多比特概率幅编码的量子衍生粒子群优化算法
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摘要
为了提高粒子群算法的优化能力,提出一种新的量子衍生粒子群优化算法.该方法采用多比特量子系统的基态概率幅对粒子编码,基于自身最优粒子和全局最优粒子确定旋转角度,采用基于张量积构造的多比特量子旋转门实施粒子的更新.在每步迭代中,只需更新粒子的一个量子比特相位,即可更新该粒子上的所有概率幅.标准函数极值优化的实验结果表明,所提出算法的单步迭代时间较长,但优化能力较同类算法有大幅度提高.
To enhance the optimization ability of the particle swarm algorithm, a novel quantum-inspired particle swarm optimization algorithm is proposed. In this method, the particles are encoded by the probability amplitudes of the basic states of the multi-qubits system. The rotation angles of multi-qubits are determined based on the local optimum particle and the global optimal particle, and the multi-qubits rotation gates are employed to update the particles. At each of iteration,updating any a qubit can lead to update all probability amplitudes of the corresponding particle. The experimental results of some benchmark functions optimization shows that, although its single step iteration consumes a long time, the optimization ability of the proposed method is significantly higher than other similar algorithms.
To enhance the optimization ability of the particle swarm algorithm, a novel quantum-inspired particle swarm optimization algorithm is proposed. In this method, the particles are encoded by the probability amplitudes of the basic states of the multi-qubits system. The rotation angles of multi-qubits are determined based on the local optimum particle and the global optimal particle, and the multi-qubits rotation gates are employed to update the particles. At each of iteration,updating any a qubit can lead to update all probability amplitudes of the corresponding particle. The experimental results of some benchmark functions optimization shows that, although its single step iteration consumes a long time, the optimization ability of the proposed method is significantly higher than other similar algorithms.
引文
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[16]赵玉新,刘立强.新兴元启发式优化算法[M].北京:科学出版社,2013:240-251.(Zhao Y X,Liu L Q.Emerging heuristic optimization algorithm[M].Beijing:Science press,2013:240-251.)
[2]Guo W Z,Chen G L,Peng S J.Hybrid particle swarm optimization algorithm for vlsi circuit partitioning[J].J of Software,2011,22(5):833-842.
[3]秦华,万云芳,张伟元,等.用粒子群算法进行单个非球面透镜的球差校正[J].计算物理,2012,29(3):426-432.(Qin H,Wan Y F,Zhang W Y,et al.Aberration correction of single aspheric lens with particle swarm algorithm[J].Chinese J of Computational Physics,2012,29(3):426-432.)
[4]Cai X J,Cui Z H,Zeng J C.Dispersed particle swarm optimization[J].Information Processing Letters,2008,105(6):231-235.
[5]Liu Y,Qin Z,Shi Z W.Center particle swarm optimization[J].Neurocomputing,2007,70(4/5/6):672-679.
[6]张英杰,邵岁锋.一种基于云模型的云变异粒子群算法[J].模式识别与人工智能,2011,24(1):90-96.(Zhang Y J,Shao S F.Cloud mutation particle swarm optimization algorithm based on cloud model[J].Pattern Recognition and Artificial Intelligence,2011,24(1):90-96.)
[7]方伟,孙俊,谢振平,等.量子粒子群优化算法的收敛性分析及控制参数研究[J].物理学报,2010,59(6):3686-3694.(Fang W,Sun J,Xie Z P,et al.Convergence analysis of quantum-behaved particle swarm optimization algorithm and study on its control parameter[J].Acta Physica Sinica,2010,59(6):3686-3694.)
[8]Sun J,Wu X J,Fang W,et al.Convergence analysis and improvements of quantum-behaved particle swarm optimization[J].Information Sciences,2012,193:81-103.
[9]Lu T C,Yu G R.An adaptive population multiobjective quantum inspired evolutionary algorithm for multi-objective 0/1 knapsack problems[J].Information Sciences,2013,243:39-56.
[10]Abdesslem L.A hybrid quantum inspired harmony search algorithm for 0-1 optimization problems[J].J of Computational and Applied Mathematics,2013,253:14-25.
[11]Gao J Q.A hybrid quantum inspired immune algorithm for multiobjective optimization[J].Applied Mathematics and Computation,2011,217(9):4754-4770.
[12]Han K H,Kim J H.Quantum-inspired evolutionary algorithm for a class of combinatorial optimization[J].IEEE Trans on Evolutionary Computation,2002,6(6):580-593.
[13]刘显德,李盼池,杨淑云.量子衍生差分进化算法的设计与实现[J].信号处理,2014,30(6):623-633.(Liu X D,Li P C,Yang S Y.Design and implementation of quantum-inspired differential evolution algorithm[J].J of Signal Processing,2014,30(6):623-633.)
[14]Eberhart R C,Shi Y.Comparing inertia weights and constriction factors in particle swarm optimization[C].Proc of IEEE Congress on Evolutionary Computation.New York:IEEE Press,2000:84-88.
[15]李盼池,王海英,宋考平.量子势阱粒子群优化算法的改进研究[J].物理学报,2012,61(6):060302.(Li P C,Wang H Y,Song K P.Research on improvement of quantum potential well-based particle swarm optimization algorithm[J].Acta Physica Sinica,2012,61(6):060302.)
[16]赵玉新,刘立强.新兴元启发式优化算法[M].北京:科学出版社,2013:240-251.(Zhao Y X,Liu L Q.Emerging heuristic optimization algorithm[M].Beijing:Science press,2013:240-251.)