Robust optimization of uncertain structures based on normalized violation degree of interval constraint

In order to improve the mechanical properties of a structure with uncertain but bounded parameters, a constrained interval robust optimization model is proposed with the center and halfwidth of its most important mechanical performance index described as objectives and the other performance indices described as constraints. The conventional indirect approaches for solving the interval optimization model will result in different optimal solutions when prescribing different satisfactory degrees of interval constraints and also deviates from the original intention of modeling the optimization problem based on interval theory. To overcome the shortcomings of indirect interval optimization approaches, a novel concept of the normalized violation degree of interval constraint (NVDIC) and the NVDIC-based preferential guidelines are proposed for directly sorting different design vectors. A direct interval robust optimization algorithm is proposed, which integrates Kriging models with inner layer genetic algorithms (GAs) to compute the interval bounds of the mechanical performance indices of various design vectors, and realizes the direct sorting of different design vectors by the outer layer non-dominated sorting genetic algorithm (NSGA) according to the NVDIC-based preferential guidelines. The validity of the proposed direct interval robust optimization algorithm is verified by a numeric example, the superiority of which to the conventional indirect one is discussed in detail. Finally, the robust optimization of a press slider with uncertain material properties demonstrates the feasibility and validity of the proposed method in engineering.