Multiobjective learning algorithm based on membrane systems for optimizing the parameters of extreme learning machine

Abstract

For adaptively learning the parameters of extreme learning machine (ELM), a novel learning algorithm is proposed on the basis of a multiobjective membrane algorithm. More specifically, first, a multiobjective mathematical model is established to learn the parameters of ELM, which is constructed by three objective functions. These objective functions include the root mean squared error, L_1 norm of output weights and the number of hidden nodes. Second, a series of the trade-off solutions with respect to the above-mentioned objective functions are found by the multiobjective membrane algorithm. Finally, a trade-off solution with the best generalization performance of ELM, which is chosen from the Pareto front obtained by the multiobjective algorithm, will become the final parameters for initializing the ELM network. The simulation experiments are run on the approximation of ‘SinC’ function, real-world regression problems and real-world classification problems. Experimental results indicate that the proposed framework is able to achieve good generalization performance in the most cases with many compact networks.