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An Interval Optimization Method Considering the Dependence between Uncertain Parameters

C. Jiang1,2, Q.F. Zhang1, X. Han1, D. Li3, J. Liu1
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City, P. R. China 410082
Corresponding author.Tel: 86-731-88823325; fax: 86-731-88822051.E-mail address: jiangc@hnu.edu.cn, jiangchaoem@yahoo.com.cn (C. Jiang)
1. Business School, Central South University, Changsha City, P. R. China 410083

Computer Modeling in Engineering & Sciences 2011, 74(1), 65-82. https://doi.org/10.3970/cmes.2011.074.065

Abstract

In this paper, an interval optimization method is developed to deal with a class of problems that there exists dependence between the interval parameters. An ellipsoidal convex model is used to model the uncertainty domain, in which the parameter dependence can be well reflected through the shape of a multi-dimensional ellipsoid. Based on an order relation and a reliability-based possibility degree of interval, the uncertain optimization can be transformed to a deterministic nesting optimization. An efficient algorithm is then constructed to solve the created nesting optimization, in which a sequence of approximate interval optimizations are created and the optimal design is obtained through an iteration process. Two numerical examples are investigated to demonstrate the effectiveness of the present method.

Keywords

interval optimization, uncertain optimization, non-probability, convex model, multi-dimensional ellipsoid, dependence

Cite This Article

Jiang, C., Zhang, Q., Han, X., Li, D., Liu, J. (2011). An Interval Optimization Method Considering the Dependence between Uncertain Parameters. CMES-Computer Modeling in Engineering & Sciences, 74(1), 65–82.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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