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This paper compares three modern and two classical multiobjective optimizers (MOOs) as applied to real-world problems in electromagnetics. The behavior of sophisticated optimizers on simple test functions has been studied exhaustively. In contrast, the algorithms here are tested on practical applications, where the function evaluations are computationally expensive, making the convergence rate a crucial factor. The examples considered include the optimization of a narrowband slot antenna, a mushroom-type electromagnetic bandgap structure, and an ultrawideband Vivaldi antenna. Another popular topic in the literature is in comparing classical MOOs on electromagnetics problems. The modern optimizers chosen in this paper are state of the art and each has a distinct design philosophy. This paper introduces two unique MOOs to the electromagnetics community: BORG, an auto-adaptive genetic algorithm and the Multi-Objective Covariance Matrix Adaptation Evolutionary Strategy (MO-CMA-ES), an extension of the popular single-objective CMA-ES. These algorithms are compared to the Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), a Chebysheff scalarization algorithm, and two classical MOOs. This paper will study the behavior of these algorithms on problems in electromagnetics with a limited number of function evaluations using five distinct metrics and will provide useful guidelines and recommended optimizer settings. [ABSTRACT FROM AUTHOR]

This paper presents the extension of framework for automatic design space exploration (FADSE) tool using a meta-optimization approach, which is used to improve the performance of design space exploration algorithms, by driving two different multiobjective meta-heuristics concurrently. More precisely, we selected two genetic multiobjective algorithms: 1) non-dominated sorting genetic algorithm-II and 2) strength Pareto evolutionary algorithm 2, that work together in order to improve both the solutions’ quality and the convergence speed. With the proposed improvements, we ran FADSE in order to optimize the hardware parameters’ values of the grid ALU processor (GAP) micro-architecture from a bi-objective point of view (performance and hardware complexity). Using our developed approach we obtained better GAP instances (a configuration has for almost the same cycles per instruction – 1.00, the hardware complexity 38% smaller/better – 35.81 versus 58.61) in half of the time compared to a classical sequential optimization approach (5 days versus 10 days). [ABSTRACT FROM PUBLISHER]

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]

Design of electromagnetic devices has multimodal, multidimensional, and constrained characteristics. Metaheuristic approaches are good choices for tackling these design problems owing to their simulation-based property. As many electromagnetic design problems require a long computing time to solve (even on modern computers) and many heuristic approaches have been created, the major goal of this paper is to improve the effectiveness and robustness of existing approaches. This paper proposes an algorithm with the ensemble of two composite differential evolution (DE) ingredients. One ingredient is biased toward exploration and the other is biased toward exploitation. The probability of choosing which ingredient to search for new solutions is adaptively updated based on the previous performance of each ingredient. The algorithm is applied to solve a loudspeaker design problem with promising performance when compared with DE, artificial bee colony, two improved artificial bee colony algorithms, and a randomly choosing ingredients algorithm. [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]

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]

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]

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]

Multimodal optimization problem (MMOP), which targets at searching for multiple optimal solutions simultaneously, is one of the most challenging problems for optimization. There are two general goals for solving MMOPs. One is to maintain population diversity so as to locate global optima as many as possible, while the other is to increase the accuracy of the solutions found. To achieve these two goals, a novel dual-strategy differential evolution (DSDE) with affinity propagation clustering (APC) is proposed in this paper. The novelties and advantages of DSDE include the following three aspects. First, a dual-strategy mutation scheme is designed to balance exploration and exploitation in generating offspring. Second, an adaptive selection mechanism based on APC is proposed to choose diverse individuals from different optimal regions for locating as many peaks as possible. Third, an archive technique is applied to detect and protect stagnated and converged individuals. These individuals are stored in the archive to preserve the found promising solutions and are reinitialized for exploring more new areas. The experimental results show that the proposed DSDE algorithm is better than or at least comparable to the state-of-the-art multimodal algorithms when evaluated on the benchmark problems from CEC2013, in terms of locating more global optima, obtaining higher accuracy solution, and converging with faster speed. [ABSTRACT FROM AUTHOR]

