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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A New Approach for the Resource Constrained Shortest Path Problem
Abstract—The Resource Constrained Shortest Path Problem
(RCSPP) seeks to determine a minimum-cost path between a
start and a goal location while ensuring that one or multiple
types of resource consumed along the path do not exceed
their limits. This problem is often solved on a graph where
a path is incrementally built from the start towards the goal
during the search. RCSPP is computationally challenging as
comparing these partial solution paths is based on multiple
criteria (i.e., the accumulated cost and resource along the path),
and in general, there does not exist a single path that optimizes
all criteria simultaneously. Consequently, the search needs to
maintain and explore a large number of partial paths in order to
find an optimal solution. While a variety of algorithms have been
developed to solve RCSPP, they either have little consideration
about efficiently comparing and maintaining the partial paths,
which reduces their overall runtime efficiency, or are restricted
to handle only one resource constraint as opposed to multiple
resource constraints. This paper develops Enhanced Resource
Constrained A* (ERCA*), a fast A*-based algorithm that can find
an optimal solution while satisfying multiple resource constraints.
ERCA* leverages both the recent advances in multi-objective
path planning to efficiently compare and maintain partial paths,
and techniques from the existing RCSPP literature. Furthermore,
ERCA* has a functional parameter to broker a trade-off between
solution quality and runtime efficiency. The results show ERCA*
often runs several orders of magnitude faster than an existing
leading algorithm for RCSPP.
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- Award ID(s):
- 2120529
- NSF-PAR ID:
- 10466861
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Intelligent Transportation Systems
- ISSN:
- 0000-0000
- Subject(s) / Keyword(s):
- Index Terms—Path Planning, Heuristic Search, Shortest Path
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TITS.2023.3293039
