A multiobjective optimization based approach for RBDO

Abstract

In this paper we present a novel algorithm in order to solve multiobjective design optimization problems of a sandwich plate when the objective functions are not smooth and when uncertainty is introduced into the material properties. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. It will be shown that a chance constraint optimization problem such as a RBDO problem can be written as a multiobjective optimization problem. Chance constraint optimization problems yields optimal designs for a fixed given level of probability for the constraint. However in real life problem it is not realistic to introduce a given probability because it is not known. It is more efficient to solve the problem for a whole range of probability in order to obtain an overview of the probability level appearing in the constraint effect on the solution. We show in this paper how to transform a chance constraint optimization problem into a multiobjective optimization problem and we give an illustration on simple examples.