One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is that optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing “experiences” to construct a prediction model via statistical machine learning approaches. However, most existing methods neglect the nonindependent and identically distributed nature of data to construct the prediction model. In this paper, we propose an algorithmic framework, called transfer learning-based dynamic multiobjective evolutionary algorithm (EA), which integrates transfer learning and population-based EAs to solve the DMOPs. This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population-based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this idea, we incorporate the proposed approach into the development of three well-known EAs, nondominated sorting genetic algorithm II, multiobjective particle swarm optimization, and the regularity model-based multiobjective estimation of distribution algorithm. We employ 12 benchmark functions to test these algorithms as well as compare them with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed design for DMOPs. [ABSTRACT FROM AUTHOR]

An optimization technique based on the combination of optimization algorithm and sensitivity analysis is discussed. The technique allows reducing the number of optimized parameters during the optimization process, which consequently reduces the search space and time of optimization. This paper explains the principle, benefits, and future challenges of this technique and illustrates its utilization with numerical experiments and a typical example. The algorithm is implemented in the framework OptiLab that represents a part of the application Agros2D developed by me. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid algorithm based on the genetic algorithm (GA) and the evolution strategy (ES) for the electromagnetic optimization problem. The GA is not good enough at times in searching the optimal solution from the view point of the convergence speed and the solution quality, while the ES has the risk of being trapped in a local minimum. The hybrid algorithm is composed of GA and ES in order to make up for these defects. First, we reached the vicinity of optimal solution using the GA. Then, the ES is used to find the accurate optimal solution. The switching point can be a main issue, which is also resolved in this paper. First, the performance of the convergence speed and the solution accuracy are comparatively tested using the known functions. In addition, the optimized design of the 2.45 GHz coplanar waveguide-fed circularly polarized antenna is carried out as a practical application. Only the GA and the hybrid algorithm reach the satisfactory value, and the more rapid convergence can be shown by the ES in this hybrid method after 380 iterations. [ABSTRACT FROM AUTHOR]

Decomposition-based evolutionary algorithms have been quite successful in solving optimization problems involving two and three objectives. Recently, there have been some attempts to exploit the strengths of decomposition-based approaches to deal with many objective optimization problems. Performance of such approaches are largely dependent on three key factors: 1) means of reference point generation; 2) schemes to simultaneously deal with convergence and diversity; and 3) methods to associate solutions to reference directions. In this paper, we introduce a decomposition-based evolutionary algorithm wherein uniformly distributed reference points are generated via systematic sampling, balance between convergence and diversity is maintained using two independent distance measures, and a simple preemptive distance comparison scheme is used for association. In order to deal with constraints, an adaptive epsilon formulation is used. The performance of the algorithm is evaluated using standard benchmark problems, i.e., DTLZ1-DTLZ4 for 3, 5, 8, 10, and 15 objectives, WFG1-WFG9, the car side impact problem, the water resource management problem, and the constrained ten-objective general aviation aircraft design problem. Results of problems involving redundant objectives and disconnected Pareto fronts are also included in this paper to illustrate the capability of the algorithm. The study clearly highlights that the proposed algorithm is better or at par with recent reference direction-based approaches for many objective optimization. [ABSTRACT FROM AUTHOR]

In this paper, a new multiobjective optimization framework based on nondominated sorting and local search (NSLS) is introduced. The NSLS is based on iterations. At each iteration, given a population P , a simple local search method is used to get a better population P' , and then the nondominated sorting is adopted on P \cup P' to obtain a new population for the next iteration. Furthermore, the farthest-candidate approach is combined with the nondominated sorting to choose the new population for improving the diversity. Additionally, another version of NSLS (NSLS-C) is used for comparison, which replaces the farthest-candidate method with the crowded comparison mechanism presented in the nondominated sorting genetic algorithm II (NSGA-II). The proposed method (NSLS) is compared with NSLS-C and the other three classic algorithms: NSGA-II, MOEA/D-DE, and MODEA on a set of seventeen bi-objective and three tri-objective test problems. The experimental results indicate that the proposed NSLS is able to find a better spread of solutions and a better convergence to the true Pareto-optimal front compared to the other four algorithms. Furthermore, the sensitivity of NSLS is also experimentally investigated in this paper. [ABSTRACT FROM AUTHOR]

