Styliani Avraamidou

On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory

In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-parametric quadratic programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the parametric solution of the dual of a convex problem.

A multi-parametric bi-level optimization strategy for hierarchical model predictive control

Abstract Hierarchical control structures consist of a hierarchy of control levels. In the case of hierarchical model predictive control (MPC) structures, each control level involves an optimization problem, with the resulting formulation typically corresponding to a multilevel programming problem. The solution of this type of problems is very challenging, even when considering only two linear optimization levels, and typically require the use of global optimization techniques. In this work, we propose the use of a novel algorithm capable of providing the exact, global and multi-parametric solution of bi-level programming problems for the solution of hierarchical control problems. The derivation of hierarchical multi-parametric/explicit MPC controllers through the proposed algorithm, allows the controller to only do simple function evaluations at every control step, instead of solving the full bi-level optimization problem. We are illustrating the proposed methodology through an example of a two level hierarchical mp-MPC of a continuous stirred tank reactor (CSTR) system.

Towards a Quantitative Food-Energy-Water Nexus Metric to Facilitate Decision Making in Process Systems: A Case Study on a Dairy Production Plant

While the importance of the Food-Energy-Water Nexus (FEW-N) has been widely accepted, a holistic approach to facilitate decision making in FEW-N systems, along with a quantitative index assessing the integrated FEW-N performance is rather lacking. In this work, we propose a FEW-N metric along with a framework to facilitate decision making for FEW-N process systems through a FEW-N integrated approach. The framework and metric are illustrated through a case study on a dairy production and processing plant. The dairy industry is a significant user of water and energy, with water being a top issue for most dairy industries and organizations worldwide. Following the framework, we develop a mixed-integer scheduling model, with alternative pathways, that faithfully replicated the major food, energy, and water aspects of a real cottage-cheese production plant. Using the developed FEW-N metric we were able to optimize the cottage-cheese plant process and observe different trade-offs between the FEW-N elements.

Land use modeling and optimization based on food-energy-water nexus: a case study on crop-livestock systems

Abstract Efficient land use in agricultural systems is a complicated decision-making problem with resource competitions and conflicting objectives. Systematic thinking based on food-energy-water (FEW) nexus is a necessity for modeling and optimization of the systems. However, challenges arise in making decisions while encountering conflicting objectives, limited data and coupling components. To address these challenges, we developed a global optimization-based land allocation framework, which provides an adaptive data-driven modeling method based on limited realistic data to predict yields for production components, a FEW index to help solve the multi-objective optimization problem and carry out assessments. Computational results indicate that the framework can provide valuable production models and a comprehensive FEW index to select strategies for optimal land allocation and limit stresses in the FEW nexus.

Development of advanced control strategies for periodic systems: An application to chromatographic separation processes

In this work we investigate the design and application of advanced control strategies to a periodic chromatographic process. For the Multicolumn Countercurrent Solvent Gradient Purification process (MCSGP), a nonlinear process described by a periodic profile, we present a step-by-step procedure that enables the seamless development of explicit advanced MPC controllers for such systems. The designed controllers assure optimal operating conditions, periodic input profiles and continuous process monitoring.