Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909968352935936 |
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| author | Trofimov, Ilya Voronkova, Daria Mironenko, Alexander Dmitriev, Anton Tulchinskii, Eduard Burnaev, Evgeny Barannikov, Serguei |
| author_facet | Trofimov, Ilya Voronkova, Daria Mironenko, Alexander Dmitriev, Anton Tulchinskii, Eduard Burnaev, Evgeny Barannikov, Serguei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization Trofimov, Ilya Voronkova, Daria Mironenko, Alexander Dmitriev, Anton Tulchinskii, Eduard Burnaev, Evgeny Barannikov, Serguei Computational Geometry Artificial Intelligence 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. |
| title | Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization |
| topic | Computational Geometry Artificial Intelligence |
| url | https://arxiv.org/abs/2512.15800 |