量子位Bloch坐标的量子人工蜂群优化算法

摘要

To solve the problems of slow convergence speed and easily getting into local optimal value for Artificial Bee Colony (ABC) algorithm, a new quantum optimization algorithm was proposed by combining quantum theory and artificial colony algorithm. This algorithm expanded the quantity of the global optimal solution and improved the probability of achieving the global optimal solution by using Bloch coordinates of quantum bit encoding food sources in the artificial colony algorithm; then food sources were updated by quantum rotation gate. This paper put forward a new method for determining the relationship between the two rotation phases in the quantum rotation gate. When the ABC algorithm searched as the equal area on the Bloch sphere, it was proved that the size of the two rotation phases in the quantum rotation gate approximated to the inverse proportion. This avoided blind arbitrary rotation and made the search regular when approaching the optimal solutions. The experiments of two typical optimization issues show that the algorithm is superior to the common Quantum Artificial Bee Colony (QABC) and the simple ABC in both search capability and optimization efficiency.%为了改善人工蜂群(ABC)算法在解决多变量优化问题时存在的收敛速度较慢、容易陷入局部最优的不足,结合量子理论和人工蜂群算法提出一种新的量子优化算法.算法首先采用量子位Bloch坐标时蜂群算法中食物源进行编码,扩展了全局最优解的数量,提高了蜂群算法获得全局最优解的概率；然后用量子旋转门实现搜索过程中的食物源更新.对于量子旋转门的转角关系的确定,提出了一种新的方法.从理论上证明了蜂群算法在Bloch球面每次以等面积搜索时,量子旋转门的两个旋转相位大小近似于反比例关系,避免了固定相位旋转的不均等性,使得搜索呈现规律性.在典型函数优化问题的实验中,所提算法在搜索能力和优化效率两个方面优于普通量子人工蜂群(QABC)算法和单一人工蜂群算法.