Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies and their associated control parameter values. Employing a trial-and-error scheme to search for the most suitable strategy and its associated parameter settings requires high computational costs. Moreover, at different stages of evolution, different strategies coupled with different parameter settings may be required in order to achieve the best performance. In this paper, we propose a self-adaptive DE (SaDE) algorithm, in which both trial vector generation strategies and their associated control parameter values are gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings can be determined adaptively to match different phases of the search process/evolution. The performance of the SaDE algorithm is extensively evaluated (using codes available from P. N. Suganthan) on a suite of 26 bound-constrained numerical optimization problems and compares favorably with the conventional DE and several state-of-the-art parameter adaptive DE variants.

Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization

In this study, a new metaheuristic optimization algorithm, called cuckoo search (CS), is introduced for solving structural optimization tasks. The new CS algorithm in combination with Levy flights is first verified using a benchmark nonlinear constrained optimization problem. For the validation against structural engineering optimization problems, CS is subsequently applied to 13 design problems reported in the specialized literature. The performance of the CS algorithm is further compared with various algorithms representative of the state of the art in the area. The optimal solutions obtained by CS are mostly far better than the best solutions obtained by the existing methods. The unique search features used in CS and the implications for future research are finally discussed in detail.

Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems

– Nature‐inspired algorithms are among the most powerful algorithms for optimization. The purpose of this paper is to introduce a new nature‐inspired metaheuristic optimization algorithm, called bat algorithm (BA), for solving engineering optimization tasks., – The proposed BA is based on the echolocation behavior of bats. After a detailed formulation and explanation of its implementation, BA is verified using eight nonlinear engineering optimization problems reported in the specialized literature., – BA has been carefully implemented and carried out optimization for eight well‐known optimization tasks; then a comparison has been made between the proposed algorithm and other existing algorithms., – The optimal solutions obtained by the proposed algorithm are better than the best solutions obtained by the existing methods. The unique search features used in BA are analyzed, and their implications for future research are also discussed in detail.

Bat algorithm: a novel approach for global engineering optimization

Differential evolution (DE) has attracted much attention recently as an effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of the mutation strategy and associated control parameters. Thus, to obtain optimal performance, time-consuming parameter tuning is necessary. Different mutation strategies with different parameter settings can be appropriate during different stages of the evolution. In this paper, we propose to employ an ensemble of mutation strategies and control parameters with the DE (EPSDE). In EPSDE, a pool of distinct mutation strategies along with a pool of values for each control parameter coexists throughout the evolution process and competes to produce offspring. The performance of EPSDE is evaluated on a set of bound-constrained problems and is compared with conventional DE and several state-of-the-art parameter adaptive DE variants.

Differential evolution algorithm with ensemble of parameters and mutation strategies

Particle swarm optimization for task assignment problem

An image clustering method that is based on the particle swarm optimizer (PSO) is developed in this paper. The algorithm finds the centroids of a user specified number of clusters, where each cluster groups together with similar image primitives. To illustrate its wide applicability, the proposed image classifier has been applied to synthetic, MRI and satellite images. Experimental results show that the PSO image classifier performs better than state-of-the-art image classifiers (namely, K-means, Fuzzy C-means, K-Harmonic means and Genetic Algorithms) in all measured criteria. The influence of different values of PSO control parameters on performance is also illustrated.

Particle swarm optimization method for image clustering

Differential Evolution (DE) is generally considered as a reliable, accurate, robust and fast optimization technique. DE has been successfully applied to solve a wide range of numerical optimization problems. However, the user is required to set the values of the control parameters of DE for each problem. Such parameter tuning is a time consuming task. In this paper, a self-adaptive DE (SDE) is proposed where parameter tuning is not required. The performance of SDE is investigated and compared with other versions of DE. The experiments conducted show that SDE outperformed the other DE versions in all the benchmark functions.

Self-adaptive differential evolution

A new dynamic clustering approach (DCPSO), based on particle swarm optimization, is proposed. This approach is applied to image segmentation. The proposed approach automatically determines the "optimum" number of clusters and simultaneously clusters the data set with minimal user interference. The algorithm starts by partitioning the data set into a relatively large number of clusters to reduce the effects of initial conditions. Using binary particle swarm optimization the "best" number of clusters is selected. The centers of the chosen clusters is then refined via the K-means clustering algorithm. The proposed approach was applied on both synthetic and natural images. The experiments conducted show that the proposed approach generally found the "optimum" number of clusters on the tested images. A genetic algorithm and random search version of dynamic clustering is presented and compared to the particle swarm version.

Dynamic clustering using particle swarm optimization with application in image segmentation

Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure Clustering is a fundamental process in many different disciplines Hence, researchers from different fields are actively working on the clustering problem This paper provides an overview of the different representative clustering methods In addition, several clustering validations indices are shown Furthermore, approaches to automatically determine the number of clusters are presented Finally, application of different heuristic approaches to the clustering problem is also investigated

Ayed A. Salman

Papers

Particle swarm optimization for task assignment problem

Particle swarm optimization method for image clustering

Self-adaptive differential evolution

Dynamic clustering using particle swarm optimization with application in image segmentation

An overview of clustering methods