发表机构
University of Modena and Reggio Emilia; Université Laval（摩德纳和雷焦艾米利亚大学; 拉瓦尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对柔性制造领域的作业排序与刀具切换问题（SSP），提出结合两种分支定界算法的组合分支定界（C-B&B）算法，辅以预处理启发式方法，成功解决了多个数十年未最优求解的基准实例。
AI 中文摘要
作业排序与刀具切换问题（SSP）是柔性制造领域中一个著名的组合优化问题。自Tang和Denardo（1988）的开创性工作以来，SSP已受到文献的广泛关注，催生了众多精确算法与启发式方法。尽管付出了这些努力，数十年前提出的仅含20个作业的数个基准实例仍未被证明最优性。本研究针对SSP提出了一种精确算法，即组合分支定界（C-B&B）算法，它结合了两种不同的分支定界算法，每种算法都引入了现有文献中未有的新特征。前者依赖于一种旨在缩小隐式枚举树规模的新分支方案，以及一组新的定界函数；后者基于Laporte等人（2004）引入的分支方案，并通过一种新的定界函数和两条支配规则对其进行强化。在C-B&B框架内，这些精确算法还辅以预处理阶段，该阶段包含一种新的基于分支定界的启发式方法，能够快速生成高质量的初始 incumbent（ incumbent 指可行解）。大量计算实验表明，C-B&B相比已发表的方法取得了重大突破，用显著更少的计算工作量证明了更多实例的最优性，并解决了数个数十年来悬而未决的基准实例。
英文摘要
The Job Sequencing and Tool Switching Problem (SSP) is a well-known combinatorial optimization problem arising in the context of flexible manufacturing. Since the seminal work of Tang and Denardo (1988), the SSP has received significant attention in the literature, leading to the development of numerous exact and heuristic approaches. Despite these efforts, several benchmark instances proposed decades ago and containing only 20 jobs have remained unsolved to proven optimality. In this work, we propose an exact algorithm for the SSP, namely the Combinatorial Branch-and-Bound (C-B\&B) algorithm, which combines two distinct branch-and-bound algorithms, each introducing novel features compared with the existing literature. The former relies on a new branching scheme designed to reduce the size of the implicit enumeration tree, together with a collection of new bounding functions. The latter builds on the branching scheme introduced by Laporte et al. (2004) and strengthens it with a new bounding function and two dominance rules. Within C-B\&B, these exact algorithms are complemented by a preprocessing phase that incorporates a new branch-and-bound-based heuristic capable of rapidly generating a high-quality initial incumbent solution. Extensive computational experiments show that C-B\&B represents a strong breakthrough over previously published approaches, proving optimality for more instances with significantly less computational effort and closing several benchmark instances that have remained open for decades.
