Quantum-behaved particle swarm optimization algorithm with Lévy mutated global best position

Abstract

This paper proposes a novel quantum-behaved particle swarm optimization (QPSO) algorithm with the global best (gbset) position subjected to Levy probability distribution. Firstly, a Gaussian mutation with the mean being the gbest position and the standard deviation being half of the distance between the mean best (mbest) position and gbest position is executed on gbest position, hence, a GGQPSO algorithm is formed. On the basis of it, by selecting a fast and accurate Levy random numbers numerical simulation algorithm and defining the ”effective standard deviation”, the only 2 parameters of Levy distribution can be determined according to empirical equations and trials respectively. Therefore, LGQPSO is taken shape. The distributions of gbest positions in LGQPSO, GGQPSO and QPSO are compared with each other. For the purpose of verifying the effectiveness of LGQPSO, QPSO algorithm with Cauchy mutated gbest position is introduced. The above four algorithms are tested on 5 test functions. It is shown by the experiment results that LGQPSO is an approach that could considerably improve performances of QPSO. LGQPSO is more likely to escape from local optimum and obtain steadier solutions in most cases.