Proceedings International Conference on Automated Planning and Scheduling, ICAPS (2022) 32 394-403

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In multi-objective search, edges are annotated with cost vectors consisting of multiple cost components. A path dominates another path with the same start and goal vertices iff the component-wise sum of the cost vectors of the edges of the former path is “less than” the component-wise sum of the cost vectors of the edges of the latter path. The Pareto-optimal solution set is the set of all undominated paths from a given start vertex to a given goal vertex. Its size can be exponential in the size of the graph being searched, which makes multi-objective search time-consuming. In this paper, we therefore study how to find an approximate Pareto-optimal solution set for a user-provided vector of approximation factors. The size of such a solution set can be significantly smaller than the size of the Pareto-optimal solution set, which enables the design of approximate multi-objective search algorithms that are efficient and produce small solution sets. We present such an algorithm in this paper, called A*pex. A*pex builds on PP-A*, a state-of-the-art approximate bi-objective search algorithm (where there are only two cost components) but (1) makes PP-A* more efficient for bi-objective search and (2) generalizes it to multi-objective search for any number of cost components. We first analyze the correctness of A*pex and then experimentally demonstrate its efficiency advantage over existing approximate algorithms for bi- and tri-objective search.

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Zhang, H., Salzman, O., Kumar, T. K. S., Felner, A., Ulloa, C. H., & Koenig, S. (2022). A*pex: Efficient Approximate Multi-Objective Search on Graphs. In *Proceedings International Conference on Automated Planning and Scheduling, ICAPS* (Vol. 32, pp. 394–403). Association for the Advancement of Artificial Intelligence. https://doi.org/10.1609/icaps.v32i1.19825

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