Comparisons with five state-of-the-art algorithms on 31 widely used test problems are carried out to test the performance of the proposed approach. The experimental results have shown the effectiveness of the proposed approach in keeping a good tradeoff between convergence and diversity. [ABSTRACT FROM AUTHOR]

In the last 20 years, evolutionary algorithms (EAs) have shown to be an effective method to solve multiobjective optimization problems (MOPs). Due to their population-based nature, multiobjective EAs (MOEAs) are able to generate a set of tradeoff solutions (called nondominated solutions) in a single algorithmic execution instead of having to perform a series of independent executions, as normally done with mathematical programming techniques. Additionally, MOEAs can be successfully applied to problems with difficult features such as multifrontality, discontinuity and disjoint feasible regions, among others. On the other hand, coevolutionary algorithms (CAs) are extensions of traditional EAs which have become subject of numerous studies in the last few years, particularly for dealing with large-scale global optimization problems. CAs have also been applied to the solution of MOPs, motivating the development of new algorithmic and analytical formulations that have advanced the state-of-the-art in CAs research, while simultaneously opening a new research path within MOEAs. This paper presents a critical review of the most representative coevolutionary MOEAs (CMOEAs) that have been reported in the specialized literature. This survey includes a taxonomy of approaches together with a brief description of their main features. In the final part of this paper, we also identify what we believe to be promising areas of future research in the field of CMOEAs. [ABSTRACT FROM AUTHOR]

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have been studied a lot and have been widely and successfully used in practice. However, there are no related theoretical studies on this kind of MOEAs. In this paper, we theoretically analyze the MOEAs based on decomposition. First, we analyze the runtime complexity with two basic simple instances. In both cases the Pareto front have one-to-one map to the decomposed subproblems or not. Second, we analyze the runtime complexity on two difficult instances with bad neighborhood relations in fitness space or decision space. Our studies show that: 1) in certain cases, polynomial-sized evenly distributed weight parameters-based decomposition cannot map each point in a polynomial sized Pareto front to a subproblem; 2) an ideal serialized algorithm can be very efficient on some simple instances; 3) the standard MOEA based on decomposition can benefit a runtime cut of a constant fraction from its neighborhood coevolution scheme; and 4) the standard MOEA based on decomposition performs well on difficult instances because both the Pareto domination-based and the scalar subproblem-based search schemes are combined in a proper way. [ABSTRACT FROM AUTHOR]

Over the last 25 years, the multiple sequence alignment (MSA) problem has attracted the attention of biologists because it is one of the major techniques used in several areas of computational biology, such as homology searches, genomic annotation, protein structure prediction, gene regulation networks, or functional genomics. This problem implicates the alignment of more than two biological sequences, and is considered as a nondeterministic polynomial time optimization problem. In this paper, we find a number of different approaches for dealing with this biological sequence alignment problem. Basically, we distinguish six main groups: 1) exact methods; 2) progressive methods; 3) consistency-based methods; 4) iterative methods; 5) evolutionary algorithms; and 6) structure-based methods. In this paper, we propose the use of evolutionary computation and multiobjective optimization for solving this bioinformatics problem. A multiobjective version of a memetic metaheuristic is presented: hybrid multiobjective metaheuristics for MSA. In order to prove the effectiveness of the new proposal, we use three structure-based benchmarks created by using empirical data as input. The results obtained by our method are compared with well-known methods published in this paper, concluding that the new approach presents remarkable accuracy when dealing with sets of sequences with a low sequence similarity, the most frequent ones in real world. [ABSTRACT FROM AUTHOR]

The design of evolutionary algorithms has typically been focused on efficiently solving a single optimization problem at a time. Despite the implicit parallelism of population-based search, no attempt has yet been made to multitask, i.e., to solve multiple optimization problems simultaneously using a single population of evolving individuals. Accordingly, this paper introduces evolutionary multitasking as a new paradigm in the field of optimization and evolutionary computation. We first formalize the concept of evolutionary multitasking and then propose an algorithm to handle such problems. The methodology is inspired by biocultural models of multifactorial inheritance, which explain the transmission of complex developmental traits to offspring through the interactions of genetic and cultural factors. Furthermore, we develop a cross-domain optimization platform that allows one to solve diverse problems concurrently. The numerical experiments reveal several potential advantages of implicit genetic transfer in a multitasking environment. Most notably, we discover that the creation and transfer of refined genetic material can often lead to accelerated convergence for a variety of complex optimization functions. [ABSTRACT FROM PUBLISHER]

