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Metamodeling is an effective method to approximate the relations between input and output parameters when significant efforts of experiments and simulations are required to collect the data to build the relations. This paper aims to develop a new sequential sampling method for adaptive metamodeling by using the data with highly nonlinear relation between input and output parameters.

In this method, the Latin hypercube sampling method is used to sample the initial data, and kriging method is used to construct the metamodel. In this work, input parameter values for collecting the next output data to update the currently achieved metamodel are determined based on qualities of data in both the input and output parameter spaces. Uniformity is used to evaluate data in the input parameter space. Leave-one-out errors and sensitivities are considered to evaluate data in the output parameter space.

This new method has been compared with the existing methods to demonstrate its effectiveness in approximation. This new method has also been compared with the existing methods in solving global optimization problems. An engineering case is used at last to verify the method further.

This paper provides an effective sequential sampling method for adaptive metamodeling to approximate highly nonlinear relations between input and output parameters.

Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. The purpose of this paper is to use support vector regression with high dimensional model representation (SVR-HDMR) model to obtain accurate metamodels for high dimensional problems with a few sampling points.

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. Support vector regression (SVR) method can approximate the underlying functions with a small subset of sample points. Dividing Rectangles (DIRECT) algorithm is a deterministic sampling method.

This paper proposes a new form of HDMR by integrating the SVR, termed as SVR-HDMR. And an intelligent sampling strategy, namely, DIRECT method, is adopted to improve the efficiency of SVR-HDMR.

Compared to other metamodeling techniques, the accuracy and efficiency of SVR-HDMR were significantly improved. The SVR-HDMR helped engineers understand the essence of underlying problems visually.

This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.

The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency.

To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations.

The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.

The purpose of this paper is to efficiently use as few sample points as possible to get a sufficiently explored design space and an accurate optimum for adaptive metamodel-based design optimization (AMBDO).

A parameterized lower confidence bounding (PLCB) scheme is proposed in which a cooling strategy is introduced to guarantee the balance between exploitation and exploration by varying weights of the predicting error and optimum of a metamodel. The proposed scheme is investigated by a set of test functions and a structural optimization problem, in which PLCB with four kinds of cooling control functions are studied. Moreover, other infill criteria (such as expected improvement and its extension versions) are taken into comparison.

Results show that the proposed PLCB (especially PLCB with the first cooling control function) based AMBDO method can find the optimum with fewer evaluations and maintain good accuracy, which means the proposed PLCB contributes to the excellent efficiency and accuracy in finding global optimal solutions.

The parameterized version of the lower confidence bound metric is proposed for AMBDO, typically used in the context of adaptive sampling in efficient global optimization.

Engineering design optimization involving computational simulations is usually a time-consuming, even computationally prohibitive process. To relieve the computational burden, the adaptive metamodel-based design optimization (AMBDO) approaches have been widely used. This paper aims to develop an AMBDO approach, a lower confidence bounding approach based on the coefficient of variation (CV-LCB) approach, to balance the exploration and exploitation objectively for obtaining a global optimum under limited computational budget.

In the proposed CV-LCB approach, the coefficient of variation (CV) of predicted values is introduced to indicate the degree of dispersion of objective function values, while the CV of predicting errors is introduced to represent the accuracy of the established metamodel. Then, a weighted formula, which takes the degree of dispersion and the prediction accuracy into consideration, is defined based on the already-acquired CV information to adaptively update the metamodel during the optimization process.

Ten numerical examples with different degrees of complexity and an AIAA aerodynamic design optimization problem are used to demonstrate the effectiveness of the proposed CV-LCB approach. The comparisons between the proposed approach and four existing approaches regarding the computational efficiency and robustness are made. Results illustrate the merits of the proposed CV-LCB approach in computational efficiency and robustness.

The proposed approach exhibits high efficiency and robustness in engineering design optimization involving computational simulations.

CV-LCB approach can balance the exploration and exploitation objectively.

The complexity and interdisciplinarity of healthcare industry problems make this industry one of the attention centers of computer-based simulation studies to provide a proper tool for interaction between decision-makers and experts. The purpose of this study is to present a metamodel-based simulation optimization in an emergency department (ED) to allocate human resources in the best way to minimize door to doctor time subject to the problem constraints which are capacity and budget.

