In this paper, we address a hybrid flow-shop scheduling problem with the objective of minimizing the makespan and the cost of delay. The concerned problem considers the diversity of the customers’ requirements, which influences the procedures of the productions and increases the complexity of the problem. The features of the problem are inspired by the real-world situations, and the problem is formulated as a mixed-integer programming model in the paper. In order to tackle the concerned problem, a hybrid metaheuristic algorithm with Differential Evolution (DE) and Local Search (LS) (denoted by DE-LS) has been proposed in the paper. The differential evolution is a state-of-the-art metaheuristic algorithm which can solve complex optimization problem in an efficient way and has been applied in many fields, especially in flow-shop scheduling problem. Moreover, the study not only combines the DE and LS, but also modifies the mutation process and provides the novel initialization process and correction strategy of the approach. The proposed DE-LS has been compared with four variants of algorithms in order to justify the improvements of the proposed algorithm. Experimental results show that the superiority and robustness of the proposed algorithm have been verified.

中文翻译：

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考虑客户多需求的混合流车间调度问题的DE-LS元启发式算法

在本文中，我们解决了一个混合流水车间调度问题，其目标是最小化完工时间和延迟成本。关注的问题考虑了客户要求的多样性，影响了生产的程序，增加了问题的复杂性。该问题的特征受到现实世界情况的启发，在论文中将问题表述为混合整数规划模型。为了解决这个问题，本文提出了一种具有差分进化（DE）和局部搜索（LS）（用DE-LS表示）的混合元启发式算法。差分进化是一种最先进的元启发式算法，可以有效地解决复杂的优化问题，并已应用于许多领域，尤其是流水车间调度问题。此外，该研究不仅结合了DE和LS，还修改了变异过程，并提供了该方法的新颖初始化过程和校正策略。所提出的 DE-LS 已与四种算法变体进行了比较，以证明所提出算法的改进是合理的。实验结果表明，该算法的优越性和鲁棒性得到了验证。