Local Search Procedures in a Multi-Objective Genetic Local Search Algorithm for Scheduling Problems

We have already proposed a multi-objective genetic local search algorithm for finding nondominated solutions of multi-objective optimization problems (Ishibuchi & Murata 1998). In our hybrid algorithm, a local search procedure is applied to each solution generated by genetic operations (i.e., selection, crossover, and mutation). Since our optimization problem involves multiple objectives, the application of the local search is not straightforward. In this paper, we examine various methods for implementing local search procedures in our multi-objective genetic local search algorithm. One method uses a weighted sum of multiple objectives as a scalar fitness function where weight values are randomly updated whenever a pair of parent solutions is selected. Such a fitness function is used in the local search as well as the selection of parent solutions. In a variant of this method, weight values for a solution in the local search are specified according to its location in the objective space. Another method uses an inequality relation between solutions based on multiple objectives when a local search procedure determines whether the current solution is to be replaced with a new solution. The performance of multi-objective genetic local search algorithms with various local search procedures is examined by computer simulations on two-objective flowshop scheduling problems.