Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization
Computational Geometry
2025-12-19 v1 Artificial Intelligence
Abstract
We introduce a topological feedback mechanism for the Travelling Salesman Problem (TSP) by analyzing the divergence between a tour and the minimum spanning tree (MST). Our key contribution is a canonical decomposition theorem that expresses the tour-MST gap as edge-wise topology-divergence gaps from the RTD-Lite barcode. Based on this, we develop a topological guidance for 2-opt and 3-opt heuristics that increases their performance. We carry out experiments with fine-optimization of tours obtained from heatmap-based methods, TSPLIB, and random instances. Experiments demonstrate the topology-guided optimization results in better performance and faster convergence in many cases.
Cite
@article{arxiv.2512.15800,
title = {Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization},
author = {Ilya Trofimov and Daria Voronkova and Alexander Mironenko and Anton Dmitriev and Eduard Tulchinskii and Evgeny Burnaev and Serguei Barannikov},
journal= {arXiv preprint arXiv:2512.15800},
year = {2025}
}