A Greedy Quantum Route-Generation Algorithm

TL;DR

This paper introduces a greedy quantum routing algorithm that constructs feasible solutions by leveraging quantum sampling data, demonstrating improved results over classical and hybrid methods in vehicle routing problems with time windows.

Contribution

It presents a novel quantum-inspired greedy algorithm that adaptively constructs feasible routes, addressing inequality constraints and noise issues in quantum computing.

Findings

Achieves lower objective values than state-of-the-art annealing methods.

Demonstrates robustness to quantum noise on D-Wave Advantage2.

Proves convergence to feasible solutions.

Abstract

Routing and scheduling problems with time windows have long been important optimization problems for logistics and planning. Many classical heuristics and exact methods exist for such problems. However, there are no satisfactory methods for generating routes using quantum computing (QC), for mainly two reasons: inequality constraints, and the trade-off of feasibility and solution quality. Inequality constraints are typically handled using slack variables; and feasible solutions are found by filtering samples. These challenges are amplified in the presence of noise inherent in QC. Here, we propose a greedy algorithm that generates routes by using information from all samples obtained from the quantum computer. By noticing the relationship between qubits in our formulation as a directed acyclic graph (DAG), we designed an algorithm that adaptively constructs a feasible solution. We prove its convergence to a feasible solution, and illustrate its efficacy by solving the Fleet Sizing Vehicle Routing Problem with Time Windows (FSVRPTW). Our computational results show that this method obtains a lower objective value than the current state-of-the-art annealing approaches, both classical and hybrid, for the same amount of time using D-Wave Hybrid Solvers. We also show its robustness to noise on D-Wave Advantage2 through computational results as compared to the filtering approach on DWaveSampler, even when the filtering approach is given a longer annealing time, and a larger sample size.