Handbook of Approxi111ation Algorith111s and Metaheuristics,

Second Edition Methodologies and Traditional Applications

Volume 1

Edited by

Teofilo F. Gonzalez

0 CRC Press Taylor & Francls Group Soca Raton London New York

CRC Press is an imprint of the Taylor & Frands Group, an lnfonna buslness

A CHAPMAN & HALL BOOK

Contents

Preface ......................................................................... xi

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Introduction, Overview, and Notation ........................................ 1 Teofilo F. Gonzalez

SECTION 1 Basic Methodologies

2 Basic Methodologies and Applications ....................................... 27 Teofilo F. Gonzalez

3 Restriction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Teofilo F. Gonzalez

4 Greedy Methods ........................................................... 55 Samir Khuller. Balaji Raghavachari, and Neal E. Young

5 Recursive Greedy Methods ....... „ . „ ... „ ... „ „ ........ „ . . . . • . • • . . . • • . . 71 GuyEven

6 Local Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Dror Rawitz

7 LP Rounding and Extensions „ „ .. „ „ „ „. „. „ „ ..... „ „ „ „ ... „ ...... 113 Daya Ram Gaur and Ramesh Krishnamurti

8 Polynomial Time Approximation Schemes .................................. 125 Hadas Shachnai and Tami Tamir

9 Rounding, Interval Partitioning and Separation .............................. 157 Sartaj Sahni

10 Asymptotic Polynomial Time Approximation Schemes ....................... 173 Rajeev Motwani, Liadan O'Callaghan, and An Zhu

11 Randomized Approximation Techniques ................................... 189 Sotiris Nikoletseas and Paul Spirakis

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viii Contents

12 Distributed Approximation Algorithms via LP-Duality and Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Devdatt Dubhashi, Fabrizio Grandoni, and Alessandro Panconesi

13 Empirical Analysis of Randomised Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Holger H. Hoos and Thomas Stützle

14 Reductions That Preserve Approximability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Giorgio Ausiello and Vangelis Th. Paschos

15 Differential Ratio Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Giorgio Ausiello and Vangelis Th. Paschos

SECTION II Local Search, Neural Networks, and Metaheuristics

16 Local Search ............................................................. 277 Roberta Solis-Oba and Nasim Samei

17 Stochastic Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Holger H. Hoos and Thomas Stützle

18 Very Large-Scale Neighborhood Search: Theory, Algorithms, and Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Ravindra K Ahuja, Özlem Ergun, James B. Orlin, and Abraham P. Punnen

19 Reactive Search: Machine Learning for Memory-Based Heuristics ............. 327 Roberto Battiti and Mauro Brunato

20 Neural Networks ......................................................... 345 Bhaskar DasGupta, Derong Liu, and Hava T. Siegelmann

21 Principles and Strategies of Tabu Search .................................... 361 Fred Glover, Manuel Laguna, and Rafael Mart{

22 Evolutionary Computation . „ .. „ . „ „ „ .. „ ..... „ ...... „ ... „ . . . . . . . . . . 379 Guillermo Leguizam6n, Christian Blum, and Enrique Alba

23 An Introduction to Ant Colony Optimization ......................... . ..... 395 Marco Dorigo and Krzysztof Socha

SECTION III Multiobjective Optimization, Sensitivity Analysis, and Stability

24 Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization: A Review ... .. .............. . ................ 411 Lufs Paquete and Thomas Stützle

25 Reoptimization of Hard Optimization Problems ............................. 427 Hans-Joachim Böckenhauer, Juraj Hromkovi~, and Dennis Komm

Contents ix

26 Sensitivity Analysis in Combinatorial Optimization .......................... 455 David Fernandez-Baca and Balaji Venkatachalam

27 Stability of Approximation ... „ ....... „. „ „ .... „ „. „ ... „ . „ . ...... „. 473 Hans-Joachim Böckenhauer, Juraj HromkoviC, and Sebastian Seibert

SECTION IV Traditional Applications

28 Performance Guarantees for One Dimensional Bin Packing ......... . ........ 491 Janos Csirik and György D6sa

2 9 Variants of Classical One Dimensional Bin Packing . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Janos Csirik and Csanad Imreh

30 Variable Sized Bin Packing and Bin Covering ....... . ........................ 539 Janos Csirik

31 Multidimensional Packing Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 Leah Epstein and Rob van Stee

32 Practical Algorithms for Two-Dimensional Packing of Rectangles ............. 571 Shinji Imahori, Mutsunori Yagiura, and Hiroshi Nagamochi

33 Practical Algorithrns for Two-Dimensional Packing of General Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Yannan Hu, Hideki Hashimoto, Shinji Imahori, and Mutsunori Yagiura

34 Prize Collecting Traveling Salesman and Related Problems . . . . . . . . . . . . . . . . . . . 611 Giorgio Ausiello, Vincenzo Bonifaci, Stefano Leonardi, and Alberto Marchetti-Spaccamela

35 A Development and Deployment Framework for Distributed Branch-and-Bound ....................................................... 629 Peter Cappello and Christopher James Coakley

36 Approximations for Steiner Minimum Trees „ .... „ ...... „ .. „ ............ 641 Ding-Zhu Du and Weili Wu

37 Practical Approximations of Steiner Trees in Uniform Orientation Metrics ........................... . .......................... 657 Andrew B. Kahng. Ion Mdndoiu, and Alexander Zelikovsky

38 Algorithms for Chromatic Sums, Multicoloring, and Scheduling Dependent Jobs „. „ ...... „ ..... „ . . ....... „ „ ....... . . „ ... 671 Magnus M. Halld6rsson and Guy Kortsarz

39 Approximation Algorithms and Heuristics for Classical Planning ..... „ . . . • . . • • • • . . . • . • . • • • • • • • • . . . . • • • • . • • • • • • • • • • • • 685 Jeremy Frank. Minh Do, and J. Benton

40 Generalized Assignment Problem .......................................... 713 Wei Wu, Mutsunori Yagiura, and Toshihide Ibaraki

x Contents

41 Linear Ordering Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 Celso S. Sakuraba and Mutsunori Yagiura

42 Submodular Functions Maximization Problems ............................. 753 Niv Buchbinderand Moran Feldman

Index ......................................................................... 789