Convergence performance and parametric sensitivity are two issues that tend to be neglected when extending differential evolution (DE) to multiobjective optimization (MO). To fill this research gap, we develop two novel mutation operators and a new parameter adaptation mechanism. A multiobjective DE variant is obtained through integration of the proposed strategies. The main innovation of this paper is the simultaneous use of individuals across generations from an objective-based perspective. Good convergence–diversity tradeoff and satisfactory exploration–exploitation balance are achieved via the hybrid cross-generation mutation operation. Furthermore, the cross-generation adaptation mechanism enables the individuals to self-adapt their associated parameters not only optimization-stage-wise but also objective-space-wise. Empirical results indicate the statistical superiority of the proposed algorithm over several state-of-the-art evolutionary algorithms in handling MO problems. [ABSTRACT FROM PUBLISHER]

Many-objective optimization has posed a great challenge to the classical Pareto dominance-based multiobjective evolutionary algorithms (MOEAs). In this paper, an evolutionary algorithm based on a new dominance relation is proposed for many-objective optimization. The proposed evolutionary algorithm aims to enhance the convergence of the recently suggested nondominated sorting genetic algorithm III by exploiting the fitness evaluation scheme in the MOEA based on decomposition, but still inherit the strength of the former in diversity maintenance. In the proposed algorithm, the nondominated sorting scheme based on the introduced new dominance relation is employed to rank solutions in the environmental selection phase, ensuring both convergence and diversity. The proposed algorithm is evaluated on a number of well-known benchmark problems having 3–15 objectives and compared against eight state-of-the-art algorithms. The extensive experimental results show that the proposed algorithm can work well on almost all the test functions considered in this paper, and it is compared favorably with the other many-objective optimizers. Additionally, a parametric study is provided to investigate the influence of a key parameter in the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Artificial gene regulatory networks (GRNs) are biologically inspired dynamical systems used to control various kinds of agents, from the cells in developmental models to embodied robot swarms. Most recent work uses a genetic algorithm (GA) or an evolution strategy in order to optimize the network for a specific task. However, the empirical performances of these algorithms are unsatisfactory. This paper presents an algorithm that primarily exploits a network distance metric, which allows genetic similarity to be used for speciation and variation of GRNs. This algorithm, inspired by the successful neuroevolution of augmenting topologies algorithm’s use in evolving neural networks and compositional pattern-producing networks, is based on a specific initialization method, a crossover operator based on gene alignment, and speciation based upon GRN structures. We demonstrate the effectiveness of this new algorithm by comparing our approach both to a standard GA and to evolutionary programming on four different experiments from three distinct problem domains, where the proposed algorithm excels on all experiments. [ABSTRACT FROM AUTHOR]

This paper discusses the genetic diversity of real-coded populations processed by an evolutionary algorithm (EA). Diversity is expressed as a variance or a covariance matrix of individuals contained in the population, in one- or multi-dimensional cases, respectively. We focus on the exploration stage of the optimization, therefore, the fitness function is modeled as noise. We prove that the expected value of genetic diversity achieves a level proportional to the mutation covariance matrix. The proportionality coefficient depends solely on the EA parameters. Formulas are derived to predict the diversity for fitness proportionate, tournament, and truncation selection, with and without arithmetic crossover and with Gaussian mutation. Experimental validation of the multidimensional case shows that prediction accuracy is satisfactory in a broad spectrum of settings of EA parameters. [ABSTRACT FROM AUTHOR]

