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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]

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]

Hybrid flow shop scheduling problems have gained an increasing attention in recent years because of its wide applications in real-world production systems. Most of the prior studies assume that the processing time of jobs is deterministic and constant. In practice, jobs’ processing time is usually difficult to be exactly known in advance and can be influenced by many factors, e.g., machines’ abrasion and jobs’ feature, thereby leading to their uncertain and variable processing time. In this paper, a dual-objective stochastic hybrid flow shop deteriorating scheduling problem is presented with the goal to minimize makespan and total tardiness. In the formulated problem, the normal processing time of jobs follows a known stochastic distribution, and their actual processing time is a linear function of their start time. In order to solve it effectively, this paper develops a hybrid multiobjective optimization algorithm that maintains two populations executing the global search in the whole solution space and the local search in promising regions, respectively. An information sharing mechanism and resource allocating method are designed to enhance its exploration and exploitation ability. The simulation experiments are carried out on a set of instances, and several classical algorithms are chosen as its peers for comparison. The results demonstrate that the proposed algorithm has a great advantage in dealing with the investigated problem. [ABSTRACT FROM AUTHOR]

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper proposes a united-based imperialist competitive algorithm (UICA) for compensatory neural fuzzy systems. The original imperialist competitive algorithm (ICA) comprises numerous empires in the population, and each empire comprises one imperialist and some colonies. Each country represents a feasible solution in the empire, and the more favorable solutions become imperialists, taking over less favorable solutions (i.e., colonies). In the ICA, each colony moves toward its relevant imperialist according to an assimilation policy. This paper proposes a UICA that focuses on this assimilation policy to explore the characteristics of the colonies. The assimilation policy consists of three major parts in this paper. In the first part, a colony searches for the best previous position of the colony. In the second part, the colony faces the best-so-far imperialist. In the third part, the colony moves toward the corresponding imperialist of the colony. The proposed UICA was applied to nonlinear system problems, and the experimental results indicated that the proposed UICA is effective. [ABSTRACT FROM PUBLISHER]

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]

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]

With the advent of electric vehicles (EVs), issues connected to the electric vehicle charging scheduling (EVCS) problem, which is $\textsf {NP}$ -hard, have become important. In previous studies, EVCS has been mainly formulated as a constrained shortest-path problem; however, such formulations have not involved variables such as charging rates, traffic congestion, scalability, and waiting time at charging station (CS), that need to be considered in practical settings. Earlier research has also tended to focus on the strengths of particular evolutionary optimization algorithms like differential evolution (DE) or particle swarm optimization (PSO) over others or traditional mathematical programming methods, with only a limited study of hybrid approaches. In this paper, fast and slow charging options at a station are considered in the EVCS problem for practical use. In previous studies, EVs have been considered to have fixed speeds; however, in order to mitigate CS congestion and thus waiting times at CSs, dynamic speed control of EVs has been considered in this work. This work also investigates the scalability of different EVCS solutions. A hybrid approach using PSO and the Firefly algorithm (FFA) with a Lévy flights search strategy is designed and implemented to solve the EVCS. Also, different hybrid methods variants of PSO and FFA have been evaluated in this paper to find the best performing hybrid variant. Experimental results validate the effectiveness of our approach on both synthetic and the real-world transportation networks. [ABSTRACT FROM AUTHOR]

Mobile edge computing (MEC) is an emerging computing paradigm that decreases the computing time and extends the lifespan of user equipments (UEs). In MEC, the computational tasks are offloaded from UEs to the base station (BS) at the edge of the network for processing. However, MEC cannot cope with environments where there are no BS or where communication facilities have been destroyed. In this paper, we study the problem of minimizing the energy consumption of UAV equipped with MEC servers as a mobile base station to serve users. The problem involves user offloading decision, UAV location and allocation with computational resources, and is a hybrid optimization problem with continuous and discrete variables. To address this problem, we propose a hybrid nature-inspired optimization algorithm (HNIO) and its version for discrete optimization, where HNIO incorporates mutation and population diversity detection mechanisms to boost its global optimization capability, and we design a probabilistic selection-based coding strategy for the discrete optimization version. The experimental study is conducted based on ten cases with different numbers of UEs. Comparing HNIO with several other state-of-the-art optimization algorithms, it is concluded from the Friedman and Wilcoxon’s test of the experimental results that HNIO shows better precision and stability in nine out of the ten cases with higher number of UEs. [ABSTRACT FROM AUTHOR]

