Mixed Integer Nonlinear Programming

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Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.

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Genre : Mathematics
Author : Jon Lee
Publisher : Springer Science & Business Media
Release : 2011-12-02
File : 687 Pages
ISBN-13 : 9781461419273


Relaxation And Decomposition Methods For Mixed Integer Nonlinear Programming

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Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many ?elds, such as process industry, engineering design, communications, and ?nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di?cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: • A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. • In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. • The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.

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Genre : Computers
Author : Ivo Nowak
Publisher : Springer Science & Business Media
Release : 2006-03-28
File : 213 Pages
ISBN-13 : 9783764373740


Convexification And Global Optimization In Continuous And Mixed Integer Nonlinear Programming

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Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

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Genre : Mathematics
Author : Mohit Tawarmalani
Publisher : Springer Science & Business Media
Release : 2013-04-17
File : 492 Pages
ISBN-13 : 9781475735321


Fast Numerical Methods For Mixed Integer Nonlinear Model Predictive Control

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Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.

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Genre : Computers
Author : Christian Kirches
Publisher : Springer Science & Business Media
Release : 2011-11-23
File : 380 Pages
ISBN-13 : 9783834882028


Nonlinear And Mixed Integer Optimization

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Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.

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Genre : Science
Author : Christodoulos A. Floudas
Publisher : Oxford University Press on Demand
Release : 1995-10-05
File : 462 Pages
ISBN-13 : 8426713335


Large Scale Optimization With Applications

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Genre : Engineering design
Author :
Publisher : Springer Science & Business Media
Release : 1997
File : 354 Pages
ISBN-13 : 0387982876


Encyclopedia Of Optimization

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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

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Genre : Mathematics
Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
Release : 2008-09-04
File : 4646 Pages
ISBN-13 : 9780387747583


Numerical Nonsmooth Optimization

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Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem’s special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book is ideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

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Genre : Business & Economics
Author : Adil M. Bagirov
Publisher : Springer Nature
Release : 2020-02-28
File : 696 Pages
ISBN-13 : 9783030349103


Machine Learning Paradigms Theory And Application

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The book focuses on machine learning. Divided into three parts, the first part discusses the feature selection problem. The second part then describes the application of machine learning in the classification problem, while the third part presents an overview of real-world applications of swarm-based optimization algorithms. The concept of machine learning (ML) is not new in the field of computing. However, due to the ever-changing nature of requirements in today’s world it has emerged in the form of completely new avatars. Now everyone is talking about ML-based solution strategies for a given problem set. The book includes research articles and expository papers on the theory and algorithms of machine learning and bio-inspiring optimization, as well as papers on numerical experiments and real-world applications.

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Genre : Technology & Engineering
Author : Aboul Ella Hassanien
Publisher : Springer
Release : 2018-12-08
File : 472 Pages
ISBN-13 : 9783030023577


Application Of Optimization In Production Logistics Inventory Supply Chain Management And Block Chain

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The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment.

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Genre : Technology & Engineering
Author : Biswajit Sarkar
Publisher : MDPI
Release : 2020-04-23
File : 618 Pages
ISBN-13 : 9783039285228