Abstract
The optimization design of engineering products involving computationally expensive simulation is usually a time-consuming or even prohibitive process. As a promising way to relieve computational burden, adaptive Kriging-based design optimization (AKBDO) methods have been widely adopted due to their excellent ability for global optimization under limited computational resource. In this paper, an entropy weight-based lower confidence bounding approach (EW-LCB) is developed to objectively make a trade-off between the global exploration and the local exploitation in the adaptive optimization process. In EW-LCB, entropy theory is used to measure the degree of the variation of the predicted value and variance of the Kriging model, respectively. Then, an entropy weight function is proposed to allocate the weights of exploration and exploitation objectively and adaptively based on the values of information entropy. Besides, an index factor is defined to avoid the sequential process falling into the local regions, which is associated with the frequencies of the current optimal solution. To demonstrate the effectiveness of the proposed EW- LCB method, several numerical examples with different dimensions and complexities and the lightweight optimization design problem of an underwater vehicle base are utilized. Results show that the proposed approach is competitive compared with state-of-the-art AKBDO methods considering accuracy, efficiency, and robustness.
Highlights
Computational simulation models, i.e., finite element analysis (FEA) and computational fluid dynamic (CFD) models, have been widely used in engineering design problems to replace physical experiments for reducing the time cost and shortening the product developing cycle
The lower confidence bounding (LCB) method is a popular adaptive Kriging-based design optimization (AKBDO) method, which can be expressed as lcb(x) = ŷ(x) − bŝ(x) where ŷ(x) and ŝ(x) are the predicted value and standard deviation, respectively. b is a factor utilized to control the weight between the ŷ(x) and ŝ(x) for the sake of balancing the exploration and the exploitation
The goal of the proposed lower confidence bounding approach based on the entropy weight algorithm (EW-LCB) is to obtain an optimal solution with less computational burden through a sequential process
Summary
Computational simulation models, i.e., finite element analysis (FEA) and computational fluid dynamic (CFD) models, have been widely used in engineering design problems to replace physical experiments for reducing the time cost and shortening the product developing cycle. There are several sorts of adaptive sampling approaches of AKBDO with different ways of making a trade-off between exploration and exploitation [19,20], such as the maximum-uncertainty adaptive sampling approaches [20], the efficient global optimization (EGO) methods [21], the lower confidence bounding (LCB) based methods [22], the aggregate-criteria adaptive sampling methods [19], and the multi-criteria adaptive approaches [23,24].
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