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In this work, a multi-output model is proposed based on extreme learning machine, which uses the regression information of training samples and the correlation of outputs to predict multiple responses for the new point. Two kernel matrices are designed to evaluate the regression relationship of training samples and the correlation of the outputs, respectively. A five-fold cross-validation method is used to assess the training error, and a heuristic algorithm is used to optimize the hyperparameters of the proposed model. The results of mathematical problems indicate that the performance of the proposed model is better with more training samples and is positively correlated with the correlation of outputs. The proposed model produces more competitive performance in terms of prediction accuracy and computational cost than the benchmark multi-output models. The proposed multi-output model is applied to the multi-objective optimization of a dental implant, showing its application potential in engineering design and optimization.

A multi-output model based on extreme learning machine with application in the multi-objective optimization of a dental implant