Cuckoo search algorithm based on three random walks

Random walk plays an important role in heuristic algorithm. The traditional Cuckoo Search used only Lévy random stemmed from Lévy distribution. This paper extends two symmetric random walk methods, named Gauss random and Cauchy random, which are consistent with α-stable distribution and can be applied to the Cuckoo Search. The characteristics of three random methods are compared and analyzed, and the Cauchy random is revised. Based on the infrastructure framework of the Cuckoo Search algorithm, two new Cuckoo Search modes using new random walk methods are constructed. By comparing with the original Cuckoo Search in solving benchmark functions optimization and pressure vessel design problem, the conclusions can be drawn that Cauchy random has a great advantage for low dimensional problems and Gauss random is quite competitive for multidimensional unimodal problems, while Lévy random is suitable for multidimensional and multimodal problems. And it has certainly guiding significance for the optimization design of algorithm and some optimization problems.