How Much Forcing Is Necessary to Let the Results of Particle Swarms Converge?
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In order to improve the behavior of Particle Swarm Optimization (PSO), the classical method is often extended by additional operations. Here, we are interested in how much “PSO” remains in this case, and how often the extension takes over the computation. We study the variant of PSO that applies random velocities (then called forced moves) as soon as the so-called potential of the swarm falls below a certain bound. We show experimentally that the number of iterations the swarm actually deviates from the classical PSO behavior is small as long as the particles are sufficiently far away from any local optimum. As soon as the swarm comes close to a local optimum, the number of forced moves increases significantly and approaches a value that depends on the swarm size and the problem dimension, but not on the actual fitness function, an observation that can be used as a stopping criterion. Additionally, we provide an explanation for the observed phenomenon in terms of the swarm’s potential.
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