A Practical View of Building Blocks

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 (Nfe) to measure the performance of models and defines the optimal model to be the one that consumes the fewest Nfe 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 existing interaction-detection metrics, including non-linearity, entropy, simultaneity, and DMC, are compared based on this definition. This paper also proposes a test problem by utilizing Bézier curve. We find that all the above metrics fail to build the correct models for the proposed problems intrinsically. This paper then proposes a new metric directly based on the idea of Nfe 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.