障害物を考慮した移動目標車両ルーティング問題に対する遅延分枝価格法による最適解
Optimal Solutions for the Moving Target Vehicle Routing Problem with Obstacles via Lazy Branch and Price
移動する目標を複数エージェントで捕捉する問題に対し、コスト計算を遅延させる分枝価格法を提案し、従来法より最大10倍高速に最適解を求めた。
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著者: Anoop Bhat, Geordan Gutow, Surya Singh, Zhongqiang Ren, Sivakumar Rathinam, Howie Choset
分類: cs.RO
原文アブストラクト
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.
