Hybrid simulated annealing–slime mould algorithm for the non-permutation flow-shop scheduling problem

The non-permutation flow-shop scheduling problem (NPFSP) is a more general type of flow-shop scheduling problem than the permutation flow-shop scheduling problem (PFSP). It features a large solution space and is highly complex. In this study, a novel metaheuristic algorithm is proposed for the NPFSP, where makespan is the scheduling objective. The specific implementation process is as follows. First, a mathematical model of the NPFSP is constructed. Secondly, the encoding and decoding rules are designed to establish the association between the solutions for PFSP and NPFSP. Subsequently, a metaheuristic hybrid simulated annealing–slime mould algorithm is proposed. Finally, a series of control experiments is conducted based on the Demirkol benchmark. The statistical results show the effectiveness of the proposed algorithm in solving the NPFSP.