Due to natural disasters or system failures, the facility has the risk of disruption, and thus improving the location reliability under uncertainty of facilities becomes an important issue. In this paper, we propose a multi-objective facility location problem under uncertainty of facilities, where two objectives on reliability are constructed and multiple coverage with variable radius is imposed to reduce the influence caused by the facility disruption. A dual-population based evolutionary algorithm is also suggested to address this problem, where one population is for the location optimization and the other population is for the radius optimization. These two populations iteratively exchange the information obtained from elite solutions during the evolution to collaboratively search for the optimal solutions of the problem. The location population provides the high-quality location schemes for radius population in evaluating the quality of radii of each location, whereas the radius population equips the proper radii for location population in determining the good location schemes. Experimental results indicate that the proposed model can effectively improve the location reliability and the proposed method can obtain higher quality optimal solutions in comparison with four state-of-the-art algorithms. Moreover, the proposed method is applied to a real-world facility location with uncertainty of express cabinets in Tianjin, China, and it produces satisfactory location schemes. [ABSTRACT FROM AUTHOR]

Core power control of a nuclear reactor during power maneuvering transients is an important issue in a nuclear power plant. This paper, for the first time, presents an optimized PID controller for a nuclear research reactor with a new model of the reactor core, which is based on the fractional neutron point kinetics (FNPK) equations. This model preserves the main dynamic properties of the neutron movement in which the relaxation time related to a quick change in the neutron flux includes a fractional order, acting as an exponent of the relaxation time, to show the dynamic characteristics of the nuclear reactor in the best way. The physical justification of the fractional exponent is associated with nonFickian impressions from the neutron diffusion equation point of view. In addition, in this paper, for the first time, feedback reactivity effects are considered for FNPK model. Genetic algorithm (GA) is used to optimize gains of the PID controller. The objective function is according to the minimization of the integral of time-weighted absolute error (ITAE). The simulation result demonstrates that this optimized control method has satisfactory performance and stability during output-tracking process for higher values of fractional order. [ABSTRACT FROM AUTHOR]

Operational indices optimization is crucial for the global optimization in beneficiation processes. This paper presents a multitasking multiobjective evolutionary method to solve operational indices optimization, which involves a formulated multiobjective multifactorial operational indices optimization (MO-MFO) problem and the proposed multiobjective MFO algorithm for solving the established MO-MFO problem. The MO-MFO problem includes multiple level of accurate models of operational indices optimization, which are generated on the basis of a data set collected from production. Among the formulated models, the most accurate one is considered to be the original functions of the solved problem, while the remained models are the helper tasks to accelerate the optimization of the most accurate model. For the MFO algorithm, the assistant models are alternatively in multitasking environment with the accurate model to transfer their knowledge to the accurate model during optimization in order to enhance the convergence of the accurate model. Meanwhile, the recently proposed two-stage assortative mating strategy for a multiobjective MFO algorithm is applied to transfer knowledge among multitasking tasks. The proposed multitasking framework for operational indices optimization has conducted on 10 different production conditions of beneficiation. Simulation results demonstrate its effectiveness in addressing the operational indices optimization of beneficiation problem. Note to Practitioners—Operational indices optimization is a typical approach to achieve global production optimization by efficiently coordinating all the indices to improve the production indices. In this paper, a multiobjective multitasking framework is developed to address the operational indices optimization, which includes a multitasking multiobjective operational indices optimization problem formulation and a multitasking multiobjective evolutionary optimization to solve the above-formulated optimization problem. The proposed approach can achieve a solution set for the decision-making. The simulation results on a real beneficiation process in China with 10 operational conditions show that the proposed approach is able to obtain a superior solution set, which is associated with a higher grade and yield of the product. [ABSTRACT FROM AUTHOR]

