Topic

# Discrete optimization

About: Discrete optimization is a(n) research topic. Over the lifetime, 4598 publication(s) have been published within this topic receiving 158297 citation(s). The topic is also known as: discrete optimisation.

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^{1}TL;DR: In this article, a new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented, which requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.

Abstract: A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.

20,354 citations

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01 Jan 2009

TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.

Abstract: Preface Table of Notation Part 1: Unconstrained Optimization Introduction Structure of Methods Newton-like Methods Conjugate Direction Methods Restricted Step Methods Sums of Squares and Nonlinear Equations Part 2: Constrained Optimization Introduction Linear Programming The Theory of Constrained Optimization Quadratic Programming General Linearly Constrained Optimization Nonlinear Programming Other Optimization Problems Non-Smooth Optimization References Subject Index.

7,016 citations

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01 Jan 1996

TL;DR: This review discusses mathematics, linear programming, and set--Constrained and Unconstrained Optimization, as well as methods of Proof and Some Notation, and problems with Equality Constraints.

Abstract: Preface. MATHEMATICAL REVIEW. Methods of Proof and Some Notation. Vector Spaces and Matrices. Transformations. Concepts from Geometry. Elements of Calculus. UNCONSTRAINED OPTIMIZATION. Basics of Set--Constrained and Unconstrained Optimization. One--Dimensional Search Methods. Gradient Methods. Newton's Method. Conjugate Direction Methods. Quasi--Newton Methods. Solving Ax = b. Unconstrained Optimization and Neural Networks. Genetic Algorithms. LINEAR PROGRAMMING. Introduction to Linear Programming. Simplex Method. Duality. Non--Simplex Methods. NONLINEAR CONSTRAINED OPTIMIZATION. Problems with Equality Constraints. Problems with Inequality Constraints. Convex Optimization Problems. Algorithms for Constrained Optimization. References. Index.

3,275 citations

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TL;DR: An overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and the ant colony optimization (ACO) metaheuristic is presented.

Abstract: This article presents an overview of recent work on ant algorithms, that is, algorithms for discrete optimization that took inspiration from the observation of ant colonies' foraging behavior, and introduces the ant colony optimization (ACO) metaheuristic. In the first part of the article the basic biological findings on real ants are reviewed and their artificial counterparts as well as the ACO metaheuristic are defined. In the second part of the article a number of applications of ACO algorithms to combinatorial optimization and routing in communications networks are described. We conclude with a discussion of related work and of some of the most important aspects of the ACO metaheuristic.

2,716 citations

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TL;DR: Discrete Choice Methods with Simulation by Kenneth Train has been available in the second edition since 2009 and contains two additional chapters, one on endogenous regressors and one on the expectation–maximization (EM) algorithm.

Abstract: Discrete Choice Methods with Simulation by Kenneth Train has been available in the second edition since 2009. The book is published by Cambridge University Press and is also available for download ...

2,586 citations