The classic problem of constrained pathfinding is a well-studied, yet challenging, topic in AI with a broad range of applications in various areas such as communication and transportation. The Weight Constrained Shortest Path Problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost-optimum path with limited weight/resource usage. Given the bi-criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi-objective search. This paper leverages the recent state-of-the-art techniques in both constrained pathfinding and bi-objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state-of-the-art algorithms in both time and space metrics. This paper also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomised graphs how bucket-based queues without tie-breaking can effectively improve the algorithmic performance of exhaustive A*-based bi-criteria searches.

翻译：经典的约束路径寻找问题是一个在人工智能领域中研究充分但依然具有挑战性的课题，在通信和交通运输等多个领域具有广泛的应用。带权约束最短路径问题作为仅含单一约束的约束路径寻找基本形式，旨在规划一条在权重/资源使用受限情况下的成本最优路径。鉴于该问题的双准则特性（即同时处理路径的成本与权重），解决WCSPP的方法与双目标搜索具有某些共同特征。本文借鉴了约束路径寻找与双目标搜索领域的最新先进技术，在A*搜索基础上提出了两种新的WCSPP求解方法，这两种方法均能在超大规模图上求解困难的WCSPP实例。我们通过一组规模较大且具有现实性的问题实例对所提算法的性能进行了实证评估，结果显示其在时间和空间指标上均优于现有先进算法。本文还探讨了优先级队列在基于A*的约束搜索中的重要性。我们通过对现实图与随机图进行大量实验证明，无平局打破机制的桶式队列如何有效提升基于穷举A*的双准则搜索算法的性能。