Dense stereo image matching in remotely sensed images is a challenging problem, though it has been studied for more than two decades, due to occlusions, discontinuities, geometric, and radiometric distortions. A novel multiobjective fitness function-based dense stereo matching approach using genetic algorithms (GAs) is proposed in this paper. The proposed method is useful for estimating dense disparity map with an improved number of inliers for a stereo image pair, despite the constraint of finding correct disparity at depth discontinuities. In this paper, the steps of GA, such as initialization of the population, fitness function, and crossover and mutation operation, are designed and implemented to effectively deal with the problem of dense stereo image matching. To initialize the population, a Scale Invariant Feature Transform (SIFT) descriptor is computed for each pixel and multiple-size window-based matching is performed, using the similarity measures: 1) Euclidean distance and 2) spectral angle mapper. The generated disparity maps are pruned to choose a suitable subset using the designed fitness functions, considering the constraints related to stereo image pair, such as epipolar constraint, which encodes the epipolar geometry and the similarity measure that is useful to decide accuracy of the correspondences. The two objective functions are the number of inliers computed using the fundamental matrix and an energy minimization function, considering discontinuities and occlusions. The usefulness of this approach for remotely sensed stereo image pairs is demonstrated by improving the number of inliers and favorably comparing with state-of-the-art dense stereo image matching methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid genetic algorithm (GA) for the optimal shape design of an axially symmetric dual-reflector antenna by combining the GA with the moving least square (MLS), which enhances the convergence rate and the global search performance. The MLS is used to construct local interpolation functions from non-uniform sample data and to estimate new superior positions. By combining these superior positions in the next generation, the MLS-GA shows better search performance for the global optimum and a faster convergence rate than those of the conventional GA. To verify the proposed MLS-GA, we applied it to the optimal shape design of the DRA at the W-band. [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]

Brain storm optimization (BSO) is a swarm intelligence optimization algorithm inspired by the collective behavior of human beings in solving problems. This paper provides a conceptual overview and detailed explanation of the BSO algorithm. For the first time, the effectiveness of BSO in electromagnetic applications is demonstrated using a Yagi–Uda antenna design and a Luneburg lens antenna design, and this effectiveness is further validated via optimization, prototyping, and measurement of a dual-band slotted patch antenna design. In addition, a novel binary version of BSO (BBSO) for optimizing discrete problems is proposed, and the process of transforming the concept of BSO into a binary language is discussed in detail. A method for selecting algorithm parameter values for BBSO is shown. Finally, BBSO is applied successfully to an array thinning example and a pixelated patch antenna design. [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]

This paper applied the finite-element method (FEM) with topological data structures to the optimization of electrical devices. A generic modifiable graph data structure is built according to the graph-theoretic foundation for these data structures. The employed topological FEM avoids rebuilding of the mesh in traditional FEM method while geometrical variations happen. It is an effective algorithm which can save computer storage and working time when applied to successive optimization. The effectiveness is verified by numerical example and comparison of the topological FEM with traditional FEM on storage load and working time is shown in this paper. [ABSTRACT FROM AUTHOR]

Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well-mixed populations, which limits the applications where this theory can be implemented. In this paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controllers. [ABSTRACT FROM PUBLISHER]

Multiple solutions are often needed because of different kinds of uncertain failures in a plan execution process and scenarios for which precise mathematical models and constraints are difficult to obtain. This paper proposes an optimization strategy for multirobot task allocation (MRTA) problems and makes efforts on offering multiple solutions with same or similar quality for switching and selection. Since the mentioned problem can be regarded as a multimodal optimization one, this paper presents a niching immune-based optimization algorithm based on Softmax regression (sNIOA) to handle it. A prejudgment of population is done before entering an evaluation process to reduce the evaluation time and to avoid unnecessary computation. Furthermore, a guiding mutation (GM) operator inspired by the base pair in theory of gene mutation is introduced into sNIOA to strengthen its search ability. When a certain gene mutates, the others in the same gene group are more likely to mutate with a higher probability. Experimental results show the improvement of sNIOA on the aspect of accelerating computation speed with comparison to other heuristic algorithms. They also show the effectiveness of the proposed GM operator by comparing sNIOA with and without it. Two MRTA application cases are tested finally. [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]

Nonlinear equations system (NES) arises commonly in science and engineering. Repulsion techniques are considered to be the effective methods to locate different roots of NES. In general, the repulsive radius needs to be given by the user before the run. However, its optimal parameter setting is difficult and problem-dependent. To alleviate this drawback, in this paper, we first propose a dynamic repulsion technique, and then a general framework based on the dynamic repulsion technique and evolutionary algorithms (EAs) is presented to effectively solve NES. The major advantages of our framework are: 1) the repulsive radius is controlled dynamically during the evolutionary process; 2) multiple roots of NES can be simultaneously located in a single run; 3) the diversity of the population is preserved due to the population reinitialization; and 4) different repulsion techniques and different EAs can be readily integrated into this framework. To extensively evaluate the performance of our framework, we choose 42 problems with diverse features as the test suite. In addition, some representative differential evolution and particle swarm optimization variants are incorporated into the framework. Our method is also compared with other state-of-the-art methods. Experimental results indicate that the dynamic repulsion technique can improve the performance of the original repulsion technique with static repulsive radius. Moreover, the proposed method is able to yield better results compared with other methods. [ABSTRACT FROM AUTHOR]

