For batch scheduling problems, more and more attentions have been paid to reducing energy consumption. In this paper, a complex batch scheduling problem on parallel batch processing machines considering time-of-use electricity price is investigated to minimize makespan and total electricity cost, simultaneously. Due to NP-hardness of the studied problem, a multi-objective evolutionary algorithm based on adaptive clustering is proposed, where an improved adaptive clustering method is incorporated to mine the distribution structure of solutions, which can be used to guide the search. Moreover, a new recombination strategy based on both distribution characteristics and mating probability is designed to select individuals for mating. In addition, to better balance exploration and exploitation, the mating probability is adaptively adjusted according to historical information. The experimental results demonstrate the competitiveness of the proposed algorithm in terms of solution quality.

对于批处理调度问题，越来越多地关注降低能耗。在本文中，研究了考虑分时电价的并行批处理机上的复杂批调度问题，以同时最小化制造周期和总电成本。针对所研究问题的NP难点，提出了一种基于自适应聚类的多目标进化算法，该算法结合了一种改进的自适应聚类方法来挖掘解的分布结构，可用于指导搜索。此外，设计了一种基于分布特征和交配概率的新重组策略来选择个体进行交配。此外，为了更好地平衡勘探与开发，根据历史信息自适应地调整交配概率。实验结果证明了该算法在解决方案质量方面的竞争力。