Xiwen Cai, Haobo Qiu, Liang Gao, Xiaoke Li and Xinyu Shao
This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.
Abstract
Purpose
This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Aibing Ji, Hui Liu, Hong-jie Qiu and Haobo Lin
– The purpose of this paper is to build a novel data envelopment analysis (DEA) model to evaluate the efficiencies of decision making units (DMUs).
Abstract
Purpose
The purpose of this paper is to build a novel data envelopment analysis (DEA) model to evaluate the efficiencies of decision making units (DMUs).
Design/methodology/approach
Using the Choquet integrals as aggregating tool, the authors give a novel DEA model to evaluate the efficiencies of DMUs.
Findings
It extends DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form. At last, the authors use the numerical examples to illustrate the performance of the proposed model.
Practical implications
The proposed DEA model can be used to evaluate the efficiency of the DMUs with multiple interactive inputs and outputs.
Originality/value
This paper introduce a new DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form.
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Xiaoke Li, Haobo Qiu, Zhenzhong Chen, Liang Gao and Xinyu Shao
Kriging model has been widely adopted to reduce the high computational costs of simulations in Reliability-based design optimization (RBDO). To construct the Kriging model…
Abstract
Purpose
Kriging model has been widely adopted to reduce the high computational costs of simulations in Reliability-based design optimization (RBDO). To construct the Kriging model accurately and efficiently in the region of significance, a local sampling method with variable radius (LSVR) is proposed. The paper aims to discuss these issues.
Design/methodology/approach
In LSVR, the sequential sampling points are mainly selected within the local region around the current design point. The size of the local region is adaptively defined according to the target reliability and the nonlinearity of the probabilistic constraint. Every probabilistic constraint has its own local region instead of all constraints sharing one local region. In the local sampling region, the points located on the constraint boundary and the points with high uncertainty are considered simultaneously.
Findings
The computational capability of the proposed method is demonstrated using two mathematical problems, a reducer design and a box girder design of a super heavy machine tool. The comparison results show that the proposed method is very efficient and accurate.
Originality/value
The main contribution of this paper lies in: a new local sampling region computational criterion is proposed for Kriging. The originality of this paper is using expected feasible function (EFF) criterion and the shortest distance to the existing sample points instead of the other types of sequential sampling criterion to deal with the low efficiency problem.
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Zheng Jiang, Haobo Qiu, Ming Zhao, Shizhan Zhang and Liang Gao
In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex…
Abstract
Purpose
In multidisciplinary design optimization (MDO), if the relationships between design variables and some output parameters, which are important performance constraints, are complex implicit problems, plenty of time should be spent on computationally expensive simulations to identify whether the implicit constraints are satisfied with the given design variables during the optimization iteration process. The purpose of this paper is to propose an ensemble of surrogates-based analytical target cascading (ESATC) method to tackle such MDO engineering design problems with reduced computational cost and high optimization accuracy.
Design/methodology/approach
Different surrogate models are constructed based on the sample point sets obtained by Latin hypercube sampling (LHS) method. Then, according to the error metric of each surrogate model, the repeated ensemble of surrogates is constructed to approximate the implicit objective functions and constraints. Under the framework of analytical target cascading (ATC), the MDO problem is decomposed into several optimization subproblems and the function of analysis module of each subproblem is simulated by repeated ensemble of surrogates, working together to find the optimum solution.
Findings
The proposed method shows better modeling accuracy and robustness than other individual surrogate model-based ATC method. A numerical benchmark problem and an industrial case study of the structural design of a super heavy vertical lathe machine tool are utilized to demonstrate the accuracy and efficiency of the proposed method.
Originality/value
This paper integrates a repeated ensemble method with ATC strategy to construct the ESATC framework which is an effective method to solve MDO problems with implicit constraints and black-box objectives.
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Zhiyuan Huang, Haobo Qiu, Ming Zhao, Xiwen Cai and Liang Gao
Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.