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Reliability-based optimization for multiple constraints with evolutionary algorithms

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Daum, David A., Deb, Kalyanmoy and Branke, Jürgen, 1969- (2007) Reliability-based optimization for multiple constraints with evolutionary algorithms. In: IEEE Congress on Evolutionary Computation, Singapore, 25-28 September 2007. Published in: IEEE Transactions on Evolutionary Computation pp. 911-918.

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Official URL: http://dx.doi.org/10.1109/CEC.2007.4424567

Abstract

In this paper, we combine reliability-based optimization with a multi-objective evolutionary algorithm for handling uncertainty in decision variables and parameters. This work is an extension to a previous study by the second author and his research group to more accurately compute a multi-constraint reliability. This means that the overall reliability of a solution regarding all constraints is examined, instead of a reliability computation of only one critical constraint. First, we present a brief introduction into this so-called 'structural reliability' aspects. Thereafter, we introduce a method for identifying inactive constraints according to the reliability evaluation. With this method, we show that with less number of constraint evaluations, an identical solution can be achieved. Furthermore, we apply our approach to a number of problems including a real-world car side impact design problem to illustrate our method.

Item Type: Conference Item (Paper)
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH): Reliability (Engineering) -- Statistical methods, Statistical decision -- Research, Evolutionary computation -- Research, Mathematical optimization, Uncertainty (Information theory)
Journal or Publication Title: IEEE Transactions on Evolutionary Computation
Publisher: IEEE
ISSN: 1089-778X
Date: 2007
Page Range: pp. 911-918
Identification Number: 10.1109/CEC.2007.4424567
Status: Not Peer Reviewed
Access rights to Published version: Open Access
Conference Paper Type: Paper
Title of Event: IEEE Congress on Evolutionary Computation
Type of Event: Conference
Location of Event: Singapore
Date(s) of Event: 25-28 September 2007
References: [1] AO. Ditlevsen, Narrow reliability bounds for structural system, J. Struct. Mech. 4 (1) 431-439, 1979. [2] M. Rosenblatt, Remarks on a multivariate transformation, Ann Math.Stat., 23 470-472, 1952. [3] AM. Hasofer, NC. Lind, An exact and invariant first order reliability format, J Eng Mech Div ASCE, 100(EM1):111U˝ 21, 1974. [4] X. Du, W. Chen, A Most Probable Point Based Method for Uncertainty Analysis, Journal of Design and Manufacturing Automation, 1, pp. 47- 66, 2001. [5] M. S. Eldred, B. J. Bichonz, B. M. Adamsx, Overview of Reliability Analysis and Design Capabilities in DAKOTA, Conference Paper, NSF Workshop on Reliable Engineering Computing (REC 2006), Savannah, GA, February 2006. [6] K. Deb, Multi-objective optimization using evolutionary algorithms, Chichester, UK: Wiley, 2001. [7] H. Agarwal, Reliability based design optimization: Formulations and Methodologies, PhD thesis, University of Notre Dame, 2004. [8] L. Gu, R. J. Yang, C. H. Tho, L. Makowski, O. Faruque, and Y. Li, Optimization and robustness for crashworthiness of side impact, International Journal of Vehicle Design, 26(4), 2001. [9] K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2):182-197, 2002. [10] K. Deb, D. Padmanabhan, S. Gupta, A. K. and Mall, Handling Uncertainties Through Reliability-Based Optimization Using Evolutionary Algorithms, Fourth International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007) pp. 66-88 Lecture Notes on Computer Science 4403, 2007. [11] O. Ditlevsen, H. O. Madsen, Structural Reliability Methods, New York: Wiley, 1996. [12] HO. Madsen, S. Krenk, NC. Lind, Methods of structural safety, Englewood Cliffs (NJ): Prentice-Hall, Inc., 1986. [13] R. Rackwitz, Reliability analysis ˚U A review and some perspectives, Structural Safety 23(4):365 ˝U 95, 2001. [14] C.A. Cornell, Bounds on the reliability of structural systems, J. Struct. Div., ASCE, 93 (ST1) 171-200, 1967. [15] K. Ramachandran, M. Baker New reliability bound for series systems, In: Konishi I, Ang AH-S, Shinozuka M, editors. Proc. ICOSSAR Š85, Kobe; p. 157U˝ 169 [Vol. I], 1985 [16] J. H. Holland, Adaptation in Natural and Artifcial Systems, Ann Arbor, MI: MIT Press, 1975. [17] D. E. Goldberg, Genetic Algorithms for Search, Optimization, and Machine Learning, Reading, MA: Addison-Wesley, 1989. [18] K. Deb, A. Srinivasan Innovization: Innovating design principles through optimizationProc. of the Genetic and Evolutionary Computation Conference (GECCO-2006), New York: The ACM Press, p. 1629–1636, 2006 [19] Henrik O. Madsen First Order vs. Second Order Reliability Analysis of Series StructuresStructural Safety, 2 207-214, 1985
URI: http://wrap.warwick.ac.uk/id/eprint/2418

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