Various evolutionary algorithms (EAs) have been proposed to address feature selection (FS) problems, in which a large number of fitness evaluations are needed. With the rapid growth of data scales, the fitness evaluation becomes time consuming, which makes FS problems expensive optimization problems. Surrogate-assisted EAs (SAEAs) have been widely used to solve expensive optimization problems. However, the SAEAs still face difficulties in solving expensive FS problems due to their high-dimensional discrete decision variables. To address this issue, we propose an SAEA with parallel random grouping for expensive FS problems, in which three main components consist. First, a constraint-based sampling strategy is proposed, which considers the influence of the constraint boundary and the number of selected features. Second, a high-dimensional FS problem is randomly divided into several low-dimensional subproblems. Surrogate models are then constructed in these low-dimensional decision spaces. After that, all the subproblems are optimized in parallel. The process of random grouping and parallel optimization continues until the termination condition is met. Finally, a final solution is chosen from the best solution in the historical search and the best solution in the last population using a random, distance-, or voting-based method. Experimental results show that the proposed algorithm generally outperforms traditional, ensemble, and evolutionary FS methods on 14 datasets with up to 10 000 features, especially when the required number of real fitness evaluations is limited.

Data-driven prediction of laminar flow and turbulent flow in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of high-fidelity data are required to describe and accurately predict the complex physical information, while reality, only limited high-fidelity data are available due to the high experimental/computational cost. Therefore, this work proposes a novel multi-fidelity learning method based on the Fourier neural operator by jointing abundant low-fidelity data and limited high-fidelity data under transfer learning paradigm. First, as a resolution-invariant operator, the Fourier neural operator is first and gainfully applied to integrate multi-fidelity data directly, which can utilize the limited high-fidelity data and abundant low-fidelity data simultaneously. Then, the transfer learning framework is developed for the current task by extracting the rich low-fidelity data knowledge to assist high-fidelity modeling training, to further improve data-driven prediction accuracy. Finally, three engineering application problems are chosen to validate the accuracy of the proposed multi-fidelity model. The results demonstrate that our proposed method has high effectiveness when compared with other high-fidelity models and has the high modeling accuracy of 99% for all the selected physical field problems. Additionally, the low-fidelity model without transfer learning has the modeling accuracy of 86%. Significantly, the proposed multi-fidelity learning method has the potential of a simple structure with high precision for fluid flow problems, which can provide a reference for the construction of the subsequent model.