The Pareto-optimal frontier for a bi-objective search problem instance consists of all solutions that are not worse than any other solution in both objectives. The size of the Pareto-optimal frontier can be exponential in the size of the input graph, and hence finding it can be hard. Some existing works leverage a user-specified approximation factor ε to compute an approximate Pareto-optimal frontier that can be significantly smaller than the Pareto-optimal frontier. In this paper, we propose an anytime approximate bi-objective search algorithm, called Anytime Bi-Objective A*-ε (A-BOA*ε). A-BOA*ε is useful when deliberation time is limited. It first finds an approximate Pareto-optimal frontier quickly, iteratively improves it while time allows, and eventually finds the Pareto-optimal frontier. It efficiently reuses the search effort from previous iterations and makes use of a novel pruning technique. Our experimental results show that A-BOA*ε substantially outperforms baseline algorithms that do not reuse previous search effort, both in terms of runtime and number of node expansions. In fact, the most advanced variant of A-BOA*ε even slightly outperforms BOA*, a state-of-the-art bi-objective search algorithm, for finding the Pareto-optimal frontier. Moreover, given only a limited amount of deliberation time, A-BOA*ε finds solutions that collectively approximate the Pareto-optimal frontier much better than the solutions found by BOA*.
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Enhanced multi-objective A* using balanced binary search trees
This work addresses a Multi-Objective Shortest Path Problem
(MO-SPP) on a graph where the goal is to find a set of
Pareto-optimal solutions from a start node to a destination
in the graph. A family of approaches based on MOA* have
been developed to solve MO-SPP in the literature. Typically,
these approaches maintain a “frontier” set at each node during
the search process to keep track of the non-dominated, partial
paths to reach that node. This search process becomes computationally
expensive when the number of objectives increases
as the number of Pareto-optimal solutions becomes large. In
this work, we introduce a new method to efficiently maintain
these frontiers for multiple objectives by incrementally
constructing balanced binary search trees within the MOA*
search framework. We first show that our approach correctly
finds the Pareto-optimal front, and then provide extensive
simulation results for problems with three, four and five objectives
to show that our method runs faster than existing
techniques by up to an order of magnitude.
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- Award ID(s):
- 2120529
- NSF-PAR ID:
- 10354018
- Editor(s):
- NA
- Date Published:
- Journal Name:
- Proceedings of the International Symposium on Combinatorial Search
- Volume:
- 15
- Issue:
- 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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