Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Advanced Quantum Annealing Approach to Vehicle Routing Problems with Time Windows

James B. Holliday, Darren Blount, Eneko Osaba, Khoa Luu

TL;DR

This paper investigates applying quantum annealing to complex routing with time windows by integrating D-Wave's Constrained Quadratic Model (CQM) into a hybrid HQTS framework. It shifts from QUBO to CQM to explicitly model time-window constraints, introduces arrival-time and sequencing variables to improve feasibility, and deploys a post-processing swapping heuristic to repair infeasible solutions. Across Solomon benchmark instances, the approach achieves an average optimality gap around $3.86\%$ and demonstrates competitive performance relative to Google OR-Tools, highlighting the potential and limitations of quantum-classical integration for real-world vehicle routing with time windows. The work emphasizes the importance of feasibility-focused post-processing in practical quantum optimization and sets a foundation for broader, scalable quantum-assisted routing research.

Abstract

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Advanced Quantum Annealing Approach to Vehicle Routing Problems with Time Windows

TL;DR

This paper investigates applying quantum annealing to complex routing with time windows by integrating D-Wave's Constrained Quadratic Model (CQM) into a hybrid HQTS framework. It shifts from QUBO to CQM to explicitly model time-window constraints, introduces arrival-time and sequencing variables to improve feasibility, and deploys a post-processing swapping heuristic to repair infeasible solutions. Across Solomon benchmark instances, the approach achieves an average optimality gap around and demonstrates competitive performance relative to Google OR-Tools, highlighting the potential and limitations of quantum-classical integration for real-world vehicle routing with time windows. The work emphasizes the importance of feasibility-focused post-processing in practical quantum optimization and sets a foundation for broader, scalable quantum-assisted routing research.

Abstract

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Paper Structure

This paper contains 14 sections, 7 equations, 6 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Routing Problems with Time Windows
  4. Quantum Annealing and Constrained Quadratic Model (CQM)
  5. Related Work
  6. Problem Formulation
  7. Traveling Salesman Problem with Time Windows (TSPTW)
  8. Capacitated Vehicle Routing Problem with Time Windows (CVRPTW)
  9. Our Proposed Method
  10. Experiments and Results
  11. Datasets and Setup
  12. TSPTW
  13. CVRPTW
  14. Conclusions

Figures (6)

  • Figure 1: Vehicle Route with Time Window Constraints
  • Figure 2: Solving the CVRPTW with a phased approach
  • Figure 3: The proposed flow of HQTS for CVRPTW
  • Figure 4: Proportion of Time Constraints Violated for Increasing Number of Stops
  • Figure 5: Comparison of Average Percent Deviation from Best Known Solution(s) for HQTS and OR-Tools on the Solomon CVRPTW Subset
  • ...and 1 more figures