Open Access

ARTICLE

An Interval Optimization Method Considering the Dependence between Uncertain Parameters

C. Jiang^1,2, Q.F. Zhang¹, X. Han¹, D. Li³, J. Liu¹
1 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
2 Corresponding author.Tel: 86-731-88823325; fax: 86-731-88822051.E-mail address: jiangc@hnu.edu.cn, jiangchaoem@yahoo.com.cn (C. Jiang)
3 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

---