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Resource Constrained Pathfinding with Enhanced Bidirectional A* Search

Saman Ahmadi, Andrea Raith, Guido Tack, Mahdi Jalili

TL;DR

This work tackles the Resource Constrained Shortest Path problem (RCSP) on large graphs, aiming to minimize the primary cost while respecting multiple resource budgets. It introduces RCEBDA*, an enhanced bidirectional A* framework that combines improved initialization, tightened dominance pruning, and a refined path-matching strategy within a perimeter search, enabling more efficient exploration. Theoretical guarantees (including Theorem 1 and supporting lemmas) establish correctness and safety of the pruning and matching procedures, while extensive empirical evaluation on large road-network benchmarks demonstrates orders-of-magnitude speedups over state-of-the-art methods. The results indicate that RCEBDA* can solve previously intractable RCSP instances in practice and provides a robust, parallelizable solution with publicly available code.

Abstract

The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade, RCSP has seen recent solutions that utilize heuristic-guided search to solve the constrained problem faster. Building upon the bidirectional A* search paradigm, this research introduces a novel constrained search framework that uses efficient pruning strategies to allow for accelerated and effective RCSP search in large-scale networks. Results show that, compared to the state of the art, our enhanced framework can significantly reduce the constrained search time, achieving speed-ups of over to two orders of magnitude.

Resource Constrained Pathfinding with Enhanced Bidirectional A* Search

TL;DR

This work tackles the Resource Constrained Shortest Path problem (RCSP) on large graphs, aiming to minimize the primary cost while respecting multiple resource budgets. It introduces RCEBDA*, an enhanced bidirectional A* framework that combines improved initialization, tightened dominance pruning, and a refined path-matching strategy within a perimeter search, enabling more efficient exploration. Theoretical guarantees (including Theorem 1 and supporting lemmas) establish correctness and safety of the pruning and matching procedures, while extensive empirical evaluation on large road-network benchmarks demonstrates orders-of-magnitude speedups over state-of-the-art methods. The results indicate that RCEBDA* can solve previously intractable RCSP instances in practice and provides a robust, parallelizable solution with publicly available code.

Abstract

The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade, RCSP has seen recent solutions that utilize heuristic-guided search to solve the constrained problem faster. Building upon the bidirectional A* search paradigm, this research introduces a novel constrained search framework that uses efficient pruning strategies to allow for accelerated and effective RCSP search in large-scale networks. Results show that, compared to the state of the art, our enhanced framework can significantly reduce the constrained search time, achieving speed-ups of over to two orders of magnitude.

Paper Structure

This paper contains 8 sections, 1 equation, 3 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Problem Definition
  3. Bidirectional Constrained A* Search
  4. An Enhanced Bidirectional RCSP Search
  5. Theoretical Results
  6. Empirical Analysis
  7. Conclusion
  8. Acknowledgement

Figures (3)

  • Figure 1: An example graph with $k=3$ and $R=\{4,4\}$. Triples inside the states denote ${\bf h}^d$. $u_2$ and $u_5$ can be seen out of bounds.
  • Figure 2: Runtime distribution of RCEBDA*par and RCEBDA* versus RCBDA* over all instances with $k=4$.
  • Figure 3: Distribution of slowdown factors for RCEBDA* initialized conventionally. Each plot shows first quartile (25% data), median, third quartile (75% of data), mean ($\blacklozenge$), minimum and maximum within the 1.5$\times$ interquartile range, and absolute maximum slowdown. Outliers are not shown.