A Computational Intelligence Approach for the Energy-Efficient Hybrid Flow Shop Scheduling Problem with Deteriorating Maintenance and Transportation Times

This paper investigates the energy-efficient hybrid flow shop scheduling problem considering deteriorating maintenance and transportation times (EHFSP-DMT), which is an NP-hard combinatorial optimization problem in complex manufacturing systems. To formulate this problem, a mixed-integer programming mathematical model is established. A computational intelligence approach, named the adaptive feedback multi-start variable neighborhood search (AFMS-VNS) algorithm, is proposed to simultaneously minimize the makespan and total energy consumption. In AFMS-VNS, a decoding strategy integrating conflict detection is designed to satisfy the mathematical constraints of equipment maintenance. A reinforcement learning (Q-learning) mechanism evaluates and adaptively selects search operators to enhance search efficiency. A search strategy based on the feedback of population distribution status is proposed to balance the optimization directions between the two conflicting objectives. An iterated greedy reconstruction strategy, guided by an elite external archive, is adopted to replace stagnant individuals. Experiments on 44 instances and Wilcoxon signed-rank tests show that AFMS-VNS outperforms five comparison algorithms in terms of inverted generational distance, hypervolume, and set coverage when solving the EHFSP-DMT.