SGOP: Surrogate-assisted global optimization using a Pareto-based sampling strategy

Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

Journal of Global Optimization ◽

10.1007/s10898-014-0184-0 ◽

2014 ◽

Vol 60 (2) ◽

pp. 123-144 ◽

Cited By ~ 88

Author(s):

Juliane Müller ◽

Christine A. Shoemaker

Keyword(s):

Global Optimization ◽

Optimization Problems ◽

Sampling Strategy ◽

Surrogate Models ◽

Black Box ◽

Solution Quality ◽

Computationally Expensive

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Metamodel-based design optimization employing a novel sequential sampling strategy

Engineering Computations ◽

10.1108/ec-01-2016-0034 ◽

2017 ◽

Vol 34 (8) ◽

pp. 2547-2564 ◽

Cited By ~ 11

Author(s):

Leshi Shu ◽

Ping Jiang ◽

Li Wan ◽

Qi Zhou ◽

Xinyu Shao ◽

...

Keyword(s):

Global Optimization ◽

Design Optimization ◽

Sequential Sampling ◽

Computational Cost ◽

Sampling Strategy ◽

Local Optimum ◽

Optimization Approach ◽

Great Ability ◽

Content Type ◽

Sample Points

Purpose Metamodels are widely used to replace simulation models in engineering design optimization to reduce the computational cost. The purpose of this paper is to develop a novel sequential sampling strategy (weighted accumulative error sampling, WAES) to obtain accurate metamodels and apply it to improve the quality of global optimization. Design/methodology/approach A sequential single objective formulation is constructed to adaptively select new sample points. In this formulation, the optimization objective is to select a sample point with the maximum weighted accumulative predicted error obtained by analyzing data from previous iterations, and a space-filling criterion is introduced and treated as a constraint to avoid generating clustered sample points. Based on the proposed sequential sampling strategy, a two-step global optimization approach is developed. Findings The proposed WAES approach and the global optimization approach are tested in several cases. A comparison has been made between the proposed approach and other existing approaches. Results illustrate that WAES approach performs the best in improving metamodel accuracy and the two-step global optimization approach has a great ability to avoid local optimum. Originality/value The proposed WAES approach overcomes the shortcomings of some existing approaches. Besides, the two-step global optimization approach can be used for improving the optimization results.

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Value-Based Global Optimization

Journal of Mechanical Design ◽

10.1115/1.4026281 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 17

Author(s):

Roxanne A. Moore ◽

David A. Romero ◽

Christiaan J. J. Paredis

Keyword(s):

Global Optimization ◽

Sequential Sampling ◽

Sampling Strategy ◽

Efficient Global Optimization ◽

Test Cases ◽

A Value ◽

New Information ◽

The Cost ◽

Analysis Models ◽

Better Than

In this paper, a value-based global optimization (VGO) algorithm is introduced. The algorithm uses kriging-like surrogate models and a sequential sampling strategy based on value of information (VoI) to optimize an objective characterized by multiple analysis models with different accuracies. VGO builds on two main contributions. The first contribution is a novel surrogate modeling method that accommodates data from any number of different analysis models with varying accuracy and cost. Rather than interpolating, it fits a model to the data, giving more weight to more accurate data. The second contribution is the use of VoI as a new metric for guiding the sequential sampling process for global optimization. Based on information about the cost and accuracy of each available model, predictions from the current surrogate model are used to determine where to sample next and with what level of accuracy. The cost of further analysis is explicitly taken into account during the optimization process, and no further analysis occurs if the expected value of the new information is negative. In this paper, we present the details of the VGO algorithm and, using a suite of randomly generated test cases, compare its performance with the performance of the efficient global optimization (EGO) algorithm (Jones, D. R., Matthias, S., and Welch, W. J., 1998, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Global Optim., 13(4), pp. 455–492). Results indicate that the VGO algorithm performs better than EGO in terms of overall expected utility—on average, the same quality solution is achieved at a lower cost, or a better solution is achieved at the same cost.

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Bi-direction multi-surrogate surrogate assisted global optimization

Engineering Computations ◽

10.1108/ec-11-2014-0241 ◽

2016 ◽

Vol 33 (3) ◽

Cited By ~ 6

Author(s):

Hu Wang ◽

Enying Li

Keyword(s):

Global Optimization ◽

Design Methodology ◽

Sample Selection ◽

Computational Cost ◽

Sampling Strategy ◽

Expected Improvement ◽

Efficient Global Optimization ◽

Bayesian Theorem ◽

Exact Function ◽

Weight Coefficients

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 (MSEGO) uses more samples generated by multiple surrogates to improve the efficiency. However, the total number of samples is commonly large. To overcome this bottleneck, a bi-direction multi-surrogate global optimization is suggested. 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. We hope this strategy help us to construct more accurate model without increasing computational cost.

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