Brain storm optimization (BSO) is a novel population-based swarm intelligence algorithm based on the human brainstorming process. BSO has been proven feasible and has been successfully applied to benchmark problems in the electromagnetic field. In this paper, inspired by the mechanism of quantum theories, a novel variant of BSO algorithm, called quantum-behaved BSO (QBSO), is proposed to solve an optimization problem modeled for Loney’s solenoid problem. The new mechanism improves the diversity of population and also utilizes the global information to generate the new individual. Simulation results show that QBSO has better ability to jump out of local optima and perform better compared with the basic BSO. [ABSTRACT FROM AUTHOR]

In the precursor paper, a many-objective optimization method (NSGA-III), based on the NSGA-II framework, was suggested and applied to a number of unconstrained test and practical problems with box constraints alone. In this paper, we extend NSGA-III to solve generic constrained many-objective optimization problems. In the process, we also suggest three types of constrained test problems that are scalable to any number of objectives and provide different types of challenges to a many-objective optimizer. A previously suggested MOEA/D algorithm is also extended to solve constrained problems. Results using constrained NSGA-III and constrained MOEA/D show an edge of the former, particularly in solving problems with a large number of objectives. Furthermore, the NSGA-III algorithm is made adaptive in updating and including new reference points on the fly. The resulting adaptive NSGA-III is shown to provide a denser representation of the Pareto-optimal front, compared to the original NSGA-III with an identical computational effort. This, and the original NSGA-III paper, together suggest and amply test a viable evolutionary many-objective optimization algorithm for handling constrained and unconstrained problems. These studies should encourage researchers to use and pay further attention in evolutionary many-objective optimization. [ABSTRACT FROM AUTHOR]

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm. [ABSTRACT FROM PUBLISHER]

Improvements to overcome premature convergence of existing wind driven optimization algorithms are proposed. The specific measures being proposed include: 1) selection of the origin point of every parcel using dynamic and random tournament selection mechanisms to guarantee that there is a good balance between exploration and exploitation searches. In this paper, the “so far searched best solution” will be exploited to guide the movement of the randomly initialized parcels by introducing a newly designed mechanism; and a probabilistic mutation is designed; and 2) full utilization of the latest information accumulated from the searched history in order to guide the search toward the potential solutions to enhance convergences, and the “so far searched worst parcel” is used to shift the new parcel away from the parcel in issue. Numerical results on three case studies are reported to showcase the feasibility and the merit of the proposed method in solving both practical engineering design problems and mathematical test functions. [ABSTRACT FROM AUTHOR]

The standard covariance matrix adaptation evolution strategy (CMA-ES) comprises two evolution paths, one for the learning of the mutation strength and one for the rank-1 update of the covariance matrix. In this paper, it is shown that one can approximately transform this algorithm in such a manner that one of the evolution paths and the covariance matrix itself disappear. That is, the covariance update and the covariance matrix square root operations are no longer needed in this novel so-called matrix adaptation (MA) ES. The MA-ES performs nearly as well as the original CMA-ES. This is shown by empirical investigations considering the evolution dynamics and the empirical expected runtime on a set of standard test functions. Furthermore, it is shown that the MA-ES can be used as a search engine in a bi-population (BiPop) ES. The resulting BiPop-MA-ES is benchmarked using the BBOB comparing continuous optimizers (COCO) framework and compared with the performance of the CMA-ES-v3.61 production code. It is shown that this new BiPop-MA-ES—while algorithmically simpler—performs nearly equally well as the CMA-ES-v3.61 code. [ABSTRACT FROM AUTHOR]

This paper proposes a hybrid, multiobjective optimization algorithm enabling global optimum tracking in permanent-magnet (PM) traction motor design. The methodology developed is based on the Artificial Bee Colony technique, strength Pareto evolutionary algorithm, and differential evolution strategy ensuring fast and reliable convergence to the optimal Pareto front. The effectiveness of the derived methodology is compared with other well-established and powerful algorithms from the literature through both appropriate test functions and an application example concerning an unequal teeth surface-mounted PM wheel motor design. [ABSTRACT FROM AUTHOR]

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach. [ABSTRACT FROM AUTHOR]

