Incorporating Lévy Flight to Distribution-Based Discrete Particle Swarm Optimization

Abstract

Particle swarm optimization (PSO) has been extended and shown to perform well on discrete optimization. Some of the extended PSOs handle continuous parameters of probability distributions over variable values of candidate solutions instead of directly handling discrete variables. These distribution-based discrete PSOs (DDPSOs) sample a variable value from a probability distribution for each variable to generate a candidate solution. This procedure can be considered as a kind of random local search centering on an intended solution, which has the highest generation probability. It has drawbacks the step size increases proportionally and the probability of producing solutions close to the intended solution decreases exponentially in high-dimensional problems. This paper proposes a novel sampling method (NS) to control the step size for DDPSO and determined the step sizes according to Lévy distribution in a similar way to Lévy flight. NS is applied to three representative DDPSOs, and they were compared in integer and categorical versions of function optimization problems and NK landscape problems. The results show NS improves the efficiency and robustness of all the DDPSO variants. In addition, NS was tested on feature selection experiments and was achieved superior results compared to some evolutionary algorithms designed for feature selection.