6 Conclusion and future work
In the current research, a no-wait flow-shop scheduling problem (NWFSP) for minimizing the makespan was discussed. This problem is known to be strongly NPhard. In this paper, ant colony algorithm with the simulated annealing as a local search method are proposed to solve this problem. Unlike most of other reported population-based algorithms in the literature, the proposed ACO–SA algorithm is simple and easy to implement and replicate. The evaluation of the proposed methods was carried out against the 8 best performing methods from the literature.
Statistical analyses and extensive experimental demonstrate the efficiency of the proposed ACO–SA algorithm owing to an average PRD of -4.85. In order to prove the efficiency of our algorithms, we use another method based on VNS for local search phase. The computational results are indicated that hybridization ACO with SA is viable and reliable method and really competitive and provides promising computational results. As the future work, other neighborhood’s structures can be applied in SA algorithm. In addition, the proposed algorithm can be used to solve the NWFSP with set-up times, maintenance of machines and transportation times. Furthermore, combining ACO with other local search-based algorithms such as Iterated local search or tabu search algorithm is possible research method.