一种新的自适应量子遗传算法

摘要

The current quantum evolution algorithms based on the Bloch spherical coordinates have slow convergence rate and poor robustness. Aiming at the two shortages, a new self-adaptive Quantum Genetic Algorithm(QGA) which is based on the characteristic of Fibonacci sequence is proposed. In the process of searching the optimal solution, a self-adaptive factorλis introduced to reflect the relative change rate which is relative to the difference of the best individual’s objective fitness between the parent generation and the child generation. The convergence rate and direction of the algorithm can be improved by adjusting the factor. It is constructed the rule of updating the rotation angleΔφandΔθwhich is based on Fibonacci sequence by studying its properties. Using the new algorithm to deal with the multidimensional complex functions, theoretical analysis of algorithm time complexity and the simulation results show that the new algorithm improves the convergence rate, efficiency and stability robustness.%现有基于 Bloch 球面坐标的量子进化算法存在收敛速度慢和鲁棒性不稳定的问题。为此，提出基于斐波那契特性更新的自适应量子遗传算法。在最优解的搜索过程中，考虑目标函数在搜索点的变化率，建立自适应因子λ，反映搜索点处目标适应度值相对于相邻两代最佳目标函数值一阶差分的变化，调整λ以改善算法收敛的方向和速度。分析量子旋转门转角步长调整策略，建立基于斐波那契数列特性的转角步长函数Δφ和Δθ的更新规则。应用该算法求解多维复杂函数的极值优化问题，时间复杂度理论分析和仿真结果证明，该算法在收敛速度、效率和稳定鲁棒性等方面均有明显改善。