A Quantum Genetic Hybrid Algorithm for Solving the Traveling Salesman Problem

– In this article we propose a Quantum inspired Genetic Algorithm (GQA) for solving the Traveling Salesman Problem (TSP). The TSP is a known combinatorial optimization problem which aims to find the shortest Hamiltonian cycle linking N cities. This algorithm is an extension of a classical genetic algorithm obtained by introducing some quantum principles such as quantum interference and states superposition. We have obtained excellent solutions in a limited number of iterations (generally about 5000 iterations). Some instances of this algorithm execution on the “gr24” TSP have given the optimal circuit given in the TSP reference site (having the length 1272).