Linkage equilibrium and genetic algorithms

The mathematical analysis of recombination/crossover in population genetics and genetic algorithms is very difficult. We investigate a result from H. Geiringer (1944), which states that by repeated applications of the recombination operator alone (with no selective pressure) the gene frequencies of diploid organisms converge to linkage equilibrium. The result is valid for any recombination/crossover scheme. It gives strong support to the conjecture that recombination is not able to explore nonlinear gene interactions. This fact explains the difficulties genetic algorithms have with optimization of fitness functions with nonlinear gene interactions.