Educational Simulator for Particle Swarm Optimization and Economic Dispatch Applications

Abstract

Optimization problems are widely encountered in various fields in science and technology. Sometimes such problems can be very complex due to the actual and practical nature of the objective function or the model constraints. Most of power system optimization problems have complex and nonlinear characteristics with heavy equality and inequality constraints. Recently, as an alternative to the conventional mathematical approaches, the heuristic optimization techniques such as genetic algorithms (GAs), Tabu search, simulated annealing, and particle swarm optimization (PSO) are considered as realistic and powerful solution schemes to obtain the global or quasi-global optimums (K. Y. Lee et al., 2002). In 1995, Eberhart and Kennedy suggested a PSO based on the analogy of swarm of bird and school of fish (J. Kennedy et al., 1995). The PSO mimics the behavior of individuals in a swarm to maximize the survival of the species. In PSO, each individual makes his decision using his own experience together with other individuals' experiences (H. Yoshida et al., 2000). The algorithm, which is based on a metaphor of social interaction, searches a space by adjusting the trajectories of moving points in a multidimensional space. The individual particles are drawn stochastically toward the present velocity of each individual, their own previous best performance, and the best previous performance of their neighbours (M. Clerc et al., 2002). The practical economic dispatch (ED) problems with valve-point and multi-fuel effects are represented as a non-smooth optimization problem with equality and inequality constraints, and this makes the problem of finding the global optimum difficult. Over the past few decades, in order to solve this problem, many salient methods have been proposed such as a hierarchical numerical method (C. E. Lin et al., 1984), dynamic programming (A. J. Wood et al., 1984), evolutionary programming (Y. M. Park et al., 1998; H. T. Yang et al., 1996; N. Sinba et al., 2003), Tabu search (W. M. Lin et al., 2002), neural network approaches (J. H. Park et al., 1993; K. Y. Lee et al., 1998), differential evolution (L. S. Coelho et al., 2006), particle swarm optimization (J. B. Park et al., 2005; T. A. A. Victoire et al., 2004; T. A. A. Victoire et al., 2005), and genetic algorithm (D. C. Walters et al., 1993). This chapter would introduce an educational simulator for the PSO algorithm. The purpose of this simulator is to provide the undergraduate students with a simple and useable tool for