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A Fast Heuristic Search Approach for Energy-Optimal Profile Routing for Electric Vehicles

Saman Ahmadi, Mahdi Jalili

TL;DR

This work tackles energy-optimal EV routing under unknown initial energy by introducing Pr-A*, a label-setting, multi-objective A* method that uses energy-profile dominance to avoid costly profile merging. Theoretical results show that energy profiles can be compactly represented by two breakpoints and that the algorithm preserves optimality while pruning dominated labels. Empirical evaluation on large, real-world road networks demonstrates that unidirectional Pr-A* variants perform close to or match energy-optimal A* with known $\mathcal{E}_{init}$, while offering a practical, scalable framework for energy-profile queries. The approach provides a simpler, yet effective, alternative to existing profile-search methods for EV routing in large-scale networks.

Abstract

We study the energy-optimal shortest path problem for electric vehicles (EVs) in large-scale road networks, where recuperated energy along downhill segments introduces negative energy costs. While traditional point-to-point pathfinding algorithms for EVs assume a known initial energy level, many real-world scenarios involving uncertainty in available energy require planning optimal paths for all possible initial energy levels, a task known as energy-optimal profile search. Existing solutions typically rely on specialized profile-merging procedures within a label-correcting framework that results in searching over complex profiles. In this paper, we propose a simple yet effective label-setting approach based on multi-objective A* search, which employs a novel profile dominance rule to avoid generating and handling complex profiles. We develop four variants of our method and evaluate them on real-world road networks enriched with realistic energy consumption data. Experimental results demonstrate that our energy profile A* search achieves performance comparable to energy-optimal A* with a known initial energy level.

A Fast Heuristic Search Approach for Energy-Optimal Profile Routing for Electric Vehicles

TL;DR

This work tackles energy-optimal EV routing under unknown initial energy by introducing Pr-A*, a label-setting, multi-objective A* method that uses energy-profile dominance to avoid costly profile merging. Theoretical results show that energy profiles can be compactly represented by two breakpoints and that the algorithm preserves optimality while pruning dominated labels. Empirical evaluation on large, real-world road networks demonstrates that unidirectional Pr-A* variants perform close to or match energy-optimal A* with known , while offering a practical, scalable framework for energy-profile queries. The approach provides a simpler, yet effective, alternative to existing profile-search methods for EV routing in large-scale networks.

Abstract

We study the energy-optimal shortest path problem for electric vehicles (EVs) in large-scale road networks, where recuperated energy along downhill segments introduces negative energy costs. While traditional point-to-point pathfinding algorithms for EVs assume a known initial energy level, many real-world scenarios involving uncertainty in available energy require planning optimal paths for all possible initial energy levels, a task known as energy-optimal profile search. Existing solutions typically rely on specialized profile-merging procedures within a label-correcting framework that results in searching over complex profiles. In this paper, we propose a simple yet effective label-setting approach based on multi-objective A* search, which employs a novel profile dominance rule to avoid generating and handling complex profiles. We develop four variants of our method and evaluate them on real-world road networks enriched with realistic energy consumption data. Experimental results demonstrate that our energy profile A* search achieves performance comparable to energy-optimal A* with a known initial energy level.

Paper Structure

This paper contains 14 sections, 20 equations, 5 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem Definition and Background
  3. Energy-optimal pathfinding with A*
  4. Pathfinding with unknown $\mathcal{E}_{init}$
  5. Energy-Optimal Profile A* Search
  6. Theoretical Results
  7. Experimental Analysis
  8. Conclusion
  9. Acknowledgments
  10. Graphs with actual energy as edge cost.
  11. Energy models based on longitudinal dynamics.
  12. Linking Energy Profiles
  13. Energy Profile Search with Backward A*
  14. Energy Profile Search with Bidirectional A*

Figures (5)

  • Figure 1: Schematic illustration of energy profiles. Horizontal axis is the $\mathcal{E}_{\mathit{init}}$ range. From left to right: positive-cost link, negative-cost link, and a generic path profile.
  • Figure 2: Dominance and non-dominance of energy profiles. In each plot, the profile of $z$ (in red) is dominated by the profile of $x$ (in blue). The profiles of $x$ and $y$ (blue and green) are non-dominated and can both contribute to the lower envelope (in gray).
  • Figure 3: Distribution of expansion differences (%) for profile-search algorithms relative to energy-optimal A*.
  • Figure 4: A schematic of distance- and energy-based heuristics.
  • Figure 5: A schematic of energy profile linking for a simple path. The linking procedure is performed in the backward direction, starting with the last edge (leftmost plot). The final energy profile of the path is shown in the rightmost plot. Maximum energy is set to $\mathcal{E}_{\mathit{max}}=5$.