求解并行机拖期与能耗成本优化调度的混合教一学算法

针对加工时间可控的并行机调度，提出了一类考虑拖期与能耗成本优化的调度问题。首先对调度问题进行了问题描述，并建立了整数线性规划模型以便于CPLEX求解。为了快速获得问题的满意解，提出了一种混合教-学算法。结合问题的性质，设计了编码与解码方法以克服标准教-学算法无法直接适用于离散问题的缺点。同时，构建了基于变邻域搜索的局部搜索算子以强化混合算法的搜索性能。最后，对加工时间可控的并行机调度问题进行了仿真实验，测试结果验证了本文构建的整数线性规划模型和混合算法的可行性和有效性。

Hybrid teaching-learning-based optimization algorithm for optimizing tardiness and energy cost on parallel machine scheduling

For the parallel machine scheduling with controllable processing times (PMS-CPT) , this paper proposed a scheduling problem for optimizing tardiness and energy cost. First, this article developed an integer linear programming (ILP) model for the proposed scheduling problem in order to facilitate the CPLEX solver. Second, this paper established a hybrid teaching-learning-based optimization (HTLBO) algorithm to quickly obtain satisfactory solutions. This algorithm adopted a new coding and decoding method according to the nature of the proposed parallel machine scheduling problem, which overcame the weakness of standard teaching-learning-based optimization algorithm that could not be directly applied to discrete problems. Meanwhile, a local optimizer was proposed based on variable neighborhood search (VNS) , which aimed to enhance the performance of the hybrid algorithm. Finally, the simulations were conducted to solve instances of PMS-CPT. The experimental results demonstrate the feasibility and validity of the proposed ILP model and hybrid algorithm.