Different algorithmic performances are required in different engineering fields for solving both the symmetric and asymmetric traveling salesman problem (STSP and ATSP), both of which are commonly referred to as TSP. In the background of small-scale TSP, according to the principle of the optimal Hamiltonian loop, this paper describes an angular bisector insertion algorithm (ABIA) that can solve TSP. The main processes of ABIA are as follows. First, the angular bisector of the point group is constructed. Second, the farthest vertex perpendicular to the angular bisector is identified as the search criterion. Finally, for both STSP and ATSP, initial loop formation rules and vertex insertion rules are constructed. Experiments were conducted for all STSP and ATSP instances with up to 100 points in the TSPLIB database. The performance of ABIA was compared with that of the 2-point farthest insertion algorithm, convex hull insertion algorithm, branch-and-bound algorithm, and a genetic algorithm. The experimental results show that, for small-scale TSP (up to 40 points), the runtime of ABIA is second only to the convex hull insertion algorithm, and the gap between ABIA and the optimal solution is second only to the exact algorithm. ABIA offers good overall performance in solving small-scale TSP.

解决对称和非对称旅行商问题（STSP 和 ATSP）在不同的工程领域需要不同的算法性能，这两种问题通常被称为 TSP。本文在小规模TSP的背景下，根据最优哈密顿回路的原理，描述了一种可以求解TSP的角平分线插入算法（ABIA）。ABIA的主要流程如下。首先，构造点群的角平分线。其次，垂直于角平分线的最远顶点被确定为搜索标准。最后，对于STSP和ATSP，构建了初始循环形成规则和顶点插入规则。对所有 STSP 和 ATSP 实例进行了实验，在 TSPLIB 数据库中最多有 100 个点。ABIA 的性能与 2 点最远插入算法、凸包插入算法、分支定界算法和遗传算法的性能进行了比较。实验结果表明，对于小规模的TSP（最多40个点），ABIA的运行时间仅次于凸包插入算法，ABIA与最优解的差距仅次于精确算法。ABIA 在解决小规模 TSP 方面提供了良好的整体性能。而ABIA与最优解的差距仅次于精确算法。ABIA 在解决小规模 TSP 方面提供了良好的整体性能。而ABIA与最优解的差距仅次于精确算法。ABIA 在解决小规模 TSP 方面提供了良好的整体性能。