Teaching–learning-based optimization (TLBO) is an intelligent optimization algorithm with relatively fewer parameters that should be determined in updating equations. For solving complex optimization problems, the local optima often appear in the evolution. To decrease the possibility of this phenomenon, a novel TLBO variant (EI-TLBO) with experience information (EI) and differential mutation is presented. In the method, neighborhood information (the best individual NTeacher and the mean individual NMean) of each learner’s neighbors is introduced to improve the exploration capability. The EI before the current iteration of each learner is introduced to make him or her accurately judge the learning behavior in future. In addition, instead of duplicate elimination to maintain the diversity of population at the end of each generation in the original TLBO, differential mutation is introduced to maintain the diversity of learners during the iterative learning process. The main contribution of this paper is to improve the convergence speed and accuracy by introducing neighborhood topology structure, EI, and differential mutation. The efficiency of the proposed algorithm is evaluated on 46 benchmark functions, among which 27 functions are selected from CEC2013. Its performance is compared with those of six other reported EAs. The results indicate that EI-TLBO algorithm can achieve superior performance. [ABSTRACT FROM PUBLISHER]

This paper explores the automated experimental control design for variable speed drives using a novel heuristic optimization algorithm. A hybrid approach, which combines desirable characteristics of two of the most widely used biologically-inspired heuristic algorithms, the genetic algorithms (GAs) and the bacterial foraging (BF) algorithms, is studied and developed in this paper. Both the structures and parameters of digital speed controllers are optimized experimentally and directly on the drive while it is subject to different types of mechanical load; the dynamics of these load profiles are generated using a programmable load emulator. The proposed hybrid bacterial foraging (HBF) algorithm is evaluated, for the purpose of control optimization for electric drives, against GA and BF, and their performances are compared and contrasted. [ABSTRACT FROM PUBLISHER]

Multiple sequence alignment (MSA) is a fundamental and key step for implementing other tasks in bioinformatics, such as phylogenetic analyses, identification of conserved motifs and domains, structure prediction, etc. Despite the fact that there are many methods to implement MSA, biologically perfect alignment approaches are not found hitherto. This paper proposes a novel idea to perform MSA, where MSA is treated as a multiobjective optimization problem. A famous multiobjective evolutionary algorithm framework based on decomposition is applied for solving MSA, named MOMSA. In the MOMSA algorithm, we develop a new population initialization method and a novel mutation operator. We compare the performance of MOMSA with several alignment methods based on evolutionary algorithms, including VDGA, GAPAM, and IMSA, and also with state-of-the-art progressive alignment approaches, such as MSAprobs, Probalign, MAFFT, Procons, Clustal omega, T-Coffee, Kalign2, MUSCLE, FSA, Dialign, PRANK, and CLUSTALW. These alignment algorithms are tested on benchmark datasets BAliBASE 2.0 and BAliBASE 3.0. Experimental results show that MOMSA can obtain the significantly better alignments than VDGA, GAPAM on the most of test cases by statistical analyses, produce better alignments than IMSA in terms of TC scores, and also indicate that MOMSA is comparable with the leading progressive alignment approaches in terms of quality of alignments. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid multi-objective optimization algorithm based on the nondominated sorting genetic algorithm II for large array thinning is presented. The iterative fast Fourier transform (IFFT) technique with a judge factor is introduced into the optimizer to accelerate the convergence. The global characteristics of a genetic algorithm show its optimization capability in the early phase of the optimization process and the powerful local search ability of IFFT works in the late phase. Thus, this proposed algorithm can not only effectively avoid being trapped into the local optimum but also possess a fast convergence for large array thinning. Several representative examples of large planar thinned arrays validate the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A finite-element analysis-based optimal design of an electric machine takes considerable time for its objective evaluation and has many local minima. Thus, selecting an appropriate global convergence optimization with fast convergence speed is necessary in the optimal design of an electric machine. In this paper, a novel global search optimization algorithm, mass ionized particle optimization (MIPO), is newly proposed. The MIPO is the population-based algorithm, which reflects the interactive force between the ionized particles. The global convergence and the convergence speed are validated by comparison with the particle swarm optimization, which have already been proved for its global convergence when applied to a well-known Goldstein–Price function as a benchmark function. In addition, the algorithm has been applied to the optimal design of an interior permanent magnet synchronous machine aiming for its torque ripple reduction. [ABSTRACT FROM AUTHOR]

