GPS: A new TSP formulation for its generalizations type QUBO

TL;DR

This paper introduces a novel QUBO formulation for the TSP that reduces variable count and is tested on a quantum annealing simulator, advancing optimization approaches for routing problems.

Contribution

The paper presents a new QUBO formulation for TSP that outperforms previous VRP formulations in variable efficiency and evaluates its effectiveness using quantum annealing simulation.

Findings

New QUBO formulation reduces variables compared to previous models.

Benchmarking shows improved constraint handling over existing formulations.

Successful testing on a quantum annealing simulator confirms correctness.

Abstract

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we tested whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave\_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations.