Estimation of Distribution Algorithm with Mixture of Bayesian Networks
Estimation of Distribution Algorithm with Mixture of Bayesian Networks
复制标题
混合贝叶斯网络的分布估计算法
DOI：
10.11394/tjpnsec.3.63
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
赤間清
中科院分区：
文献类型：
--
作者：
堀伸哉;棟朝雅晴;赤間清
本文提出了一种新的估计分布算法（EDA）--混合分布贝叶斯优化算法（BOA-MD），它利用多个贝叶斯网络的混合来解决复杂问题。为了解决由多个具有隐变量的贝叶斯网络建模的复杂问题，原始BOA需要大量的计算成本来将多个概率结构建模为大型复杂的贝叶斯网络。BOA-MD试图用期望最大化（EM）方法建立考虑隐变量的贝叶斯网络的多个模型，以表达概率分布的所有结构。贝叶斯网络的混合是由一个隐变量C和一些贝叶斯网络组成的。每一个贝叶斯网络都可以表达多个分布的问题结构。我们用两个测试函数：交叉陷阱函数和三重陷阱函数进行了数值实验。这两个测试函数用于表示多个分布的问题。BOA-MD方法比BOA方法具有更少的适应度评价次数和更大的建模开销。这是因为BOA-MD需要大量的计算时间来构建贝叶斯网络的混合。当每个适应度评价的重叠较大时，BOA-MD比原BOA能更快地解决问题。在Triple-Trap功能下，BOA-MD可以检测到比BOA更好的解决方案。
This paper proposes a new method of Estimation Distribution Algorithm (EDA) named Bayesian Optimization Algorithm with Mixture Distribution (BOA-MD) that employs mixture of multiple Bayesian Networks to solve complex problems. In order to solve complex problems that are modeled by multiple Bayesian networks with hidden variables, the original BOA needs a large computation cost to model multiple probabilistic structures as a large, complex Bayesian network. The BOA-MD tries to build multiple models of Bayesian networks considering hidden variables with Expectation Maximization (EM) method to express all the structures of probabilistic distribution. The mixture of Bayesian networks is composed of a hidden variable C and some Bayesian Networks. Each composed Bayesian network can express each problem structure of multiple distributions. We perform numerical experiments by two test functions: Cross-Trap function and Triple-Trap function. These two test functions are to represent problems with multiple distributions. BOA-MD can solve these test problems with smaller number of fitness evaluations and larger modeling overheads than those by BOA for Cross-Trap5 function. This is because BOA-MD needs large computation time to construct Mixture of Bayesian Network. The BOA-MD can solve the problem faster than the original BOA when the overhands of each fitness evaluation becomes larger. At Triple-Trap function, BOA-MD can detect better solution than BOA.