Resource Constrained Pathfinding with A* and Negative Weights
Saman Ahmadi, Andrea Raith, Mahdi Jalili
TL;DR
This work addresses the Resource Constrained Shortest Path Problem (RCSP) in networks with potential negative edge costs but no negative cycles. It introduces NWRCA*, an $A^*$-based constrained search framework that constructs high-quality heuristics via backward cost-optimal searches for each cost component and employs powerful dominance and truncation-based pruning to enumerate all non-dominated ${cost_1}$-optimal start-to-goal paths under multiple resource budgets. Theoretical guarantees (Lemmas 1–5 and Theorem 1) establish correctness and safe pruning under the assumption of a consistent heuristic and the absence of negative cycles. Empirically, NWRCA* significantly outperforms state-of-the-art RCSP methods on large DIMACS instances, achieving up to two orders of magnitude speedups and higher solved-instance rates, illustrating its practical impact for large-scale constrained pathfinding with negative weights.
Abstract
Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained Shortest Path Problem (RCSP), aims to plan a cost-optimum path subject to limited usage of resources. Given the recent advances in constrained and multi-criteria search with A*, this paper introduces a new resource constrained search framework on the basis of A* to tackle RCSP in large networks, even in the presence of negative cost and negative resources. We empirically evaluate our new algorithm on a set of large instances and show up to two orders of magnitude faster performance compared to state-of-the-art RCSP algorithms in the literature.