Ali Asghar Mohammadi - Islamic Azad University – Zanjan Branch, Zanjan
Javad Mohammadi - Payam Noor University of MahmoudAbad Mazandaran
Morteza Khalilzadeh - Islamic Azad University, Science and Research East Azarbaijan Branch
Moslem Hoseinzadeh - Islamic Azad University – Zanjan Branch, Zanjan, Iran,

A Bayesian Network (BN) is a probabilistic approach for reasoning under uncertainty, and has become a popular knowledge representation scheme in several fields such as data mining and knowledge discovery. A BN is a graphical model which denotes a joint probabilistic distribution of given variables under their dependence relationships. In this paper, We use a multi-objective evaluation strategy with a genetic algorithm. The multi-objective criteria are a network’s probabilistic score and structural complexity score. Our use of Pareto ranking is ideal for this application, because it naturally balances the effect of the likelihood and structural simplicity terms used in the BIC network evaluation heuristic. We use a basic structural scoring formula, which tries to keep the number of links in the network approximately equivalent to the number of variables. We also use a simple representation that favors sparsely connected networks similar in structure to those modeling biological phenomenon. Our experiments show promising results when evolving networks ranging from 10 to 30 variables, using a maximal connectivity of between 3 and 4 parents per node.The results from the multi-objective GA were superior to those obtained with a single objective GA.

Genetic Algorithms (GA), Bayesian Networks(BN), Structure Learning, Directed Acyclic Graph(DAG), Dynamic Bayesian Network (DBN), Bayesian Information Criterion (BIC), Minimal Description Length (MDL), Likelihood, Multi-Objective