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 arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

Recent advances in differential evolution – An updated survey

The firefly algorithm has become an increasingly important tool of Swarm Intelligence that has been applied in almost all areas of optimization, as well as engineering practice. Many problems from various areas have been successfully solved using the firefly algorithm and its variants. In order to use the algorithm to solve diverse problems, the original firefly algorithm needs to be modified or hybridized. This paper carries out a comprehensive review of this living and evolving discipline of Swarm Intelligence, in order to show that the firefly algorithm could be applied to every problem arising in practice. On the other hand, it encourages new researchers and algorithm developers to use this simple and yet very efficient algorithm for problem solving. It often guarantees that the obtained results will meet the expectations.

A comprehensive review of firefly algorithms

Differential Evolution (DE) is a simple and efficient optimizer, especially for continuous optimization. For these reasons DE has often been employed for solving various engineering problems. On the other hand, the DE structure has some limitations in the search logic, since it contains too narrow a set of exploration moves. This fact has inspired many computer scientists to improve upon DE by proposing modifications to the original algorithm. This paper presents a survey on DE and its recent advances. A classification, into two macro-groups, of the DE modifications is proposed here: (1) algorithms which integrate additional components within the DE structure, (2) algorithms which employ a modified DE structure. For each macro-group, four algorithms representative of the state-of-the-art in DE, have been selected for an in depth description of their working principles. In order to compare their performance, these eight algorithm have been tested on a set of benchmark problems. Experiments have been repeated for a (relatively) low dimensional case and a (relatively) high dimensional case. The working principles, differences and similarities of these recently proposed DE-based algorithms have also been highlighted throughout the paper. Although within both macro-groups, it is unclear whether there is a superiority of one algorithm with respect to the others, some conclusions can be drawn. At first, in order to improve upon the DE performance a modification which includes some additional and alternative search moves integrating those contained in a standard DE is necessary. These extra moves should assist the DE framework in detecting new promising search directions to be used by DE. Thus, a limited employment of these alternative moves appears to be the best option in successfully assisting DE. The successful extra moves are obtained in two ways: an increase in the exploitative pressure and the introduction of some randomization. This randomization should not be excessive though, since it would jeopardize the search. A proper increase in the randomization is crucial for obtaining significant improvements in the DE functioning. Numerical results show that, among the algorithms considered in this study, the most efficient additional components in a DE framework appear to be the population size reduction and the scale factor local search. Regarding the modified DE structures, the global and local neighborhood search and self-adaptive control parameter scheme, recently proposed in literature, seem to be the most promising modifications.

Recent advances in differential evolution: a survey and experimental analysis

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In this paper we investigate a Self-Adaptive Differential Evolution algorithm (jDE) where F and CR control parameters are self-adapted and a multi-population method with aging mechanism is used. The performance of the jDE algorithm is evaluated on the set of benchmark functions provided for the CEC 2009 special session on evolutionary computation in dynamic and uncertain environments.

https://www.cs.le.ac.uk/people/syang/ECiDUE/Competition09-Papers/4982976.pdf

Dynamic optimization using Self-Adaptive Differential Evolution

In this paper we investigate a self-adaptive differential evolution algorithm (jDEdynNP-F) where F and CR control parameters are self-adapted and a population size reduction method is used. Additionally the proposed jDEdynNP-F algorithm uses a mechanism for sign changing of F control parameter with some probability based on the fitness values of randomly chosen vectors, which are multiplied by the F control parameter (scaling factor) in the mutation operation of DE algorithm. The performance of the jDEdynNP-F algorithm is evaluated on the set of 7 benchmark functions provided for the CECpsila2008 special session on high-dimensional real-parameter optimization.

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High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction

In this paper, an optimization algorithm is formulated and its performance assessment for large scale global optimization is presented. The proposed algorithm is named DEwSAcc and is based on Differential Evolution (DE) algorithm, which is a floating-point encoding evolutionary algorithm for global optimization over continuous spaces. The original DE is extended by log-normal self-adaptation of its control parameters and combined with cooperative co-evolution as a dimension decomposition mechanism. Experimental results are given for seven high-dimensional test functions proposed for the Special Session on Large Scale Global Optimization at 2008 IEEE World Congress on Computational Intelligence.

Large Scale Global Optimization using Differential Evolution with self-adaptation and cooperative co-evolution

This paper presents insight into an adaptation and self-adaptation mechanism within differential evolution, covering not only how but moreover – when this mechanism generates new values for control parameters, focusing on the iteration-temporal randomness of the self-adaptive control parameters. In particular, this randomness is controlled by a randomness level parameter, which influences the control parameters values׳ dynamics and their propagation through suitable individuals׳ improvement contributions during ellitistic selection. Thereby, the randomness level parameter defines the chaotic behavior of self-adaptive control parameter values׳ instances. A Differential Evolution (DE) algorithm for Real Parameter Single Objective Optimization is utilized as an application of this mechanism, to analyze the impact of the randomness level parameter as used inside the evolutionary algorithm parameter adaptation and control mechanism, yielding statistically significant different algorithm performances and ranks on different randomness level parameter values. Moreover, the impacts of different randomness configurations on the number of improvements, improvement scales, and adaptation frequencies, are shown, in order to present a deeper insight into the influences and causes using different randomness level parameter configurations, to present the influence of randomization frequency on propagation stability. Since DE variant algorithms with the mechanism of control parameters self-adaptation are widely applied, this study might help in increasing the performances of these different variants and their applications.

Self-adaptive control parameters׳ randomization frequency and propagations in differential evolution

This paper presents performance assessment of differential evolution for multiobjective optimization with self adaptation algorithm, which uses the self adaptation mechanism from evolution strategies to adapt F and CR parameters of the candidate creation in DE. Results for several runs on CEC2007 special session test functions are presented and assessed with different performance metrics. Based on these metrics, algorithm strengths and weaknesses are discussed.

Aleš Zamuda

Papers

Dynamic optimization using Self-Adaptive Differential Evolution

High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction

Large Scale Global Optimization using Differential Evolution with self-adaptation and cooperative co-evolution

Self-adaptive control parameters׳ randomization frequency and propagations in differential evolution

Differential evolution for multiobjective optimization with self adaptation