Case Studies in Applying Fitness Distributions in Evolutionary Algorithms. II. Comparing the Improvements from Crossover and Gaussian Mutation on Simple Neural Networks

Previous efforts in applying fitness distributions of Gaussian mutation for optimizing simple neural networks in the XOR problem are extended by conducting a similar analysis for three types of crossover operators. Onepoint, two-point, and uniform crossover are applied to the best-evolved neural networks at each generation in an evolutionary trial. The maximum expected improvement under Gaussian mutation with a single fixed standard deviation is then compared to that which can be obtained using crossover. The results indicate that the benefits of each type of crossover varies as a function of the generation number. Furthermore, these fitness profiles are notably similar (i.e., there is little functional difference between the various crossover operators). This does not support a “building block hypothesis” for explaining the gains that can be made via recombination. The results indicate cases where mutation alone can outperform recombination and vice versa.