Energy-efficient scheduling for multi-objective flexible job shops with variable processing speeds by grey wolf optimization

Abstract In recent years, confronted with serious global warming and rapid exhaustion of non-renewable resources, green manufacturing has become an increasingly important theme in the world. As a significant way to achieve the purpose of green manufacturing, the energy-efficient scheduling has been intensively studied by both academia and industry due to its ability to keep a compromise between production efficiency and environmental impacts. To this end, this study investigates the multi-objective flexible job shop scheduling problem (MOFJSP) with variable processing speeds aiming at minimizing the makespan and total energy consumption simultaneously. An elaborately-designed multi-objective grey wolf optimization (MOGWO) algorithm is proposed to address this issue. Specifically, a three-vector representation corresponding to three sub-problems including machine assignment, speed assignment and operation sequence is utilized for chromosome encoding. A new decoding method ( N D M ) is presented to obtain active schedules and reach a trade-off between two conflicting criteria. In consideration of the multi-objective problem nature, two Pareto-based mechanisms are developed to determine the leader wolves and the lowest (worst) wolves so that the hierarchy of a wolf pack can be constructed. Finally, to avoid premature convergence and maintain population diversity, a new position updating mechanism ( N P U M ), which integrates information from both the leader wolves and the lowest wolves based on a comprehensive point of view, is developed to guide the other wolves in the searching space. Extensive numerical experiments on 35 different scale benchmarks have not only verified the effectiveness of N D M and N P U M but also demonstrated that the proposed MOGWO is more effective than well-known multi-objective evolutionary algorithms such as NSGA-II and SPEA-II.