IEEE Trans Cybern. 2023 Jul;53(7):4079-4093. doi: 10.1109/TCYB.2021.3135539. Epub 2023 Jun 15.
In this article, we focus on a biobjective hot strip mill (HSM) scheduling problem arising in the steel industry. Besides the conventional objective regarding penalty costs, we have also considered minimizing the total starting times of rolling operations in order to reduce the energy consumption for slab reheating. The problem is complicated by the inevitable uncertainty in rolling processing times, which means deterministic scheduling models will be ineffective. To obtain robust production schedules with satisfactory performance under all possible conditions, we apply the robust optimization (RO) approach to model and solve the scheduling problem. First, an RO model and an equivalent mixed-integer linear programming model are constructed to describe the HSM scheduling problem with uncertainty. Then, we devise an improved Benders' decomposition algorithm to solve the RO model and obtain exactly optimal solutions. Next, for coping with large-sized instances, a multiobjective particle swarm optimization algorithm with an embedded local search strategy is proposed to handle the biobjective scheduling problem and find the set of Pareto-optimal solutions. Finally, we conduct extensive computational tests to verify the proposed algorithms. Results show that the exact algorithm is effective for relatively small instances and the metaheuristic algorithm can achieve satisfactory solution quality for both small- and large-sized instances of the problem.
本文聚焦于钢铁行业中出现的双目标热轧带钢轧机（HSM）调度问题。除了传统的惩罚成本目标外，我们还考虑了最小化轧制操作的总启动时间，以减少板坯再加热的能耗。由于轧制加工时间不可避免的不确定性，使得该问题变得复杂，这意味着确定性调度模型将不再适用。为了在所有可能的条件下获得具有令人满意性能的稳健生产计划，我们应用鲁棒优化（RO）方法对调度问题进行建模和求解。首先，构建了一个 RO 模型和一个等效的混合整数线性规划模型，以描述具有不确定性的 HSM 调度问题。然后，设计了一种改进的 Benders 分解算法来求解 RO 模型，并获得了精确的最优解。接下来，为了处理大规模实例，提出了一种带有嵌入式局部搜索策略的多目标粒子群优化算法来处理双目标调度问题，并找到帕累托最优解集。最后，进行了广泛的计算测试来验证所提出的算法。结果表明，精确算法对于较小的实例有效，而元启发式算法对于该问题的小和大规模实例都能获得令人满意的求解质量。
