[Paper Review] Two-Phase Bicriterion Search for Finding Fast and Efficient Electric Vehicle Routes

Michael T. Goodrich, Paweł Pszona|arXiv (Cornell University)|Sep 10, 2014

Algorithms and Data Compression6 references4 citations

TL;DR

This paper proposes a two-phase bicriterion search algorithm that efficiently finds electric vehicle routes balancing driving time and energy consumption by splitting paths into two driving styles—initially optimizing for speed, then for efficiency. The method runs in O(n log n + m) time for non-negative weights and achieves near-optimal reachability (over 99%) with minimal performance overhead, even when incorporating charging stations.

ABSTRACT

The problem of finding an electric vehicle route that optimizes both driving time and energy consumption can be modeled as a bicriterion path problem. Unfortunately, the problem of finding optimal bicriterion paths is NP-complete. This paper studies such problems restricted to two-phase paths, which correspond to a common way people drive electric vehicles, where a driver uses one driving style (say, minimizing driving time) at the beginning of a route and another driving style (say, minimizing energy consumption) at the end. We provide efficient polynomial-time algorithms for finding optimal two-phase paths in bicriterion networks, and we empirically verify the effectiveness of these algorithms for finding good electric vehicle driving routes in the road networks of various U.S. states. In addition, we show how to incorporate charging stations into these algorithms, in spite of the computational challenges introduced by the negative energy consumption of such network vertices.

Motivation & Objective

• To address the challenge of finding optimal trade-offs between driving time and energy consumption in electric vehicle routing.
• To model real-world driving behavior where drivers switch between time-optimized and energy-optimized driving styles.
• To develop a polynomial-time algorithm that outperforms existing NP-complete approaches for bicriterion path problems.
• To integrate charging stations into route planning despite computational challenges from negative energy consumption at stations.
• To empirically validate the algorithm’s performance and solution quality on real U.S. road networks.

Proposed method

• Formalize the problem as a two-phase bicriterion path problem, where the first segment optimizes for one criterion (e.g., time) and the second for another (e.g., energy).
• Use a modified Dijkstra’s algorithm to compute shortest paths under two distinct criteria, then combine results via a two-phase traversal strategy.
• Apply a two-phase search that identifies optimal transition points between driving styles using efficient priority-queue-based computations.
• Handle charging stations by modeling them as vertices with negative energy consumption, and extend the algorithm to support multiple stations with minimal overhead.
• Use a labeling technique to track both time and energy costs per path, ensuring dominance checks are performed efficiently.
• Optimize performance by precomputing paths between charging stations and leveraging existing speed-up techniques for Dijkstra’s algorithm.

Experimental results

Research questions

• RQ1 Can a two-phase bicriterion path approach achieve near-optimal route quality while maintaining polynomial-time complexity?
• RQ2 How does the two-phase method compare to exact pseudo-polynomial algorithms in terms of solution quality and running time?
• RQ3 To what extent can charging stations be effectively integrated into bicriterion route planning without degrading performance?
• RQ4 How does the number of charging stations affect the running time and reachability of the two-phase algorithm?
• RQ5 Can the two-phase approach support real-world electric vehicle driving patterns with practical performance on large-scale road networks?

Key findings

• The two-phase algorithm achieves over 99% reachability of vertices reachable by energy-efficient algorithms, demonstrating near-optimal solution quality.
• On the Nevada road network (261,155 vertices, 311,043 edges), the algorithm found feasible routes for 92.6% of origin-destination pairs with an 85 kWh battery and 10 charging stations, in under 35 seconds on average.
• With a 60 kWh battery and 10 charging stations, the algorithm achieved 92.6% reachability in under 35 seconds, showing strong scalability.
• The algorithm’s running time scales primarily with the number of charging stations, and performance can be further improved by precomputing inter-charging-station paths.
• Even on a modest 2.2 GHz CPU, the algorithm computed routes in under 35 seconds for large-scale networks, indicating strong practical feasibility.
• The method supports realistic driving behavior with only two driving styles and a single transition point, making it easier for drivers to follow than complex multi-criteria routes.