Real-world optimization problems are usually multimodal which require optimization algorithms to keep a balance between exploration and exploitation. Therefore, multimodal optimization is one of the main opportunities as well as one of the main challenges for evolutionary algorithms. In this paper, a loser-out tournament-based fireworks algorithm (LoTFWA) is proposed for solving multimodal optimization problems. The search manner of the conventional fireworks algorithm (FWA) is based on the cooperation of several fireworks. While in the LoTFWA, we propose competition as a new manner of interaction, in which the fireworks are compared with each other not only according to their current status but also according to their progress rate. If the fitness of a certain firework cannot catch up with the best one with its current progress rate, it is considered a loser in the competition. The losers will be eliminated and reinitialized because it is vain to continue their search processes. Reinitializing these fireworks would greatly reduce the probability of being trapped in local minima for the algorithm. Experimental results show that the proposed algorithm is very powerful in optimizing multimodal functions. It not only outperforms previous versions of the FWA, but also outperforms several famous evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Fitness landscape analysis (FLA) is an important approach for studying how hard problems are for metaheuristic algorithms to solve. Static FLA focuses on extracting the properties of a problem and does not consider any information about the optimization algorithms; thus, it is not adequate for indicating whether a particular algorithm is suitable for solving a problem. By contrast, dynamic FLA considers the behavior of algorithms in combination with the properties of an optimization problem to determine the effectiveness of a given algorithm for solving that problem. However, previous dynamic FLA approaches are all individually based and lack statistical significance. In this paper, the concept of population evolvability is presented, as an extension of dynamic FLA, to quantify the effectiveness of population-based metaheuristic algorithms for solving a given problem. Specifically, two measures of population evolvability are defined that describe the probability that a population will obtain improved solutions to a problem and its ability to do so. Then, a combined measure is derived from these two measures to represent the overall population evolvability. Subsequently, the significance and validity of the proposed measures are investigated through analytical and experimental studies. Finally, the utility of the proposed measures is illustrated in an application of algorithm selection for black-box optimization problems. High accuracy in selecting the best algorithm is observed in a statistical analysis, with a low computational cost in terms of fitness evaluations. [ABSTRACT FROM AUTHOR]

Tchebycheff decomposition represents one of the most widely used decomposition approaches that can convert a multiobjective optimization problem into a set of scalar optimization subproblems. Nevertheless, the geometric properties of the subproblem objective functions in Tchebycheff decomposition have not been explicitly studied. This paper proposes a Tchebycheff decomposition with lp -norm constraint on direction vectors in which the subproblem objective functions are endowed with clear geometric property. Especially, the Tchebycheff decomposition with l2 -norm constraint on direction vectors is taken as an example to illustrate its advantage. A new unary R2 indicator is also introduced to approximate the hyper-volume metric and justify the efficiency of the proposed Tchebycheff decomposition. A resultant Tchebycheff decomposition-based multiobjective evolutionary algorithm (MOEA) with l2 -norm constraint and a new population update strategy is proposed to solve multiobjective optimization problems. The experimental results on both benchmark and real-world multiobjective optimization problems show that the proposed algorithm is capable of obtaining high quality solutions compared with other state-of-the-art MOEAs. [ABSTRACT FROM PUBLISHER]

Existing studies on dynamic multiobjective optimization (DMO) focus on problems with time-dependent objective functions, while the ones with a changing number of objectives have rarely been considered in the literature. Instead of changing the shape or position of the Pareto-optimal front/set (PF/PS) when having time-dependent objective functions, increasing or decreasing the number of objectives usually leads to the expansion or contraction of the dimension of the PF/PS manifold. Unfortunately, most existing dynamic handling techniques can hardly be adapted to this type of dynamics. In this paper, we report our attempt toward tackling the DMO problems with a changing number of objectives. We implement a dynamic two-archive evolutionary algorithm which maintains two co-evolving populations simultaneously. In particular, these two populations are complementary to each other: one concerns more about the convergence while the other concerns more about the diversity. The compositions of these two populations are adaptively reconstructed once the environment changes. In addition, these two populations interact with each other via a mating selection mechanism. Comprehensive experiments are conducted on various benchmark problems with a time-dependent number of objectives. Empirical results fully demonstrate the effectiveness of our proposed algorithm. [ABSTRACT FROM PUBLISHER]

