An uncertain multidisciplinary design optimization method using interval convex models

Abstract

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.

Keywords:

• multidisciplinary design optimization (MDO)
• multi-objective optimization
• interval model
• uncertainty
• multidisciplinary feasible (MDF) method

Acknowledgements

This work is partially supported by Chancellor's Research Fellowship (2032062), University of Technology, Sydney (UTS), National Natural Science Foundation of China (NSFC) (10872036), ‘863’ High-Tech Research Program of China (2008AA04Z118) and Open Foundation of the Key Lab. of Manufacture and Test Techniques for Automobile Parts, Chongqing University of Technology, China.