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Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering = = Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering =/
Reminder of title:	Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos.
Author:	Bernal Neira, David E.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	573 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
Subject:	Chemical engineering. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28496316
ISBN:	9798516060847

Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering = = Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos.
Bernal Neira, David E.

Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering =Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 573 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--Carnegie Mellon University, 2021.

This item must not be sold to any third party vendors.

Nonlinear discrete optimization problems arise in many different disciplines, given the modeling versatility associated with nonlinear constraints and discrete decision variables. In Process Systems Engineering, such problems appear in applications ranging from optimal process design and synthesis, process planning, scheduling, and control, and molecular design. Albeit their many applications that arise from its universal modeling capabilities, finding optimal solutions to these optimization problems is a challenging task, given the computational complexity associated with their solution. The design of novel algorithms and the correct modeling of these problems arise among the different ways to overcome this complexity. In particular, tackling these problems with the correct combination of mathematical modeling and solution procedure is an efficient strategy to address them. The objective of this Thesis is to propose new solutions and modeling methods for nonlinear discrete optimization problems, which lead to improvements with respect to the existing solution approaches.We initially pose the discrete nonlinear optimization problems in the context of Mathematical Programming. The problems that we consider solving here can be classified as Mixed-Integer Nonlinear Programming (MINLP) problems. In Chapter 2 we provide a review on the different solution algorithms and existing software to deterministically solve a subclass of MINLP problems called convex MINLP. Among those algorithms, we consider the Outer-approximation (OA) method, which decomposes the MINLP into a Mixed-Integer Nonlinear Programming (MILP) problem and a Nonlinear Programming (NLP) problem. We perform a large computational study comparing the performance of more than sixteen different software implementations, solvers, by solving over 350 convex MINLP problems from benchmark library MINLPLib. This large study allowed us to identify how the different solvers perform based on features from the problem to be solved.Chapter 3 presents the implementation of the feasibility pump algorithm in the commercial MINLP solver DICOPT. This algorithm is being used as a preprocessing step to enhance the solver's capabilities to find feasible solutions early in the search for the optimal solutions. The approach described and implemented in this chapter improved the solver performance becoming the default setting for DICOPT when solving convex MINLP problems.In Chapter 4 we propose a new algorithm for convex MINLP, the Center-cut algorithm. Using a decomposition of the problem similar to OA, this algorithm relies on finding the Chebyshev center of the linear approximation of the nonlinear constraints. Although this algorithm is deterministic, in the sense that we provide convergence guarantees for it, it behaved remarkably well in finding feasible solutions quickly.Chapter 5 presents the derivation of scaled quadratic underestimators for convex functions and their usage in an OA framework, denoted Outer-approximation with quadratic cuts (OA-QCUT). Using those quadratic underestimators, the decomposition in OA then requires the solution of a Mixed-Integer Quadratically Constrained Programming (MIQCP) problem, which more closely underestimates the nonlinearities in convex MINLP problems, achieving a reduction in iterations when solving these problems.Chapter 6 then presents another modification of OA, where auxiliary Mixed-Integer Quadratic Programming (MIQP) problems are solved at each iteration of OA. These auxiliary MIQP problems minimize a quadratic distance metric to the best-found solution in the algorithm while guaranteeing an improvement in the estimated objective function, hence stabilizing the OA method. These methods are successful at reducing the total number of iterations in OA at the expense of the solution of the auxiliary problem, which we prove needs not be solved to optimality, leading to performance improvements of the OA method when solving convex MINLP.Chapter 7 generalizes the concepts of Chapter 6 by showing that the auxiliary mixed-integer problem can have any regularization objective function. We prove the convergence guarantees of this method and show its equivalence of integrating a trust-region constraint in OA. This method is denoted Regularized Outer-approximation (ROA). We implemented these algorithms as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo - MindtPy and tested them extensively with all convex MINLP problems in the library MINLPLib. The results suggest an improvement of the existing OA and LP/NLP methods by using regularization.Chapter 8 tackles the more efficient solution of convex MINLP problems from a different perspective, its modeling. Having identified that one of the primary sources of convex MINLP problems is problems that enforce nonlinear constraints given a discrete choice, we consider a higher level modeling alternative known as Generalized Disjunctive Programming (GDP). The GDP modeling framework uses logical variables and disjunctions to represent these nonlinear discrete optimization problems, which later can be transformed into MINLP problems via reformulations. One of the reformulations is the Hull reformulation (HR), which derives a higher dimensional description of the disjunctive set whose projection into the space of the original variables yields its. (Abstract shortened by ProQuest).

