Concepts of Combinatorial Optimization

ISBN-13: 9781848216563 / Angielski / Twarda / 2014 / 408 str.

Vangelis T. Paschos

Opis

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization.

Concepts of Combinatorial Optimization, is divided into three parts:
- On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity;
- Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming;
- Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.

Spis treści

Preface xiii

Vangelis Th. Paschos

Part I Complexity of Combinatioral Optimization Problems 1

Chapter 1 Basic Concepts in Algorithms and Complexity Theory 3
Vangelis Th. Paschos

Chapter 2 Randomized Complexity 21
Jérémy Barbay

Part II Classic Solution Methods 39

Chapter 3 Branch–and–Bound Methods 41
Irène Charon and Olivier Hudry

Chapter 4 Dynamic Programming 71
Bruno Escoffier and Olivier Spanjaard

Part III Elements from Mathematical Programming 101

Chapter 5 Mixed Integer Linear Programming Models for Combinatorial Optimization Problems 103
Frédérico Della Croce

Chapter 6 Simplex Algorithms for Linear Programming 135
Frédérico Della Croce and Andrea Grosso

Chapter 7 A Survey of Some Linear Programming Methods 157
Pierre Tolla

Chapter 8 Quadratic Optimization in 0–1 Variables 189
Alain Billionnet

Chapter 9 Column Generation in Integar Linear Programming 235
Irène Loiseau, Alberto Ceselli, Nelson Maculan and Matteo Salani

Chapter 10 Polyhedral Approaches 261
Ali Ridha Mahjoub

Chapter 11 Constaint Programming 325
Claude Le Pape

General Bibliography 339

List of Authors 363

Index 367

Summary of Other Volumes in the Series 371

O autorze

Vangelis T. Paschos is Professor of Computer Science at the University of Paris–Dauphine and Chairman of the LAMSADE (Laboratory for the Modeling and the Analysis of Decision Aiding Systems). His research interests include complexity theory, the theory of the polynomial approximation of NP–hard problems, probabilistic combinatorial optimization and on–line computation. He is the author of more than a 100 research papers and is a member of the editorial board of several international scientific journals.