A neutral mutated operator applied for DE algorithms
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ORIGINAL RESEARCH
A neutral mutated operator applied for DE algorithms Chuan Ma1,2 · Yancheng Liu1 · Chuan Wang1 · Qinjin Zhang1 Received: 29 May 2019 / Accepted: 11 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract As an easily used and powerful heuristic search technique based on population, differential evolution (DE) algorithm has been widely used for many optimization and real engineering projects. Similar to other evolutionary algorithms (EA), DE could not avoid from premature convergence due to over concentrated population, which could be called losing population diversity. To improve the performance, a neutral mutation (NM) operator for DE algorithm is proposed. The proposed operator is inspired by neutral theory of molecular evolution, which claims that most mutations are neutral at the level of molecular. The NM operator maintains slightly deleterious trial vectors with a certain probability in the conventional selection operator of DE. At the same time, two control parameters of Neutral Mutation operator are investigated and a dynamic neutral mutation rate tuning strategy is designed. Besides, some of these trial vectors have a chance to be mutated neutrally within the search domain randomly. As a result, the population is diversified with costing negligible function evaluations. Comprehensive experimental results demonstrate that the presented NM operator could improve population diversity to some extent, especially when the population is not divergent at all. Moreover, a real word problem is used to further evaluate NM operator. Also, this operator can be easily used in other EAs to keep population diversity. Keywords Differential evolution · Neutral mutation operator · Population diversity · Neutral theory of molecular evolution · IEEE bus 57
1 Introduction Since it was first proposed in 1997, the algorithm of Differential Evolution (DE) has been used on wide spreading areas (Storn and Price 1997; Zhu et al. 2013), such as pattern recognition (Das and Sil 2010), data mining (Das et al. 2008), power system (Wang et al. 2010), financial market (Hachicha et al. 2011) and combinatorial optimization (Tasgetiren et al. 2010), due to the powerful searching capability and satisfying performance. In Das and Suganthan (2011), most widely used DE methods are summarized in detail (Gong et al. 2011a, b). Although many achievements have been obtained on DE algorithms, a few weaknesses are still not overcome yet. One of these weaknesses is that the population is gradually losing diversity and gathering in a certain area during optimizing * Chuan Wang [email protected] 1
Marine Engineering College, Dalian Maritime University, Dalian 116026, China
Engineering Department, Qingdao Ocean Shipping Mariners College, Qingdao 266071, China
2
process. Like other population-based methods, successes of the methods depend on their abilities to balance exploration and exploitation. If all the individuals could not find any better solution in fitness landscape, i.e., the population me
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