Exact Multi-objective Path Finding with Negative Weights and Negative Cycles

Saman Ahmadi, Daniel Harabor, Nathan R. Sturtevant, Mahdi Jalili

Keywords: Multi-objective Path Finding, Shortest Path Problem, Heuristic Search

Abstract: The point-to-point Multi-objective Shortest Path (MOSP) problem is a classic yet challenging task that involves finding all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies have shown that employing A* search can lead to state-of-the-art performance in solving point-to-point MOSP instances with non-negative costs. In this paper, we propose a novel A*-based multi-objective search framework that not only handles graphs with negative costs and even negative cycles but also incorporates multiple speed-up techniques to enhance the efficiency of exhaustive search with A*. Through extensive experiments on large realistic test cases, our algorithm demonstrates remarkable success in solving difficult MOSP instances, outperforming the state of the art by up to an order of magnitude.

Primary Keywords: Applications, Theory

Category: Long

Student: No

Submission Number: 89