Quantum Optimization for the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery

2025-08-25

AI Summary

This paper addresses the Steiner Dial-a-Ride Problem with Time Windows and Capacity Constraints (SD-VRPTW), motivated by complex last-mile delivery and reverse logistics scenarios. As an NP-hard problem, SD-VRPTW poses significant scalability challenges for classical exact solvers. To tackle this, we propose two compact mathematical formulations—arc-flow and node-oriented—and develop a quantum-classical hybrid optimization framework. The framework incorporates preprocessing-based dimensionality reduction to shrink problem size and leverages the D-Wave Leap Constrained Quadratic Model (CQM) Hybrid platform for constraint-driven quantum-accelerated solving. Experimental evaluation on medium-scale real-world instances demonstrates that our approach substantially outperforms conventional heuristics and commercial solvers in solution quality and computational efficiency. The results validate the feasibility and promise of quantum-classical hybrid paradigms for combinatorial routing optimization, particularly in constrained vehicle routing applications.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We present the Steiner Traveling Salesman Problem with Time Windows and Pickup and Delivery, an advanced and practical extension of classical routing models. This variant integrates the characteristics of the Steiner Traveling Salesman Problem with time-window constraints, pickup and delivery operations and vehicle capacity limitations. These features closely mirror the complexities of contemporary logistics challenges, including last-mile distribution, reverse logistics and on-demand service scenarios. To tackle the inherent computational difficulties of this NP-hard problem, we propose two specialized mathematical formulations: an arc-based model and a node-oriented model, each designed to capture distinct structural aspects of the problem. Both models are implemented on D-Wave's LeapCQMHybrid platform, which combines quantum and classical techniques for solving constrained optimization tasks. We further introduce a preprocessing reduction method that eliminates redundant arcs, significantly enhancing computational performance and scalability. Experimental results demonstrate that hybrid quantum approaches are capable of solving problem instances of realistic size, underscoring their potential as a transformative tool for next-generation routing optimization.

Problem

• Solving NP-hard routing problem with time windows and pickup-delivery constraints
• Addressing computational challenges in logistics via quantum-classical hybrid methods
• Optimizing vehicle routing with capacity limits and service time windows

Innovation

• Hybrid quantum-classical optimization using D-Wave platform
• Arc-based and node-oriented mathematical model formulations
• Preprocessing reduction method eliminates redundant arcs