Optimization of Nonlinear Manufacturing Systems under Uncertainty

A new algorithm for the optimization of nonlinear systems under uncertainty is presented. The algorithm, based on a parametric programming framework, gives a complete map of the optimal solution in the space of the uncertain parameters, solving a minimum number of NLP subproblems and simplified multiparametric linear master problems. Through cumulative outer-approximations obtained from the solution of deterministic NLP at fixed values of the uncertain parameters, the master problem provides valid lower bounds that converge to the optimal values as the number of approximations is increased. Several heuristics are proposed to guide the mathematical algorithm, drastically reducing the computational requirements, still ensuring convergence to the optimal solution.