Due to its practical relevance, the hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature with the objectives related to production efficiency. However, studies regarding energy consumption and environmental effects have rather been limited. This paper addresses the trade-off between makespan and total energy consumption in hybrid flowshops, where machines can operate at varying speed levels. A bi-objective mixed-integer linear programming (MILP) model and a bi-objective constraint programming (CP) model are proposed for the problem employing speed scaling. Since the objectives of minimizing makespan and total energy consumption are conflicting with each other, the augmented epsilon (ε)-constraint approach is used for obtaining the Pareto-optimal solutions. While close approximations for the Pareto-optimal frontier are obtained for small-sized instances, sets of non-dominated solutions are obtained for large instances by solving the MILP and CP models under a time limit. As the problem is NP-hard, two variants of the iterated greedy algorithm, a variable block insertion heuristic and four variants of ensemble of metaheuristic algorithms are also proposed, as well as a novel constructive heuristic. The performances of the proposed seven bi-objective metaheuristics are compared with each other as well as the MILP and CP solutions on a set of well-known HFSP benchmarks in terms of cardinality, closeness, and diversity of the solutions. Initially, the performances of the algorithms are tested on small-sized instances with respect to the Pareto-optimal solutions. Then, it is shown that the proposed algorithms are very effective for solving large instances in terms of both solution quality and CPU time.

由于其实用性，混合流水车间调度问题（HFSP）已在文献中进行了广泛研究，其目标与生产效率有关。但是，有关能源消耗和环境影响的研究相当有限。本文探讨了混合流水车间中制造时间和总能耗之间的权衡问题，在混合流水车间中，机器可以以不同的速度运行。针对采用速度缩放的问题，提出了双目标混合整数线性规划（MILP）模型和双目标约束规划（CP）模型。由于最小化制造时间和总能耗的目标相互冲突，因此使用增强的ε约束方法来获得帕累托最优解。对于小型实例，可以得到帕累托最优边界的近似值，对于大型实例，可以通过在时间限制下求解MILP和CP模型来获得非主导解集。由于问题是NP难的，因此还提出了迭代贪婪算法的两个变体，可变块插入启发式算法和元启发式算法集合的四个变体，以及一种新颖的构造启发式算法。拟议的七种双目标元启发式方法的性能以及MILP和CP解决方案在一组知名的HFSP基准上的基数，紧密度和多样性都进行了比较。最初，针对帕累托最优解，在小型实例上测试了算法的性能。然后，