Optimal population size under constant computation cost

Abstract

Optimal setting of genetic algorithm parameters has been the subject of numerous studies; however, the optimality of a population size is still a controversial subject. This work addresses the issue of optimal population size under the constraint of a constant computation cost. Given a problem P to be solved, a GA (genetic algorithm) as a problem solver, and a computation cost C to spend, how should we schedule the problem solving? Under the constant C, there is a trade-off between a population size s. and the number r of GA runs. Focusing on this trade-off, the present paper claims there exists the optimal s _opt for the given P and GA under the constant C; here, the optimality means maximum of the expected probability of obtaining acceptable solutions. To explain how the optimality comes about we propose the statistical model of GA runs, prove the existence of s _opt and get more insight in a specific case. Then experiments were performed using a difficult job shop scheduling problem. The experiments showed the plausibility of the proposed model.