Adaptive approximation in multi-objective optimization for full stochastic fatigue design problem

Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases

“…In order to obtain the reliable Pareto frontiers, the accuracy of Pareto solutions are iteratively checked and the corresponding Kriging models are updated consistently [55][56][57]. Then, the converged Pareto sets subjected to the different single impact angles θ¼01, 101, 201 and 301 are obtained and the normalized values d EA and d F (used for MOPSO) are converted to the absolute values for comparison of these different SLCs (as shown in Fig.…”

On design of multi-cell tubes under axial and oblique impact loads

“…In this paper, the MOPSO proposed by Coello et al [45] is utilized to produce Pareto frontiers for the optimization problems of multi-cell tubes. In this problem, we iteratively check the accuracy of Pareto solutions and update the Kriging models until the Pareto frontiers become stable [48][49][50][51]. The converged Pareto frontiers for optimization problems of individual angle of θ¼0, 10, 20 and 30°are plotted together in Fig.…”

Crashworthiness design of foam-filled bitubal structures with uncertainty

“…This strategy is intended to enhance the accuracy of the metamodels at above-mentioned extreme regions by conducting two AASOs for seeking the respective optimums, separately, which will be used herein. More details of combine AASO-AAMO can be found in [53,55]. …”