Reducing the surrogate model-based method computation without loss of prediction accuracy remains a significant challenge in structural reliability analysis. The unbalanced probability density, important information in critical region and information redundancy of added sample points are ignored in most of traditional surrogate-based methods, resulting in heavy computational burden. In this work, an active learning combining adaptive Kriging method and weighted penalty (AK-WP) is proposed to analyze the reliability of engineering structures. Firstly, an active learning and weighted penalty function (WPLF) is the result of integrating active learning method, weighted function and penalty function, which is proposed to find the most probable point (MPP). Meanwhile, to avoid redundant information, the best suitable MPP is determined by a proposed distance law established between the found MPP and the existing design of experiment (DoE). Secondly, the Kriging model is refined according to best suitable MPP in each iteration. Thirdly, the failure probability is estimated by the Monte Carlo sample points from the n-ball domain until the convergence condition is satisfied. The accuracy and efficiency of the proposed method are demonstrated by some numerical examples including the highly nonlinear, the small probability problems and implicit function, as well as a real engineering application.

No abstract

Surrogate-assisted evolutionary algorithms (SAEAs) are one effective method for solving expensive optimization problems. However, there has been little attention to expensive many-objective irregular problems. To address this issue, we propose an ensemble surrogate-assisted adaptive reference point guided evolutionary algorithm for dealing with expensive many-objective irregular problems. Firstly, a reference point adaptation method is adopted in the proposed algorithm to adjust the reference point for calculating indicators and guide the search process. Secondly, the enhanced inverted generational distance (IGD-NS) indicator is improved by using the modified distance to obey the Pareto compliant, which can maintain a balance between convergence and diversity in the population. Thirdly, an infill sampling criterion is designed to select elite individuals for re-evaluation in case the Pareto fronts are irregular. The added elite individuals update the ensemble surrogate model, which is expected to assist the algorithm in efficiently finding the Pareto optimal solutions in a limited computational resource. Finally, experimental results on several benchmark problems demonstrate that the proposed algorithm performs well in solving expensive many-objective optimization problems with irregular and regular Pareto fronts. A real-world application problem also confirms the effectiveness and competitiveness of the proposed algorithm.

PurposeSurrogate-assisted evolutionary algorithms (SAEAs) are the most popular algorithms used to solve design optimization problems of expensive and complex engineering systems. However, it is difficult for fixed surrogate models to maintain their accuracy and efficiency in the face of different issues. Therefore, the selection of an appropriate surrogate model remains a significant challenge. This paper aims to propose a dynamic adaptive hybrid surrogate-assisted particle swarm optimization algorithm (AHSM-PSO) to address this issue.Design/methodology/approachA dynamic adaptive hybrid selection method (AHSM) is proposed. This method can identify multiple ensemble models formed by integrating different numbers of excellent individual surrogate models. Then, according to the minimum root-mean-square error, the best suitable surrogate model is dynamically selected in each generation and is used to assist PSO.FindingsExperimental studies on commonly used benchmark problems, and two real-world design optimization problems demonstrate that, compared with existing algorithms, the proposed algorithm achieves better performance.Originality/valueThe main contribution of this work is the proposal of a dynamic adaptive hybrid selection method (AHSM). This method uses the advantages of different surrogate models and eliminates the shortcomings of experience selection. Furthermore, the empirical results of the comparison of the proposed algorithm (AHSM-PSO) with existing algorithms on commonly used benchmark problems, and two real-world design optimization problems demonstrate its competitiveness.