求解数值优化问题的自适应粒子群算法研究(论文17000字)
摘要：鸟是自然界中一种以群体为活动单位的生物，虽然它们以个体出现时行为简单，但当它们进行群体觅食时表现出了分工明确，共同协作等复杂的群体智能行为。研究人员通过对鸟群这种特性的研究，于1995年提出了粒子群优化算法(Particle Swarm Optimization, PSO)。此后PSO在国内外学术界及工程界引起了极大的关注。但早期的算法在技术层面还存在一些不足，诸多学者对其进行了改进。本文重点研究了其中的一种改进算法PSO-MAM，PSO-MAM重点侧重于解决粒子群算法两个方面的不足之处，第一是粒子群算法空间搜索的随机性，第二是粒子群算法存在的早熟收敛性。为了解决第一个问题，PSO-MAM通过融合多种搜索方法来增强粒子群算法。在这个方面，对两个搜索技术进行了研究：非均匀变异方法和自适应的梯度方法。为解决粒子群的早熟收敛的问题，PSO-MAM又进一步利用了自适应的柯西变异法。最终，提出了具有多级适应性的粒子群算法（PSO-MAM）。与原来的粒子群算法相比，提出的粒子群算法在性能上表现出了极大的优势，但也存在一个比较大的缺陷，即在对函数进行测试时，需要人工将该函数的梯度求出再对程序进行相应地修改。由于有些函数无法求梯度，所有该算法无法广泛适用于所有函数，即适用度不高。为了改进该算法的函数适应度，本论文在该算法的基础上剔除了子梯度法再结合差分进化算法（Differential Evolution Algorithms, DE）对其进行了策略修改，通过一系列的对比试验后提出了一种可以广泛适用于所有函数并可以得到有效解的新的算法，即普适自适应多级粒子群算法（PSO-UMAM）。
关键词：粒子群；非均匀变异方法；自适应；差分进化；多级适应性；柯西变异
Research on Numerical Adaptive Particle Swarm Optimization Problems
ABSTRACT：Bird is a kind of creatures which works as a group in the nature. Although their individual behaviors are simple, but when they are foraging as a group, they can show some swarm intelligence behaviors like clear division of labor and collaborate. Researchers have studied about that features, in 1995, they proposed Particle Swarm Optimization (PSO). Thereafter it has aroused great concern in the academic circle and engineer circle all over the world in the past two decades. But PSO in its early time has some deficiencies in the technical level and many scholars have tried to improve it, until now. This paper focuses on one of their improved algorithm, PSO-MAM. PSO-MAM focuses on two aspects of PSO's shortcomings. The first one is that most existent PSO are proposed for a specific search space therefore there is lacking an algorithm, which is performing well on a diverse set of problems. The second one is that PSO suffers premature convergence. In order to solve the first problem, PSO-MAM proposes to use the fusion of multiple search methods to augment PSO. Based on an effectiveness index to trigger appropriate search methods, an intelligent selection mechanism is developed. Two search techniques in this research have been studied: a non-uniform mutation-based method and an adaptive sub-gradient method. In order to further improve the proposed PSO,weuse adaptive Cauchy mutation to prevent premature convergence. As a result, an augment PSO with multiple adaptive methods (PSO-MAM) is proposed. Compared with the original PSO, this one performs a great advantage on algorithms. However,there is also a large defect about this algorithm, that is, when you do a new function test, you need to get its gradient by person and then modify the code accordingly. The problem is that some functions’ gradient cannot be evaluated, so the algorithm’s fitness is low. In order to change the PSO-MAM’s fitness, we combined it with the Differential Evolution Algorithms(DE) to modify the strategies. After do a series of comparative tests, we proposed Particle Swarm Optimization with Universal Multilevel Adaptive Method (PSO-UMAM). This algorithm can be widely applied to all functions and can get an effective solution.
Keywords: Particle Swarm; non-uniform variation method; adaptive; differential variation method; adaptive multistage; Cauchy mutation
目录
1 绪论 1
1.1研究背景 1
1.2 研究目标及意义 2
1.3 论文研究内容及组织结构 2
2 粒子群优化算法概述 4
2.1 基本的粒子群优化算法原理 4
2.2 算法流程 4
2.3 粒子群优化算法的拓扑结构 5
2.4 本章小结 6
3 关的改进工作 7
3.1 参数改进的粒子群算法 7
3.1.1 标准粒子群优化算法 7
3.1.2 添加收缩因子的粒子群算法 7
3.2 离散粒子群优化算法 7
3.3 拓扑结构改进的粒子群算法 8
3.3.1 邻域拓扑改进的PSO算法 8
3.3.2 动态邻域的PSO算法 9
3.4 混合粒子群算法 9
3.5 新的粒子群学习策略 10
3.6 其它粒子群改进方法 11
3.7 本章小结 11
4 普适自适应多级粒子群算法 12
4.1 智能多种搜索方式 12
4.1.1 非均匀变异方法 13
4.1.2 差分进化算法 14
4.1.3 智能选择策略 15
4.2 柯西变异 16
4.3 本章小结 16
5 实验分析及结果 17
5.1 二十四种方法的组合 17
5.2 30维函数的对照实验 18
5.3 测试函数选取 18
5.4 测试结果 27
5.5 方法对比分析 32
5.6 实验结论 34
5.7 本章小结 34
6 结论与展望 36
6.1 结论 36
6.2 展望 36
参考文献 38
致谢 43
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