Genetic algorithms and permutation problems: a comparison of recombination operators for neural net structure specification

The specification of neural net architectures by genetic algorithm (GA) is thought to be hampered by difficulties with crossover. This is the `permutation´ or `competing conventions´ problem: similar nets may have the hidden units defined in different orders so that they have very dissimilar genetic strings, preventing successful recombination of building blocks. Previous empirical tests of a number of recombination operators using a simulated net-building task indicated the superiority of one that sorts hidden unit definitions by overlap prior to crossover. However, simple crossover also fared well, suggesting that the permutation problem is not serious in practice. This is supported by an observed reduction in performance when the permutation problem is removed. The GA is shown to be able to resolve the permutations, so that the advantages of an increase in the number of maxima outweigh the difficulties of recombination