Abstract
<jats:p>The Traveling Salesman Problem (TSP) is a representative NP-hard combinatorial optimization problem whose search space grows rapidly with the number of cities. Classical ant colony optimization (ACO) is attractive because of its distributed construction process and positive-feedback search, but its performance deteriorates on large instances owing to probability dilution, pheromone concentration, search stagnation, and the cost of optimizing a complete tour with a single colony. This paper proposes Collaborative Attention Ant Colony Optimization (CAACO), which integrates sparse coordinate-based graph attention, random-offset collaborative subpath optimization, a memetic MAX–MIN Ant System, and adaptive double-bridge stagnation escape. The method is evaluated against FACO, BCACO, and CCACO on nine symmetric Euclidean TSP instances, with every algorithm executed independently 30 times per instance. CAACO obtains the lowest mean GAP on all nine instances, with an average instance-level mean GAP of 3.193%, compared with 12.587%, 22.177%, and 23.826% for the three baselines. Per-instance two-sided Mann–Whitney U tests with Holm correction show significant differences in all 27 comparisons (pHolm &lt; 10−10), and the Vargha–Delaney effect size is A12=1.000 throughout. These results demonstrate a consistently favorable solution-quality distribution for the proposed framework, while the runtime analysis shows a quality–efficiency trade-off relative to the efficiency-oriented baseline. A 30-run ablation study further shows that removing attention, dynamic slicing, and double-bridge escape increases the average mean GAP from 3.199% to 4.525%, 5.863%, and 3.813%, respectively; all 27 module-level comparisons remain significant after Holm correction.</jats:p>