A Simple Proof for the Usefulness of Crossover in Black-Box Optimization

The idea to recombine two or more search points into a new solution is one of the main design principles of evolutionary computation (EC). Its usefulness in the combinatorial optimization context, however, is subject to a highly controversial discussion between EC practitioners and the broader Computer Science research community. While the former, naturally, report significant speedups procured by crossover, the belief that sexual reproduction cannot advance the search for high-quality solutions seems common, for example, amongst theoretical computer scientists. Examples that help understand the role of crossover in combinatorial optimization are needed to promote an intensified discussion on this subject.

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