Parametric optimization of MILP programs and a framework for the parametric optimization of MINLPs

Abstract

Development of parametric optimization tools are essential in process design as they can offer significant analytical results to problems related either to uncertainty or multiple objective optimization. In fact the solution of the pertinent parametric optimization problems is the complete and exact solution of the former ones from the mathematical point of view. Although sensitivity analysis and parametric optimization problems have been addressed successfully in the linear programming case(Gal 1979) they are still the subject of ongoing research for the mathematical programs that involve integer variables in their formulation (MILP and MINLP). This paper addresses the scalar parameterization of such problems by presenting first a sensitivity analysis algorithm for the MILP case, which when iterated provides the parametric optimization results of this problem. For the MINLP case, an algorithm that provides a succession of improving parametric lower and upper bounds is presented that involves the ϵ-approximate solution of parametric NLP subproblems and the exact solution of parametric MILP master problems within the general framework of the Outer Approximation/Equation Relaxation algorithm.