Hypercube-Based Crowding Differential Evolution with Neighborhood Mutation for Multimodal Optimization

Hypercube-Based Crowding Differential Evolution with Neighborhood Mutation for Multimodal Optimization

Haihuang Huang (Guangdong University of Education, Guangzhou, China), Liwei Jiang (Sun Yat-sen University, Guangzhou, China), Xue Yu (Sun Yat-sen University, Guangzhou, China) and Dongqing Xie (Guangzhou University, Guangzhou, China)
Copyright: © 2018 |Pages: 13
DOI: 10.4018/IJSIR.2018040102
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In reality, multiple optimal solutions are often necessary to provide alternative options in different occasions. Thus, multimodal optimization is important as well as challenging to find multiple optimal solutions of a given objective function simultaneously. For solving multimodal optimization problems, various differential evolution (DE) algorithms with niching and neighborhood strategies have been developed. In this article, a hypercube-based crowding DE with neighborhood mutation is proposed for such problems as well. It is characterized by the use of hypercube-based neighborhoods instead of Euclidean-distance-based neighborhoods or other simpler neighborhoods. Moreover, a self-adaptive method is additionally adopted to control the radius vector of a hypercube so as to guarantee the neighborhood size always in a reasonable range. In this way, the algorithm will perform a more accurate search in the sub-regions with dense individuals, but perform a random search in the sub-regions with only sparse individuals. Experiments are conducted in comparison with an outstanding DE with neighborhood mutation, namely NCDE. The results show that the proposed algorithm is promising and computationally inexpensive.
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1. Introduction

In practical optimization problems, it is not uncommon that multiple global and local optima need to be located for a given objective function. Therefore, multimodal optimization is proposed to deal with optimization tasks that involve finding multiple optima of a problem rather than a single best solution. Recently, in the field of optimization, there have been lots of theory and application researches on evolutionary algorithms (EAs) such as particle swarm optimization (PSO) (Jordehi, 2015; Jordehi et al., 2015), differential evolution (DE) (Storn et al., 1997; Das et al., 2011). Particularly, the research of evolutionary multimodal optimization algorithms (Wong, 2015; Das et al., 2011) is quite popular since most EAs are population-based and they are naturally excelling at parallel search to find multiple optima. Different evolutionary multimodal optimization algorithms have been developed based on different EAs, such as multimodal genetic algorithm (GA) (Yao et al., 2010; Kamyab et al., 2013, 2016), multimodal PSO (Chang, 2015; Li, 2011; Zhang et al., 2015), multimodal estimation of distribution algorithm (EDA) (Yang, et al., 2017) and multimodal DE (Liang et al., 2014; Qu et al., 2012; Zhang. et al., 2015). Among those EAs, DE has been widely researched and adopted to tackle optimization problems in various areas (Cheng et al., 2014; Pan et al., 2015; Rocca et al., 2011), due to its simplicity and high efficiency. Thus, in this study, we devote efforts to further research on DE for multimodal optimization.

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