QUANTUM ANT COLONY OPTIMIZATION ALGORITHM BASED ON BLOCH SPHERICAL SEARCH

Abstract

In the existing quantum-behaved optimization algorithms, almost all of the individuals are encoded by qubits described on plane unit circle. As qubits con- tain only a variable parameter, quantum properties have not been fully embodied, which limits the optimization ability rise further. In order to solve this problem, this paper proposes a quantum ant colony optimization algorithm based on Bloch sphere search. In the proposed algorithm, the positions of ants are encoded by qubits described on Bloch sphere. First, the destination to move is determined according to the select probability constructed by the pheromone and heuristic information, then, the rotation axis is established with Pauli matrixes, and the evolution search is realized with the rotation of qubits on Bloch sphere. In or- der to avoid premature convergence, the mutation is performed with Hadamard gates. Finally, the pheromone and the heuristic information are updated in the new positions of ants. As the optimization process is performed in n-dimensional hypercube space (−1, 1) n , which has nothing to do with the specific issues, hence, the proposed method has good adaptability for a variety of optimization prob- lems. The simulation results show that the proposed algorithm is superior to other quantum-behaved optimization algorithms in both search ability and optimization efficiency.