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 PPA*, a state-of-the-art approximate bi-objective search algorithm (where there are only two cost components) but (1) makes PPA* 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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Bounded-Cost Bi-Objective Heuristic Search [Short Paper]
There are many settings that extend the basic shortest-path search problem. In Bounded-Cost Search, we are given a constant bound, and the task is to find a solution within the bound. In Bi-Objective Search, each edge is associated with two costs (objectives), and the task is to minimize both objectives. In this paper, we combine both settings into a new setting of Bounded-Cost Bi-Objective Search. We are given two bounds, one for each objective, and the task is to find a solution within these bounds. We provide a scheme for normalizing the two objectives, introduce several algorithms for this new setting and compare them experimentally.
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- Award ID(s):
- 2121028
- PAR ID:
- 10350233
- Date Published:
- Journal Name:
- Proceedings of the Symposium on Combinatorial Search (SoCS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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