发表机构
LIMOSE Laboratory, University of M’hamed Bougara（穆哈梅德·布加拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无固定仓库的双目标服务导向TSP，改进MTZ公式并线性化，提出结合模糊推理更新参考环的节点移位编码遗传算法，在TSPLIB基准上性能优于经典NSE方法。
AI 中文摘要
旅行商问题（TSP）仍是组合优化领域的一个关键研究方向，在物流、制造和服务交付中具有广泛应用。本文研究了一个双目标服务导向型旅行商问题，其中客户在配送路径中的排名至关重要。与传统的基于仓库的TSP公式不同，所考虑的问题不假设存在特定的仓库或固定的环起点。为解决这一设定，我们改进了基于Miller–Tucker–Zemlin（MTZ）的公式，并推导出所得模型的原始线性化形式，从而能够使用现成的整数线性规划求解器进行求解。这种改进避免了传统MTZ公式所强加的刚性环起点，因为固定起始节点虽然不影响环成本，但在客户排名敏感的TSP中可能影响目标值。为解决该问题，我们提出了一种基于节点移位编码（NSE）的遗传算法，并辅以模糊推理在整个进化过程中更新参考环。在TSPLIB基准上的实验评估表明，与经典NSE方法相比，所提方法实现了更优的性能。
英文摘要
The Travelling Salesman Problem (TSP) remains a key area of research in combinatorial optimization, with applications in logistics, manufacturing, and service delivery. This paper addresses a bi-objective service-oriented TSP in which the clients' ranks in the delivery path matter. Unlike conventional depot-based TSP formulations, the considered problem does not assume a distinguished depot or a fixed tour origin. To address this setting, we adapt the Miller--Tucker--Zemlin (MTZ)-based formulation and derive an original linearization of the resulting model, enabling its solution with off-the-shelf integer linear programming solvers. This adaptation avoids the rigid tour origin imposed by the conventional MTZ formulation, for which fixing the starting node does not affect the tour cost but can affect the objective in a customer-rank-sensitive TSP. To solve this problem, we present a Node-Shift-Encoding (NSE)-based Genetic Algorithm augmented with fuzzy reasoning to update the reference tour throughout the evolutionary process. Experimental evaluation on TSPLIB benchmarks demonstrates that the proposed method achieves improved performance compared with the classical NSE approach.
Comments22 pages, 13 figures
