Towards Analyzing Recombination Operators in Evolutionary Search

Recombination (also called crossover) operators are widely used in EAs to generate offspring solutions. Although the usefulness of recombination has been well recognized, theoretical analysis on recombination operators remains a hard problem due to the irregularity of the operators and their complicated interactions to mutation operators. In this paper, as a step towards analyzing recombination operators theoretically, we present a general approach which allows to compare the runtime of an EA turning the recombination on and off, and thus helps to understand when a recombination operator works. The key of our approach is the Markov Chain Switching Theorem which compares two Markov chains for the first hit of the target. As an illustration, we analyze some recombination operators in evolutionary search on the LeadingOnes problem using the proposed approach. The analysis identifies some insight on the choice of recombination operators, which is then verified in experiments.