Optimization under uncertainties is an evolving field during the last decade, and it's studied by researchers in different mechanical engineering domains especially in due to the irreducible presence of uncertainties in variables and environmental parameters like as tolerance and ambient temperature. Reliability-based optimization (RBO) and robust optimization (RO) are the two principal types of optimization under uncertainties, the first aims to find optimums that respect problem's constraints with high reliability despite the presence of uncertainties, the second aims to find optimums that are less sensible to inputs' uncertainties. The main challenge in this optimization types mainly in RO is the high computational cost, the three principal sources of this cost are firstly the numerical simulation cost to evaluate objective functions, and secondly the cost of uncertainty propagation technique which is used to propagate uncertainties from inputs (variables and environmental parameters) to outputs of the problem (objective functions and constraint functions) and finally the cost of the optimization algorithm used.

In this work we propose a new efficient framework for Robust and reliability based optimization by using a polynomial meta-model to replace numerical simulation, and we use analytic calculation for uncertainty propagation which is the fastest and the only exact method, and finally a combination algorithm of “Normal boundary intersection” method and “Epsilon constraint” method (NBI-Epsilon) is used to solve the optimization problem.

We apply this framework to a composite hat-stiffened panel that is used in aerospace and marine structures due to its high stiffness to weight ratio and its resistance to corrosion and fatigue, the results show the necessity of the optimization under uncertainties for this kind of problems and show the insufficiency of deterministic optimization, and the proposed framework demonstrates its efficiency after a comparison with a multi-objective genetic algorithm NSGAII which is very used in multi-objective optimizations.