Clustering and learning Gaussian distribution for continuous optimization

Since the Estimation of Distribution Algorithm (EDA) was introduced, different approaches in continuous domains have been developed. Initially, the single Gaussian distribution was broadly used when building the probabilistic models, which would normally mislead the search when dealing with multimodal functions. Some researchers later constructed EDAs that take advantage of mixture probability distributions by using clustering techniques. But their algorithms all need prior knowledge before applying clustering, which is unreasonable in real life. In this paper, two new EDAs for continuous optimization are proposed, both of which incorporate clustering techniques into estimation process to break the single Gaussian distribution assumption. The new algorithms, Clustering and Estimation of Gaussian Network Algorithm based on BGe metric and Clustering and Estimation of Gaussian Distribution Algorithm, not only show great advantage in optimizing multimodal functions with a few local optima, but also overcome the restriction of demanding prior knowledge before clustering by using a very reliable clustering technique, Rival Penalized Competitive Learning. This is the first time that EDAs have the ability to detect the number of global optima automatically. A set of experiments have been implemented to evaluate the performance of new algorithms. Besides the improvement over some multimodal functions, according to the No Free Lunch theory, their weak side is also showed.