Ignoble Trails - Where Crossover Is Provably Harmful
نویسندگان
چکیده
Beginning with the early days of the genetic algorithm and the schema theorem it has often been argued that the crossover operator is the more important genetic operator. The early Royal Road functions were put forth as an example where crossover would excel, yet mutation based EAs were subsequently shown to experimentally outperform GAs with crossover on these functions. Recently several new Royal Roads have been introduced and proved to require expected polynomial time for GAs with crossover, while needing exponential time to optimize for mutation-only EAs. This paper does the converse, showing proofs that GAs with crossover require exponential optimization time on new Ignoble Trail functions while mutation based EAs optimize them efficiently.
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Mutation and crossover are the main search operators of different variants of evolutionary algorithms. Despite the many discussions on the importance of crossover nobody has proved rigorously for some explicitly defined fitness functions fn : {0, 1} n → R that a genetic algorithm with crossover (but without idealization) can optimize fn in expected polynomial time while all evolution strategies...
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