Identifying Variables Interaction for Black-box Continuous Optimization with Mutual Information of Multiple Local Optima

Identifying the interaction of search variables of black-box optimization problem and exploiting the learned interaction structure back to optimization process is a very meaningful research topic. Evaluating the interaction between variables based on information theory is a popular and effective method. However, very little research pay attention to what kind of data can help identify interactions between variables. In this paper, we propose a method to identify the interaction between variables by using the local optima solutions of the objective function. First, a multimodal optimization algorithm is used to search for multiple local optima of the optimization problem. Then, hierarchical clustering is used to cluster and discretize local optima. Finally, the interaction between variables is quantified using the mutual information of local optima. Experimental results show that the proposed method can use the information of local optima to identify the interaction of search variables.