Neural Networks Multiobjective Learning With Spherical Representation of Weights

This article presents a novel representation of artificial neural networks (ANNs) that is based on a projection of weights into a new spherical space defined by a radius r and a vector of angles . This spherical representation of ANNs further simplifies the multiobjective learning problem, which is usually treated as a constrained optimization problem that requires great computational effort to maintain the constraints. With the proposed spherical representation, the constrained optimization problem becomes unconstrained, which simplifies the formulation and computational effort required. In addition, it also allows the use of any nonlinear optimization method for the multiobjective learning of ANNs. Results presented in this article show that the proposed spherical representation of weights yields more accurate estimates of the Pareto set than the classical multiobjective approach. Regarding the final solution selected from the Pareto set, our approach was effective and outperformed some state-of-the-art methods on several data sets.