Some Comments on Evolutionary Algorithm Theory

The development of a sound theory that predicts and veriies existing evolutionary algorithms is one of the most important research issues in the eld today. In mathematical proofs, the assumption of spherical symmetry is probably one of the most widely-used simpliications. This paper discusses to which extend spherical symmetry is appropriate for certain evolutionary algorithms. It turns out that spherical symmetry leads to simpliications in (self-adaptive) evolutionary algorithms, but that spherical symmetry seems inappropriate for certain genetic algorithm variants, since small mutation rates bias a search algorithm toward the coordinate axes. This paper also argues that current test suites are weak in that they do not provide problems with signiicant epistasis, which describes the interaction between diierent parameters. Consequently, when using empirical test for pushing existing theory beyond its limits, benchmark functions should include more epistatic interaction or at least should use coordinate rotations.