ISBN: 9798516060847Subjects--Topical Terms:

560457
Chemical engineering.
Subjects--Index Terms:

Discrete Nonlinear Optimization

Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering = = Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos.
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245 1 0 $a Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering = $b Enfoques Computacionales Modernos a la Optimizacion Discreta No Lineal y Aplicaciones en la Ingenieria de Procesos.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 573 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Grossmann, Ignacio E.
502 $a Thesis (Ph.D.)--Carnegie Mellon University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Nonlinear discrete optimization problems arise in many different disciplines, given the modeling versatility associated with nonlinear constraints and discrete decision variables. In Process Systems Engineering, such problems appear in applications ranging from optimal process design and synthesis, process planning, scheduling, and control, and molecular design. Albeit their many applications that arise from its universal modeling capabilities, finding optimal solutions to these optimization problems is a challenging task, given the computational complexity associated with their solution. The design of novel algorithms and the correct modeling of these problems arise among the different ways to overcome this complexity. In particular, tackling these problems with the correct combination of mathematical modeling and solution procedure is an efficient strategy to address them. The objective of this Thesis is to propose new solutions and modeling methods for nonlinear discrete optimization problems, which lead to improvements with respect to the existing solution approaches.We initially pose the discrete nonlinear optimization problems in the context of Mathematical Programming. The problems that we consider solving here can be classified as Mixed-Integer Nonlinear Programming (MINLP) problems. In Chapter 2 we provide a review on the different solution algorithms and existing software to deterministically solve a subclass of MINLP problems called convex MINLP. Among those algorithms, we consider the Outer-approximation (OA) method, which decomposes the MINLP into a Mixed-Integer Nonlinear Programming (MILP) problem and a Nonlinear Programming (NLP) problem. We perform a large computational study comparing the performance of more than sixteen different software implementations, solvers, by solving over 350 convex MINLP problems from benchmark library MINLPLib. This large study allowed us to identify how the different solvers perform based on features from the problem to be solved.Chapter 3 presents the implementation of the feasibility pump algorithm in the commercial MINLP solver DICOPT. This algorithm is being used as a preprocessing step to enhance the solver's capabilities to find feasible solutions early in the search for the optimal solutions. The approach described and implemented in this chapter improved the solver performance becoming the default setting for DICOPT when solving convex MINLP problems.In Chapter 4 we propose a new algorithm for convex MINLP, the Center-cut algorithm. Using a decomposition of the problem similar to OA, this algorithm relies on finding the Chebyshev center of the linear approximation of the nonlinear constraints. Although this algorithm is deterministic, in the sense that we provide convergence guarantees for it, it behaved remarkably well in finding feasible solutions quickly.Chapter 5 presents the derivation of scaled quadratic underestimators for convex functions and their usage in an OA framework, denoted Outer-approximation with quadratic cuts (OA-QCUT). Using those quadratic underestimators, the decomposition in OA then requires the solution of a Mixed-Integer Quadratically Constrained Programming (MIQCP) problem, which more closely underestimates the nonlinearities in convex MINLP problems, achieving a reduction in iterations when solving these problems.Chapter 6 then presents another modification of OA, where auxiliary Mixed-Integer Quadratic Programming (MIQP) problems are solved at each iteration of OA. These auxiliary MIQP problems minimize a quadratic distance metric to the best-found solution in the algorithm while guaranteeing an improvement in the estimated objective function, hence stabilizing the OA method. These methods are successful at reducing the total number of iterations in OA at the expense of the solution of the auxiliary problem, which we prove needs not be solved to optimality, leading to performance improvements of the OA method when solving convex MINLP.Chapter 7 generalizes the concepts of Chapter 6 by showing that the auxiliary mixed-integer problem can have any regularization objective function. We prove the convergence guarantees of this method and show its equivalence of integrating a trust-region constraint in OA. This method is denoted Regularized Outer-approximation (ROA). We implemented these algorithms as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo - MindtPy and tested them extensively with all convex MINLP problems in the library MINLPLib. The results suggest an improvement of the existing OA and LP/NLP methods by using regularization.Chapter 8 tackles the more efficient solution of convex MINLP problems from a different perspective, its modeling. Having identified that one of the primary sources of convex MINLP problems is problems that enforce nonlinear constraints given a discrete choice, we consider a higher level modeling alternative known as Generalized Disjunctive Programming (GDP). The GDP modeling framework uses logical variables and disjunctions to represent these nonlinear discrete optimization problems, which later can be transformed into MINLP problems via reformulations. One of the reformulations is the Hull reformulation (HR), which derives a higher dimensional description of the disjunctive set whose projection into the space of the original variables yields its. (Abstract shortened by ProQuest).
