Anoop Bhat

Anoop Bhat, Geordan Gutow, Zhongqiang Ren et al.

The Moving Target Vehicle Routing Problem (MT-VRP) seeks trajectories for several agents that intercept a set of moving targets, subject to speed, time window, and capacity constraints. We introduce an exact algorithm, Branch-and-Price with Relaxed Continuity (BPRC), for the MT-VRP. The main challenge in a branch-and-price approach for the MT-VRP is the pricing subproblem, which is complicated by moving targets and time-dependent travel costs between targets. Our key contribution is a new labeling algorithm that solves this subproblem by means of a novel dominance criterion tailored for problems with moving targets. Numerical results on instances with up to 25 targets show that our algorithm finds optimal solutions more than an order of magnitude faster than a baseline based on previous work, showing particular strength in scenarios with limited agent capacities.

Anoop Bhat, Geordan Gutow, Surya Singh et al.

The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it must be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. We introduce Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), which finds optimal solutions for the MT-VRP-O. Lazy BPRC applies the branch-and-price framework for VRPs, which alternates between a restricted master problem (RMP) and a pricing problem. The RMP aims to select a sequence of target-time window pairings (called a tour) for each agent to follow, from a limited subset of tours. The pricing problem adds tours to the limited subset. Conventionally, solving the RMP requires computing the cost for an agent to follow each tour in the limited subset. Computing these costs in the MT-VRP-O is computationally intensive, since it requires collision-free motion planning between moving targets. Lazy BPRC defers cost computations by solving the RMP using lower bounds on the costs of each tour, computed via motion planning with relaxed continuity constraints. We lazily evaluate the true costs of tours as-needed. We compute a tour's cost by searching for a shortest path on a Graph of Convex Sets (GCS), and we accelerate this search using our continuity relaxation method. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.

Anoop Bhat, Geordan Gutow, Bhaskar Vundurthy et al.

The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.