New strategies for flexibility analysis and design under uncertainty

Abstract

Process flexibility and design under uncertainty have been researched extensively in the literature. Problem formulations for flexibility include nested optimization problems and these can often be refined by substituting the optimality conditions for these nested problems. However, these reformulations are highly constrained and can be expensive to solve. In this paper we extend algorithms to solve these reformulated NLP problem under uncertainty by introducing two contributions to this approach. These are the use of a Constraint Aggregation function (KS function) and Smoothing Functions. We begin with basic properties of KS function. Next, we review a class of parametric smooth functions, used to replace the complementarity conditions of the KKT conditions with a well-behaved, smoothed nonlinear equality constraint. In this paper we apply the previous strategies to two specific problems: i) the'worst case algorithm', that assesses design under uncertainty and, ii) the flexibility index and feasibility test formulations. In the first case, two new algorithms are derived, one of them being single level optimization problem. Next using similar ideas, both flexibility index and feasibility test are reformulated leading to a single non linear programming problem instead of a mixed integer non linear programming one. The new formulations are demonstrated on five different example problems where a CPU time reduction of more than 70 and 80% is demonstrated.