Notes on the Distinction of Gaussian and Cauchy Mutations

In evolutionary computation, Gaussian and Cauchy mutations are two popular mutation techniques and completely discussed in this study. It is known that Cauchy mutation has the better ability of escaping local optima, and Gaussian mutation is excellent in local convergence. However, there still exist some vague characteristics in the abilities of local escape/convergence for these two mutations. Therefore, four closed-form equations of probability to clarify those vague behaviors of Gaussian and Cauchy mutations are derived in this paper, and successfully apply to explain the simulated results of benchmark functions. Finally, this paper verifies that Cauchy mutation can prevent the dilemma problem of choosing a proper mutation step size and achieve the acceptable performance except for some specific conditions for evolutionary computation.