## Handbook on Modelling for Discrete OptimizationGautam M. Appa, Leonidas S. Pitsoulis, H. Paul Williams The primary reason for producing this book is to demonstrate and commu nicate the pervasive nature of Discrete Optimisation. It has applications across a very wide range of activities. Many of the applications are only known to specialists. Our aim is to rectify this. It has long been recognized that ''modelling" is as important, if not more important, a mathematical activity as designing algorithms for solving these discrete optimisation problems. Nevertheless solving the resultant models is also often far from straightforward. Although in recent years it has become viable to solve many large scale discrete optimisation problems some problems remain a challenge, even as advances in mathematical methods, hardware and software technology are constantly pushing the frontiers forward. The subject brings together diverse areas of academic activity as well as di verse areas of applications. To date the driving force has been Operational Re search and Integer Programming as the major extention of the well-developed subject of Linear Programming. However, the subject also brings results in Computer Science, Graph Theory, Logic and Combinatorics, all of which are reflected in this book. We have divided the chapters in this book into two parts, one dealing with general methods in the modelling of discrete optimisation problems and one with specific applications. The first chapter of this volume, written by Paul Williams, can be regarded as a basic introduction of how to model discrete optimisation problems as Mixed Integer Programmes, and outlines the main methods of solving them. |

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### Contents

2 | 39 |

3 | 61 |

4 | 103 |

5 | 129 |

6 | 150 |

7 | 193 |

variable and predecision state variable in time periods | 214 |

8 | 227 |

platforms Iyer et al 1998 | 292 |

1 | 313 |

Ferris Robert R Meyer and Warren DSouza | 316 |

The Gamma Knife Treatment Unit A focusing helmet | 321 |

plan and b d the reoptimized plan a and b show | 332 |

12 | 341 |

back b hierarchical architecture with feedback and | 344 |

frametoframe matching | 354 |

### Other editions - View all

Handbook on Modelling for Discrete Optimization Gautam M Appa,Leonidas S. Pitsoulis,H. Paul Williams No preview available - 2010 |

Handbook on Modelling for Discrete Optimization Gautam M. Appa,Leonidas S. Pitsoulis,H. Paul Williams No preview available - 2006 |

### Common terms and phrases

aggregate algorithm alignment applications approach architecture arcs assignment problem binary variables brachytherapy capacity cardinality combinatorial configurations constraints convex hull correlation cost cuts cycle decisions decomposition defined denote discrete Discrete Mathematics disjunction dose dynamic programming edge example Figure formulation frame-to-frame matching Gamma Knife genome given global track graph Grossmann haplotypes heuristic inequalities iteration Lagrangian relaxation Laporte Latin square Linear Programming logic-based lower bound LP relaxation Mathematical Programming matrix maximum method MILP mixed integer programming multiple frame multiple hypothesis nodes nonlinear NP-hard objective function obtained oilfield Operations Research optimal solution optimization problems pairs period proposed protein queue radiation resource scenarios scheduling sensor sequence SMIP solved source track source-correlated tracks source-to-source stochastic structure subproblem subset supply chain Tabu Search target tion track fusion treatment planning update upper bound Vehicle Routing Problem voxels