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

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 (NDM) 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 (NPUM), 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 NDM and NPUM but also demonstrated that the proposed MOGWO is more effective than well-known multi-objective evolutionary algorithms such as NSGA-II and SPEA-II.