A surrogate-assisted evolutionary algorithm with solution sets classification based on inter-dimensional correlation and its applications

Abstract

To effectively mine the complex long-term dependencies correlations between high-dimensional decision variables, improve the quality of the candidate and real solution sets for evaluation, and expedite the efficiency of fitting the objective function, the paper proposes an algorithm called a surrogate-assisted evolutionary algorithm (SAEA) with solution sets classification based on inter-dimensional correlation for expensive multi-objective optimization (DCSCSAEA) in this study. The paper develops a surrogate model with inter-dimensional correlation called DCBiLSTM, which can carry out nonlinear fitting at a low computational cost, to mine the long-term dependencies correlations between high-dimensional decision variables. A step classification axis is designed based on the reference solutions screened by the division of the radial space, predicting the dominant relationship between the solutions in the space and the reference solutions on the classification axis, in order to classify solutions in the space of the solution set. The paper then divides the uncertainty in the prediction space and develop an adaptive “checkers” model infill criterion to determine the interval in which the predictive error falls. The paper uses the results to choose the corresponding strategy for screening the set of candidate solutions. Experiments on expensive multi-objective optimization problems (EMOPs) (20–100 variables) show DCSCSAEA outperforms five state-of-the-art SAEAs, yielding well-converged, diverse solutions. In real-world weld defect detection (21 variables), DCSCSAEA optimizes the network faster, reducing computational complexity and detection time by 52.14% and 20.39% respectively while maintaining comparable accuracy to state-of-the-art SAEAs.