基于演化计算的网络社区发现研究

复杂网络是表征现实世界中大型复杂系统的有效工具，已成为数学、物理学、数据科学等领域的研究热点。在复杂网络的研究中，“社区”的概念受到越来越多的关注。事实上，社区可看作组成网络的基本模块，将一个网络划分为若干社区实际达到了将一个复杂系统分解为若干相互独立的子系统的目的。为更方便地研究复杂系统的组成与结构，网络社区发现技术应运而生。现实中的复杂网络有多种类型，催生出了不同种类的社区发现问题。近年来，国内外学者针对不同的社区发现问题提出了一系列解决方法，但都存在一些不足。在现有社区发现方法中，模块度优化法因其社区划分质量高和适用范围广的特点受到广泛关注，而演化计算作为一种新兴的优化工具十分适合解决这类高维离散的优化问题。因此，本文以模块度优化为基本原理，以演化计算为基本优化工具，在分析现有方法不足之处的基础上，针对局部社区发现、全局社区发现和多层网络社区发现这三类核心社区发现问题展开深入研究，分别提出相应的解决算法。本文的主要研究工作概括如下：

（1）针对现有局部社区发现算法缺乏网络整体认识的局限，将局部社区发现重新建模为全局二进制优化问题并利用二进制演化算法解决，通过设计一系列演化算子和优化机制，提出了一种演化局部社区发现算法，该算法能够利用已知网络的全局信息搜索指定节点所在的局部社区。在复杂网络上的测试结果表明该算法与现有局部社区发现算法相比具有更高的准确度。

（2）针对演化算法在复杂崎岖解空间中容易陷入局部最优解的缺陷，提出一种简化适应度空间引导的演化优化方法，即通过构造原优化问题的简化模型来改进其适应度空间，使算法更容易获取全局最优解。首先针对连续优化问题，提出一种利用机器学习模型来平滑目标函数适应度空间的方法，研究了各种模型对复杂优化函数的平滑效果。在此基础上提出了一种简化适应度空间引导的演化优化框架。在连续函数上的测试结果表明该方法能显著提高演化算法在粗糙崎岖解空间中的全局优化能力。

（3）针对演化算法在模块度空间中容易陷入局部最优解，进而导致全局社区划分质量下降的缺陷，提出一种代理网络引导的全局社区发现方法。该方法首先基于原网络谱信息构造代理网络，以实现对网络模块度空间的简化，然后利用代理网络来引导原网络的模块度优化，进而帮助演化算法发现网络中隐藏的不明显的社区结构。实验结果表明该方法能够提高演化计算发现复杂网络全局社区结构的能力。

（4）针对现有多层网络社区发现算法检测层内社区时忽略各层拓扑相关性的缺陷，将多层网络的层内社区发现建模为一个多任务优化问题并采用演化多任务优化算法解决。为克服现有演化多任务优化算法难以实现对各优化进程的独立监测与控制的缺陷，提出一种新型多任务优化算法——头脑风暴多任务优化。该算法采用多种群优化机制，能够独立监测和控制各任务的进行，且容易并行化实现。为设计该算法，首先将头脑风暴由单任务模式拓展至多任务模式，提出多任务问题头脑风暴处理模型，以该模型为基础，设计出算法的框架并开发出一系列演化算子和机制。之后，通过研究算法的优化过程，提出一种信息转移控制策略并应用于算法中，形成了改进版的多任务头脑风暴算法，提高了对转移信息的利用效率。在多任务优化问题集上的测试结果表明多任务头脑风暴算法与现有算法相比具有更优异的优化性能。最后，以改进版的多任务头脑风暴为基本优化算法，在充分利用各层拓扑相似性的基础上，实现了多层网络各层社区结构的联合检测，提高了层内社区发现的效率。

（5）针对现有多层网络联合社区发现算法的准确度较低且容易造成误差累积的缺陷，提出了一种基于演化多任务聚类的多层网络联合社区发现方法。该方法首先基于层内社区发现的结果和多层网络的各层信息来构造一致性网络，然后采用演化算法优化该网络的广义模块度，最终获得联合社区划分。最终，通过将该方法和基于多任务优化的层内社区发现相结合，构造出新型多层网络社区发现算法——头脑风暴多层社区发现。实验结果表明，与现有算法相比，该算法在层内社区和联合社区的检测上均具有更好的效果。

综上，本文旨在建立利用演化计算技术解决复杂网络社区发现问题的理论体系和方法。此外，本文在解决网络社区发现问题的过程中提出了一些较现有算法效果更好的通用型演化计算模型与算法。因此，本文的研究在社区发现领域和演化计算领域均具有一定的理论与应用价值。

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