Advanced Quantum Annealing Approach to Vehicle Routing Problems with Time Windows

2025-03-31

AI Summary

This work addresses two NP-hard combinatorial optimization problems: the Traveling Salesman Problem with Time Windows (TSPTW) and the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). To overcome the rapid degradation of time-window feasibility in large-scale instances on quantum annealers, we propose a quantum-classical hybrid solving framework. Our method leverages D-Wave quantum annealing hardware and Constraint Quadratic Modeling (CQM), augmented by classical heuristics for co-optimization. The key contribution is the first quantum solution post-processing heuristic specifically designed to repair time-window violations—achieved via localized sequence swaps that restore feasibility while preserving solution quality. Evaluated on standard benchmarks, the framework achieves an average optimality gap of 3.86%, significantly improving both time-window satisfaction rates and solution quality for large-scale instances.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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%.

Problem

• Quantum annealing for vehicle routing with time windows
• Solving NP-Hard problems using hybrid quantum-classical framework
• Improving feasibility in large-scale routing via heuristic swaps

Innovation

• Uses D-Wave Quantum Annealer for routing
• Applies Constrained Quadratic Model solver
• Implements heuristic swapping for feasibility