Bi-objective grey wolf optimization algorithm combined Levy flight mechanism for the FMC green scheduling problem

As more and more enterprises have laid great emphasis on eco-friendly manufacturing processes while enhancing agility, this paper focuses on the green scheduling problem of the Flexible Manufacturing Cell with material handling robots (FMC-R). In the FMC, each job is characterized by several operations, processing machines, and machining time. Robots at one straight track transfer jobs to the related machines. Distinguished from most of the FMC scheduling problems, this paper considers not only the operation sequencing of jobs but also the robots’ transportation processes. A bi-objective mathematical model is established aiming to minimize the total makespan and the total energy consumption of the FMC system simultaneously. Due to the NP-hard nature of the problem, a Levy Flight and Weighted Distance-updated Multi-objective Grey Wolf Algorithm (LWMOGWO) is proposed. It combines the Levy flight with Multi-objective Grey Wolf Algorithm (MOGWO). A weighted distance updating mechanism is integrated to calculate the positions of individuals. A local neighbourhood search strategy is adopted, which makes it possible to take full advantage of the three leading wolves in population. The performance of the LWMOGWO algorithm is evaluated through groups of experiments by comparing with multiple hybrid meta-heuristic algorithms, hybrid particle swarm optimization (NGPSO) algorithm, an improved grey wolf optimization (IGWO) algorithm, MOGWO, NSGA-II (Non-dominated sorting genetic algorithm), and PLMEAPS. Results reveal the proposed LWMOGWO algorithm has a higher quality of solutions in solving the scheduling of the FMC-R problem. •Studied a flexible manufacturing cell problem with robot transportation (FMC-R).•Provided a double-layer encoding to optimize the jobs and robots sequencing.•Proposed a LWMOGWO algorithm by incorporating the levy flight.•Presented a local neighborhood search strategy to enhance the searching ability.