Integrated Working-Age Maintenance to the Unrelated Parallel Machine Scheduling with Sequence-Dependent Setup Times

This paper focus on unrelated parallel machine scheduling problem with sequence-dependent setup times and working-age preventive maintenance (PM-UPMST). Taking the working-age of machines as the decision variable, a joint mathematical model is proposed aiming to minimize the makespan and total tardiness time simultaneously, and then, a Pareto-based hybrid discrete particle swarm optimization algorithm (PHDPSO) is presented. To address this NP-Hardness problem, a heuristic initialization scheme is introduced to ensure the quality and diversity of the generated initial population. Taking into account the discrete nature of this problem, three discrete update mechanisms are developed to identify optimal solutions, and a problem-specific variable neighborhood descending search mechanism is excogitated to enhance the exploitation capability. Besides, a refined particle dominated measure is proposed to guarantee the diversity of Pareto solutions during the evolutionary process. Extensive numerical experiments conducted on various scales continually confirm the robustness and effectiveness of the proposed PHDPSO algorithm in comparison with other well-known algorithms.