抄録
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.