This paper presents fuzzy ${c}$ -means-based yield estimation (FUZYE), a methodology that reduces the time impact caused by Monte Carlo (MC) simulations in the context of analog integrated circuits (ICs) yield estimation, enabling it for yield optimization with population-based algorithms, e.g., the genetic algorithm (GA). MC analysis is the most general and reliable technique for yield estimation, yet the considerable amount of time it requires has discouraged its adoption in population-based optimization tools. The proposed methodology reduces the total number of MC simulations that are required, since, at each GA generation, the population is clustered using a fuzzy ${c}$ -means (FCMs) technique, and, only the representative individual (RI) from each cluster is subject to MC simulations. This paper shows that the yield for the rest of the population can be estimated based on the membership degree of FCM and RIs yield values alone. This new method was applied on two real circuit-sizing optimization problems and the obtained results were compared to the exhaustive approach, where all individuals of the population are subject to MC analysis. The FCM approach presents a reduction of 89% in the total number of MC simulations, when compared to the exhaustive MC analysis over the full population. Moreover, a ${k}$ -means-based clustering algorithm was also tested and compared with the proposed FUZYE, with the latest showing an improvement up to 13% in yield estimation accuracy. [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]

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]

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]

The improved differential evolutionary algorithm (EA) discussed in this paper is used to solve high-dimensional big data. Specifically, the algorithm improves population diversity by expanding the searching scope of the population, prevents premature deaths of the population through wider and more specific searches, and aims to solve the high-dimensional issue. To achieve this improvement goal, the paper suggests a multilayer hierarchical architecture on the basis of the above-mentioned heuristic mechanism. In each layer of the hierarchical architecture in the dynamic subpopulation, individuals who are more suitable for isolated evolution can better coexist with the original main population. We propose a new multiobjective optimization algorithm based on nondominated sorting and bidirectional local search (NSBLS). The algorithm takes the local beam search as the main body. NSBLS outputs the nondominated solution set through a continuous iterative search when the iteration termination condition is satisfied. It is worthy to note that the iteration of NSBLS is similar to the generation of the EA; therefore, this paper uses generation to represent the iterations. An algorithm introduces a new distribution maintaining strategy based on the sampling theory to combine with the fast nondominated sorting algorithm in order to select a new population into the next iteration. NSBLS will compare with three classical algorithms: NSGA-II, MOEA/D-DE, and MODEA through a series of bi-objective test problems. The proposed nondominated sorting and local search is able to find a better spread of solutions and better convergence to the true Pareto-optimal front compared to the other four algorithms. The outstanding performance of the proposed technology was proven in well-known benchmark problems. [ABSTRACT FROM PUBLISHER]

Lightning is considered one of the main causes of faults in overhead distribution networks. Direct strokes usually lead to flashovers due to the insulation levels that are used. Induced overvoltages caused by indirect lightning are usually lower and can be efficiently reduced by metal–oxide surge arresters. Hence, its associated flashover rate can be reduced. In this paper, a heuristic method is proposed to optimize the number of surge arresters as well as their locations. The method presented is based on genetic algorithms and an economic approach is taken into account by means of evaluating the cost of insulation flashover. [ABSTRACT FROM AUTHOR]

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]

Scalable compact models for passive elements are important in the Analog/RF circuit design and optimization. Traditional scalable modeling methods are mainly physical and manual based methods, which usually require deep physical insight and extensive human intervention. In this paper, an automatic scalable compact modeling method for generic passive elements is established. The proposed method is a unified parameter extraction and scalable modeling scheme with novel inner-loop correlated parameter extraction and outer-loop adaptive boundary compression techniques. Experimental results show that both accuracy and scalability have been achieved by the proposed method for industrial inductors and transformers with an acceptable computational cost. [ABSTRACT FROM PUBLISHER]

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]

