An exact schema theorem for adaptive genetic algorithm and its application to machine cell formation

This paper proposes an exact schema theorem that is able to predict the expected number of copies of schemas in the next GA generation. It focuses on two-point crossover, which is widely used in many GA applications. As two important GA control parameters, crossover probability (pc) and mutation probability (pm) affect the performance of GAs drastically. A set of good GA parameters help in improving the ability of a GA to search for near global optimal solutions. This work shows that optimal pc and pm do not exist in most cases. As a result, a compromised pair of pc and pm may help improve the performance of GA. A multiple population search strategy enabled fuzzy c-means based evolutionary approach, which embeds the proposed exact schema theorem, to machine cell formation is then proposed. The approach enables the crossover and mutation probabilities of GAs to be made adaptive to suit different stages of the search for near optimal solutions. Three case studies were conducted. The proposed approach was able to provide better solutions consistently.

Research highlights
► Exact schema theorem to predict exact number of copies of schemas.
► Analysis of crossover and mutation probabilities using the proposed exact schema theorem.
► GA and tabu search for fuzzy c-means.