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Research Papers

An Improved Kriging-Assisted Multi-Objective Genetic Algorithm

[+] Author and Article Information
Mian Li

 University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China e-mail: mianli@sjtu.edu.cn

J. Mech. Des 133(7), 071008 (Jul 18, 2011) (11 pages) doi:10.1115/1.4004378 History: Received April 22, 2010; Accepted May 27, 2011; Published July 18, 2011; Online July 18, 2011

Although Genetic Algorithms (GAs) and Multi-Objective Genetic Algorithms (MOGAs) have been widely used in engineering design optimization, the important challenge still faced by researchers in using these methods is their high computational cost due to the population-based nature of these methods. For these problems it is important to devise MOGAs that can significantly reduce the number of simulation calls compared to a conventional MOGA. An improved kriging-assisted MOGA, called Circled Kriging MOGA (CK-MOGA), is presented in this paper, in which kriging metamodels are embedded within the computation procedure of a traditional MOGA. In the proposed approach, the decision as to whether the original simulation or its kriging metamodel should be used for evaluating an individual is based on a new and advanced objective switch criterion and an adaptive metamodeling technique. The effect of the possible estimated error from the metamodel is mitigated by applying the new switch criterion. Five numerical and engineering examples with different degrees of difficulty are used to illustrate applicability of the proposed approach, with the verification using different quality measures. The results show that, on the average, CK-MOGA outperforms both a conventional MOGA and a previously developed Kriging MOGA in terms of the number of simulation calls.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Dominance status in a two-objective case

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Figure 2

Kriging metamodeling for response prediction

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Figure 4

Conventional MOGA (left) with CK-MOGA addition (right)

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Figure 5

MD criterion for accepting the predicted value

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Figure 6

Possible failure of the criterion in Eq. 7

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Figure 7

Pareto solutions for OSY

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Figure 8

Nsc versus run number for OSY

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Figure 9

Quality metrics (a) HD and (b) OS

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Figure 10

MD from simulation and kriging metamodel

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Figure 11

Real and predicted uncertainty for (a) f1 and (b) f2 for OSY in the 10th generation

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Figure 12

Obtained Pareto solutions using MOGA, K-MOGA, and CK-MOGA for cabinet design

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Figure 13

Statistic results (or probability density functions) for test examples

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