Differential evolution has been shown to be an effective methodology for solving optimization problems over continuous space. In this paper, we propose an eigenvector-based crossover operator. The proposed operator utilizes eigenvectors of covariance matrix of individual solutions, which makes the crossover rotationally invariant. More specifically, the donor vectors during crossover are modified, by projecting each donor vector onto the eigenvector basis that provides an alternative coordinate system. The proposed operator can be applied to any crossover strategy with minimal changes. The experimental results show that the proposed operator significantly improves DE performance on a set of 54 test functions in CEC 2011, BBOB 2012, and CEC 2013 benchmark sets. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to investigate the capability of genetic programming to select and extract linearly separable features when the evolutionary process is guided to achieve the same and to propose an integrated system for that. We decompose a c-class problem into c binary classification problems and evolve c sets of binary classifiers employing a steady-state multiobjective genetic programming with three minimizing objectives. Each binary classifier is composed of a binary tree and a linear support vector machine (SVM). The features extracted by the feature nodes and some of the function nodes of the tree are used to train the SVM. The decision made by the SVM is considered the decision of the corresponding classifier. During crossover and mutation, the SVM-weights are used to determine the usefulness of the corresponding nodes. We also use a fitness function based on Golub’s index to select useful features. To discard less frequently used features, we employ unfitness functions for the feature nodes. We compare our method with 34 classification systems using 18 datasets. The performance of the proposed method is found to be better than 432 out of 570, i.e., 75.79% of comparing cases. Our results confirm that the proposed method is capable of achieving our objectives. [ABSTRACT FROM AUTHOR]

The performance of decomposition-based multiobjective evolutionary algorithms (MOEAs) often deteriorates clearly when solving multiobjective optimization problems with irregular Pareto fronts (PFs). The main reason is the improper settings of reference vectors and scalarizing functions. In this paper, we propose a decomposition-based MOEA guided by a growing neural gas network, which learns the topological structure of the PF. Both reference vectors and scalarizing functions are adapted based on the topological structure to enhance the evolutionary algorithm’s search ability. The proposed algorithm is compared with eight state-of-the-art optimizers on 34 test problems. The experimental results demonstrate that the proposed method is competitive in handling irregular PFs. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) have shown remarkable performance in various real-world applications. Unfortunately, the promising performance of CNNs can be achieved only when their architectures are optimally constructed. The architectures of state-of-the-art CNNs are typically handcrafted with extensive expertise in both CNNs and the investigated data, which consequently hampers the widespread adoption of CNNs for less experienced users. Evolutionary deep learning (EDL) is able to automatically design the best CNN architectures without much expertise. However, the existing EDL algorithms generally evaluate the fitness of a new architecture by training from scratch, resulting in the prohibitive computational cost even operated on high-performance computers. In this paper, an end-to-end offline performance predictor based on the random forest is proposed to accelerate the fitness evaluation in EDL. The proposed performance predictor shows the promising performance in term of the classification accuracy and the consumed computational resources when compared with 18 state-of-the-art peer competitors by integrating into an existing EDL algorithm as a case study. The proposed performance predictor is also compared with the other two representatives of existing performance predictors. The experimental results show the proposed performance predictor not only significantly speeds up the fitness evaluations but also achieves the best prediction among the peer performance predictors. [ABSTRACT FROM AUTHOR]

A large number of prediction strategies are specific to a dynamic multiobjective optimization problem (DMOP) with only one type of the Pareto set (PS) change. However, a continuous DMOP with more than one type of the unknown PS change has been seldom investigated. We present a multimodel prediction approach (MMP) realized in the framework of evolutionary algorithms (EAs) to tackle the problem. In this paper, we first detect the type of the PS change, followed by the selection of an appropriate prediction model to provide an initial population for the subsequent evolution. To observe the influence of MMP on EAs, optimal solutions obtained by three classical dynamic multiobjective EAs with and without MMP are investigated. Furthermore, to investigate the performance of MMP, three state-of-the-art prediction strategies are compared on a large number of dynamic test instances under the same particle swarm optimizer. The experimental results demonstrate that the proposed approach outperforms its counterparts under comparison on most optimization problems. [ABSTRACT FROM AUTHOR]

