AIob Lab

Combinatorial Route Optimization (CRO) problems, such as the Vehicle Routing Problem (VRP) or the Travelling Salesman Problem (TSP), are commonly seen in scheduling, logistics, and transportation. While current machine learning (ML) methods can overcome certain limitations of traditional approaches, including exact and heuristic algorithms, they typically require substantial computational resources, large training datasets, and carefully designed models, thereby limiting their scalability and practical deployment. In this paper, we develop a method to address such concerns in a data-efficient and near-training-free manner using foundation models. We select TSP, one of the most well-known combinatorial optimization problems, to solve in our experiments and employ the Tabular Prior-Data Fitted Network (TabPFN), one of the newly designed foundation models. Specifically, we develop a node-based formulation that converts TSP into a sequence of localized prediction tasks and constructs a complete route through in-context learning provided by TabPFN. The proposed method enables TabPFN, a model developed for regression and classification, to be applied to CRO problems with only one TSP sample for fine-tuning. We evaluate the proposed method across varying TSP instance sizes and demonstrate that our approach generalizes effectively without retraining, maintains competitive solution quality, and exhibits promising scalability. These findings suggest that CRO problems can be approached through foundation models, enabling scalability as well as generating rapidly deployable solutions with near-training-free adaptation.

Double-Deck Multi-Agent Pickup and Delivery (DD-MAPD) models the multi-robot shelf rearrangement problem in automated warehouses. MAPF-DECOMP is a recent framework that first computes collision-free shelf trajectories with a MAPF solver and then assigns agents to execute them. While efficient, it enforces strict trajectory dependencies, often leading to poor execution quality due to idle agents and unnecessary shelf switching. We introduce CREST, a new execution framework that achieves more continuous shelf carrying by proactively releasing trajectory constraints during execution. Experiments on diverse warehouse layouts show that CREST consistently outperforms MAPF-DECOMP, reducing metrics related to agent travel, makespan, and shelf switching by up to 40.5%, 33.3%, and 44.4%, respectively, with even greater benefits under lift/place overhead. These results underscore the importance of execution-aware constraint release for scalable warehouse rearrangement. Code and data are available at https://github.com/ChristinaTan0704/CREST.

We study GCS-TSP, a variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS)—a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by a sparse graph. In GCS-TSP, edge costs are not fixed but depend on the specific trajectory passing through each convex region, making classical TSP methods inapplicable. We introduce GHOST, a hierarchical framework that optimally solves GCS-TSP by combining combinatorial tour search with convex trajectory optimization. GHOST systematically explores tours on a complete graph induced by the GCS, using a novel abstract-path-unfolding algorithm to compute admissible lower bounds that guide best-first search at both the high level (over tours) and the low level (over feasible GCS paths realizing the tour). These bounds provide strong pruning power, reducing unnecessary optimization calls. We prove that GHOST guarantees optimality and present a bounded-suboptimal variant for time-critical settings. Experiments show that GHOST is orders-of-magnitude faster than unified mixed-integer convex programming baseline while uniquely handling complex problems involving high-order continuity constraints and incomplete GCSs.

We address the Multi-Robot Motion Planning (MRMP) problem of computing collision-free trajectories for multiple robots in shared continuous environments. While existing frameworks effectively decompose MRMP into singlerobot subproblems, spatiotemporal motion planning with dynamic obstacles remains challenging, particularly in cluttered or narrow-corridor settings. We propose Space-Time Graphs of Convex Sets (ST-GCS), a novel planner that systematically covers the collision-free space-time domain with convex sets instead of relying on random sampling. By extending Graphs of Convex Sets (GCS) into the time dimension, ST-GCS formulates time-optimal trajectories in a unified convex optimization that naturally accommodates velocity bounds and flexible arrival times. We also propose Exact Convex Decomposition (ECD) to "reserve" trajectories as spatiotemporal obstacles, maintaining a collision-free space-time graph of convex sets for subsequent planning. Integrated into two prioritized-planning frameworks, ST-GCS consistently achieves higher success rates and better solution quality than state-of-the-art sampling-based planners—often at orders-of-magnitude faster runtimes—underscoring its benefits for MRMP in challenging settings. Project page: https://sites.google.com/view/stgcs.