Sensor network localization based on connectivity can be modeled as a nonconvex optimization problem. However, current models only consider the convex constraints, i.e., connections among the nodes. The proposed method considers not only the connection constraints but the disconnection constraints, which are nonconvex in nature, as well. It is argued that the connectivity-based localization problem should be represented as an optimization problem with both convex and nonconvex constraints. In this paper, an algorithm combining a modified differential evolution (DE) algorithm and heuristics is presented for the situation in which the communication range value is unknown. The developed algorithm has a new crossover procedure, with refined procedures to produce a new generation of individuals/candidates. A “single node treatment” procedure is also designed for the search procedure to formulate a new set of coordinate locations to jump out from the local minimum. The final solution can reach the most suitable configuration of the unknown nodes (nodes without knowing their location) because all the information on the constraints has been used. Simulation results have shown that better solutions can be obtained when compared with other convex-constraint methods. The proposed method also gets better results than other general nonconvex optimization methods. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms have been successfully applied for exploring both converged and diversified approximate Pareto-optimal fronts in multiobjective optimization problems, two- or three-objective in general. However, when solving problems with many objectives, nearly all algorithms perform poorly due to the loss of selection pressure in fitness evaluation. An extremely large objective space could inadvertently deteriorate the effect of an evolutionary operator. In this paper, we propose a new approach to directly handle the challenges to solve many-objective optimization problems (MaOPs). This novel design includes two stages: first, the whole population quickly approaches a small number of “target” points near the true Pareto front; then, the proposed diversity improvement strategy is applied to facilitate these individuals to spread and well distribute. As a case study, the proposed algorithm based on this design is compared with five state-of-the-art algorithms. Experimental results show that the proposed method exhibits improved performance in both convergence and diversity for solving MaOPs. [ABSTRACT FROM PUBLISHER]

Multiobjective evolutionary algorithms have become prevalent and efficient approaches for solving multiobjective optimization problems. However, their performances deteriorate severely when handling many-objective optimization problems (MaOPs) due to the loss of selection pressure to drive the search toward the Pareto front and the ineffective design in diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm (MaOEA) based on directional diversity (DD) and favorable convergence (FC). The main features are the enhancement of two selection schemes to facilitate both convergence and diversity. In the algorithm, a mating selection based on FC is applied to strengthen selection pressure while an environmental selection based on DD and FC is designed to balance diversity and convergence. The proposed algorithm is tested on 64 instances of 16 MaOPs with diverse characteristics and compared with seven state-of-the-art algorithms. Experimental results show that the proposed MaOEA performs competitively with respect to chosen state-of-the-art designs. [ABSTRACT FROM PUBLISHER]

Hyper-heuristic approaches aim to automate heuristic design in order to solve multiple problems instead of designing tailor-made methodologies for individual problems. Hyper-heuristics accomplish this through a high-level heuristic (heuristic selection mechanism and an acceptance criterion). This automates heuristic selection, deciding whether to accept or reject the returned solution. The fact that different problems, or even instances, have different landscape structures and complexity, the design of efficient high-level heuristics can have a dramatic impact on hyper-heuristic performance. In this paper, instead of using human knowledge to design the high-level heuristic, we propose a gene expression programming algorithm to automatically generate, during the instance-solving process, the high-level heuristic of the hyper-heuristic framework. The generated heuristic takes information (such as the quality of the generated solution and the improvement made) from the current problem state as input and decides which low-level heuristic should be selected and the acceptance or rejection of the resultant solution. The benefit of this framework is the ability to generate, for each instance, different high-level heuristics during the problem-solving process. Furthermore, in order to maintain solution diversity, we utilize a memory mechanism that contains a population of both high-quality and diverse solutions that is updated during the problem-solving process. The generality of the proposed hyper-heuristic is validated against six well-known combinatorial optimization problems, with very different landscapes, provided by the HyFlex software. Empirical results, comparing the proposed hyper-heuristic with state-of-the-art hyper-heuristics, conclude that the proposed hyper-heuristic generalizes well across all domains and achieves competitive, if not superior, results for several instances on all domains. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms have been shown to be powerful for solving multiobjective optimization problems, in which nondominated sorting is a widely adopted technique in selection. This technique, however, can be computationally expensive, especially when the number of individuals in the population becomes large. This is mainly because in most existing nondominated sorting algorithms, a solution needs to be compared with all other solutions before it can be assigned to a front. In this paper we propose a novel, computationally efficient approach to nondominated sorting, termed efficient nondominated sort (ENS). In ENS, a solution to be assigned to a front needs to be compared only with those that have already been assigned to a front, thereby avoiding many unnecessary dominance comparisons. Based on this new approach, two nondominated sorting algorithms have been suggested. Both theoretical analysis and empirical results show that the ENS-based sorting algorithms are computationally more efficient than the state-of-the-art nondominated sorting methods. [ABSTRACT FROM AUTHOR]

