This paper focuses on a cascaded flowshop joint scheduling problem (CFJSP) based on an investigation of the printed circuit board manufacturing industry, aiming at total tardiness minimization. Unlike single flowshop scheduling problems, the CFJSP can be regarded as a scheduling problem consisting of two sub-problems, , distributed permutation flowshop scheduling problem (DPFSP) and hybrid flowshop scheduling problem (HFSP). The optimization process between DPFSP and HFSP becomes the key to solving this problem. We first formulate its working principle and establish a mixed-integer linear programming model. Second, we propose a population-based iterated greedy (PBIG) algorithm, whose search space alternates sequentially from phase 1 to phase 2 to explore near-optimal solutions. Meanwhile, we present an NEH-based heuristic to generate a high-quality initial solution, and a finite skip boundary reconstruction operator to explore more promising search space and reduce computational effort. The parameters and operators of the PBIG algorithms are calibrated and analyzed using the experiment design and evaluation method. We generate an applicable benchmark instance set to evaluate the PBIG algorithm against five state-of-the-art metaheuristics. Statistically sound results demonstrate the effectiveness of the proposed PBIG algorithm for solving the CFJSP with the total tardiness objective.

中文翻译：

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级联流水车间联合调度问题：一种数学模型和基于群体的迭代贪婪算法，以最小化总迟到率

本文基于对印刷电路板制造行业的调查，重点研究了级联流水车间联合调度问题（CFJSP），旨在实现总延误最小化。与单一流水车间调度问题不同，CFJSP 可以看作是由两个子问题组成的调度问题：分布式排列流水车间调度问题（DPFSP）和混合流水车间调度问题（HFSP）。DPFSP和HFSP之间的优化过程成为解决该问题的关键。我们首先阐述其工作原理并建立混合整数线性规划模型。其次，我们提出了一种基于群体的迭代贪婪（PBIG）算法，其搜索空间从第一阶段到第二阶段顺序交替，以探索接近最优的解决方案。同时，我们提出了一种基于 NEH 的启发式方法来生成高质量的初始解决方案，并提出了一种有限跳跃边界重建算子来探索更有前景的搜索空间并减少计算量。利用实验设计和评估方法对PBIG算法的参数和算子进行了标定和分析。我们生成一个适用的基准实例集来根据五种最先进的元启发法评估 PBIG 算法。统计上可靠的结果证明了所提出的 PBIG 算法在解决具有总迟到目标的 CFJSP 方面的有效性。