Lévy flight search patterns in particle swarm optimization

There has been a growing interest in studying of random search strategies. In many industries including manufacturing, logistics, computer etc., researchers use evolutionary algorithms to solve sophisticated optimization problems which have stationary or shifty optimal values. These problems could hardly be solved with precise mathematical methods, called non-deterministic Polynomial-time hard (NP-hard) problems. Particle swarm optimization (PSO) is one of those algorithm and attracts extra attention. In this paper, we put forward a new model to explore the step length of search process of PSO, via statistics methods. Typical two-dimensional and multi-dimensional benchmark functions are used to generate empirical data for further analysis. Levy flight search patterns finally proved to play an important role in the searching process. Then the relationship between the values of scaling parameters in power law distributions and the efficiency of PSO is discussed. More interesting results are given in discussion.