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

Since genetic algorithm (GA) presented decades ago, large amount of intelligent algorithms and their improvements and mixtures have been putting forward one after another. However, little works have been done to extend their applications and verify their competence in different problems. For each specific complex problem, people always take a long time to find appropriate intelligent algorithm and develop improvements. To overcome these shortcomings, new dynamic configuration methods for intelligent algorithms (DC-IA) is presented in this paper on the basis of the requirements of three kinds of algorithm users. It separates the optimization problems and intelligent algorithms, modularizes each step of algorithms and extracts their core operators. Based on the coarse-grained operator modules, three-layer dynamical configurations, i.e., parameter-based configuration, operator-based configuration and algorithm-based configuration, are fully exploited and implemented. Under these methods, dozens of hybrid and improved intelligent algorithms can be easily produced in a few minutes just based on several configurable operator modules. Also, problem-oriented customizations in configurations can further extend the application range and advance the efficiency of the existing operators enormously. Experiments based on the established configuration platform verify the new configuration ways of applying and improving intelligent algorithm for both numerical and combinatorial optimization problems in industries on aspects of flexibility, robustness, and reusability. [ABSTRACT FROM PUBLISHER]

The optimization of electrical machines and energy-harvesting devices has been one of the hot topics of research in recent years. In this context, advanced computational intelligence algorithms are suitable design tools, since they are able to optimize complex systems with a large number of constraints and free design parameters. This paper presents the social network optimization (SNO): a new population-based algorithm developed to guarantee an effective and faster exploration of the solution domain with respect to traditional optimization techniques. The proposed technique will be described and validated with a benchmark case study. Finally, the optimization problem of a tubular permanent magnet linear generator will be formulated in the context of vehicular energy-harvesting systems. [ABSTRACT FROM PUBLISHER]

In this paper we present a multi-objective optimization approach to subarrayed linear antenna arrays design. We define this problem as a bi-objective one. We consider two objective functions for directivity maximization and sidelobe level minimization. Memetic algorithms (MAs) are hybrid algorithms that combine the benefits of a global search Evolutionary Algorithm (EA) with a local search method. In this paper, we introduce a new memetic multi-objective evolutionary algorithm namely the memetic generalized differential evolution (MGDE3). This algorithm is a memetic extension of the popular generalized differential evolution (GDE3) algorithm. Another popular MOEA is the nondominated sorting genetic algorithm-II (NSGA-II). MGDE3, GDE3 and NSGA-II are applied to the synthesis of uniform and nonuniform subarrayed linear arrays, providing an extensive set of solutions for each design case. Depending on the desired array characteristics, the designer can select the most suitable solution. The results of the proposed method are compared with those reported in the literature, indicating the advantages and applicability of the multi-objective approach. [ABSTRACT FROM PUBLISHER]

Selection strategy, including mating selection and environmental selection, is a key ingredient in the design of evolutionary multiobjective optimization algorithms. Existing approaches, which have shown competitive performance in low-dimensional multiobjective optimization problems with two or three objectives, often encounter considerable challenges in many-objective optimization, where the number of objectives exceeds 3. This paper first provides a comprehensive analysis on the selection strategies in the current evolutionary many-objective optimization algorithms. Afterward, we propose a coordinated selection strategy to improve the performance of evolutionary algorithms in many-objective optimization. This selection strategy considers three crucial factors: 1) the new mating selection criterion considers both the quality of each selected parent and the effectiveness of the combination of selected parents; 2) the new environmental selection criterion directly focuses on the performance of the whole population rather than single individual alone; and 3) both selection steps are complement to each other and the coordination between them in the evolutionary process can achieve a better performance than each of them used individually. Furthermore, in order to handle the curse of dimensionality in many-objective optimization problems, a new convergence measure by distance and a new diversity measure by angle are developed in both selection steps. Experimental results on both DTLZ and WFG benchmark functions demonstrate the superiority of the proposed algorithm in comparison with six state-of-the-art designs in terms of both solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization (ACO) algorithms in preserving high diversity, this paper intends to extend ACO algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ACO algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima. [ABSTRACT FROM AUTHOR]

