Collaborative Attention Ant Colony Optimization for Large-Scale Traveling Salesman Problems

Collaborative Attention Ant Colony Optimization (CAACO) integrates a deterministic coordinate-based attention prior with subpath decomposition, memetic MAX–MIN Ant System search, and double-bridge perturbation for the symmetric Euclidean Traveling Salesman Problem. The attention prior combines coordinate-direction compatibility and distance information to guide candidate selection without model training. Random-offset slicing organizes endpoint-constrained subpath search, while local improvement and perturbation refine and diversify the tour. An exploratory comparison of Full CAACO and CAACO-KNN uses 30 recorded runs per configuration on each of eight EUC_2D benchmark instances. Average instance-level mean GAP values are 2.945% and 3.222%, respectively, with a lower mean for Full CAACO on six instances. A two-sided exact Wilcoxon signed-rank test over the eight instance means gives p=0.0391; four per-instance comparisons remain significant after Holm correction. The results characterize configuration-level performance on the selected benchmarks and motivate further controlled evaluation of attention-guided search.