Title: Optimization under Uncertainty – Recent Advances in Multi-Parametric Mixed Integer Linear Programming and its Applications
Speaker: Martina Wittmann-Hohlbein
Affiliation: CPSE – Department of Chemical Engineering – Imperial College London
Location: 219A William Penney Lab (entrance from walkway)
Time: 4:00pm
Abstract. In optimization under uncertainty, multi-parametric programming is a powerful tool to account for the presence of uncertainty in mathematical models. Its objective is to derive the optimal solution as a function of the parameters without exhaustively enumerating the parameter space. We consider the general multi-parametric mixed integer linear programming (mp-MILP) problem. The presence of uncertainty in mixed integer linear programming models employed in widespread application fields, including planning/scheduling, process synthesis and hybrid control, significantly increases the complexity and computational effort in retrieving optimal solutions. A particular difficulty arises when uncertainty is simultaneously present in the coefficients of the objective function, the constraint matrix and the constraint vector, which transforms the original linear model into a nonlinear and non-convex one with respect to both the optimization variables and the parameters. Here, we discuss two novel methods for the solution of the general mp-MILP problem. The first approach deals with the global solution of the general mp-MILP model. Exploiting the special structure of the problem, we outline the steps of a parametric branch and bound procedure. The second approach is a two-stage method for the approximate solution of the general mp-MILP problem which combines state-of-the-art robust optimization and multi-parametric programming techniques. The two-stage method is applied to short-term batch process scheduling under uncertainty and we demonstrate its potential in the construction of a pro-active scheduling policy.
About the speaker. Martina Wittmann-Hohlbein obtained a Diploma in Mathematics and Economics at Martin-Luther-University Halle-Wittenberg, Germany, in 2007. She joined CPSE at Imperial College in 2009.