APULSE: A Scalable Hybrid Algorithm for the RCSPP on Large-Scale Dense Graphs

TL;DR

APULSE tackles RCSPP on large-scale dense graphs with a unidirectional, A*-guided search augmented by Pulse-style pruning and time bucketing. The method uses Phase 1 heuristic pre-computation and Phase 2 guided exploration with multi-level pruning, plus auto-tuned temporal granularity, to achieve near-optimal solutions with substantial speedups over exact solvers. Empirical results on a large UGV planning graph show APULSE often outperforming state-of-the-art exact solvers in runtime while maintaining near-optimal or optimal quality, enabling interactive decision support and dynamic replanning. This work demonstrates a scalable, robust approach for dense-grid path planning under time and risk constraints, with potential extensions to additional resources and multi-agent settings.

Abstract

The resource-constrained shortest path problem (RCSPP) is a fundamental NP-hard optimization challenge with broad applications, from network routing to autonomous navigation. This problem involves finding a path that minimizes a primary cost subject to a budget on a secondary resource. While various RCSPP solvers exist, they often face critical scalability limitations when applied to the large, dense graphs characteristic of complex, real-world scenarios, making them impractical for time-critical planning. This challenge is particularly acute in domains like mission planning for unmanned ground vehicles (UGVs), which demand solutions on large-scale terrain graphs. This paper introduces APULSE, a hybrid label-setting algorithm designed to efficiently solve the RCSPP on such challenging graphs. APULSE integrates a best-first search guided by an A* heuristic with aggressive, Pulse-style pruning mechanisms and a time-bucketing strategy for effective state-space reduction. A computational study, using a large-scale UGV planning scenario, benchmarks APULSE against state-of-the-art algorithms. The results demonstrate that APULSE consistently finds near-optimal solutions while being orders of magnitude faster and more robust, particularly on large problem instances where competing methods fail. This superior scalability establishes APULSE as an effective solution for RCSPP in complex, large-scale environments, enabling capabilities such as interactive decision support and dynamic replanning.

Figures (6)

• Figure 1: Conceptual illustration of the data layers associated with each node in the graph. Each node encapsulates geospatial attributes (terrain type, slope) and a computed risk value, forming the basis for the multi-cost pathfinding problem.
• Figure 2: Illustration of the time bucketing mechanism. Multiple labels arriving at node $v$ are grouped into discrete time buckets. For each state $(v,b)$, only the label with the minimum log-risk (green dot) is retained, while all others (red dots) are pruned.
• Figure 3: Operational test area (30 km2) within the Santa Margarida military training field. The red boundary denotes the region used to construct the experimental graph.
• Figure 4: Runtime evolution across instance scales ($\alpha=0.10$). APULSE becomes consistently faster from the 1$\to$5000 configuration onwards, confirming the crossover point.
• Figure 5: Runtime performance of APULSE compared to reference algorithms under two factors. (a) Effect of increasing budget slack $\alpha$ on runtime (Medium instance, 1$\to$15k). (b) Runtime scaling across instance sizes for a fixed slack $\alpha=0.5$.