Acknowledgement Advisor

ii Existing estimation of distribution algorithms (EDAs) learn linkages starting from pairwise interactions of variables and construct models from the linkages. The char-acteristic function of models which indicates the relations among variables are bi-nary. In other words, the characteristic function indicates that there exist or not interactions among variables. Empirically, it can occur that two variables should be sometimes related but sometimes not. This thesis introduces a real-valued charac-teristic function to illustrate this property of fuzziness. We examine all the possible binary models and real-valued models on test problems. The results show that EDAs using optimal real-valued models outperforms the one using optimal binary models. This thesis also proposes two recombination algorithms which are able to utilize the information provided by real-valued models. Experiments show that the proposed pairwise crossover could reduce function evaluations by three quarters. Moreover, this thesis proposes an effective method to find a threshold for entropy based linkage-learning metric and a method to generate real-valued models. Experiments show that the proposed crossover with generated real-valued models works well