Particle Swarm Optimization - A Survey <s> Locality in Search Space <s> In recent years population based methods such as genetic algorithms, evolutionary programming, evolution strategies and genetic programming have been increasingly employed to solve a variety of optimisation problems. Recently, another novel population based optimisation algorithm - namely the particle swarm optimisation (PSO) algorithm, was introduced by R. Eberhart and J. Kennedy (1995). Although the PSO algorithm possesses some attractive properties, its solution quality has been somewhat inferior to other evolutionary optimisation algorithms (P. Angeline, 1998). We propose a number of techniques to improve the standard PSO algorithm. Similar techniques have been employed in the context of self organising maps and neural-gas networks (T. Kohonen, 1990; T.M. Martinez et al., 1994). <s> BIB001 </s> Particle Swarm Optimization - A Survey <s> Locality in Search Space <s> In this paper we present a new definition of neighborhood for particle swarm optimization (PSO) methods called area of influence. Area of influence (AOI) derives from the observation that in nature the effective exchange of information between individuals of a society deteriorates as their physical distance increases. In PSO with AOI, the loss of information exchange, ability with distance is simulated by making the exchange of information a function of the physical distance between particles in hyperspace. In this paper, we compare the AOI method to the standard PSO neighborhood methods, global best, local best, and von Neumann. We also introduce a local search method using reinitialization of velocity components based on the current search range. We show that AOI along with local search and a time-varying constriction coefficient provides strong benefits to several PSO algorithms. Results are presented using the standard benchmark functions from the PSO literature. <s> BIB002
In contrast to these static neighborhoods based on predefined index topology, Suganthan BIB001 proposed to dynamically redefine them using the immediate particle positions in the search space D while running the PSO. The neighborhood S i of particle c i was redefined as a set of particles inside a hypersphere in D centered at x i . In addition, the radius of the hypersphere will gradually grow, eventually becoming a gbest-type PSO. Experimental results show that this method found better solutions in average, when it was compared with the conventional gbest-type PSO. Binkley and Hagiwara BIB002 also used locality in the search space by augmenting the gbest factor in Eq. (17) with a function of immediate particle distances. They also found improvements over the methods with index-based neighborhoods on some benchmark functions.