Journal ArticleDOI
Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques
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TLDR
In this article, a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, such as Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form is presented.Abstract:
This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.read more
Citations
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Proceedings ArticleDOI
An approach for QoS-aware service composition based on genetic algorithms
TL;DR: Genetic Algorithms, while being slower than integer programming, represent a more scalable choice, and are more suitable to handle generic QoS attributes.
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An algorithmic framework for convex mixed integer nonlinear programs
Pierre Bonami,Lorenz T. Biegler,Andrew R. Conn,Gérard Cornuéjols,Ignacio E. Grossmann,Carl D. Laird,Jon Lee,Andrea Lodi,François Margot,Nicolas Sawaya,Andreas Wächter +10 more
TL;DR: A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented and Computational results that demonstrate the effectiveness of this framework are reported.
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State-of-the-art review of optimization methods for short-term scheduling of batch processes
TL;DR: The main goal of this paper is to provide an up-to-date review of the state-of-the-art in this challenging area of short-term batch scheduling, with a general classification for scheduling problems of batch processes as well as for the corresponding optimization models.
Journal ArticleDOI
Branching and bounds tighteningtechniques for non-convex MINLP
TL;DR: An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver.
Journal ArticleDOI
Mixed-integer nonlinear optimization
TL;DR: An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.
References
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Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Journal ArticleDOI
GAMS, a user's guide
TL;DR: JuMP is an open-source modeling language that allows users to express a wide range of ideas in an easy-to-use manner.
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Branch-And-Price: Column Generation for Solving Huge Integer Programs
Cynthia Barnhart,Ellis L. Johnson,George L. Nemhauser,Martin W. P. Savelsbergh,Pamela H. Vance +4 more
TL;DR: In this paper, column generation methods for integer programs with a huge number of variables are discussed, including implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree.
Journal ArticleDOI
Generalized Benders decomposition
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.
Journal ArticleDOI
Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
TL;DR: For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented to exclude from consideration regions where the global minimizer cannot exist.