Inertia weight control strategies for PSO algorithms

Abstract

Particle swarm optimization (PSO) is a stochastic population-based algorithm which was originally introduced by Kennedy and Eberhart [1]. This optimization algorithm is motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. As in most of the metaheuristic optimization algorithms, in PSO, a population of individuals, known as particles, are evolved through successive iterations. The most important advantages of PSO, compared to other optimization strategies, are its easy implementation and few parameters requiring adjustment. Since the initial development of PSO by Kennedy and Eberhart, several variants of this algorithm have been proposed by researchers. The first modification was introducing an inertia weight parameter in the velocity update equation of the initial PSO-a PSO model which is now accepted as the global best PSO algorithm [2]. The goal of the inertia weight parameter is to balance the exploration and exploitation characteristics of PSO. Generally, large inertia weight values are expected to increase the velocity of the particles and improve the long-range exploration of the PSO algorithm, while low inertia values increase the short-range exploration. Due to the strong effect of the inertia weight on the performance of PSO, many researchers have investigated different inertia weight control approaches during the past decades, and many different strategies have been proposed. Various inertia weighting strategies can be categorized into three main classes (Figure 7.1): (1) constant or random, (2) time-varying, and (3) adaptive inertia weights. The first class contains strategies in which the value of the inertia weight is constant during the search or is determined randomly. In the second class, the inertia weight is defined as a function of time (iteration number), and hence these strategies are referred to as time-varying inertia weight strategies. These methods are not considered adaptive since they do not monitor the situation of the particles in the search space, and the value of the inertia weight in each iteration is known before the execution of the algorithm. The third class of the inertia weight strategies consists of those methods which use a feedback parameter to monitor the state of the algorithm and adjust the value of the inertia weight based on the feedback parameter's value. This chapter presents the major existing inertia weight control strategies in the above three categories and discusses examples of each category in detail. The remainder of this chapter is organized as follows. The next section gives a short review of the PSO algorithm, and the role ofthe inertia weight parameter in the velocity update equation. Sections 7.2-7.4 review the three groups of inertia weight strategies, constant or random, time-varying, and adaptive models. Section 7.5 reports some experimental evaluations of different inertia weight models. Finally, Section 7.6 concludes this chapter. A short description of the symbols frequently used in this chapter is shown in Table 7.1.