IEEE Trans Cybern. 2019 Mar;49(3):1097-1109. doi: 10.1109/TCYB.2018.2796119. Epub 2018 Feb 2.
Flexible job shop scheduling problem (FJSP) has been extensively considered; however, multiobjective FJSP with energy consumption threshold is seldom investigated, the goal of which is to minimize makespan and total tardiness under the constraint that total energy consumption does not exceed a given threshold. Energy constraint is not always met and the threshold is difficult to be decided in advance. These features make it more difficult to solve the problem. In this paper, a two-phase meta-heuristic (TPM) based on imperialist competitive algorithm (ICA) and variable neighborhood search (VNS) is proposed. In the first phase, the problem is converted into FJSP with makespan, total tardiness and total energy consumption and the new FJSP is solved by an ICA, which uses some new methods to build initial empires and do imperialist competition. In the second phase, new strategies are provided for comparing solutions and updating the nondominated set of the first phase and a VNS is used for the original problem. The current solution of VNS is periodically replaced with member of the set Ω to improve solution quality. An energy consumption threshold is obtained by optimization. Extensive experiments are conducted to test the performance of TPM finally. The computational results show that TPM is a very competitive algorithm for the considered FJSP.
柔性作业车间调度问题（FJSP）得到了广泛的研究；然而，很少有研究涉及带能耗阈值的多目标 FJSP，其目标是在总能耗不超过给定阈值的约束下最小化最大完工时间和总延迟。能耗约束并不总是满足的，而且阈值很难提前确定。这些特点使得问题更难解决。本文提出了一种基于帝国主义竞争算法（ICA）和变邻域搜索（VNS）的两阶段元启发式算法（TPM）。在第一阶段，将问题转化为最大完工时间、总延迟和总能耗的 FJSP，并使用 ICA 求解新的 FJSP，ICA 采用了一些新的方法来构建初始帝国并进行帝国主义竞争。在第二阶段，为比较解和更新第一阶段的非支配集提供了新的策略，并使用 VNS 求解原始问题。VNS 的当前解会定期用集合Ω中的成员替换，以提高解的质量。通过优化获得能耗阈值。最后进行了广泛的实验来测试 TPM 的性能。计算结果表明，TPM 是一种非常有竞争力的算法，可以用于考虑的 FJSP。
