Over decades of Traveling Salesperson Problem (TSP) research, powerful heuristics have been developed that efficiently solve many TSP instances. Among them, the local search optimizer LKH and the genetic algorithm EAX stand out as the two complementary state-of-the-art solvers. Yet, the links between instance structures and solver complementarity remain obscure, i.e., it is often unclear how instance structures affect solver performance and behavior.
While visualization techniques have advanced our understanding of TSP instance structures, there is still no general method to assess the behavior of TSP heuristics directly based on the structural characteristics of the instance to be solved.
Existing approaches, such as search trajectory networks, are often optimized for graph-theoretic properties that may not reflect true similarities between tours. Consequently, visually comparing solvers remains difficult, especially when few identical solutions are encountered.
This paper introduces a framework for visualizing the search behavior of TSP heuristics, aiming to illuminate the still poorly understood key differences in their search behavior. To this end, we adapt the dimensionality reduction technique PaCMAP to map intermediate solutions into two-dimensional space, preserving distances that meaningfully reflect tour similarity. To support exploration, we provide an interactive dashboard that allows users to inspect individual tours and visually compare selected tour pairs. The resulting visualizations reveal fundamental differences in how LKH and EAX explore the search space, including their initialization strategies and trajectory structures. We further show that a recent EAX-inspired and performance-improved LKH variant still behaves similarly to LKH, highlighting the untapped potential for further algorithmic improvements.