MINLP model and two-stage algorithm for the simultaneous synthesis of heat exchanger networks, utility systems and heat recovery cycles

This work proposes a novel approach for the simultaneous synthesis of Heat Exchanger Networks (HEN) and Utility Systems of chemical processes and energy systems. Given a set of hot and cold process streams and a set of available utility systems, the method determines the optimal selection, arrangement and design of utility systems and the heat exchanger network aiming to rigorously consider the trade-off between efficiency and capital costs. The mathematical formulation uses the SYNHEAT superstructure for the HEN, and ad hoc superstructures and nonlinear models to represent the utility systems. The challenging nonconvex MINLP is solved with a two-stage algorithm. A sequential synthesis algorithm is specifically developed to generate a good starting solution. The algorithm is tested on a literature test problem and two industrial problems, the optimization of the Heat Recovery Steam Cycle of a Natural Gas Combined Cycle and the heat recovery system of an Integrated Gasification Combined Cycle. (C) 2017 Elsevier Ltd. All rights reserved

Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

L'abstract è presente nell'allegato / the abstract is in the attachmen

Subgradient-based Decomposition Methods for Stochastic Mixed-integer Programs with Special Structures

The focus of this dissertation is solution strategies for stochastic mixed-integer programs with special structures. Motivation for the methods comes from the relatively sparse number of algorithms for solving stochastic mixed-integer programs. Two stage models with finite support are assumed throughout. The first contribution introduces the nodal decision framework under private information restrictions. Each node in the framework has control of an optimization model which may include stochastic parameters, and the nodes must coordinate toward a single objective in which a single optimal or close-to-optimal solution is desired. However, because of competitive issues, confidentiality requirements, incompatible database issues, or other complicating factors, no global view of the system is possible. An iterative methodology called the nodal decomposition-coordination algorithm (NDC) is formally developed in which each entity in the cooperation forms its own nodal deterministic or stochastic program. Lagrangian relaxation and subgradient optimization techniques are used to facilitate negotiation between the nodal decisions in the system without any one entity gaining access to the private information from other nodes. A computational study on NDC using supply chain inventory coordination problem instances demonstrates that the new methodology can obtain good solution values without violating private information restrictions. The results also show that the stochastic solutions outperform the corresponding expected value solutions. The next contribution presents a new algorithm called scenario Fenchel decomposition (SFD) for solving two-stage stochastic mixed 0-1 integer programs with special structure based on scenario decomposition of the problem and Fenchel cutting planes. The algorithm combines progressive hedging to restore nonanticipativity of the first-stage solution, and generates Fenchel cutting planes for the LP relaxations of the subproblems to recover integer solutions. A computational study SFD using instances with multiple knapsack constraint structure is given. Multiple knapsack constrained problems are chosen due to the advantages they provide when generating Fenchel cutting planes. The computational results are promising, and show that SFD is able to find optimal solutions for some problem instances in a short amount of time, and that overall, SFD outperforms the brute force method of solving the DEP

Multi-fidelity Bayesian Optimization in Engineering Design

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization

Robust simulation and optimization methods for natural gas liquefaction processes

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 313-324).Natural gas is one of the world's leading sources of fuel in terms of both global production and consumption. The abundance of reserves that may be developed at relatively low cost, paired with escalating societal and regulatory pressures to harness low carbon fuels, situates natural gas in a position of growing importance to the global energy landscape. However, the nonuniform distribution of readily-developable natural gas sources around the world necessitates the existence of an international gas market that can serve those regions without reasonable access to reserves. International transmission of natural gas via pipeline is generally cost-prohibitive beyond around two thousand miles, and so suppliers instead turn to the production of liquefied natural gas (LNG) to yield a tradable commodity. While the production of LNG is by no means a new technology, it has not occupied a dominant role in the gas trade to date. However, significant growth in LNG exports has been observed within the last few years, and this trend is expected to continue as major new liquefaction operations have and continue to become operational worldwide. Liquefaction of natural gas is an energy-intensive process requiring specialized cryogenic equipment, and is therefore expensive both in terms of operating and capital costs. However, optimization of liquefaction processes is greatly complicated by the inherently complex thermodynamic behavior of process streams that simultaneously change phase and exchange heat at closely-matched cryogenic temperatures. The determination of optimal conditions for a given process will also generally be nontransferable information between LNG plants, as both the specifics of design (e.g. heat exchanger size and configuration) and the operation (e.g. source gas composition) may have significantly variability between sites. Rigorous evaluation of process concepts for new production facilities is also challenging to perform, as economic objectives must be optimized in the presence of constraints involving equipment size and safety precautions even in the initial design phase. The absence of reliable and versatile software to perform such tasks was the impetus for this thesis project. To address these challenging problems, the aim of this thesis was to develop new models, methods and algorithms for robust liquefaction process simulation and optimization, and to synthesize these advances into reliable and versatile software. Recent advances in the sensitivity analysis of nondifferentiable functions provided an advantageous foundation for the development of physically-informed yet compact process models that could be embedded in established simulation and optimization algorithms with strong convergence properties. Within this framework, a nonsmooth model for the core unit operation in all industrially-relevant liquefaction processes, the multi-stream heat exchanger, was first formulated. The initial multistream heat exchanger model was then augmented to detect and handle internal phase transitions, and an extension of a classic vapor-liquid equilibrium model was proposed to account for the potential existence of solutions in single-phase regimes, all through the use of additional nonsmooth equations. While these initial advances enabled the simulation of liquefaction processes under the conditions of simple, idealized thermodynamic models, it became apparent that these methods would be unable to handle calculations involving nonideal thermophysical property models reliably. To this end, robust nonsmooth extensions of the celebrated inside-out algorithms were developed. These algorithms allow for challenging phase equilibrium calculations to be performed successfully even in the absence of knowledge about the phase regime of the solution, as is the case when model parameters are chosen by a simulation or optimization algorithm. However, this still was not enough to equip realistic liquefaction process models with a completely reliable thermodynamics package, and so new nonsmooth algorithms were designed for the reasonable extrapolation of density from an equation of state under conditions where a given phase does not exist. This procedure greatly enhanced the ability of the nonsmooth inside-out algorithms to converge to physical solutions for mixtures at very high temperature and pressure. These models and submodels were then integrated into a flowsheeting framework to perform realistic simulations of natural gas liquefaction processes robustly, efficiently and with extremely high accuracy. A reliable optimization strategy using an interior-point method and the nonsmooth process models was then developed for complex problem formulations that rigorously minimize thermodynamic irreversibilities. This approach significantly outperforms other strategies proposed in the literature or implemented in commercial software in terms of the ease of initialization, convergence rate and quality of solutions found. The performance observed and results obtained suggest that modeling and optimizing such processes using nondifferentiable models and appropriate sensitivity analysis techniques is a promising new approach to these challenging problems. Indeed, while liquefaction processes motivated this thesis, the majority of the methods described herein are applicable in general to processes with complex thermodynamic or heat transfer considerations embedded. It is conceivable that these models and algorithms could therefore inform a new, robust generation of process simulation and optimization software.by Harry Alexander James Watson.Ph. D