A bi-population cooperative scatter search algorithm for distributed hybrid flow shop scheduling with machine breakdown

The occurrence of machine breakdowns is a frequent and dynamic phenomenon in the production process. The implementation of effective preventive measures can mitigate such events and result in reduced production costs. This paper investigates the distributed hybrid flow shop scheduling problem with machine breakdown (DHFSSPB) considering short maintenance time. The bi-population cooperative scatter search (BCSS) algorithm is proposed to address the DHFSSPB, wherein the search for the optimal scheduling sequence is transformed into genetic evolution aiming to obtain a gene chain with both minimum lower bound and minimum cost attributes. Firstly, the DHFSSPB problem is modeled through a combination of predictive maintenance strategy and rightshift rescheduling rule. Subsequently, a diversification approach is developed to facilitate attribute inheritance, enhance the efficiency of job allocation, and establish a reference set. The reference set is partitioned into two subpopulations based on lower bound attributes and cost attributes, respectively. The corresponding hybrid search strategies are designed to enhance the efficiency of job sorting and machine selection for subpopulations with distinct attributes. The cooperative evolution between subpopulations occurs through the competitive interaction and fusion of individuals. An enhanced reinforcement learning approach is proposed to expedite the acceleration of individual attribute evolution by leveraging evolutionary knowledge acquired from populations, thereby effectively guiding the evolutionary trajectories of individuals. Additionally, a method for evaluating the population during the learning process is developed based on problem characteristics to enhance learning efficiency. Experimental results demonstrate that BCSS outperforms the comparative algorithm in solving the DHFSSPB.