Decomposability-Guided Cooperative Coevolution for Large-Scale Itinerary Planning

Large-scale routing often requires visiting clusters of nodes in a prescribed order, giving rise to the Ordered Clustered Traveling Salesman Problem (OCTSP). Optimizing each cluster independently seems natural, but misses non-local dependencies. We introduce the COMPASS algorithm for OCTSP, which combines search with learning-accelerated routing by orchestrating parallel sub-solvers. COMPASS has no quality ceiling and its solutions keep improving with compute. It exploits the clustered structure, and can reach exact solutions in time exponential in cluster size rather than instance size. Empirically, COMPASS consistently outperforms alternative methods. Unlike common large-scale routing solvers, COMPASS consumes general distance matrices and is not limited to coordinate inputs. We demonstrate scaling to 100K synthetic nodes and to 28.5K real e-commerce nodes. To our knowledge, the latter is the largest reported routing solution over asymmetric distances, 9x beyond established ATSP benchmarks.

In large urban areas, planning multi-day travel itineraries is challenging due to the abundance of Points of Interest (POIs), diverse user preferences, and constraints such as opening hours. Effective solutions must dynamically accommodate diverse traveler requirements while optimizing for satisfaction and feasibility within limited computation time. This paper addresses these challenges through introducing an innovative framework that integrates Large Language Models (LLMs) to dynamically capture user requirements with precision and flexibility, and an enhanced Greedy Randomized Adaptive Search Procedure (GRASP) algorithm as a well-suited preference-aware planner to generate feasible multi-day itineraries. The effectiveness of our integrated approach is demonstrated through extensive experiments on two real-world urban datasets from Beijing and Tianjin. Our framework significantly outperforms state-of-the-art (SOTA) methods, improving the average total itinerary score by at least 4.52% and 11.09% across 5,040 user cases with diverse preferences in the two datasets. Furthermore, through end-to-end algorithmic enhancements, it achieves notable average improvements of 17.95% and 26.07% in the computed metrics, while also delivering substantial gains in time efficiency -- realizing average performance increases of 4.64% and 25.55% within shorter computation times compared to suboptimal methods that require multiple iterations. These outcomes underscore our method's superiority in delivering both enhanced itinerary quality and computational efficiency over existing methodologies.

Routing problems, like the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP), are NP-hard and slow to solve for large instances. Diffusion-based solvers can be trained in a supervised way using sets of optimal solutions, and then quickly solve new test instances. However, for large instances, optimal solutions are hard to find, and diffusion models fail to generalize to instance sizes outside their training distribution. Here we describe ResizeCO, a label free size-generalization approach that addresses both the change in statistical properties of larger instances, and the computational challenge of solving them quickly. It uses reinforcement learning on large-scale instances to adapt a diffusion model trained on small instances. Specifically, we adapt GRPO to this problem, using route length as the training signal. ResizeCO also formulates k-opt as a tree search, solved by a beam search on the GPU. In size-generalization experiments on TSP and CVRP instances with up to 10000 nodes, ResizeCO achieves a Pareto front over route quality and time that dominates learned solvers, and also outperforms other solvers at short run times, setting a new state of the art.