Multiparametric programming

Explicit mapping from parameters to decisions

Multiparametric programming enables the explicit representation of the dependence of the optimal solution on the parameters of an optimization problem, providing valuable insights into the sensitivity and trade-offs among different decision variables.
Critical regions of the multiparametric programming solution
Our contributions include proposing a novel approach for efficient reactive scheduling by utilizing multiparametric programming. This approach incorporates uncertainty and covers all possible outcomes, resulting in improved scheduling efficiency and avoiding complex optimization problems during uncertain events. Additionally, a solution framework is proposed for various scheduling problems under different types of uncertainty, addressing complexity and providing effective solutions.

Relevant publications:
  • Z. Li, M.G. Ierapetritou. A method for solving the general parametric linear complementarity problem. Annals of Operations Research, 2010, 181, 485-501.
  • Z. Li, M.G. Ierapetritou. A new methodology for the general multiparametric mixed-integer linear programming (MILP) problems Industrial & Engineering Chemistry Research, 2007, 46, 5141-5151.
  • Z. Li, M.G. Ierapetritou. Process scheduling under uncertainty using multiparametric programming. AIChE Journal, 2007, 53, 3183-3203.
  • Z. Li, M.G. Ierapetritou. Reactive scheduling using parametric programming. AIChE Journal, 2008, 54, 2610-2623.