ISSN 1000-1239 CN 11-1777/TP

计算机研究与发展 ›› 2017, Vol. 54 ›› Issue (8): 1644-1654.doi: 10.7544/issn1000-1239.2017.20170155

所属专题: 2017人工智能前沿进展专题

• 人工智能 • 上一篇    下一篇

求解大尺度优化问题的学生t-分布估计算法

王豫峰1,2,董文永1,董学士1,王浩3   

  1. 1(武汉大学计算机学院 武汉 430072);2(南阳理工学院软件学院 河南南阳 473000);3(岩土力学与工程国家重点实验室(中国科学院武汉岩土力学研究所) 武汉 430071) (wangyufeng@whu.edu.cn)
  • 出版日期: 2017-08-01
  • 基金资助: 
    国家自然科学基金项目(61170305,61672024,41472288);河南省高等学校重点科研项目计划(17A520046)

Adaptive Estimation of Student’s t-Distribution Algorithm for Large-Scale Global Optimization

Wang Yufeng1,2, Dong Wenyong1, Dong Xueshi1, Wang Hao3   

  1. 1(Computer School, Wuhan University, Wuhan 430072);2(Software School, Nanyang Institute of Technology, Nanyang, Henan 473000);3(State Key Laboratory of Geomechanics and Geotechnical Engineering (Institute of Rock and Soil Mechanics, Chinese Academy of Sciences), Wuhan 430071)
  • Online: 2017-08-01

摘要: 针对处理大尺度全局优化问题,提出一种基于自适应t-分布的分布估计算法(EDA-t).该算法不仅求解效果良好,而且求解速度也比同类型算法快.其基本思想是:在迭代搜索过程,首先利用期望最大化算法对演化种群进行概率主成分分析,然后根据得到的概率隐变量建立算法的概率模型,并通过t-分布自由度自适应方法,在算法收敛停滞时跳出局部最优.由于在构建模型时进行了数据降维,在不影响算法求解精度的前提下,其计算开销得到了明显降低.通过和目前主流的演化算法在大尺度优化测试函数上的仿真实验和分析,验证了所提算法的有效性和适用性.

关键词: 概率主成分分析, 学生t-分布, 分布估计算法, 大尺度全局优化, 最大期望算法

Abstract: In this paper, an adaptive estimation of student’s t-distribution algorithm (EDA-t) is proposed to deal with the large-scale global optimization problems. The proposed algorithm can not only obtain optimal solution with high precision, but also run faster than EDA and their variants. In order to reduce the number of the parameters in student’s t-distribution, we adapt its closed-form in latent space to replace it, and use the expectation maximization algorithm to estimate its parameters. To escape from local optimum, a new strategy adaptively tune the degree of freedom in the t-distribution is also proposed. As we introduce the technology of latent variable, the computational cost in EDA-t significantly decreases while the quality of solution can be guaranteed. The experimental results show that the performance of EDA-t is super than or equal to the state-of-the-art evolutionary algorithms for solving the large scale optimization problems.

Key words: probabilistic PCA, student’s t-distribution, estimation of distribution algorithm (EDA), large scale global optimization (LSGO), expectation maximization (EM) algorithm

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