Fitness distributions in evolutionary computation: motivation and examples in the continuous domain

Evolutionary algorithms are, fundamentally, stochastic search procedures. Each next population is a probabilistic function of the current population. Various controls are available to adjust the probability mass function that is used to sample the space of candidate solutions at each generation. For example, the step size of a single-parent variation operator can be adjusted with a corresponding effect on the probability of finding improved solutions and the expected improvement that will be obtained. Examining these statistics as a function of the step size leads to a 'fitness distribution', a function that trades off the expected improvement at each iteration for the probability of that improvement. This paper analyzes the effects of adjusting the step size of Gaussian and Cauchy mutations, as well as a mutation that is a convolution of these two distributions. The results indicate that fitness distributions can be effective in identifying suitable parameter settings for these operators. Some comments on the utility of extending this protocol toward the general diagnosis of evolutionary algorithms is also offered.