Mixed-integer multi-level optimization through multi-parametric programming

Optimization problems involving a set of nested optimization problems over a single feasible region are referred to as multi-level programming problems. The control over the decision variables is divided among different optimization levels, but all decision variables can affect the objective function of all optimization levels. This class of problems has attracted considerable attention across a broad range of research communities, including economics, sciences and engineering. Multi-level programming problems are very challenging to be solved even when considering just two linear decision levels. For classes of problems where the lower level problems also involve discrete variables, the difficulty is further increased, typically requiring global optimization methods for its solution. In this thesis, we present novel algorithms for the exact and global solution of different classes of multi-level programming problems containing both integer and continuous variables at all optimization levels, namely (i) bi-level mixed-integer linear programming problems, (ii) bi-level mixed-integer quadratic programming problems, (iii) tri-level mixed-integer linear and quadratic programming problems, (iv) bi-level multi-follower mixed-integer linear and quadratic programming problems and (v) multi-level non-linear programming problems. Based on multi-parametric programming theory, the main idea behind the algorithms presented in Chapters 3, 5 and 6, is to recast the lower level problems as multi-parametric programming problems, in which the optimization variables of the upper level problems are considered as parameters for the lower level. The proposed algorithms are implemented in a MATLAB based toolbox, B-POP, presented in Chapter 4, and computational studies were performed to highlight the capabilities of the algorithms. B-POP was found to be much more efficient for the solution of multi-level mixed-integer linear problems than the quadratic ones. The number of constraints was also a key factor for the difficulty of each test problem, and it was shown that by increasing the number of constraints the time required to solve the bi-level problems is increased. For all classes of problems solved, it was clearly observed that the limiting step of the algorithms, and more time consuming, is the solution of the lower level multi-parametric problem. A data-driven algorithm for the solution of large scale bi-level mixed-integer non-linear programming problems is presented in Chapter 7. The main idea behind this algorithm is to approximate the bi-level problem into a single level problem by collecting data from the optimality of the lower level problem. This algorithm was tested by solving a set of bi-level test problems from the literature. The algorithm was able to converge to the global solution for many problems, and was able to find a near optimal or sub-optimal feasible solution for the rest of the problems. Furthermore, multi-level programming was applied to a variety of real-world problems, including classical bi-level problems such as the integration of production planning and distribution planning, and other novel applications such as a hierarchical economic model predictive controller and a class of robust optimization.Open Acces

A Neural Network Based Superstructure Optimization Approach to Reverse Osmosis Desalination Plants

An ever-growing population together with globally depleting water resources pose immense stresses for water supply systems. Desalination technologies can reduce these stresses by generating fresh water from saline water sources. Reverse osmosis (RO), as the industry leading desalination technology, typically involves a complex network of membrane modules that separate unwanted particles from water. The optimal design and operation of these complex RO systems can be computationally expensive. In this work, we present a modeling and optimization strategy for addressing the optimal operation of an industrial-scale RO plant. We employ a feed-forward artificial neural network (ANN) surrogate modeling representation with rectified linear units as activation functions to capture the membrane behavior accurately. Several ANN set-ups and surrogate models are presented and evaluated, based on collected data from the H2Oaks RO desalination plant in South-Central Texas. The developed ANN is then transformed into a mixed-integer linear programming formulation for the purpose of minimizing energy consumption while maximizing water utilization. Trade-offs between the two competing objectives are visualized in a Pareto front, where indirect savings can be uncovered by comparing energy consumption for an array of water recoveries and feed flows

Decentralized Multiparametric Model Predictive Control for Domestic Combined Heat and Power Systems

In an effort to provide affordable and reliable power and heat to the domestic sector, the use of cogeneration methods has been rising in the past decade. We address the issue of optimal operation of a domestic cogeneration plant powered by a natural gas, internal combustion engine via the use of explicit/multiparametric model predictive control. More specifically, we take advantage of the natural division of a combined heat and power (CHP) cogeneration system into two distinct but interoperable subsystems, namely, the power generation subsystem and the heat recovery subsystem, in order to derive a decentralized, two-mode model predictive control scheme that specifically targets the production of either electrical power or usable heat at a given time. We follow our recently developed PAROC framework for the design of the controllers, and we apply it in a decentralized manner. We show how the CHP system can efficiently operate in both modes of operation through closed-loop validation of the control scheme against a high-fidelity CHP process model

A Food-Energy-Water Nexus approach for land use optimization

Allocation and management of agricultural land is of emergent concern due to land scarcity, diminishing supply of energy and water, and the increasing demand of food globally. To achieve social, economic and environmental goals in a specific agricultural land area, people and society must make decisions subject to the demand and supply of food, energy and water (FEW). Interdependence among these three elements, the Food-Energy-Water Nexus (FEW-N), requires that they be addressed concertedly. Despite global efforts on data, models and techniques, studies navigating the multi-faceted FEW-N space, identifying opportunities for synergistic benefits, and exploring interactions and trade-offs in agricultural land use system are still limited. Taking an experimental station in China as a model system, we present the foundations of a systematic engineering framework and quantitative decision-making tools for the trade-off analysis and optimization of stressed interconnected FEW-N networks. The framework combines data analytics and mixed-integer nonlinear modeling and optimization methods establishing the interdependencies and potentially competing interests among the FEW elements in the system, along with policy, sustainability, and feedback from various stakeholders. A multi-objective optimization strategy is followed for the trade-off analysis empowered by the introduction of composite FEW-N metrics as means to facilitate decision-making and compare alternative process and technological options. We found the framework works effectively to balance multiple objectives and benchmark the competitions for systematic decisions. The optimal solutions tend to promote the food production with reduced consumption of water and energy, and have a robust performance with alternative pathways under different climate scenarios. (c) 2018 Elsevier B.V. All rights reserved.</p

Quantifying the Environmental Benefits of a Solvent-Based Separation Process for Multilayer Plastic Films

Food packaging often appears in the form of multilayer (ML) plastic films, which leverage the functional properties of different polymers to achieve specific food protection goals (e.g., oxygen, water, and temperature barriers). These properties are essential to enable long shelf lives, reduce refrigeration usage, mitigate food waste, and increase food accessibility. However, ML f film production processes generate large amounts of plastic waste that cannot be mechanically recycled. Recently, we have proposed a process, which we call solvent-targeted recovery and precipitation (STRAP), that enables the separation and recycling of the constituent polymers of ML films. This technology uses a series of solvent washes that selectively dissolve and precipitate target polymers. Quantifying the environmental benefits of STRAP over virgin resin production is essential for the commercial deployment of this technology. This work uses life cycle assessment (LCA) methods to evaluate these impacts in terms of carbon footprint, energy use, water use, and toxicity. We analyze three STRAP process variants that use anti-solvent and temperature-driven precipitation and that target different types of ML films. Our analysis reveals that a couple of STRAP process variants can provide environmental benefits over virgin film production and also provides valuable insight into the key components of ML films and of the STRAP process that are responsible for the highest impacts. Ultimately, we believe that the proposed analysis framework can lead to the design of more environmentally-friendly ML films and recycling processes