Using Opposition-based Learning with Particle Swarm Optimization and Barebones Differential Evolution

Particle swarm optimization (PSO) (Kennedy & Eberhart, 1995) and differential evolution (DE) (Storn & Price, 1995) are two stochastic, population-based optimization methods, which have been applied successfully to a wide range of problems as summarized in Engelbrecht (2005) and Price et al. (2005). A number of variations of both PSO and DE have been developed in the past decade to improve the performance of these algorithms (Engelbrecht, 2005; Price et al. 2005). One class of variations includes hybrids between PSO and DE, where the advantages of the two approaches are combined. The barebones DE (BBDE) is a PSO-DE hybrid algorithm proposed by Omran et al. (2007) which combines concepts from the barebones PSO (Kennedy 2003) and the recombination operator of DE. The resulting algorithm eliminates the control parameters of PSO and replaces the static DE control parameters with dynamically changing parameters to produce an almost parameter-free, self-adaptive, optimization algorithm. Recently, opposition-based learning (OBL) was proposed by Tizhoosh (2005) and was successfully applied to several problems (Rahnamayan et al., 2008). The basic concept of OBL is the consideration of an estimate and its corresponding opposite estimate simultaneously to approximate the current candidate solution. Opposite numbers were used by Rahnamayan et al. (2008) to enhance the performance of Differential Evolution. In addition, Han and He (2007) and Wang et al. (2007) used OBL to improve the performance of PSO. However, in both cases, several parameters were added to the PSO that are difficult to tune. Wang et al. (2007) used OBL during swarm initialization and in each iteration with a user-specified probability. In addition, Cauchy mutation is applied to the best particle to avoid being trapping in local optima. Similarly, Han and He (2007) used OBL in the initialization phase and also during each iteration. However, a constriction factor is used to enhance the convergence speed. In this chapter, OBL is used to improve the performance of PSO and BBDE without adding any extra parameter. The performance of the proposed methods is investigated when applied to several benchmark functions. The experiments conducted show that OBL improves the performance of both PSO and BBDE. The remainder of the chapter is organized as follows: PSO is summarized in Section 2. DE is presented in Section 3. Section 4 provides an overview of BBDE. OBL is briefly reviewed in