摘要： 基于实数编码和目标函数梯度信息的双链量子遗传算法可增加种群的多样性、扩大解空间的搜索域、加速算法的进化进程、避免早熟收敛现象，但没有从理论上证明该算法的收敛性。为此，给出相应的定理，利用定理从理论上证明该算法的收敛性，通过仿真实例，论述量子编码和量子旋转门对算法收敛性和优化效率的影响。结果表明，该研究丰富和完善了双链量子遗传理论。

关键词: 量子遗传算法, 量子比特, 量子旋转门, 量子非门, 优化算法, 马尔可夫链, 收敛性

Abstract: The double chains quantum genetic algorithm based on real-coded and gradient of objective function increases the diversity of population, expands the search field about space, accelerates the algorithm evolutionary process, avoids the premature convergence phenomenon, is an effective optimization algorithm, but does prove theoretically convergence. This paper gives the corresponding theorem on the basis of previous work, theoretically proves the convergence of the algorithm by the theorem, and discusses the effects of the quantum coding and quantum rotation gate in terms of the algorithm convergence and optimization efficiency by simulation example. Results show that his research enriches and improves the double chains quantum genetic theory.

Key words: quantum genetic algorithm, quantum-bit, quantum rotating gate, quantum not gate, optimization algorithm, Markov chain, convergence

中图分类号: 

• TP301