Enhanced Methods for the Weight Constrained Shortest Path Problem

TL;DR

This paper introduces two novel A*-based algorithms for the Weight Constrained Shortest Path Problem, demonstrating improved efficiency on large, realistic graphs through extensive empirical evaluation.

Contribution

It presents new solution methods leveraging bi-objective search techniques for WCSPP, outperforming existing algorithms in large-scale instances.

Findings

Algorithms solve hard WCSPP instances efficiently.

Bucket-based priority queues improve A* search performance.

Empirical results show advantages over state-of-the-art methods.

Abstract

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.