Energy-efficient distributed permutation flow shop scheduling problem using a multi-objective whale swarm algorithm

Production scheduling is of great significance in improving production effectiveness while the energy-efficient problem is one of most concerned problems for researchers and manufacturers. Thus, this study investigates the energy-efficient distributed permutation flow shop scheduling problem (DPFSP) with the objectives of makespan and energy consumption. The DPFSP is an extension of permutation flow shop problem (PFSP) considering a set of identical factories. This paper presents a multi-objective mixed integer programming model based on the three sub-problems: allocating jobs among factories, scheduling the jobs in each factory and determining speed upon each job. A multi-objective whale swarm algorithm (MOWSA) is proposed to solve this energy-efficient DPFSP. A new problem-dependent local search is developed to improve the exploitation capability of MOWSA. Moreover, the updating exploitation mechanism is presented to enhance energy efficiency without affecting production efficiency. Finally, the extensive comparison experiments are designed to demonstrate the effectiveness of proposed MOWSA, problem-dependent local search and updating exploitation mechanism. The results indicate the effectiveness of MOWSA and the superior performance over NSGA-II, SPEA2, PAES and MDEA, and also demonstrate that the proposed algorithm can significantly reduce the energy consumption compared with other algorithms.