Hybridization of Genetic Algorithm with Local Search in Multiobjective Function Optimization: Recommendation of GA then LS

Abstract

It is well known that local search (LS) improves the performance of genetic algorithms (GA) in single objective optimization, and it has recently been reported that the hybridization of GA with LS is effective in multiobjective combinatorial optimization as well. In most studies of this kind, LS is applied to the solutions of each generation of GA, which is the scheme called ``GA with LS'' herein. Another scheme, in which LS is applied to the solutions obtained with GA, has also been studied, which is called ``GA then LS'' herein. It seems there is no consensus in the literature as to which scheme is better. The situation in the multibojective function optimization literature is even more unclear since the number of such studies in the field has been small. However, some argue that LS contributes marginally to improving the performance of GA in multiobjective function optimization. This paper, assuming that objective functions are differentiable, reveals the reasons why GA is not necessarily effective in finding solutions of high precision, and hence hybridizing it with LS is indeed effective in multiobjective function optimization. It also suggests that the hybridization scheme which maximally exploits both GA and LS is GA then LS. Experiments confirmed that GA is not suitable for obtaining solutions of high precision, and GA then LS performs better than GA and GA with LS on many benchmark problems.