New strategies for flexibility analysis and design under uncertainty

Process flexibility and design under uncertainty have been researched exten sively in the literature. Problem formulations for flexibility include nest ed optimization problems and these can often be refined by substituting the optimality conditions for these nested problems. However, these reformulat ions are highly constrained and can be expensive to solve. In this paper we extend algorithms to solve these reformulated NLP problem under uncertaint y 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 para metric smooth functions, used to replace the complementarity conditions of the KKT conditions with a well-behaved, smoothed nonlinear equality constra int. In this paper we apply the previous strategies to two specific problem s: i) the 'worst case algorithm', that assesses design under uncertainty an d, ii) the flexibility index and feasibility test formulations. In the firs t case, two new algorithms are derived, one of them being single level opti mization problem. Next using similar ideas, both flexibility index and feas ibility test are reformulated leading to a single non linear programming pr oblem instead of a mixed integer non linear programming one. The new formul ations are demonstrated on five different example problems where a CPU time reduction of more than 70 and 80% is demonstrated. (C) 2000 Elsevier Scien ce Ireland Ltd. All rights reserved.