Function approximations by coupling neural networks and genetic programming trees with oblique decision trees

Abstract This paper is concerning the development of the hybrid system of neural networks and genetic programming (GP) trees for problem domains where a complete input space can be decomposed into several different subregions, and these are well represented in the form of oblique decision tree. The overall architecture of this system, called federated agents, consists of a facilitator, local agents, and boundary agents. Neural networks are used as local agents, each of which is expert at different subregions. GP trees serve as boundary agents. A boundary agent refers to the one that specializes at only the borders of subregions where discontinuities or a few different patterns may coexist. The facilitator is responsible for choosing the local agent that is suitable for given input data using the information obtained from oblique decision tree. However, there is a large possibility of selecting the invalid local agent as result of the incorrect prediction of decision tree, provided that input data is close enough to the boundaries. Such a situation can lead the federated agents to produce a higher prediction error than that of a single neural network trained over the whole input space. To deal with this, the approach taken in this paper is that the facilitator selects the boundary agent instead of the local agent when input data is closely located at certain border of subregions. In this way, even if decision tree yields an incorrect prediction, the performance of the system is less affected by it. The validity of our approach is examined by applying federated agents to the approximation of the function with discontinuities and the configuration of the midship section of bulk cargo ships.