Research on Order-of-Addition in the Traveling Salesman Problem
诗棋 曾 · Advances in Applied Mathematics · 2025
针对复杂多因子试验顺序优化中存在的路径成本高、实验迭代次数多等难题，本文提出一种基于邻接关系模型的双循环排序算法。通过构建全循环模型矩阵与基线约束条件，结合主因子分割策略，实现了最优试验序列的快速确定与实验次数的最小化。理论分析表明：该算法将传统旅行商问题的应用边界拓展至试验设计领域。这项研究为化学工程和生物医学研究等领域的实验序列优化提供了理论框架和跨学科解决方案。To address the challenges of high path costs and excessive experimental iterations in complex multi-factor trial sequence optimization, this study proposes a dual-loop sorting algorithm based on an Adjacency Relationship Model. By constructing a full-cycle model matrix with baseline constraints and integrating a principal component partitioning strategy, the algorithm achieves rapid determination of the optimal trial sequence while minimizing experimental iterations. Theoretical analysis demonstrates that the algorithm extends the application scope of the traditional Traveling Salesman Problem to experimental design domains. This research provides a robust theoretical framework and an interdisciplinary solution for experimental sequence optimization in fields such as chemical engineering and biomedical studies.