Quantum-Inspired Estimation Of Distribution Algorithm To Solve The Travelling Salesman Problem

Abstract

A novel Quantum-Inspired Estimation of Distribution Algorithm (QIEDA) is proposed to solve the Travelling Salesman Problem (TSP). The QIEDA uses a modified version of the W state quantum circuits to sample new solutions during the algorithm runtime. The algorithm behaviour is compared with other state-of-the-art population-based algorithms. QIEDA convergence is faster than other algorithms, and the obtained solutions improve as the size of the problem increases. Moreover, we show that quantum noise enhances the search of an optimal solution. Because quantum computers differ from each other, partly due to the topology that distributes the qubits, the computational cost of executing the QIEDA in different topologies is analyzed and an ideal topology is proposed for the TSP solved with the QIEDA.