Design and analysis of computer experiments

Kuhnt, Sonja; Steinberg, David M.

doi:10.1007/s10182-010-0143-0

Cited by 30 publications

(10 citation statements)

References 9 publications

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“…The kriging method is a geostatistics technique which has many different types [ 29 , 30 , 31 ], and each type has its own special features. The regression kriging method is a type of kriging method, which was first introduced as a surrogate model by Sacks [ 32 , 33 ]. Many researchers now use the regression kriging method to establish the surrogate model.…”

Section: Study Area and Methodsmentioning

confidence: 99%

Surrogate Model Application to the Identification of Optimal Groundwater Exploitation Scheme Based on Regression Kriging Method—A Case Study of Western Jilin Province

Cheng

2015

IJERPH

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This paper introduces a surrogate model to identify an optimal exploitation scheme, while the western Jilin province was selected as the study area. A numerical simulation model of groundwater flow was established first, and four exploitation wells were set in the Tongyu county and Qian Gorlos county respectively so as to supply water to Daan county. Second, the Latin Hypercube Sampling (LHS) method was used to collect data in the feasible region for input variables. A surrogate model of the numerical simulation model of groundwater flow was developed using the regression kriging method. An optimization model was established to search an optimal groundwater exploitation scheme using the minimum average drawdown of groundwater table and the minimum cost of groundwater exploitation as multi-objective functions. Finally, the surrogate model was invoked by the optimization model in the process of solving the optimization problem. Results show that the relative error and root mean square error of the groundwater table drawdown between the simulation model and the surrogate model for 10 validation samples are both lower than 5%, which is a high approximation accuracy. The contrast between the surrogate-based simulation optimization model and the conventional simulation optimization model for solving the same optimization problem, shows the former only needs 5.5 hours, and the latter needs 25 days. The above results indicate that the surrogate model developed in this study could not only considerably reduce the computational burden of the simulation optimization process, but also maintain high computational accuracy. This can thus provide an effective method for identifying an optimal groundwater exploitation scheme quickly and accurately.

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Section: Study Area and Methodsmentioning

confidence: 99%

Surrogate Model Application to the Identification of Optimal Groundwater Exploitation Scheme Based on Regression Kriging Method—A Case Study of Western Jilin Province

Cheng

2015

IJERPH

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“…Gaussian process [30] (also known as Kriging [4] or DACE [21]) is popular to be used as a model in the surrogateassisted evolutionary algorithms because it can provide both the approximated value and the uncertainty of the approximation. However, GP is impeded to be widely applied due to the expensive cost to optimize the hyperparameters of GP, especially the dimension of decision space of the problem is high.…”

Section: Radial Basis Function Networkmentioning

confidence: 99%

Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

Qin

Sun

et al. 2021

Complex Intell. Syst.

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Surrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

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“…This is mirrored in AStA, and we refer exemplary to some special issues of the last years, which reflect the statistical zeitgeist. With the overwhelming developments in computer science, computer experiments have replaced classical experiments in many areas, which was covered in a special issue in 2010 (see Kuhnt and Steinberg 2010). Panel data and their interdisciplinary focus were treated in 2011 (see Haupt and Hsiao 2011).…”

Section: Dear Readers Dear Colleaguesmentioning

confidence: 99%