Rithwik J Cherian¹ (rcherian@ur.rochester.edu), Ralf M Haefner¹, Dora Biro¹; ¹University of Rochester

Humans solve the Traveling Salesman Problem (TSP)—a classic optimization problem of finding the shortest path through a set of locations—with remarkable proficiency, producing near-optimal tours with minimal effort and training. This ability is particularly surprising given the problem's computational complexity, yet the underlying mechanisms remain poorly understood. Theories and models of human performance on TSP emphasize perceptual processes such as boundary detection and hierarchical clustering, but direct evidence linking visual processing to spatial optimization is limited (MacGregor and Chu, 2011). Traditional TSP studies rely on manual reporting via pen-and-paper or mouse clicks, requiring deliberate route construction that engages both perceptual and cognitive processes. We introduce a novel paradigm using eye movements as the reporting modality, allowing us to directly capture the perceptual system's implicit spatial optimization strategies as they unfold in real-time, bypassing explicit planning and working memory demands. We examined scanpath efficiency using a vanishing-dots paradigm where participants explored displays of randomly distributed points (5-25 points) that disappeared after sustained fixation (100ms). This gaze-contingent design provides immediate feedback while reducing visual working memory demands and encouraging complete spatial coverage. Using high-precision eye tracking, we extracted scanpaths and compared them to optimal and heuristic TSP solutions. We found that scanpaths exhibited systematic spatial efficiency. Performance, measured as percent above optimal, ranged from 3-15%, degrading predictably as problem size increased. Participants terminated their routes closer to optimal endpoints than expected by chance, suggesting multi-step saccade planning. Median fixation duration remained approximately constant (230-280ms) within participants across problem sizes, indicating consistent local processing independent of global complexity. These results demonstrate that the visual system produces spatially efficient scanpaths even without explicit goals, establishing eye tracking as a powerful paradigm for studying the perceptual foundations of human spatial optimization abilities with increased ecological validity and temporal resolution compared to traditional manual reporting methods.