Hybridization with local search (LS) is known to enhance the performance of genetic algorithms (GA) in single objective optimization and have also been studied in the multiobjective combinatorial optimization literature. In most such studies, 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, let alone the reasoning for it. The situation in the multiobjective function optimization literature is even more unclear since the number of such studies in the field has been small.This paper, assuming that objective functions are differentiable, reveals the reasons why GA is not suitable for obtaining solutions of high precision, thereby justifying hybridization of GA and LS. It also suggests that the hybridization scheme which maximally exploits both GA and LS is GA then LS. Experiments conducted on many benchmark problems verified our claims.