Optimization of uncertain structures using non-probabilistic models

This paper deals with the problem of uncertain optimization, i.e. problems where a level of uncertainty is accounted for. While this class of problems is usually solved using probabilistic optimization, a different strategy which makes use of anti-optimization is used here. Anti-optimization may be a valid alternative when the amount of information available on the uncertain parameters is not enough to accurately define the probability distribution functions. It consists in defining only bounds for the uncertain variables and to build a closed domain of variation. The worst case is searched over this domain and used to verify the constraints of the optimization problem. The aim of the present paper is to compare two different approaches which make use of anti-optimization, namely a nested optimization, where the search for worst case is integrated with the main optimization and a two step optimization, where anti-optimization is solved once for all constraints before starting the optimization allowing a great computational saving with respect to the first. The method has been applied to the optimization of a ten-bar truss where the loads are considered varying within a polyhedron box. (C) 1998 Elsevier Science Ltd. All rights reserved.