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Research Papers

An Evolutionary Algorithm Based Approach to Design Optimization Using Evidence Theory

[+] Author and Article Information
Rupesh Kumar Srivastava

Graduate Student
Dalle Molle Institute for AI (IDSIA),
CH-6928, Manno-Lugano, Switzerland
e-mail: rupesh@idsia.ch

Kalyanmoy Deb

Koenig Endowed Chair Professor
Department of Electrical and Computer Engineering,
Professor, Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824;
Professor, Department of Computer Science and Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: kdeb@egr.msu.edu

Rupesh Tulshyan

Research Associate
Kanpur Genetic Algorithms Laboratory,
Indian Institute of Technology
Kanpur, 208016 Uttar Pradesh, India
e-mail: tulshyan@iitk.ac.in

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 14, 2011; final manuscript received February 23, 2013; published online June 10, 2013. Assoc. Editor: Zissimos P. Mourelatos.

J. Mech. Des 135(8), 081003 (Jun 10, 2013) (12 pages) Paper No: MD-11-1233; doi: 10.1115/1.4024223 History: Received May 14, 2011; Revised February 23, 2013

For problems involving uncertainties in design variables and parameters, a bi-objective evolutionary algorithm (EA) based approach to design optimization using evidence theory is proposed and implemented in this paper. In addition to a functional objective, a plausibility measure of failure of constraint satisfaction is minimized. Despite some interests in classical optimization literature, this is the first attempt to use evidence theory with an EA. Due to EA's flexibility in modifying its operators, nonrequirement of any gradient, its ability to handle multiple conflicting objectives, and ease of parallelization, evidence-based design optimization using an EA is promising. Results on a test problem and two engineering design problems show that the modified evolutionary multi-objective optimization algorithm is capable of finding a widely distributed trade-off frontier showing different optimal solutions corresponding to different levels of plausibility failure limits. Furthermore, a single-objective evidence-based EA is found to produce better optimal solutions than a previously reported classical optimization algorithm. Furthermore, the use of a graphical processing unit (GPU) based parallel computing platform demonstrates EA's performance enhancement around 160–700 times in implementing plausibility computations. Handling uncertainties of different types are getting increasingly popular in applied optimization studies and this EA based study is promising to be applied in real-world design optimization problems.

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Figures

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Fig. 1

Various methods of handling incomplete information in RBDO

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Fig. 3

Results obtained for the two-variable test problem

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Fig. 4

Results obtained for the modified two-variable test problem

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Fig. 5

A mirrored S shaped Pareto-optimal front and likely preferred point (A) and set (BC) are illustrated. The point B is obtained by drawing a tangent line from A on to the Pareto-optimal front.

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Fig. 6

Obtained trade-off front for the cantilever design problem

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Fig. 7

Obtained trade-off front for the pressure vessel design problem

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Fig. 8

Effect of varying number of threads per block (tcount) for the cantilever problem run for 30 generations

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