Differential evolution (DE) algorithm with a small population size is called Micro-DE (MDE). A small population size decreases the computational complexity but also reduces the exploration ability of DE by limiting the population diversity. In this paper, we propose the idea of combining ensemble mutation scheme selection and opposition-based learning concepts to enhance the diversity of population in MDE at mutation and selection stages. The proposed algorithm enhances the diversity of population by generating a random mutation scale factor per individual and per dimension, randomly assigning a mutation scheme to each individual in each generation, and diversifying individuals selection using opposition-based learning. This approach is easy to implement and does not require the setting of mutation scheme selection and mutation scale factor. Experimental results are conducted for a variety of objective functions with low and high dimensionality on the CEC Black- Box Optimization Benchmarking 2015 (CEC-BBOB 2015). The results show superior performance of the proposed algorithm compared to the other micro-DE algorithms.
A novel type of ensemble DE, called MPEDE, is proposed in @cite_28 . It is a multi-population based approach which deploys a dynamic ensemble of multiple mutation strategies. It controls parameters of the algorithms such as mutation scale factor and crossover rate @cite_35 . This method uses the current-to-pbest 1", current-to-rand 1", and rand 1" mutation schemes @cite_28 . Another method for unconstrained continuous optimization problems is @math JADE @cite_38 . It is an adaptive DE with a small population size approach. The @math JADE uses a new mutation operator, called current-by-rand-to-pbest @cite_38 .
@cite_28 @cite_35 @cite_38
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A multi-population based approach is proposed to realize the adapted ensemble of multiple strategies of differential evolution.The control parameters of each mutation strategy are adapted independently.Extensive experiments are conducted to test the performance of multi-population ensemble DE (MPEDE). Differential evolution (DE) is among the most efficient evolutionary algorithms (EAs) for global optimization and now widely applied to solve diverse real-world applications. As the most appropriate configuration of DE to efficiently solve different optimization problems can be significantly different, an appropriate combination of multiple strategies into one DE variant attracts increasing attention recently. In this study, we propose a multi-population based approach to realize an ensemble of multiple strategies, thereby resulting in a new DE variant named multi-population ensemble DE (MPEDE) which simultaneously consists of three mutation strategies, i.e., "current-to-pbest 1" and "current-to-rand 1" and "rand 1". There are three equally sized smaller indicator subpopulations and one much larger reward subpopulation. Each constituent mutation strategy has one indicator subpopulation. After every certain number of generations, the current best performing mutation strategy will be determined according to the ratios between fitness improvements and consumed function evaluations. Then the reward subpopulation will be allocated to the determined best performing mutation strategy dynamically. As a result, better mutation strategies obtain more computational resources in an adaptive manner during the evolution. The control parameters of each mutation strategy are adapted independently as well. Extensive experiments on the suit of CEC 2005 benchmark functions and comprehensive comparisons with several other efficient DE variants show the competitive performance of the proposed MPEDE (Matlab codes of MPEDE are available from http: guohuawunudt.gotoip2.com publications.html). This paper proposes a new differential evolution (DE) algorithm for unconstrained continuous optimisation problems, termed @math μJADE, that uses a small or micro' ( @math μ) population. The main contribution of the proposed DE is a new mutation operator, current-by-rand-to-pbest.' With a population size less than 10, @math μJADE is able to solve some classical multimodal benchmark problems of 30 and 100 dimensions as reliably as some state-of-the-art DE algorithms using conventionally sized populations. The algorithm also compares favourably to other small population DE variants and classical DE.