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arXiv · 2603.26564

A Canceling Heuristic for the Directed Traveling Salesman Problem

Steffen Borgwardt·Zachary Sorenson
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Abstract

The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal tour, such as a local optimum found using a classic heuristic. Minimum Cost Flow Problems can be solved efficiently through linear programming or combinatorial algorithms based on cycle canceling. We investigate the potential of flow-canceling in the context of the TSP. Through a restriction of the search space to cycles and circulations that alternate between arcs in- and outside of the tour, practical results exhibit that only a low number of subtours is created, and a lightweight patching step suffices for a high success rate and gap closure towards an optimum.

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Steffen Borgwardt, Zachary Sorenson. 2026-03-27. A Canceling Heuristic for the Directed Traveling Salesman Problem. https://arxiv.org/abs/2603.26564

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