Title: Edge-wise topological divergence gaps: guiding search in combinatorial optimization
Primary area: optimization
Keywords: Travelling Salesman Problem, Topological Data Analysis, Combinatorial Optimization

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, expressing 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.

TL;DR: We use topological divergence between a tour and an MST as a signal guiding solution of a TSP problem