Improving Distribution-Based Discrete Particle Swarm Optimization Using Lévy Flight

Abstract

Some metaheuristic algorithms such as particle swarm optimization (PSO) are extended and have been shown to perform very well in a wide range of optimization domains though they are originally designed for continuous optimization. In discrete optimization, some extended algorithms handle continuous parameters of a probability distribution, which assumes variable values of a candidate solution instead of directly handling discrete variables. These distribution-based discrete PSOs (DDPSO) sample a variable value from a distribution for every variable to generate a candidate solution. This procedure can be considered as a kind of local search centered on an intended solution, which has the highest probability to be generated. Step length from the intended solution increases proportionally and the probability of producing an intended solution decreases exponentially in high-dimensional problems. We propose a novel sampling method to control the step size for DDPSO. In this paper, we describe our new sampling method to control the step size with Lévy distribution in a similar way to Lévy flight. The proposed method is applied to three representative methods of DDPSOs and performance is compared with original algorithms. In our discrete optimization experiments, we demonstrate that our algorithm increases DDPSO’s search performance and robustness to dimensionality.