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 and uses random input weights and biases while learning the output weights. However, ELDR requires high computation time as the problem dimensionality and the number of hidden neurons increase, making its applicability to high-dimensional problems difficult. A surrogate model should be computationally efficient and enable rapid fitness estimations. Therefore, this study proposes a fast implementation technique, i.e., a learning method for ELDR (fELDR) that achieves mathematically equivalent learning results with small computational complexity. Additionally, we propose a pointwise score function to reuse the prediction results. The experimental results confirmed the effectiveness of fELDR 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 large dimensionality problem. Moreover, owing to the reusable prediction results, the computation time of the fELDR-assisted SAEA can be further decreased by 79.5% compared with that of the original ELDR-assisted SAEA. The reduced training time and reusable prediction results of fELDR make it feasible to apply ELDR to high-dimensional optimization problems and use high prediction accuracy with a large number of hidden neurons.

Surrogate-assisted evolutionary algorithms (SAEAs) have attracted considerable attention for reducing the computation time required by an EA on computationally expensive optimization problems. In such algorithms, a surrogate model estimates the solution evaluation with a low computing cost and is used to obtain promising solutions to which the accurate evaluation with an expensive computation cost is then applied. This study proposes a novel pairwise ranking surrogate model called the Extreme Learning-machine-based DirectRanker (ELDR). ELDR integrates two machine learning models: extreme learning machine (ELM) and DirectRanker (DR). ELM is a single-layer neural network capable of fast learning, whereas DR uses pairwise learning to rank using a neural network developed mainly for information retrieval. To investigate the effectiveness of the proposed surrogate model, this study first examined the estimation accuracy of ELDR. Subsequently, ELDR was incorporated into a state-of-the-art SAEA and compared with existing SAEAs on well-known real-valued optimization benchmark problems. The experimental results revealed that ELDR has a high estimation accuracy even on high-dimensional problems with a small amount of training data. In addition, the SAEA using ELDR exhibited the highest search performance compared with other existing SAEAs, especially on high-dimensional problems.