Existing differential evolution (DE) algorithms often face two challenges. The first is that the optimization performance is significantly affected by the ad hoc configurations of operators and parameters for different problems. The second is the long runtime for real-world problems whose fitness evaluations are often expensive. Aiming at solving these two problems, this paper develops a novel double-layered heterogeneous DE algorithm and realizes it in cloud computing distributed environment. In the first layer, different populations with various parameters and/or operators run concurrently and adaptively migrate to deliver robust solutions by making the best use of performance differences among multiple populations. In the second layer, a set of cloud virtual machines run in parallel to evaluate fitness of corresponding populations, reducing computational costs as offered by cloud. Experimental results on a set of benchmark problems with different search requirements and a case study with expensive design evaluations have shown that the proposed algorithm offers generally improved performance and reduced computational time, compared with not only conventional and a number of state-of-the-art DE variants, but also a number of other distributed DE and high-performing evolutionary algorithms. The speedup is significant especially on expensive problems, offering high potential in a broad range of real-world applications. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel optimization scheme by hybridizing an artificial bee colony optimizer (HABC) with a bee life-cycle mechanism, for both stationary and dynamic optimization problems. The main innovation of the proposed HABC is to develop a cooperative and population-varying scheme, in which individuals can dynamically shift their states of birth, foraging, death, and reproduction throughout the artificial bee colony life cycle. That is, the bee colony size can be adjusted dynamically according to the local fitness landscape during algorithm execution. This new characteristic of HABC helps to avoid redundant search and maintain diversity of population in complex environments. A comprehensive experimental analysis is implemented that the proposed algorithm is benchmarked against several state-of-the-art bio-inspired algorithms on both stationary and dynamic benchmarks. Then the proposed HABC is applied to the real-world applications including data clustering and image segmentation problems. Statistical analysis of all these tests highlights the significant performance improvement due to the life-cycle mechanism and shows that the proposed HABC outperforms the reference algorithms. [ABSTRACT FROM PUBLISHER]

This paper presents a cooperative framework for fireworks algorithm (CoFFWA). A detailed analysis of existing fireworks algorithm (FWA) and its recently developed variants has revealed that ( $i$ ) the current selection strategy has the drawback that the contribution of the firework with the best fitness (denoted as core firework) overwhelms the contributions of all other fireworks (non-core fireworks) in the explosion operator, ($ii$ ) the Gaussian mutation operator is not as effective as it is designed to be. To overcome these limitations, the CoFFWA is proposed, which significantly improves the exploitation capability by using an independent selection method and also increases the exploration capability by incorporating a crowdness-avoiding cooperative strategy among the fireworks. Experimental results on the CEC2013 benchmark functions indicate that CoFFWA outperforms the state-of-the-art FWA variants, artificial bee colony, differential evolution, and the standard particle swarm optimization SPSO2007/SPSO2011 in terms of convergence performance. [ABSTRACT FROM PUBLISHER]

Automatic data clustering, whose goal is to recover the proper number of clusters as well as appropriate partitioning of data sets, is a fundamental yet challenging problem in unsupervised learning. In this paper, adaptive multisubpopulation competition (AMC) and multiniche crowding are proposed and incorporated into a memetic algorithm to tackle the problem. The AMC mechanism is developed to ensure a diverse search over solution subspaces corresponding to different numbers of clusters while allowing more promising subspaces to be more intensively searched. In this mechanism, the amount of individuals to be migrated between subpopulations is adaptively controlled according to the performance of subpopulations as well as the diversity of cluster numbers in population. Further, the migration is restricted to occur between subpopulations with relatively similar performances. Additionally, subpopulations with different performances are devised to search their corresponding subspaces with different exploration powers. The adaptive multiniche crowding scheme is designed to promote a diverse search of the subspace while allowing an efficient convergence of the corresponding subpopulation. This is achieved by dynamically adjusting parameter values of a multiniche crowding method to form and maintain diverged niches of high fitness within the subpopulation. The performance of proposed algorithm has been demonstrated through a series of experiments on both artificial and real data, and compared with existing methods. The results reveal that our proposed algorithm can achieve superior clustering performance and outperform related methods. [ABSTRACT FROM PUBLISHER]