Particle Swarm Optimization - A Survey <s> Mutation <s> In this paper we present particle swarm optimization with Gaussian mutation combining the idea of the particle swarm with concepts from evolutionary algorithms. This method combines the traditional velocity and position update rules with the ideas of Gaussian mutation. This model is tested and compared with the standard PSO and standard GA. The comparative experiments have been conducted on unimodal functions and multimodal functions. PSO with Gaussian mutation is able to obtain a result superior to GA. We also apply the PSO with Gaussian mutation to a gene network. Consequently, it has succeeded in acquiring better results than those by GA and PSO alone. <s> BIB001 </s> Particle Swarm Optimization - A Survey <s> Mutation <s> The particle swarm optimization algorithms converges rapidly during the initial stages of a search, but often slows considerably and can get trapped in local optima. This paper examines the use of mutation to both speed up convergence and escape local minima. It compares the effectiveness of the basic particle swarm optimization scheme (BPSO) with each of BPSO with mutation, constriction particle swarm optimization (CPSO) with mutation, and CPSO without mutation. The four test functions used were the Sphere, Ackley, Rastrigin and Rosenbrock functions of dimensions 10, 20 and 30. The results show that mutation hinders the motion of the swarm on the sphere but the combination of CPSO with mutation provides a significant improvement in performance for the Rastrigin and Rosenbrock functions for all dimensions and the Ackley function for dimensions 20 and 30, with no improvement for the 10 dimensional case. <s> BIB002 </s> Particle Swarm Optimization - A Survey <s> Mutation <s> Behavior and search performance of the proposed cautious particle swarm, in which the particles are cautious about imitating the best successful one, are investigated with a question: ldquoIs it really the best strategy for a group that every individual in which obediently imitates the top one?rdquo Their neutral or disobedient attitudes to the global best are expressed by replacing the conventional uniform distribution for random numbers with either of the two probability distributions: slided uniform distribution and asymmetrical normal distribution. Empirical analyses on the behavior of such a single particle in one-dimensional search space have aroused an expectation that appropriate cautiousness balance may accomplish both exploration-oriented search for avoiding local minima and exploitation-oriented search for finding the global optimum near the global best. For discussion on the optimization performance of the cautious particle swarm, experiments in typical test functions were performed. The experimental results have presented an acceptable parameter range of obedience for appropriate cautiousness. <s> BIB003
Mutation operations common in real-valued genetic algorithms (GA) have been introduced to PSO as well. Injection of randomness in the positional updates of particles have been done using Gaussian mutation (Higashi and Iba BIB001 ) and Cauchy mutation (Stacy et al. BIB002 ). Improvements for both benchmark objective functions and real-world problems have been reported. Someya BIB003 reports that the search tendencies (exploratory vs. exploiting) could be controlled by modifying an asymmetric normal distribution for the density of randomness for the diagonal elements of R in the last term of Eq. (2).