A Novel Mutation Strategy for Differential Evolution

1. Introduction

Many real world applications Storn and Price (1997), Price et al. (2006), Joshi and Sanderson (1999), Zhang et al. (2008), Zhang et al. (2010), shows that Differential Evolution (DE) is an efficient algorithm for dealing with a variety of problems. DE was first introduced by Storn and Price in 1995, with the strategy DE/rand/1/bin which is still widely used among the researchers. Gämperle et al. (2002) and Zhang et al. (2007) shows that the performance of DE mostly depends on mutation factor and crossover probability. So, a change in these parameters affects the performance of DE in all aspects. Later on, different DE strategies were proposed by Storn (1996), Price (1999) and it was observed by Storn and Price (1997) and Gämperle et al. (2002) that the strategies in which there are two difference vectors such as DE/rand/2/bin and DE/best/2/bin are better than the strategies having difference vector, as diversity increases by adding more trial vectors as stated by Lampinen and Zelinka (2000). DE/best/1/bin and DE/rand-to-best/1/bin converges fast on easy optimization problems, but become reckless for highly multi-modal problems. DE/target-to-best/1/bin variant was proposed with the concept of neighborhood of each population so as to balance exploration and exploitation Das et al. (2009). DE/current-to-rand/1/bin can solve rotated problems more easily as compared to other strategies, Iorio and Li (2005).

A lot of research has been done to further enhance the performance of DE. Researchers have experimented with the setting of parameters Price et al. (2006), Gämperle et al. (2002), Gämperle (2006) and have also suggested adaptive and self-adaptive DE algorithms Qin and Suganthan (2005) and Huang et al. (2006). Some recently suggested DE variants and their applications in various engineering fields are given in Box 1.