An Analysis of Two-Parent Recombinations for Real-Valued Chromosomes in an Infinite Population

This paper concerns recombinations which produce offspring from two parents. We assume an infinite population and regard recombinations as transformations of stochastic variables represented as chromosomes. We then formalize recombinations with the probability density functions of stochastic variables represented as the parameters and describe the change of the probability density functions of chromosomes before and after recombination. Our formalization includes various proposed recombinations, such as multi-point, uniform, and linear crossover, as well as BLX-alpha. We also derive certain properties of the operators, such as diversification and decorrelation.