POP – Parametric Optimization Toolbox

Abstract

In this paper, we describe POP, a MATLAB toolbox for parametric optimization. It features (a) efficient implementations of multiparametric programming problem solvers for multiparametric linear and quadratic programming problems and their mixed-integer counter-parts, (b) a versatile problem generator capable of creating random multiparametric programming problems of arbitrary size, and (c) a comprehensive library of multiparametric programming test problems featuring benchmark test sets for multiparametric linear, quadratic, mixed-integer linear, and mixedinteger quadratic programming problems. In addition, POP is equipped with a graphical user interface which enables the userfriendly use of all functionalities of POP and a link to the solvers of the Multi-Parametric Toolbox (MPT), as well as the ability to design explicit MPC problems. These features are demonstrated in detailed computational studies providing insights into the versatility and applicability of POP. Additionally, the example of a periodic chromatographic system is used to show the scalability of multiparametric programming in general and POP, in particular.Article pubs.acs.org/IECR

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…In particular, it o ers tools for the formulation and solution of multi-parametric programming problems. Based on POP [258], it contains state-of-the-art algorithms which allow for an e cient solution of mp-LP, mp-QP, mp-MILP and mp-MIQP problems. Furthermore, its interconnection with gPROMS R • ModelBuilder (see below) makes the use of the PAROC framework straightforward and allows for an intuitive approach for design, operation and control problems.…”

“…The multi-parametric model predictive controller problem is formulated and solved using POP where the optimal control action is generated as a map of solutions and as a function of the problem parameters [34,258]. The problem formulation is based on Equation 4.5 and the tuning of the controller is presented in Table 6.3.…”

“…The multi-parametric model predictive controller problem is formulated based on Equation 4.5 and solved with POP [258]. The objective of the mp-MPC is to minimize the concentration of the reactants at the outlet of the reactor.…”

“…The multi-parametric model predictive controller problem (based on Equation 4.5) is formulated and solved with POP [258]. The tuning of the controller is presented in Table 6.8.…”

“…•toolbox [258]. The parameters in this case are the disturbances introduced to the system and the system operation (commonly denoted by the states variables of the state-space model).…”