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Li E.,Central South University | Wang H.,Hunan University | Wang H.,Joint Center for Intelligent New Energy Vehicle
Engineering Computations (Swansea, Wales) | Year: 2016

Purpose - For global optimization, an important issue is a trade-off between exploration and exploitation within limited number of evaluations. Efficient global optimization (EGO) is an important algorithm considering such condition termed as expected improvement (EI). One of major bottlenecks of EGO is to keep the diversity of samples. Recently, Multi-Surrogate EGO uses more samples generated by multiple surrogates to improve the efficiency. However, the total number of samples is commonly large. The purpose of this paper is to suggest a bi-direction multi-surrogate global optimization to overcome this bottleneck. Design/methodology/approach - As the name implies, two different ways are used. The first way is to EI criterion to find better samples similar to EGO. The second way is to use the second term of EI to find accurate regions. Sequentially, the samples in these regions should be evaluated by multiple surrogates instead of exact function evaluations. To enhance the accuracy of these samples, Bayesian inference is employed to predicted the performance of each surrogate in each iteration and obtain the corresponding weight coefficients. The predicted response value of a cheap sample is evaluated by the weighted multiple surrogates combination. Therefore, both accuracy and efficiency can be guaranteed based on such frame. Findings - According to the test functions, it empirically shows that the proposed algorithm is a potentially feasible method for complicated underlying problems. Originality/value - A bi-direction sampling strategy is suggested. The first way is to use EI criterion to generate samples similar to the EGO. In this way, new samples should be evaluated by real functions or simulations called expensive samples. Another way is to search accurate region according to the second term of EI. To guarantee the reliability of samples, a sample selection scenario based on Bayesian theorem is suggested to select the cheap samples. The authors hope this strategy help them to construct more accurate model without increasing computational cost. © Emerald Group Publishing Limited. Source


Li E.,Central South University | Wang H.,Hunan University | Wang H.,Joint Center for Intelligent New Energy Vehicle
Advances in Engineering Software | Year: 2016

Differential Evolution (DE) is one of the most powerful stochastic real parameter optimizers. An alternative adaptive DE algorithm called Expected Improvement (EI)-High Dimensional Model Representation (HDMR)-DE is suggested. The EI criterion and the Kriging-HDMR are used to adjust scale factor F and crossover constant Cr, respectively. Considering the expensive computational cost of evaluation, the Kriging is integrated to evaluate the objective function when an accuracy criterion is met. To compare the performance, the suggested method, it has been compared with four popular adaptive DE algorithms over 25 standard numerical benchmarks derived from the IEEE Congress on Evolutionary Computation 2005 competition. To verify the feasibility of the suggested algorithm, a real-world application, time-dependent variable Blank Hold Force (BHF) optimization problem is also carried out by the EI-HDMR-DE. The results show that the EI-HDMR-DE improves the performance of adaptive DE and has potential capability to solve some complicated real-world applications. © 2016 Elsevier Ltd. All rights reserved. Source


Li E.,Central South University | Wang H.,Hunan University | Wang H.,Joint Center for Intelligent New Energy Vehicle | Ye F.,Hunan University | Ye F.,Joint Center for Intelligent New Energy Vehicle
Applied Soft Computing Journal | Year: 2016

Curse of dimensionality is a key issue in engineering optimization. When the dimension increases, distribution of samples becomes sparse due to expanded design space. To obtain accurate and reliable results, the amount of samples often grows exponentially with the dimensions. To improve the efficiency of the surrogate with limited samples, a Two-level Multi-surrogate Assisted Optimization (TMAO) is suggested. The framework of the TMAO is to decompose a complicated problem into separable and non-separable components. In the first-level, High Dimensional Model Representation (HDMR) is utilized to determine the correlations among input variables. Then, a high dimensional problem can be decomposed into separable and non-separable components. Thus, the dimension of the original problem might be reduced significantly. Moreover, considering noises and outliers, Support Vector Regression (SVR)-HDMR is utilized to obtain more reliable surrogate. Expected Improvement (EI) criterion is suggested to generate new samples to save computational cost. In the second-level, to handle the non-separable component, a multi-surrogate assisted sampling strategy is suggested. Compared with other methods, the distinctive characteristic of the suggested sampling strategy is to use different surrogates to search potential uncertain regions. Considering the diversity of surrogates, more feature samples might be generated close to the local optimum. Even though it is still difficult to find a global solution, it could help us to find a feasible solution in practice. To verify the performance of the suggested method, several high dimensional mathematical functions are tested by the suggested method. The results demonstrate that all test functions can be successfully solved. © 2016 Elsevier B.V. All rights reserved. Source


Gao G.,Hunan University | Wang H.,Hunan University | Wang H.,Joint Center for Intelligent New Energy Vehicle | Li E.,Central South University | And 2 more authors.
Computers and Structures | Year: 2015

Abstract This paper presents an alternative reanalysis algorithm based on the block matrix to address problems with local modifications. In this method, the modified stiffness can be classified as three parts: influenced region, stationary region and an interface region between them. The main computation cost concentrates on the influenced region by this specific blocked strategy. Compared with popular reanalysis methods, the proposed method can achieve an accurate response for large modification with lower computation cost. Several practical engineering problems are analyzed and the results are exactly as that performed by full analysis. © 2015 Elsevier Ltd. Source


Li G.,Hunan University | Li G.,Joint Center for Intelligent New Energy Vehicle | Zhang Z.,Hunan University | Sun G.,Hunan University | And 3 more authors.
Thin-Walled Structures | Year: 2015

Abstract This paper provides a comparative study on the crashworthiness of different functionally-graded thin-wall tubes under multiple loading angles, which include hollow uniform thickness (H-UT), hollow functionally graded thickness (H-FGT), foam-filled uniform thickness (F-UT) and foam-filled functionally graded thickness (F-FGT) configurations. First, finite element analyses of these differently graded circular tubes reveal that the F-FGT tube has the best crashworthiness under multiple loading angles. Second, parametric study on the F-FGT tube indicates that the thickness gradient and variation range significantly influence its crashworthiness. Third, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the F-FGT tube, in which the optimal thickness variation is sought for maximizing specific energy absorption (SEA) and minimizing initial peak force (IPF) under multiple loading angles. The optimized F-FGT tube exhibits better crashworthiness than other three equivalent tube configurations, indicating that the F-FGT tube can be a potential energy absorber when oblique impact loading is inevitable. © 2015 Elsevier Ltd. Source

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