A dynamic search method for jobshop scheduling using Lagrange relaxation method and genetic algorithms

This paper deals with an approximate solution method by decomposing a search space dynamically combined with genetic algorithm (GA) and Lagrangian relaxation (LR) method for solving a job-shop scheduling problem. In this method a subspace of a search space is constructed by using information on partial processing order relations between operations which use same resources. We search these subspaces by using GA. We evaluate each subspace with lower bound obtained by using LR method and with minimum value of the set-up cost obtained by the structure of subspace. We reduce the size of solution space gradually, and search a feasible solution in the subspace finally obtained. Some numerical experiments are included to evaluate the proposed method.