Magnetotactic bacteria is a kind of polyphyletic group of prokaryotes with the characteristics of magnetotaxis that make them orient and swim along geomagnetic field lines. Its distinct biology characteristics are useful to design new optimization technology. In this paper, a new bionic optimization algorithm named Magnetotactic Bacteria Moment Migration Algorithm (MBMMA) is proposed. In the proposed algorithm, the moments of a chain of magnetosomes are considered as solutions. The moments of relative good solutions can migrate each other to enhance the diversity of the MBMMA. It is compared with variants of PSO on standard functions problems. The experiment results show that the MBMMA is effective in solving optimization problems. It shows better or competitive performance compared with the variants of PSO on most of the tested functions in this paper. [ABSTRACT FROM PUBLISHER]

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]

This paper presents the fast topology optimization methods for rotating machines based on deep learning. The cross-sectional image of electric motors and their performances obtained during a multi-objective topology optimization based on the finite-element method and genetic algorithm (GA) is used for training of the convolutional neural network (CNN). Two different approaches are proposed: 1) CNN trained by preliminary optimization with a small population for GA is used for the main optimization with a large population and 2) CNN is used for screening of torque performances in the optimization with respect to the motor efficiency. [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]

Decomposition has become an increasingly popular technique for evolutionary multiobjective optimization (EMO). A decomposition-based EMO algorithm is usually designed to approximate a whole Pareto-optimal front (PF). However, in practice, a decision maker (DM) might only be concerned in her/his region of interest (ROI), i.e., a part of the PF. Solutions outside that might be useless or even noisy to the decision-making procedure. Furthermore, there is no guarantee that the preferred solutions will be found when many-objective problems. This paper develops an interactive framework for the decomposition-based EMO algorithm to lead a DM to the preferred solutions of her/his choice. It consists of three modules, i.e., consultation, preference elicitation, and optimization. Specifically, after every several generations, the DM is asked to score a few candidate solutions in a consultation session. Thereafter, an approximated value function, which models the DM's preference information, is progressively learned from the DM's behavior. In the preference elicitation session, the preference information learned in the consultation module is translated into the form that can be used in a decomposition-based EMO algorithm, i.e., a set of reference points that are biased toward the ROI. The optimization module, which can be any decomposition-based EMO algorithm in principle, utilizes the biased reference points to guide its search process. Extensive experiments on benchmark problems with three to ten objectives fully demonstrate the effectiveness of our proposed method for finding the DM's preferred solutions. [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]

Pattern mining (PM) refers to the process of discovering patterns of interest to users from data. However, most studies have considered only one pattern, such as frequent pattern or high-utility pattern. With the continuous requirement of businesses in various industries, the single-objective PM methods are difficult to meet the increasingly diverse needs of users. In this paper, a multi-objective problem model for high quality pattern mining (HQPM) is proposed, where the objectives are support, occupancy, and utility. In order to solve the proposed three-objective problem efficiently, an improved multi-objective evolutionary algorithm for HQPM (MOEA-PM) is proposed. Two kinds of population initialization strategies are designed, which is used to ensure the population is effectively distributed in the feasible solution space. By taking the properties of the model into consideration, an auxiliary tool is proposed to accelerate the convergence of the algorithm. Experimental results on real-world datasets show that the proposed three-objective problem model with the MOEA-PM algorithm can discover patterns that are both frequently occurring and has a high utility in the transaction datasets, while at the same time being relatively complete. Compared with the state-of-the-art MOEA-based HQPM algorithms, MOEA-PM has better performance in terms of efficiency, quality, and convergence speed. [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]

Distribution feeder reconfiguration (DFR) is a precious operation strategy that can improve the system from different aspects including total cost, reliability, and power quality. Nevertheless, the high complexity of the new smart grids has resulted in much uncertainty in the DFR problem that necessities the use of a sufficient stochastic framework to deal with them. In this way, this paper proposes a new stochastic framework based on cloud theory to account the uncertainties associated with multiobjective DFR problem from the reliability point of view. Cloud theory is constructed based on fuzzy theory and probability idea. In comparison with the Monte Carlo simulation method, cloud models can give more information on the uncertainties associated with the problem. This special aspect of cloud models makes it possible to integrate the fuzziness and randomness of qualitative concepts through the cloud drops and then transforms them to the quantitative model. In order to solve the proposed problem, a fast and powerful optimization technique is required. To deal with this issue, a new optimization algorithm designated as \theta -bat algorithm is proposed in this paper. The feasibility and satisfying performance of the proposed method are examined on the 32-bus and 69-bus IEEE distribution test system. [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]