This paper proposes a new prediction-based dynamic multiobjective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for solving dynamic multiobjective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three subpopulations based on different strategies. The first subpopulation is created by moving nondominated individuals using a simple linear prediction model with different step sizes. The second subpopulation consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third subpopulation comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These subpopulations are tailored to form a population for the new environment. The experimental results carried out on a variety of bi- and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Running time analysis is a fundamental problem of critical importance in evolutionary computation. However, the analysis results have rarely been applied to advanced evolutionary algorithms (EAs) in practice, let alone their variants for continuous optimization. In this paper, an experimental method is proposed for analyzing the running time of EAs that are widely used for solving continuous optimization problems. Based on Glivenko–Cantelli theorem, the proposed method simulates the distribution of gain, which is introduced by average gain model to characterize progress during the optimization process. Data fitting techniques are subsequently adopted to obtain a desired function for further analyses. To verify the validity of the proposed method, experiments were conducted to estimate the upper bounds on expected first hitting time of various evolutionary strategies, such as (1, λ) evolution strategy, standard evolution strategy, covariance matrix adaptation evolution strategy, and its improved variants. The results suggest that all estimated upper bounds are correct. Backed up by the proposed method, state-of-the-art EAs for continuous optimization will have identical results about the running time as simplified schemes, which will bridge the gap between theoretical foundation and applications of evolutionary computation. [ABSTRACT FROM AUTHOR]

Neighborhood information plays an important role in improving the performance of evolutionary computation in various optimization scenarios, particularly in the context of multimodal optimization. Several neighborhood concepts, i.e., index-based neighborhood, nearest neighborhood, and fuzzy neighborhood, have been studied and engaged in the design of niching methods. However, the use of these neighborhood concepts requires the specification of some problem-related parameters, which is difficult to determine without a prior knowledge. In this paper, we introduce a new neighborhood concept based on a geometrical construction called Voronoi diagram. The new concept offers two advantages at the expense of increasing the computational complexity to a higher level. It eliminates the need of additional parameters and it is more informative than the existing ones. The information provided by the Voronoi neighbors of an individual can be exploited to estimate the evolutionary state. Based on the information, we divide the population into three groups and assign each group a different reproduction strategy to support the exploration and exploitation of the search space. We show the use of the concept in the design of an effective evolutionary algorithm for multimodal optimization. The experiments have been conducted to investigate the performance of the algorithm. The results reveal that the proposed algorithm compare favorably with the state-of-the-art algorithms designed based on other types of neighborhood concepts. [ABSTRACT FROM AUTHOR]

Two-echelon vehicle routing problem (2E-VRP) is a challenging problem that involves both the strategic and tactical planning decisions on both echelons. The satellite locations and the customer distribution affect the cost of different components on the second echelon, thus the possibilities of satellite-to-customer assignment complicates the problem. In this paper, we propose a graph-based fuzzy evolutionary algorithm for solving 2E-VRP. The proposed method integrates a graph-based fuzzy assignment scheme into an iteratively evolutionary learning process to minimize the total cost. To resolve the possibilities of the satellite-to-customer assignment, graph-based fuzzy operator is used to take advantage of population evolution and avoid excessive fitness evaluations of unpromising moves in different satellites. Each offspring is produced via graph-based fuzzy assignment procedure out of an assignment graph from parent individuals, and fuzzy local search procedure is used to further improve the offspring. The experimental results on the public test sets demonstrate the competitiveness of the proposed method. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems by evolutionary algorithms, the core issue is to balance constraints and objective function. This paper is the first attempt to utilize the correlation between constraints and objective function to keep this balance. First of all, the correlation between constraints and objective function is mined and represented by a correlation index. Afterward, a weighted sum updating approach and an archiving and replacement mechanism are proposed to make use of this correlation index to guide the evolution. By the above process, a novel constrained optimization evolutionary algorithm is presented. Experiments on a broad range of benchmark test functions indicate that the proposed method shows better or at least competitive performance against other state-of-the-art methods. Moreover, the proposed method is applied to the gait optimization of humanoid robots. [ABSTRACT FROM AUTHOR]

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark (MPB) and show its nonseparable nature irrespective of its number of peaks. We then propose a composite MPB suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower-dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200-D, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems. [ABSTRACT FROM AUTHOR]

