Optimization with genetic algorithms in multispecies environments

We discuss a converging ´scaled coevolutionary genetic algorithm´ (scGA) in a setting where populations contain fixed numbers of interacting creatures of several types. The interaction defines a population-dependent fitness function. The scGA employs multiple-spot mutation, various crossover operators and power-law scaled proportional fitness selection. In particular, the Vose-Liepins version of mutation-crossover is included. To achieve convergence, the mutation and crossover rates have to be annealed to zero in proper fashion, and power-law scaling is used with logarithmic growth in the exponent. If creatures of specific types exist that have maximal fitness in every population they reside in, then the scGA described here converges asymptotically to a probability distribution over multiuniform populations containing only such maximal creatures wherever they exist.