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Research Papers: Design Automation

A Kriging Metamodel Assisted Multi-Objective Genetic Algorithm for Design Optimization

[+] Author and Article Information
M. Li, G. Li

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742

S. Azarm1

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742azarm@umd.edu

1

Corresponding author.

J. Mech. Des 130(3), 031401 (Feb 04, 2008) (10 pages) doi:10.1115/1.2829879 History: Received May 30, 2006; Revised July 16, 2007; Published February 04, 2008

The high computational cost of population based optimization methods, such as multi-objective genetic algorithms (MOGAs), has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise methods that can significantly reduce the number of simulation (objective∕constraint functions) calls. We present a new multi-objective design optimization approach in which the Kriging-based metamodeling is embedded within a MOGA. The proposed approach is called Kriging assisted MOGA, or K-MOGA. The key difference between K-MOGA and a conventional MOGA is that in K-MOGA some of the design points are evaluated on-line using Kriging metamodeling instead of the actual simulation model. The decision as to whether the simulation or its Kriging metamodel should be used for evaluating a design point is based on a simple and objective criterion. It is determined whether by using the objective∕constraint functions’ Kriging metamodels for a design point, its “domination status” in the current generation can be changed. Seven numerical and engineering examples with different degrees of difficulty are used to illustrate applicability of the proposed K-MOGA. The results show that on the average K-MOGA converges to the Pareto frontier with an approximately 50% fewer number of simulation calls compared to a conventional MOGA.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flowchart of MOGA (left dashed block) and proposed addition (right dashed block) of K-MOGA

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Figure 2

Predicted errors in (a) objective space and (b) constraint space

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Figure 3

Pareto solutions for the ZDT2 example

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Figure 4

No. of simulation calls versus run number for the ZDT2 example

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Figure 5

Quality metrics (a) HD and (b) OS

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Figure 6

(a) MMDf1 and (b) MMDf2 based on simulation and Kriging metamodel

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Figure 7

Real error and predicted error for (a) f1 and (b) f2 for the ZDT2 example in the tenth generation

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Figure 8

Pareto solutions for cabinet problem using MOGA and proposed K-MOGA

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