Mathematical optimization models for solving computational problems

Abstract

Introduction. The current research is framed in the introduction of new computational methods of mathematical optimization for multitarget regression problems. Methods. A group of proposals of learning algorithms are included, efficiently modeled by means of optimization methods adjusted to each problem and their applications in the multitarget regression. The introduction of appropriate regularizers is efficiently solved for the simultaneous training of several low range learning structures and distance metric learning. Results and Discussion. It was tested experimentally, on 18 sets of available data. The results show the superiority of the proposal with respect to the state-of-the-art algorithms MSLR and MMR in that the execution times are significantly lower. The meta-heuristic algorithms based on continuation methods proposed in the present work obtain a lower value of the generalization error and training error, with statistically significant difference, with respect to the Stochastic Gradient Descent algorithm in the training of Artificial Neural Networks. The results of introducing the DMLMTP algorithm demonstrate a significant improvement over the KNN-SP algorithm previously proposed as part of the instance-based learning. As some conclusions, modern mathematical optimization methods are proposed for the solution of prediction problems of multiple indicators possibly correlated which improve the accuracy results of the state of the art as their design denotes high efficiency. Concrete applications are achieved in the estimation of the short- and long-term forecasting of COVID-19 that validate the research.