论文总字数：27175字

摘 要

2014 年 05月10号

摘要

本文首先对染色体编码空间、量子旋转门、变异算子、局部搜索的基本原理及搜索性能进行了分析和对比。在此基础上，将编码空间的动态调整，量子旋转门角度的动态调整，Pauli组合变异算子，局部搜索算子应用到量子遗传算法中，设计出了一种改进的量子遗传算法。该算法在进化过程中，能根据所求问题精度动态确定量子染色体基因长度的编码方法，该编码方法考虑了计算解的精度和搜索效率的一种平衡关系。动态调整变搜索步长，从而尽量保证算法在进化中有较强的搜索效率。通过对量子变异操作的组合增强种群的多样性，确保算法在合理的计算代价内有潜能搜索到高精度的解。理论分析和实验数据表明：本文算法在求解函数优化问题时，与传统量子遗传算法相比，在求解精度和稳定性等方面有了较大的改进。

Abstract

Quantum information science is an interdisciplinary field of information science and quantum mechanics theory. Quantum bits used to represent quantum states. Genetic algorithm is an artificial intelligence algorithm which imitates the biological and genetic mechanism of natural selection and construct with a random searching. Quantum genetic algorithm is a combination of Quantum computing and genetic algorithm. On solving a number of specific problems with Quantum genetic algorithm the prior knowledge of the problem does not require,only rely on the fitness function information, while not subject to the requirements of the problem derivative, continuity constraints conditions in the search space and so om Quantum genetic algorithm is to use the revolving gate to evolution algorithm.

Quantum genetic algorithm bas been widely used in function optimization and combinatorial optimization problems, but due to the specific problems, the function complex, diverse, some is easily to converge, and some is difficult to converge. Quantum genetic algorithm is still a lot of problems to solve. The most prominent issue main features: easy to fall into premature, and it is difficult break away from the local optimal solution and so on. Only by enhancing the ability of local search algorithms and global search capability can resolve.

First this paper analyzes and compares chromosome space, quantum rotation gate, mutation operator, the basic principles of local search and search efficiency. On this basis, the dynamic adjustment of the encoding space, the quantum dynamics of adjustment of the revolving gate, Pauli combination of mutation operators, local search operator applied to the quantum genetic algorithm, we designed an improved quantum genetic algorithm. In the evolutionary process,the issue of accuracy according to the request to dynamically determine the quantum chromosome length coding method, it takes into account the accuracy of the solution and the calculation of a balance between search efficiency. Dynamic adjustment of variable search step to try to ensure the search efficiency. Through a combination of quantum mutation operation the mutation in a larger context of the neighborhood search make sure the algorithm within a reasonable computational cost has the potential to search for high-precision solution. Theoretical analysis and experimental data show that: In solving continuous function optimization, the algorithm compared with the traditional quantum genetic algorithm in the solution accuracy and stability and have been greatly improved.

毕业设计说明书 I

摘要 II

Abstract III

第一章绪论 1

1.1课题背景及意义 1

1.2国内外现状 2

1.3本文研究内容及结构安排 3

第二章量子遗传算法及相关理论 5

2.1量子比特 5

2.2量子遗传算法编码解码 6

2.2.1二进制编码解码 6

2.2.2浮点数值编码解码 7

2.3量子态的测量 8

2.4量子旋转门 8

2.5量子遗传算法基本步骤 9

2.6本章小结 11

第三章改进的量子遗传算法 12

3.1概述 12

3.2改进的量子遗传算法及其描述 12

3.2.1算法改进思路 12

3.2.2染色体基因长度的自适应计算 13

3.2.3量子旋转角度动态调整 14

3.2.4 Pauli组合变异算子 15

3.2.5局部搜索策略 17

3.2.6改进的量子遗传算法设计 19

3.3本章小结 20

第四章算法测试 22

4.1测试函数特性 22

4.2测试参数设置 23

4.3测试结果与分析 23

4.4本章小结 25

第五章总结与展望 26

5.1论文总结 26

5.2工作展望 26

参考文献 28

致谢 31

第一章绪论

1.1课题背景及意义

近年来国内外存量子情息学领域的研究进展，不仅向我们展示了未来量于信息处理技术的光明前景，同时也启发我们从量子理论的角度重新去研究一些传统算法，以达到改进其性能的目的。

遗传算法（Genetic Aigorithrn．GA)是在模拟达尔文的进化论和孟德尔的遗传学理论基础上，产生和发展起来的种优化问题求解的随机优化方法[1]。由于GA不受问题本身的性质、优化准则形式、模型结构形式、控优化参数数目和有无约束等因素的限制，仅用目标函数在概率准则引导下进行并行全局自适应搜索，就能够处理许多传统优化方法难以解决的复杂问题，且具有极高鲁棒性和广泛适用性，因而CA在各个优化领域得到了广泛应用并成为跨学科研究的热点[2,3]。

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