# Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity

## TL;DR

This paper introduces a novel QUBO formulation for the capacitated vehicle routing problem that incorporates time, capacity, and state constraints, enabling quantum annealing solutions with D-Wave 2000Q.

## Contribution

It presents a new QUBO model for CVRP that includes time-evolution, capacity adjustments, and vehicle states, expanding the scope of quantum annealing applications.

## Key findings

- Successful formulation of CVRP as QUBO with time and capacity constraints
- Demonstration of quantum annealing on D-Wave 2000Q for the problem
- Enhanced modeling of vehicle states and traveling rules

## Abstract

We propose a brand-new formulation of capacitated vehicle routing problem (CVRP) as quadratic unconstrained binary optimization (QUBO). The formulated CVRP is equipped with time-table which describes time-evolution of each vehicle. Therefore, various constraints associated with time are successfully realized. With a similar method, constraints of capacities are also introduced, where capacitated quantities are allowed to increase and decrease according to the cities which vehicles arrive. As a bonus of capacity-qubits, one also obtains a description of state, which allows us to set a variety of traveling rules, depending on each state of vehicles. As a consistency check, the proposed QUBO formulation is also evaluated by quantum annealing with D-Wave 2000Q.