Multiobjective Optimization of Mixed-Integer Linear Programming Problems: A Multiparametric Optimization Approach.

Industrial process systems need to be optimized, simultaneously satisfying financial, quality and safety criteria. To meet all those potentially conflicting optimization objectives, multiobjective optimization formulations can be used to derive optimal trade-off solutions. In this work, we present a framework that provides the exact Pareto front of multiobjective mixed-integer linear optimization problems through multiparametric programming. The original multiobjective optimization program is reformulated through the well-established ϵ-constraint scalarization method, in which the vector of scalarization parameters is treated as a right-hand side uncertainty for the multiparametric program. The algorithmic procedure then derives the optimal solution of the resulting multiparametric mixed-integer linear programming problem as an affine function of the ϵ parameters, which explicitly generates the Pareto front of the multiobjective problem. The solution of a numerical example is analytically presented to exhibit the steps of the approach, while its practicality is shown through a simultaneous process and product design problem case study. Finally, the computational performance is benchmarked with case studies of varying dimensionality with respect to the number of objective functions and decision variables.

Integrated Data-Driven Process Monitoring and Explicit Fault-Tolerant Multiparametric Control.

We propose a novel active fault-tolerant control strategy that combines machine learning based process monitoring and explicit/multiparametric model predictive control (mp-MPC). The strategy features (i) data-driven fault detection and diagnosis models by using the support vector machine (SVM) algorithm, (ii) ranking via a nonlinear, kernel-dependent, SVM-based feature selection algorithm, (iii) data-driven regression models for fault magnitude estimation via the random forest algorithm, and (iv) a parametric optimization and control (PAROC) framework for the design of the explicit/multiparametric model predictive controller. The resulting explicit control strategies correspond to affine functions of the system states and the magnitude of the detected fault. A semibatch process, an example for penicillin production, is presented to demonstrate how the proposed framework ensures smart operation for which rapid switches between a priori computed explicit control action strategies are enabled by continuous process monitoring information.