Exact Multi-objective Path Finding with Negative Weights

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 MOSP instances with non-negative costs. This paper proposes 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, our algorithm demonstrates remarkable success in solving difficult MOSP instances, outperforming leading solutions by several factors.