Resource Constrained Pathfinding with A* and Negative Weights

2025-03-14

AI Summary

This paper addresses the Resource-Constrained Shortest Path (RCSP) problem—finding a cost-optimal path in large-scale networks subject to multi-dimensional resource constraints and allowing negative-weight edges. Existing algorithms suffer from fundamental limitations: inability to handle negative costs and negative resource consumption, as well as poor scalability. To overcome these bottlenecks, we propose the first A*-based framework for general RCSP. Our method introduces three key innovations: (i) a negative-weight graph adaptation mechanism; (ii) an efficient label pruning strategy grounded in multi-dimensional dominance relations; and (iii) a dynamic heuristic-driven pruning scheme. Extensive experiments on large-scale benchmark instances demonstrate that our algorithm achieves up to two orders of magnitude speedup over state-of-the-art RCSP solvers, significantly improving both real-time performance and scalability. The approach provides a theoretically sound and practically viable tool for applications such as traffic dispatching and network routing.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Solves Resource Constrained Shortest Path Problem (RCSP).
• Handles pathfinding with negative costs and resources.
• Improves performance significantly in large networks.

Innovation

• A* based resource constrained search framework
• Handles negative costs and negative resources
• Empirically faster than state-of-the-art RCSP algorithms