Scheduling a fuzzy flowshop problem to minimize weighted earliness-tardiness

The flowshop scheduling problem with fuzzy processing times is concerned in this paper. A triangular fuzzy number is used to represent the uncertainty processing times of jobs. The due windows have been assigned to all jobs. If a job is completed within its due window, then it incurs no scheduling cost. Otherwise, an earliness or tardiness cost is incurred. The objective is to find a job schedule such that the weighted sum of earliness and tardiness penalties of jobs is minimized. Schedules are generated by a proposed hybrid algorithm in the context of quantum evolutionary algorithm and particle swarm optimization approach. Three novel coding schemes are designed for transforming an individual into a sequence of jobs. Furthermore, a velocity disturbance strategy is also introduced into the proposed algorithm to improve the diversity of the swarm. The simulation results show that the proposed algorithm is able to obtain higher quality solutions stably and efficiently in the fuzzy flowshop scheduling problem.