Multi-Objective Hybrid Flow Shop Scheduling with Sequence-Dependent Setup Times and Multi-Skilled Workers

In multi-variety, small-batch electric oven manufacturing, sequence-dependent setup times (SDST) and worker skill heterogeneity jointly affect makespan, labor cost, and energy consumption. This study addresses a multi-objective hybrid flow shop scheduling problem with SDST and multi-skilled worker assignment (HFSP-SDST), in which symmetry and asymmetry coexist: the three objectives require balanced trade-offs, whereas sequence-dependent setups and skill–speed compatibility impose asymmetric constraints. A mixed-integer linear programming model is formulated to minimize the three objectives, embedding a skill–speed downward compatibility mechanism that couples worker assignment with processing time, power demand, and labor cost. To solve it, a hybrid algorithm integrating NSGA-II, variable neighborhood search (VNS), and multi-objective simulated annealing (MOSA) is designed on a four-matrix encoding with problem-specific crossover, neighborhood, and feasibility-repair operators. On 24 test instances of varied scale and structure, NSGA-II-VNS-MOSA attains the highest mean hypervolume (2.05) and the best average rank (2.07) against classical and recent Q-learning-guided algorithms, with its advantage growing as setup asymmetry intensifies; an ablation study shows that VNS and MOSA jointly increase hypervolume by 89.5% and reduce the inverted generational distance (IGD) by 45.2% relative to baseline NSGA-II. A real electric oven case confirms that the resulting Pareto set offers decision-makers actionable trade-offs among the three objectives.