Efficiency of crossover in genetic algorithms

Question

I\'ve implemented a number of genetic algorithms to solve a variety of a problems. However I\'m still skeptical of the usefulness of crossover/recombination.

I usually f

Answer 1

John Holland's two seminal works "Adaptation in Natural and Artificial Systems" and "Hidden Order" (less formal) discuss the theory of crossover in depth. IMO, Goldberg's "Genetic Algorithms in Search, Optimization, and Machine Learning" has a very approachable chapter on mathematical foundations which includes such conclusions as:

With both crossover and reproduction....those schemata with both above-average performance and short defining lengths are going to be sampled at exponentially increasing rates.

Another good reference might be Ankenbrandt's "An Extension to the Theory of Convergence and a Proof of the Time Complexity of Genetic Algorithms" (in "Foundations of Genetic Algorithms" by Rawlins).

I'm surprised that the power of crossover has not been apparent to you in your work; when I began using genetic algorithms and saw how powerfully "directed" crossover seemed, I felt I gained an insight into evolution that overturned what I had been taught in school. All the questions about "how could mutation lead to this and that?" and "Well, over the course of so many generations..." came to seem fundamentally misguided.