To obtain the objective of this research, first the data are collected from a public hospital ED in Brazil, and then an agent-based simulation is designed and constructed. Afterwards, three machine-learning approaches, namely, adaptive neuro-fuzzy inference system (ANFIS), feed forward neural network (FNN) and recurrent neural network (RNN), are used to build an ensemble metamodel through adaptive boosting. Finally, the results from the metamodel are applied in a discrete imperialist competitive algorithm (ICA) for optimization.

Analyzing the results shows that the yellow zone section is considered as a potential bottleneck of the ED. After 100 executions of the algorithm, the results show a reduction of 24.82 per cent in the door to doctor time with a success rate of 59 per cent.

This study fulfils an identified need to optimize human resources in an ED with less computational time.

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

The purpose of this paper is to introduce a new method to carry out the design optimization of the tool head system in the heavy‐duty machine tool where closed hydrostatic guideways with multiple pockets are employed.

A more accurate method of pressure calculation for closed hydrostatic guideways is introduced. Then, a multidisciplinary design optimization (MDO) model is formulated for design of a tool head system, which minimizes the highest pocket pressure under some constraints from machining accuracy and vibration resistance requirements as well as constraints from ballscrew design specifications. Finally, a metamodel‐based design space alternation (DSA) strategy is proposed to solve the optimization problem.

The results show that the maximum pocket pressure in a tool head system can be reduced over 47 percent with a proper design while all the constraints are satisfied. As a consequence, the tool head system can safely work under the maximum output pressure of oil supply system.

This paper introduces a more accurate method of pressure calculation for multi‐pocket closed hydrostatic guideways, develops a metamodel‐based MDO model for the tool head system, and proposes a DSA strategy to solve the MDO problem.

Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the EMD need to be perfectly modeled using a complex numerical model. However, these fine models demand a high computational time. Alternatively, less accurate coarse models can be used with a demerit of the high expected recovery errors. The purpose of this paper is to present an efficient methodology to reduce the effect of stochastic modeling errors in the inverse problem solution.

The recovery error in the electromagnetic inverse problem solution is reduced using the Bayesian approximation error approach coupled with an adaptive Kriging-based model. The accuracy of the forward model is assessed and adapted a priori using the cross-validation technique.

The adaptive Kriging-based model seems to be an efficient technique for modeling EMDs used in inverse problems. Moreover, using the proposed methodology, the recovery error in the electromagnetic inverse problem solution is largely reduced in a relatively small computational time and memory storage.

The proposed methodology is capable of not only improving the accuracy of the inverse problem solution, but also reducing the computational time as well as the memory storage. Furthermore, to the best of the authors knowledge, it is the first time to combine the adaptive Kriging-based model with the Bayesian approximation error approach for the stochastic modeling error reduction.

This study aims to suggest and develops a global sensitivity analysis-assisted multi-level sequential optimization method for the heat transfer problem.

Compared with other surrogate-assisted optimization methods, the distinctive characteristic of the suggested method is to decompose the original problem into several layers according to the global sensitivity index. The optimization starts with the several most important design variables by the support vector regression-based efficient global optimization method. Then, when the optimization process progresses, the filtered design variables should be involved in optimization one by one or the setting value. Therefore, in each layer, the design space should be reduced according to the previous optimization result. To improve the accuracy of the global sensitivity index, a novel global sensitivity analysis method based on the variance-based method incorporating a random sampling high-dimensional model representation is introduced.

The advantage of this method lies in its capability to solve complicated problems with a limited number of sample points. Moreover, to enhance the reliability of optimum, the support vector regression-based global efficient optimization is used to optimize in each layer.

The developed optimization tool is built by MATLAB and can be integrated by commercial software, such as ABAQUS and COMSOL. Lastly, this tool is integrated with COMSOL and applied to the plant-fin heat sink design. Compared with the initial temperature, the temperature after design is over 49°. Moreover, the relationships among all design variables are also disclosed clearly.

The D-MORPH-HDMR is integrated to obtain the coupling relativities among the design variables efficiently. The suggested method can be decomposed into multiplier layers according to the GSI. The SVR-EGO is used to optimize the sub-problem because of its robustness of modeling.