[Paper Review] Speed-up Heuristic for an On-Demand Ride-Pooling Algorithm

Roman Engelhardt, Florian Dandl+1 more|arXiv (Cornell University)|Jul 29, 2020

Transportation and Mobility InnovationsEngineering14 references17 citations

TL;DR

This paper proposes a speed-up heuristic for an on-demand ride-pooling algorithm to reduce computational time in large-scale dynamic vehicle routing while preserving solution quality. By introducing a three-rule vehicle selection heuristic that prunes the search space, the method achieves a 2.5x overall speed-up—especially reducing the most expensive step by a factor of 8—while maintaining 70% of the distance savings and nearly all served requests compared to the full multi-step algorithm.

ABSTRACT

With ongoing developments in digitalization and advances in the field of autonomous driving, on-demand ride pooling is a mobility service with the potential to disrupt the urban mobility market. Nevertheless, to apply this kind of service successfully efficient algorithms have to be implemented for effective fleet management to exploit the benefits associated with this mobility service. Especially real time computation of finding beneficial assignments is a problem not solved for large problem sizes until today. In this study, we show the importance of using advanced algorithms by comparing a fast, but simple insertion heuristic algorithm with a state-of-the-art multi-step matching algorithm. We test the algorithms in various scenarios based on private vehicle trip OD-data for Munich, Germany. Results indicate that in the tested scenarios by using the multi-step algorithm up to 8$\%$ additional requests could be served while also 10$\%$ additional driven distance could be saved. However, computational time for finding optimal assignments in the advanced algorithm exceeds real time rather fast as problem size increases. Therefore, several aspects to reduce the computational time by decreasing redundant checks of the advanced multi step algorithm are introduced. Finally, a refined vehicle selection heuristic based on three rules is presented to furthermore reduce the computational effort. In the tested scenarios this heuristic can speed up the most cost intensive algorithm step by a factor of over 8, while keeping the number of served requests almost constant and maintaining around 70$\%$ of the driven distance saved in the system. Considering all algorithm steps, an overall speed up of 2.5 could be achieved.

Motivation & Objective

• Address the computational bottleneck in large-scale on-demand ride-pooling systems, where NP-hard matching problems explode in complexity with fleet size.
• Improve real-time feasibility of advanced multi-step matching algorithms by reducing redundant computations in the vehicle-to-request matching phase.
• Maintain high solution quality—especially in request acceptance rate and distance savings—while drastically cutting runtime for practical deployment.
• Develop a heuristic-based vehicle selection strategy that leverages spatial and temporal request patterns to limit candidate vehicles per request.
• Enable scalable, real-time ride-pooling operations in dense urban environments like Munich, Germany, using optimized algorithmic design.

Proposed method

• Adapt the multi-step ODRP algorithm from Alonso-Mora et al. (2015), which decouples the problem using shareability networks and time-expanded routing.
• Introduce a vehicle selection heuristic based on three rules: (1) proximity to origin, (2) expected travel time to pickup, and (3) route compatibility with existing requests.
• Cache and reuse previously computed feasible vehicle-to-request-bundle (V2RB) combinations across time steps to avoid recomputation.
• Apply the heuristic specifically to the most computationally intensive step—building the V2RB database—where it reduces time by a factor of 8.
• Use a hybrid approach: combine the fast insertion heuristic as a baseline with the optimized multi-step algorithm to compare performance trade-offs.
• Implement a simulation framework using real private vehicle trip OD-data from Munich to evaluate performance under varying demand levels (5%, 10%, 15%).

Experimental results

Research questions

• RQ1 To what extent can a heuristic-based vehicle selection strategy reduce computational time in a multi-step on-demand ride-pooling algorithm without sacrificing solution quality?
• RQ2 How does the performance of the advanced multi-step algorithm compare to a simple insertion heuristic in terms of request acceptance and distance savings?
• RQ3 What is the impact of search space pruning via vehicle selection rules on the scalability of the algorithm as fleet size and demand increase?
• RQ4 Can caching previously computed V2RBs across time steps significantly reduce redundant computation in dynamic ride-pooling?
• RQ5 How does the heuristic’s effectiveness vary across different demand densities, particularly during peak hours?

Key findings

• The multi-step algorithm outperforms the insertion heuristic by serving up to 8% more requests and saving 10% more driven distance in tested Munich scenarios.
• The proposed vehicle selection heuristic reduces the time to build the V2RB database by a factor of 8, which is the most computationally intensive step.
• Despite the aggressive pruning, the heuristic maintains 70% of the distance savings achieved by the full algorithm and preserves nearly all served requests.
• The overall algorithm achieves a 2.5x speed-up across all steps, with the greatest gains in the most expensive computational phases.
• The heuristic is most effective during high-demand periods due to increased route overlap and better convergence of vehicle selection rules.
• The speed-up is expected to increase with larger problem sizes, as the heuristic targets exponentially scaling components, while unaffected steps scale quadratically.