There are many target methods that are efficient to tackle the robustness and immunization problem, in particular, to identify the most influential nodes in a certain complex network. Unfortunately, owing to the diversity of networks, none of them could be accounted as a universal approach that works well in a wide variety of networks. Hence, in this paper, from a percolation perspective, we connect the immunization and robustness problem with an evolutionary algorithm, i.e., a framework of an evolutionary algorithm for investigation of influential nodes in complex networks, in which we have developed procedures of selection, mutation, and initialization of population as well as maintaining the diversity of population. To validate the performance of the proposed framework, we conduct intensive experiments on a large number of networks and compare it to several state-of-the-art strategies. The results demonstrate that the proposed method has significant advantages over others, especially on empirical networks in most of which our method has over 10% advantages of both optimal immunization threshold and average giant fraction, even against the most excellent existing strategies. Additionally, our discussion reveals that there might be better solutions with various initial methods. [ABSTRACT FROM AUTHOR]

Optimization problems with variable-length decision space are a class of challenging optimization problems derived from some real-world applications, such as the composite laminate stacking problem and the sensor coverage problem. Unlike other optimization problems, the solutions in these problems might be represented as the vectors with different variable size (i.e., dimensionality). So far, some research efforts have been done on the use of evolutionary algorithms (EAs) for solving single objective variable-length optimization problems. In fact, the variable-length problem difficulty can also exist in multiobjective optimization. However, such challenging problems have not yet gained much attention in the area of evolutionary multiobjective optimization. To facilitate the research on the variable-length Pareto optimization, we first suggest a systematic toolkit for constructing benchmark multiobjective test problems with variable-length feature in this paper. Then, we also propose a variable-length multiobjective EA based on a two-level decomposition strategy, which decomposes a multiobjective optimization problem in terms of the penalty boundary intersection search directions and the dimensionality of variables. The performance of our proposed algorithm and the other three state-of-the-art algorithms on these problems are compared. To further show the effectiveness of our proposed algorithm, some experimental results on a bi-objective laminate stacking optimization problem are also reported and analyzed. [ABSTRACT FROM AUTHOR]

The balance between convergence and diversity is the cornerstone of evolutionary multiobjective optimization (EMO). The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multiobjective optimization. In particular, the one-one stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, is claimed to strike a balance between convergence and diversity. However, the original stable marriage model has a high risk of matching a solution with an unfavorable subproblem, which finally leads to an imbalanced selection result. In this paper, we introduce the concept of incomplete preference lists into the stable matching model to remedy the loss of population diversity. In particular, each solution is only allowed to maintain a partial preference list consisting of its favorite subproblems. We implement two versions of stable matching-based selection mechanisms with incomplete preference lists: one achieves a two-level one-one matching and the other obtains a many-one matching. Furthermore, an adaptive mechanism is developed to automatically set the length of the incomplete preference list for each solution according to its local competitiveness. The effectiveness and competitiveness of our proposed methods are validated and compared with several state-of-the-art EMO algorithms on 62 benchmark problems. [ABSTRACT FROM PUBLISHER]

Metaheuristics have yielded very promising results for the frequency assignment problem (FAP). However, the results obtainable using currently published methods are far from ideal in complex, large-scale instances. This paper applies and extends some of the most recent advances in evolutionary algorithms to two common variants of the FAP, and shows how, in traditional techniques, two common issues affect their performance: 1) premature convergence and 2) the way in which neutral networks are handled. A recent replacement-based diversity management strategy is successfully applied to alleviate the premature convergence drawback. Additionally, by properly defining a distance metric, the performance in the presence of neutrality can also be greatly improved. The replacement strategy combines the principle of transforming a single-objective problem into a multiobjective one by considering diversity as an additional objective, with the idea of adapting the balance induced between exploration and exploitation to the requirements of the different optimization stages. Tests with 44 publicly available instances yield very competitive results. New best-known frequency plans were generated for 11 instances, whereas in the remaining ones the best-known solutions were replicated. Comparisons with a large number of strategies designed to delay convergence of the population clearly show the advantages of our novel proposals. [ABSTRACT FROM PUBLISHER]