Abstract
The determination of vehicle routes fulfilling connectivity, time, and operational constraints is a well-studied combinatorial optimization problem. The NP-hard complexity of vehicle routing problems has fostered the adoption of tailored exact approaches, matheuristics, and metaheuristics on classical computing devices. The ongoing evolution of quantum computing hardware and the recent advances of quantum algorithms (i.e., VQE, QAOA, and ADMM) for mathematical programming make decision-making for routing problems an avenue of research worthwhile to be explored on quantum devices. In this article, we propose several mathematical formulations for inventory routing cast as vehicle routing with time windows and comment on their strengths and weaknesses. The optimization models are compared from a quantum computing perspective, specifically with metrics to evaluate the difficulty in solving the underlying quadratic unconstrained binary optimization problems. Finally, the solutions obtained on simulated quantum devices demonstrate the relative benefits of different algorithms and their robustness when put into practice.
Highlights
Routing problems encompass a wide range of problems in logistics and operations research
The ongoing evolution of quantum computing hardware and the recent advances of quantum algorithms for mathematical programming make decision-making for routing problems an avenue of research worthwhile to be explored on quantum devices
The continuous problems of the alternating direction method of multipliers (ADMM) converge to a local stationary point, and the overall ADMM strategy will remain a heuristic in general, but with the advantage that it limits the introduction of auxiliary binary decision variables in the quadratic unconstrained binary optimization (QUBO) subproblems and makes the solution of mixed binary optimization (MBO) on quantum devices a computationally tractable task
Summary
Routing problems encompass a wide range of problems in logistics and operations research. This article aims to bring together different formulations for solving routing problems on quantum devices, with specific focus on timing constraints, expressed either in a discrete or continuous form. These formulations are largely inspired by the classical operations research literature, but we introduce them here in order to obtain QUBO representations suitable for quantum algorithms. While Irie et al [23] have introduced a formulation that handles timing constraints, we are not aware of any work that collects VRPTW approaches together and compares them in the context of quantum algorithms (see [24] for a comparison of different formulations in a classical setting). Diag(v) denotes a square matrix with v on its diagonal and zeros elsewhere
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
