Existing EDAs learn linkages starting from pairwise interactions. The characteristic function which indicates the relations among variables are binary. 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 paper introduces a real-valued characteristic function to illustrate this property of fuzziness. We examine all the possible binary models and real-valued models on a test problem. The results show that the optimal real-valued model is better than all the binary models. This paper also proposes a crossover method which is able to utilize the real-valued information. Experiments show that the proposed crossover could reduce the number of function evaluations up to four times. Moreover, this paper proposes an effective method to find a threshold for entropy based interaction-detection metric and a method to learn real-valued models. Experiments show that the proposed crossover with the learned real-valued models works well.
Multi-variate estimation of distribution algorithms (EDAs) build models via detecting interactions between genes and estimate the distributions to solve problems. EDAs have been applied for real world applications, but whether the models given by EDAs match what are really needed to solve the problems is yet unknown. This paper proposes using the number of function evaluation (N f e ) to measure the performance of models and defines the optimal model to be the one that consumes the fewest N f e for EDAs to solve the problem. Then the building blocks (BBs) that construct the optimal model are defined as the correct BBs. The capabilities of some existing interaction-detection metrics are compared based on this definition. This paper also proposes a test problem by utilizing Bézier curve. We find that all the mentioned metrics fail to identify the correct BBs for the proposed problems intrinsically. This paper then proposes a new metric directly based on the idea of N f e to enhance the existing interaction-detection mechanisms. Empirical results show that the new metric is able to build the optimal models. The preliminary success suggests another view on learning linkage.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.