Personal Best Oriented Particle Swarm Optimizer

Abstract

Optimization problems are frequently encountered in many engineering, economic or scientific fields that engineers or researchers are seeking to minimize cost or time, or to maximize profit, quality or efficiency, of a specific problem. For example, economic dispatch of power generation, optimal allocation of resources for manufacture, design optimal plant to maximize production, and so many which are unable to enumerate completely. In addition, many optimization problems are very complex and hard to solve by conventional gradient-based techniques, particularly the objective function and constraint are not in closed forms. Thus, the development of a good optimization strategy or algorithm is of great value. In the past decade, particle swarm optimization (PSO) algorithm [Eberhart & Kennedy 1995, Kennedy and Eberhart 1995] attracts many sights around the world due to its powerful searching ability and simplicity. PSO simulates the swarm behavior of birds flocking and fish schooling that swarms work in a collaborative manner to search for foods as efficient and quick as possible. There are three different types of PSO which are frequently encountered in literature. They are constriction type PSO, constant inertia weight PSO and linearly decreasing inertia weight PSO. Each of them has been successfully applied to many optimization problems. While empirical studies have proven PSO’s usefulness as an optimization algorithm, it does not always fit all problems. Sometimes, it may also get stuck on local optimal. In order to improve the performance, many variants of PSO have been proposed. Some of the proposed algorithms adopted new operations and some of the modifications hybridized with other algorithm. Although they are claimed better than original PSO algorithm, most of them will introduce extra mathematical or logical operations, which, in turn, making algorithm more complicate and spending more computing time. Especially, they, in general, did not present any theoretical models to describe its behavior and support such modifications. Many researchers have devoted to study how PSO works. They intended to discover the implicit properties of PSO and its weakness and strength via theoretical analysis. The first attempt to analysis PSO is made by Kenndey [Kennedy, 1998]. Meanwhile, Ozcan and Mohan showed that a particle in a simple one-dimensional PSO system follows a path defined by a sinusoidal wave with random amplitude and frequency. However, the effects of inertia weight are not addressed in that paper [Ozcan & Mohan, 1999]. In order to analyze