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IV COMPUTATIONAL SWARM INTELLIGENCE
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Slime moulds consist of very simple cellular organisms with limited abilities However, in times of food shortage they aggregate to form a mobile slug with the ability to transport the assembled individuals to new feeding areas The objective of computational swarm intelligence models is to model the simple behaviors of individuals, and the local interactions with the environment and neighboring individuals, in order to obtain more complex behaviors that can be used to solve complex problems, mostly optimization problems For example, particle swarm optimization (PSO) models two simple behaviors: each individual (1) moves toward its closest best neighbor, and (2) moves back to the state that the individual has experienced to be best for itself As a result, the collective behavior that emerges is that of all individuals converging on the environment state that is best for all individuals On the other hand, ant colony optimization models the very simple pheromone trailfollowing behavior of ants, where each ant perceives pheromone concentrations in its local environment and acts by probabilistically selecting the direction with the highest pheromone concentration From this emerges the behavior of nding the best alternative (shortest path) from a collection of alternatives Models of the local behavior of ants attending to cemeteries result in the complex behavior of grouping similar objects into clusters This part is devoted to the two computational swarm intelligence paradigms, particle swarm optimization (PSO), presented in 16, and ant algorithms (AA), presented in 17 The former was inspired from models of the ocking behavior of birds, while the latter was inspired from a number of models of di erent behaviors observed in ant and termite colonies
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16
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Particle Swarm Optimization
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The particle swarm optimization (PSO) algorithm is a population-based search algorithm based on the simulation of the social behavior of birds within a ock The initial intent of the particle swarm concept was to graphically simulate the graceful and unpredictable choreography of a bird ock [449], with the aim of discovering patterns that govern the ability of birds to y synchronously, and to suddenly change direction with a regrouping in an optimal formation From this initial objective, the concept evolved into a simple and e cient optimization algorithm In PSO, individuals, referred to as particles, are own through hyperdimensional search space Changes to the position of particles within the search space are based on the social-psychological tendency of individuals to emulate the success of other individuals The changes to a particle within the swarm are therefore in uenced by the experience, or knowledge, of its neighbors The search behavior of a particle is thus a ected by that of other particles within the swarm (PSO is therefore a kind of symbiotic cooperative algorithm) The consequence of modeling this social behavior is that the search process is such that particles stochastically return toward previously successful regions in the search space The remainder of this chapter is organized as follows: An overview of the basic PSO, ie the rst implementations of PSO, is given in Section 161 The very important concepts of social interaction and social networks are discussed in Section 162 Basic variations of the PSO are described in Section 163, while more elaborate improvements are given in Section 165 A discussion of PSO parameters is given in Section 164 Some advanced topics are discussed in Section 166
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Basic Particle Swarm Optimization
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Individuals in a particle swarm follow a very simple behavior: to emulate the success of neighboring individuals and their own successes The collective behavior that emerges from this simple behavior is that of discovering optimal regions of a high dimensional search space A PSO algorithm maintains a swarm of particles, where each particle represents a potential solution In analogy with evolutionary computation paradigms, a swarm is
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Computational Intelligence: An Introduction, Second Edition AP Engelbrecht c 2007 John Wiley & Sons, Ltd
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