Evolutionary Functional Network Model And Learning Algorithm

Different from neural network(NN), functional network(FN) resolves general functional models, its neural functions are not fixed but learnable, generally expressed as a linear combination of set of fixed basis functions. Like NN, until now, there's no system method for designing approximation functional network structure. As a branch of evolutionary algorithm(EA), genetic programming(GP) can dynamically change the structure and with flexible encoding method, but until now there is no rigorous or integral theory and evaluating rule to help to design the encoding method of GP. How to design the encoding method has been one of the applied difficulties of EA.This paper incorporates the approximation properties of EA and FN, proposes a novel evolutionary functional network(EFN) model. Firstly, generalized basis function(GBF) is introduced, then according to the approximation problem, the individual structure of GP is designed, i.e., individuals in the form of sequences of GBFs are encoded by general tree structure. After genetic operartions, the group is evaluated by least square method, each individual is approximated by a linear combination of GBFs, through evolutions the optimum model is achieved. This model is used to solve tested data and practical data, the results are very satisfied. According to problems of function approximation and numerical integration, choose different kinds of base function sets and different number of GBFs to approximate, the experiment results show that this algorithm is efficiently flexible and with strong generalization.