An MO‐GVNS algorithm for solving a multiobjective hybrid flow shop scheduling problem

Abstract This paper addresses the multiobjective hybrid flow shop (MOHFS) scheduling problem. In the MOHFS problem considered here, we have a set of jobs that must be performed in a set of stages. At each stage, we have a set of unrelated parallel machines. Some jobs may skip stages. The evaluation criteria are the minimizations of makespan, the weighted sum of the tardiness, and the weighted sum of the earliness. For solving it, an algorithm based on the multiobjective general variable neighborhood search (MO‐GVNS) metaheuristic, named adapted MO‐GVNS, is proposed. This work also presents and compares the results obtained by the adapted MO‐GVNS with those of four other algorithms: multiobjective reduced variable neighborhood search, nondominated sorting genetic algorithm II (NSGA‐II), and NSGA‐III, and another MO‐GVNS from the literature. The results were evaluated based on the Hypervolume, Epsilon, and Spacing metrics, and statistically validated by the Levene test and confidence interval charts. The results showed the efficiency of the proposed algorithm for solving the MOHFS problem.