Parallelizing Multi-objective A* Search

TL;DR

This work tackles the multi-objective shortest path (MOSP) problem by introducing a parallel MOA* framework that runs MOA* with different objective orderings simultaneously across $k$ threads. A novel cross-thread upper-bounding mechanism reduces the effective search dimensionality, often collapsing it toward a single dimension and enabling significant pruning. Theoretical results establish correctness and global upper-bounding properties, while experiments on NYC-DIMACS MOSP instances show that parallelization yields speedups proportional to the number of objectives, solving more instances and delivering substantial runtime reductions at higher $k$. The approach delivers practical gains for large MOSP instances and lays groundwork for further scaling with additional objective orderings and tighter inter-thread coordination.

Abstract

The Multi-objective Shortest Path (MOSP) problem is a classic network optimization problem that aims to find all Pareto-optimal paths between two points in a graph with multiple edge costs. Recent studies on multi-objective search with A* (MOA*) have demonstrated superior performance in solving difficult MOSP instances. This paper presents a novel search framework that allows efficient parallelization of MOA* with different objective orders. The framework incorporates a unique upper bounding strategy that helps the search reduce the problem's dimensionality to one in certain cases. Experimental results demonstrate that the proposed framework can enhance the performance of recent A*-based solutions, with the speed-up proportional to the problem dimension.

Figures (2)

• Figure 1: Runtime distribution of NWMOA* and LTMOA* versus their parallelized variant over instances with $k=4$.
• Figure 2: Cactus plot of LTMOA*'s performance versus its virtual best variant, parallelized variant with and without upper bounding (denoted noub). Instances are sorted by runtime.