Feasibility Analysis and Optimal Design Using a Chance Constrained Programming Framework

We propose a new framework to address feasibility analysis and optimal design problems under uncertainty. This approach is based on nonlinear chance constrained programming. The feasibility analysis problem is defined as the maximization of the achievable confidence level of satisfying all constraints for a given design. The solution can provide clear information about the dependence of the reliability of a nonlinear convex system on the values of the design variables. This offers a priori the feasible region for the design optimization problem. A feature of this approach is that for a design with a 100% confidence level the solution does not depend on the distribution of the uncertain variables. Moreover, the critical constraint which cuts off the largest part of the design space can be identified so that, if necessary, a decision can be made to relax this constraint to achieve a meaningful design. The chance constrained program will be relaxed to a single level nonlinear optimization problem (NLP). The scope of this approach is demonstrated with a nonlinear design problem.