A novel worst case approach for robust optimization of large scale structures

Abstract

In robust optimization, an optimum solution of a system is obtained when some uncertainties exist in the system. The uncertainty can be defined by probabilistic characteristics or deterministic intervals (uncertainty ranges or tolerances) that are the main concern in this study. An insensitive objective function is obtained with regard to the uncertainties or the worst case is considered for the objective function within the intervals in robust optimization. A supreme value within the uncertainty interval is minimized. The worst case approach has been extensively utilized in the linear programming (LP) community. However, the method solved only small scale problems of structural optimization where nonlinear programming (NLP) is employed. In this research, a novel worst case approach is proposed to solve large scale problems of structural optimization. An uncertainty interval is defined by a tolerance range of a design variable or problem parameter. A supreme value is obtained by optimization of the objective function subject to the intervals, and this process yields an inner loop. The supremum is minimized in the outer loop. Linearization of the inner loop is proposed to save the computational time for optimization. This technique can be easily extended for constraints with uncertainty intervals because the worst case of a constraint should be satisfied. The optimum sensitivity is utilized for the sensitivity of a supremum in the outer loop. Three examples including a mathematical example and two structural applications are presented to validate the proposed idea.