Fast implementation of extreme learning machine-based directRanker for surrogate-assisted evolutionary algorithms

Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used to solve computationally expensive optimization problems. The extreme learning machine-based DirectRanker (ELDR) is a single-layer feed-forward neural network surrogate model designed for SAEAs. ELDR estimates the superiority of two solutions with a high estimation accuracy, even in high-dimensional problems. However, ELDR requires a long computation time as the problem dimensionality and the number of hidden neurons increase, thus making it difficult to apply it to high-dimensional problems. A surrogate model should be computationally efficient and enable rapid fitness estimations. Therefore, this paper proposes a fast implementation technique, i.e., fast version ELDR (fELDR) that achieves mathematically equivalent learning results with low computational complexity. Additionally, this paper proposes a pointwise score function to render the prediction results reusable. The experimental results confirmed the effectiveness of fELDR when compared with the original ELDR. The learning results of the proposed fELDR were equivalent to those of the original ELDR while reducing the training time by up to 97%, especially when using a large hidden layer on a high dimensionality problem. Moreover, due to the reusable prediction results, the computation time of the fELDR-assisted SAEA can be further decreased by 79.5% when compared with that of the original ELDR-assisted SAEA. The reduced training time and reusable prediction results of fELDR render it feasible to apply ELDR to high-dimensional optimization problems and realize a high prediction accuracy with a large number of hidden neurons.