A hybrid algorithm to minimize makespan for the permutation flow shop scheduling problem

This paper deals with the permutation flow shop scheduling problem. The objective is to minimize the maximum completion time, or makespan. To solve this problem which has been proved to be strongly NP-hard, a combination between an ant colony algorithm, a heuristic algorithm and a local search procedure is proposed and presented. The hybrid approach is to use artificial ants to construct solutions by applying a stochastic greedy rule based on the Gupta’s heuristic and pheromone trails. A local search is then performed to improve the performance quality of constructed solutions. Once all ants have terminated their generations, the pheromone trails are modified according to a global updating rule. The proposed algorithm is applied to benchmark problems taken from the literature and compared with other metaheuristics. Computational experiments are given to demonstrate the superiority of the algorithm in the quality of solution and CPU time.