Energy-efficient Flexible Job Shop Scheduling Problem Considering Preventive Maintenance and Transportation Times

The flexible job shop scheduling problem (FJSP) has been extensively researched over the past decade. However, the integration of preventive maintenance (PM), transportation times, and energy efficiency remains under-explored. This paper addresses the energy-efficient flexible job shop scheduling problem with preventive maintenance and transportation times (EFJSP-PMT). To minimize both makespan and total energy consumption, a multi-population optimization algorithm with adaptive strategy and competition (MPOA-ASC) is proposed, featuring distinct early and later evolution phases. In the early evolution phase, we develop a hybrid heuristic initialization method, a new population division strategy, an adaptive mechanism for crossover and mutation probabilities, and three specialized local search operators. In the later phase, a novel inter-population competition mechanism is introduced to optimize the allocation of computational resources and enhance convergence performance. Extensive experimental results demonstrate that the proposed MPOA-ASC significantly outperforms state-of-the-art algorithms in solving the EFJSP-PMT.