Abstract
Abstract The distributed permutation flow shop scheduling problem with sequence dependent setup times (DPFSP_SDST) is a generalization of permutation flow shop scheduling problem with sequence dependent setup times (PFSP_SDST), where there exists a set of identical factories in a PFSP_SDST structure. It is concerned with first assignment of jobs to factories, and then scheduling jobs in each factory. In this paper, we try to find a trade-off between makespan and total energy consumption in a DPFSP_SDST environment, where machines are assumed to operate at varying speed levels. A multi-objective mixed integer linear programming model is presented based on (1) allocating jobs among factories, (2) determining velocity upon each machine, and (3) scheduling the jobs in each factory. Due to the NP-complete nature of the problem, a multi-objective whale swarm algorithm (MOWSA) is presented to solve this complex multi-objective DPFSP_SDST. We propose a problem specific encoding scheme, crossover and mutation operators as well as a very effective local search in MOWSA. The extensive experimental results show the effectiveness of MOWSA over NSGA-II, SPEA2 and PAES for approximating the Pareto front solution sets.
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