In the existing quantum intelligent optimization algorithms,almost all of the individuals are encoded by qubits described on plane unit circle.Since there is only one adjustable parameter,quantum properties have not been fully embodied,which limits the improvement of the optimization ability further.To address this issue,a chaos quantum immune algorithm based on Bloch sphere is proposed.In the proposed algorithm,the antibodies are encoded by qubits described on Bloch sphere,the axis of rotation is designed by using Pauli matrix,the clone of the excellent antibodies is performed by rotating qubits on Bloch sphere,and the local searching is achieved by employing the chaos variables in the rotation angles.The global searching is achieved by the mutations of the inferior individuals based on the Hadamard gates.The simulation results show that the proposed algorithm is superior to other quantum intelligent optimization algorithms in both search capability and optimization efficiency.
In the existing quantum intelligent optimization algorithms,almost all of the individuals are encoded by qubits described on plane unit circle.Since there is only one adjustable parameter,quantum properties have not been fully embodied,which limits the improvement of the optimization ability further.To address this issue,a chaos quantum immune algorithm based on Bloch sphere is proposed.In the proposed algorithm,the antibodies are encoded by qubits described on Bloch sphere,the axis of rotation is designed by using Pauli matrix,the clone of the excellent antibodies is performed by rotating qubits on Bloch sphere,and the local searching is achieved by employing the chaos variables in the rotation angles.The global searching is achieved by the mutations of the inferior individuals based on the Hadamard gates.The simulation results show that the proposed algorithm is superior to other quantum intelligent optimization algorithms in both search capability and optimization efficiency.
To enhance optimization ability of quantum potential well-based particle swarm optimization algorithm,a quantum particle swarm optimization algorithm based on Bloch spherical search is proposed by analyzing the design of quantum potential well-based particle swarm optimization algorithms.Firstly,particles are expressed with qubits,axis of rotation is established with Pauli matrix,the angle of rotation is obtained with a model of Delta potential well,and search is realized with rotation of qubits in Bloch sphere.Then,to avoid premature convergence,mutation of particles is achieved with Hadamard gates.Such rotation makes current qubit approximates target qubit along with the biggest circle on Bloch sphere,which accelerates optimization process.It shows that the proposed algorithm is superior to the original one in optimization ability.
To enhance the performance of the intelligent optimization algorithm, a new model of performing search on the Bloch sphere is proposed. Then, by integrating the model into the artificial fish swarm optimization, we present a quantum-inspired artificial fish swarm optimization algorithm. In proposed method, the fishes are encoded with the qubits described on the Bloch sphere. The vector product theory is adopted to establish the axis of rotation, and the Pauli matrices are used to construct the rotation matrices. The four fish behaviors, such as moving, tracking, capturing, aggregating, are achieved by rotating the current qubit about the rotation axis to the target qubit on the Bloch sphere. The Bloch coordinates of qubit can be obtained by measuring with the Pauli matrices, and the optimization solutions can be presented through the solution space transformation. The highlight advantages of this method are the ability to simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method obviously outperforms the classical one in convergence speed and achieves better levels for some benchmark functions.
To enhance the optimization performance of differential evolution algorithm, by studying the implementation mechanism of differential evolution algorithm, a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper. In the proposed approach, the individuals are encoded by qubits described on Bloch sphere, and the rotation angles of qubits in current individual are obtained by differential strategy. The axis of rotation is designed by using vector product theory, and the rotation matrixes are constructed by using Pauli matrixes. Taking the corresponding qubits in current best individual as targets, the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere. The Hadamard gates are used to mutate individuals. The simulation results of optimizing the minimum value of functions indicate that, for an iterative step, the average time of the proposed approach is 13 times as long as that of the classical differential evolution algorithm. When the same limited steps are applied in two approaches, the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches, the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm. These results suggest that the proposed approach is inefficient in computational ability; however, it is obviously efficient in optimization ability, and the overall optimization performance is better than that of the classical differential evolution algorithm.
To enhance the optimization performance of differential evolution algorithm,by studying the implementation mechanism of differential evolution algorithm,a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper.In the proposed approach,the individuals are encoded by qubits described on Bloch sphere,and the rotation angles of qubits in current individual are obtained by differential strategy.The axis of rotation is designed by using vector product theory,and the rotation matrixes are constructed by using Pauli matrixes.Taking the corresponding qubits in current best individual as targets,the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere.The Hadamard gates are used to mutate individuals.The simulation results of optimizing the minimum value of functions indicate that,for an iterative step,the average time of the proposed approach is 13times as long as that of the classical differential evolution algorithm.When the same limited steps are applied in two approaches,the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches,the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm.These results suggest that the proposed approach is inefficient in computational ability; however,it is obviously efficient in optimization ability,and the overall optimization performance is better than the classical differential evolution algorithm.
To improve the efficiency of particle swarm optimization, a quantum particle swarm optimization algorithm is proposed on the basis of analyzing the search process of particle swarm optimization algorithm. In the proposed algorithm, particles are endoded by qubits described on the Bloch sphere, each particle occupy three locations of the search space, and each location represents a optimization solution. By employing the search method of general PSO to adjust the two parameters of qubit, the qubits rotation are performed on the Bloch sphere, which can simultaneously update three locations occupied by a qubit and quickly approach the global optimal solution. The experimental results of standard test function extreme optimization and fuzzy controller parameters optimization show that the proposed algorithm is superior to other similar algorithm in optimization ability and optimization efficiency.
To enhance the performance of the artificial bee colony optimization by integrating the quantum computing model into bee colony optimization, we present a quantum-inspired bee colony optimization algorithm. In our method, the bees are encoded with the qubits described on the Bloch sphere. The classical bee colony algorithm is used to compute the rotation axes and rotation angles. The Pauli matrices are used to construct the rotation matrices. The evolutionary search is achieved by rotating the qubit about the rotation axis to the target qubit on the Bloch sphere. By measuring with the Pauli matrices, the Bloch coordinates of qubit can be obtained, and the optimization solutions can be presented through the solution space transformation. The proposed method can simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method is obviously superior to the classical one for some benchmark functions.