A metaheuristic algorithmic framework for solving the hybrid flow shop scheduling problem with unrelated parallel machines

The hybrid flow shop scheduling problem (HFSP), as a realistic extension of the classical flow shop scheduling problem, widely exists in real-world industrial production systems. In practice, the fact that machines are unrelated is important and cannot be neglected. This study focuses on the HFSP with unrelated parallel machines (HFSP-UPM) to minimize the makespan. To address this problem, a hybrid representation that combines single-sequence coding and full-sequence coding is developed to search for solution space that is not covered by common encoding methods. An initialization block integrating random heuristic strategies is proposed for improving the quality of the initial sparrow swarm. To improve the diversity of a sparrow swarm further, a perturbation block embedded with a set of historical best positions and an enhancement strategy are developed. A critical set based local search block is designed for high-intensity local exploitation of promising regions when necessary. Several benchmark cases from the literature as well as some randomly generated instances characterized by the distribution of real data from factory studies are employed to participate in the test. The test results reveal the effectiveness of the proposed perturbation block and local search block. Compared to state-of-the-art metaheuristic algorithms, the enhanced sparrow search algorithm (ESSA) demonstrates higher convergence accuracy when handling instances. The value of the gap between a solution found by the ESSA and a feasible solution found by the mixed-integer programming (MIP) model can reach 0.6%.