520 $a Los problemas de optimizacion discreta no lineal surgen en muchas disciplinas, dada la versatilidad de modelado asociada con las restricciones no lineales y las variables de decision discretas. En Ingenieria de Sistemas de Procesos, estos problemas aparecen en aplicaciones que van desde el diseno y sintesis optimos de procesos, la planeacion y control de procesos y el diseno molecular. A pesar de sus muchas aplicaciones, que surgen a partir de sus capacidades de modelamiento universal, encontrar soluciones optimas a estos problemas de optimizacion es una tarea desafiante, dada la complejidad computacional asociada con su solucion. El diseno de algoritmos novedosos y el correcto modelado de estos problemas surgen entre las diferentes formas de superar esta complejidad. En particular, abordar estos problemas con la combinacion correcta de modelos matematicos y procedimientos de solucion es una estrategia eficaz para abordarlos. El objetivo de esta Tesis es proponer nuevas soluciones y metodos de modelado para problemas de optimizacion discretos no lineales, que conduzcan a mejoras con respecto a los enfoques de solucion existentes.Inicialmente planteamos los problemas de optimizacion discreta no lineal en el contexto de la Programacion Matematica.Los problemas que consideramos resolver aqui se pueden clasificar como problemas de programacion mixto entero no lineal (Mixed-Integer Nonlinear Programming MINLP). En el Capitulo 2 proporcionamos una revision de los diferentes algoritmos de solucion y el software existente para resolver deterministicamente una subclase de problemas MINLP llamados MINLP convexos. Los problemas MINLP convexos tienen la cualidad de que sus restricciones no lineales son convexas, lo que da lugar a algoritmos de solucion eficientes. Entre esos algoritmos, consideramos el metodo de aproximacion externa (Outer Approximation OA), que descompone el MINLP en un problema de programacion no lineal de enteros mixtos (Mixed-Integer Linear Programming MILP) y un problema de programacion no lineal (Nonlinear Programming NLP). Realizamos un gran estudio computacional comparando el rendimiento de mas de dieciseis implementaciones de software diferentes, solvers, resolviendo mas de 350 problemas MINLP convexos de la biblioteca de referencia MINLPLib. Este gran estudio nos permitio identificar como se desempenan los diferentes solucionadores en funcion de las caracteristicas del problema a resolver.El Capitulo 3 presenta la implementacion del algoritmo de bomba de factibilidad en el solver comercial para MINLP, DICOPT. Este algoritmo se utiliza como un paso de preprocesamiento para mejorar las capacidades del solver encontrando soluciones factibles al principio de la busqueda de las soluciones optimas. El enfoque descrito e implementado en este capitulo mejoro el rendimiento del solver convirtiendose en la configuracion predeterminada para DICOPT al resolver problemas de MINLP convexos.En el Capitulo 4 proponemos un nuevo algoritmo para MINLP convexo, el algoritmo de corte central. Usando una descomposicion del problema similar a OA, este algoritmo se basa en encontrar el centro de Chebyshev de la aproximacion lineal de las restricciones no lineales. Aunque este algoritmo es deterministico, en el sentido de que le damos garantias de convergencia, se comporto notablemente bien en la busqueda rapida de soluciones factibles.El Capitulo 5 presenta la derivacion de subestimadores cuadraticos escalados para funciones convexas y su uso en el metodo de OA, denotado por aproximacion externa con cortes cuadraticos (OA-QCUT). Usando esos subestimadores cuadraticos, la descomposicion en OA luego requiere la solucion de un problema de programacion mixto entero con restricciones cuadraticas (Mixed-Integer Quadratically Contstrained Programming MIQCP), que subestima mas de cerca las no linealidades en los problemas convexos MINLP, logrando una reduccion en las iteraciones al resolver estos problemas.El Capitulo 6 luego presenta otra modificacion de OA, donde problemas auxiliares de programacion mixta etnera cuadratica (Mixed-Integer Quadratic Programming MIQP) se resuelven en cada iteracion de OA. Estos problemas auxiliares MIQP minimizan una metrica de distancia cuadratica a la mejor solucion encontrada en el algoritmo al tiempo que garantizan una mejora en la funcion objetivo estimada, estabilizando asi el metodo OA.El Capitulo 7 generaliza los conceptos del Capitulo 6 mostrando que el problema auxiliar de mixto entero puede tener cualquier funcion objetivo de regularizacion. Demostramos las garantias de convergencia de este metodo y mostramos su equivalencia de integrar una restriccion de region de confianza en OA. Este metodo se denomina Aproximacion externa regularizada (ROA).Implementamos estos algoritmos como parte del codigo abierto Mixed-integer nonlinear decomposition toolbox for Pyomo - MindtPy y fueron probados extensamente con todos los problemas de MINLP convexos en la biblioteca MINLPLib. Los resultados sugieren una mejora de los metodos de OA y LP/NLP existentes mediante el uso de la regularizacion.El Capitulo 8 aborda la solucion mas eficiente de problemas convexos MINLP desde una perspectiva diferente, su modelado. Habiendo identificado que una de las principales fuentes de problemas convexos del MINLP son los problemas que imponen restricciones no lineales. (Abstract shortened by ProQuest).
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