Integer Optimization by Local Search : A Domain-Independent Approach - H. Kautz

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Integer Optimization by Local Search

A Domain-Independent Approach

By: H. Kautz (Foreword by), Joachim P. Walser

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Paperback | 4 August 1999

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164 Pages

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Integer Optimization addresses a wide spectrum of practically important optimization problems and represents a major challenge for algorithmics. The goal of integer optimization is to solve a system of constraints and optimization criteria over discrete variables.
Integer Optimization by Local Search introduces a new approach to domain-independent integer optimization, which, unlike traditional strategies, is based on local search. It develops the central concepts and strategies of integer local search and describes possible combinations with classical methods from linear programming. The surprising effectiveness of the approach is demonstrated in a variety of case studies on large-scale, realistic problems, including production planning, timetabling, radar surveillance, and sports scheduling. The monograph is written for practitioners and researchers from artificial intelligence and operations research.

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Introduction	p. 1
Integer Optimization and Heuristics	p. 1
Integer Local Search	p. 5
Experimental Results	p. 7
Research Contributions	p. 9
Frameworks for Combinatorial Optimization	p. 11
Integer Programming Branch- and- Bound	p. 11
Finite Domain Constraint Programming	p. 13
Local Search	p. 15
Meta- heuristics	p. 16
RISC and CISC Local Search	p. 17
Local Search for SAT	p. 18
Application Domains of SAT Local Search	p. 20
Modeling Languages	p. 21
Search Relaxations and Integer Local Search	p. 21
Local Search for Integer Constraints	p. 25
Over- Constrained Integer Programs	p. 25
Definition	p. 27
Relation to Integer Linear Programs	p. 28
Constraint-Bounds	p. 31
Integer Local Search: Wsat(oip)	p. 32
The Score	p. 33
The Main Loop	p. 34
Move Selection and Tabu Search Extensions	p. 34
Combinations with Linear Programming	p. 37
Bounds from LP Relaxations	p. 37
Initialization by Rounding LP Solutions	p. 38
Search Space Reduction Using LP Reduced Costs	p. 40
Implementation Issues	p. 41
A Graphical Interpretation	p. 43
Related Work	p. 47
Integer Programming Heuristics	p. 48
Local Search in Constraint Satisfaction	p. 51
Summary	p. 51
Case Studies Methodology	p. 53
Optimization in Practice: Criteria of Success	p. 53
Scaling with Increasing Problem Size	p. 54
Scaling with Increasing Constrainedness	p. 55
Flexibility and Residual Robustness	p. 56
The Problem Class Selection	p. 56
The Empirical Comparisons	p. 57
Time-Tabling and Sports Scheduling	p. 59
The Progressive Party Problem	p. 59
Problem Description and Formulation	p. 60
Experimental Results and Comparison	p. 62
The ACC Basketball Scheduling Problem	p. 64
Double Round Robin Scheduling	p. 65
Problem Specification of ACC97/98	p. 66
Integer Local Search Formulation	p. 68
Redundant Constraints	p. 71
Previous (Multi- stage) Approaches	p. 72
Experimental Results under Varied Constrainedness	p. 73
Minimal Distortion Mirroring	p. 76
Conclusions	p. 78
Covering and Assignment	p. 81
Radar Surveillance Covering	p. 81
Problem Description and Formulation	p. 81
Experimental Results under Varied Problem Size	p. 83
Course Assignment	p. 87
Problem Description and Formulation	p. 87
Experimental Results under Varied Problem Size	p. 89
A Related Application: Reviewer Assignment	p. 91
Conclusions	p. 93
Capacitated Production Planning	p. 95
Capacitated Lot- Sizing	p. 96
Integer Local Search Formulation	p. 98
Mixed Integer Programming Formulation	p. 99
Lagrangean Relaxation Approach	p. 100
Restricting the Problem	p. 101
Experimental Results	p. 101
Comparison of Results	p. 101
Lower Bounds	p. 104
Conclusions	p. 105
Extensions	p. 107
Current Limitations	p. 107
An Alternative Scoring Scheme	p. 108
Future Research	p. 111
Conclusions	p. 112
A Complete AMPL Model for ACC97/98	p. 115
References	p. 122
Index	p. 135
Table of Contents provided by Publisher. All Rights Reserved.

Integer Optimization by Local Search

A Domain-Independent Approach

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