Variable-Fidelity Lower Confidence Bounding Approach for Engineering Optimization Problems with Expensive Simulations

Abstract

Engineering design optimization with expensive simulations is usually a computationally prohibitive process. As one of the most famous efficient global optimization approaches, the lower confidence bounding (LCB) approach has been widely applied to relieve this computational burden. However, the LCB approach can be used only for design optimization problems with the single-fidelity level. In this paper, a variable-fidelity lower confidence bounding (VF-LCB) approach is developed to extend the LCB approach to engineering problems with multifidelity levels. First, a VF-LCB function is analytically derived to adaptively select LF or HF samples according to the predicted values and uncertainty from the VF metamodel. Then the coefficient of variations (CoV) of the predicted values and uncertainty of the VF model, which can reflect the degree of dispersion of the prediction values and uncertainty, respectively, are introduced to balance the global exploration and local exploitation objectively. To illustrate the effectiveness and merits of the proposed VF-LCB approach, eight numerical examples, and the design of micro-aerial vehicle (MAV) fuselage are tested. Comparative results between the proposed approach and the other five existing methods show that the average cost savings are about 25% for eight numerical examples and about 45% for the MAV problem compared with the other five existing methods.