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

This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http://www.alimirjalili.com/SCA.html .

SCA: A Sine Cosine Algorithm for solving optimization problems

Salp Swarm Algorithm

A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Grasshopper Optimisation Algorithm

Research on the single objective optimization algorithms is the basis of the research on the more complex optimization algorithms such as multi-objective optimizations algorithms, niching algorithms, constrained optimization algorithms and so on. All new evolutionary and swarm algorithms are tested on single objective benchmark problems. In addition, these single objective benchmark problems can be transformed into dynamic, niching composition, computationally expensive and many other classes of problems. In the recent years various kinds of novel optimization algorithms have been proposed to solve real-parameter optimization problems, including the CEC'05 and CEC'13 Special Session on Real-Parameter Optimization [1][2]. Considering the comments on the CEC'13 test suite, we organize a new competition on real parameter single objective optimization. For this competition, we are developing benchmark problems with several novel features such as novel basic problems, composing test problems by extracting features dimension-wise from several problems, graded level of linkages, rotated trap problems, and so on. This competition excludes usage of surrogates or meta-models. There is a sub-competition to test the algorithms with a very small number of function evaluations in order emulate the computationally expensive optimization scenario. This sub-competition encourages the usage of surrogates and other approximation approaches. This special session is devoted to the approaches, algorithms and techniques for solving real parameter single objective optimization without making use of the exact equations of the test functions. We encourage all researchers to test their algorithms on the CEC'14 test suite which includes 30 benchmark functions. The participants are required to send the final results in the format specified in the technical report to the organizers. The organizers will present an overall analysis and comparison based on these results. We will also use statistical tests on convergence performance to compare algorithms that generate similar final solutions eventually. Papers on novel concepts that help us in understanding problem characteristics are also welcome.

Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization

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Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Optimization

Parameters identification of photovoltaic models using an improved JAYA optimization algorithm

In this paper, a neighborhood mutation strategy is proposed and integrated with various niching differential evolution (DE) algorithms to solve multimodal optimization problems. Although variants of DE are highly effective in locating a single global optimum, no DE variant performs competitively when solving multi-optima problems. In the proposed neighborhood based differential evolution, the mutation is performed within each Euclidean neighborhood. The neighborhood mutation is able to maintain the multiple optima found during the evolution and evolve toward the respective global/local optimum. To test the performance of the proposed neighborhood mutation DE, a total of 29 problem instances are used. The proposed algorithms are compared with a number of state-of-the-art multimodal optimization approaches and the experimental results suggest that although the idea of neighborhood mutation is simple, it is able to provide better and more consistent performance over the state-of-the-art multimodal algorithms. In addition, a comparative survey on niching algorithms and their applications are also presented.

Boyang Qu

Papers

Multiobjective evolutionary algorithms: A survey of the state of the art

Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization

Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Optimization

Parameters identification of photovoltaic models using an improved JAYA optimization algorithm

Differential Evolution With Neighborhood Mutation for Multimodal Optimization