Exact and Heuristic Methods in Combinatorial Optimization 2nd Edition by Rafael Martí, Gerhard Reinelt ISBN 9783662648766 3662648768

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ISBN 10: 3662648768
ISBN 13: 9783662648766
Author: Rafael Martí, Gerhard Reinelt

Exact and Heuristic Methods in Combinatorial Optimization 2nd Edition Table of contents:

Chapter 1 Introduction

1.1 The Linear Ordering Problem

1.1.1 Applications

1.1.2 The LOLIB Library of Benchmark Instances

1.2 The Maximum Diversity Problem

1.2.1 Diversity measures and models

1.2.2 The MDPLIB Library of Benchmark Instances

Chapter 2 Heuristic Methods

2.1 Introduction

2.1.1 Assessing the Quality of Heuristics

2.2 Construction Heuristics

2.2.1 Early LOP Methods

2.2.2 Reconstruction in the MDP

2.2.3 General Insertions

2.2.4 Numerical Experiments

2.3 Local Search

2.3.1 Insertions in permutation problems

2.3.2 Exchanges in binary problems

2.3.3 LOP methods

2.4 Multi-Start Procedures

2.4.1 Variants of Multi-Start

2.4.2 Numerical Experiments

Chapter 3 Meta-Heuristics

3.1 Introduction

3.2 GRASP

3.2.1 Construction Phase

3.2.2 Improvement Phase

3.3 Strategic Oscillation and Iterated Greedy

3.4 Tabu Search

3.4.1 Short Term Memory

3.4.2 Long Term Memory

3.5 Simulated Annealing

3.6 Variable Neighborhood Search

3.6.1 VNS implementations for the LOP

3.6.2 VNS implementations for the MDP

3.7 Scatter Search

3.7.1 Reference Set Creation

3.7.2 Reference Set Update

3.7.3 Reference Set Rebuild

3.8 Genetic and Memetic Algorithms

3.9 Matheuristics

3.10 Experiments with the LOP

3.11 Experiments with the MDP

Chapter 4 Branch-and-Bound

4.1 Introduction

4.2 Branch-and-Bound with Partial Orderings for the LOP

4.3 Lexicographic Search

4.4 Extension of Lexicographic Search to Branch-and-Bound

4.5 Branch-and-Bound with Lagrangean Relaxation

4.6 Improved MDP formulations

4.7 Branch-and-Bound with Partial Selections for the MDP

Chapter 5 Branch-and-Cut for the LOP

5.1 Integer Programming

5.2 Cutting Plane Algorithms

5.3 Branch-and-Cut with 3-Dicycle Cuts

5.3.1 Solving the 3-Diycle Relaxation

5.3.2 An LP Based Heuristic

5.3.3 Computational Results with 3-Dicycles

5.4 Generation of Further Cuts

5.4.1 Chvátal-Gomory Cuts

5.4.2 Maximally Violated Mod-k Cuts

5.4.3 Mod-2 Cuts

5.5 Implementation of Branch-and-Cut

5.5.1 Initialization

5.5.2 Active Variables

5.5.3 Local Upper Bound

5.5.4 Branching

5.5.5 Fixing and Setting of Variables

5.5.6 Logical Implications

5.5.7 Selection of Nodes

5.5.8 Lower Bounds

5.5.9 Separation

5.5.10 Elimination of Constraints

5.5.11 Constraint Pool

5.5.12 Pricing

5.5.13 Infeasible LPs

5.5.14 Addition of Variables

5.6 Some Computational Results

Chapter 6 The Linear Ordering Polytope

6.1 Polyhedral Combinatorics and Basic Results

6.2 Facets of the Linear Ordering Polytope

6.3 Computation of Complete Descriptions

6.4 Differences between Facets

6.5 Separation of Small Facets

6.6 Computational Experiments with Small Facets

6.6.1 Comparison of Heuristics

6.6.2 Cutting Plane Selection

6.6.3 Number of Classes Taken into Account

6.6.4 Facet Selection

6.7 Local Cuts and Target Cuts

Chapter 7 Further Aspects

7.1 Approximative Algorithms

7.2 Integrality Gaps of LP Relaxations

7.3 Degree of Linearity

7.4 Semidefinite Relaxations

7.5 Context Independent Solvers

7.6 Difficulty of LOP Instances

7.7 Multiple Optimal Rankings

7.8 Sparse Problems

7.9 A Simple Dual Heuristic

7.10 Future Research on the LOP

7.11 Extensions of the MDP

References

Index

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Tags: Rafael Martí, Gerhard Reinelt, Heuristic Methods, Combinatorial Optimization