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Handbook on Modelling for Discrete Optimization

Gautum Appa, Leonidas Pitsoulis, H Paul Williams (eds)
Springer (July 2006)

The primary objective underlying this book is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this.

It has long been recognised that 'modelling' is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modelling with the hot area of discrete optimization. It will be done in an academic handbook treatment outlining the state-of-the-art for researchers across the domains of computer science, math programming, applied mathematics, engineering and operations research. Including in the book's treatment are results from graph theory, logic, computer science and combinatorics.

The book is divided into two parts: one dealing with general methods in the modelling of discrete optimization problems and the other with specific applications. The first chapter of this volume, written by H Paul Williams, can be regarded as a basic introduction of how to model discrete optimization problems as mixed integer problems, and outlines the main methods of solving them. In the second part of the book, various real life applications are presented, most of them formulated as mixed integer linear or nonlinear programming problems. These applications include network problems, constant logic problems, many engineering problems, computer design, finance problems, medical diagnosis and metical treatment problems, applications of the Genome project, an array of transportation scheduling problems and other applications.

The book contains chapters by 27 authors including Dr Gautam Appa, Professor Paul Williams and Dr Katerina Papadaki from LSE's Operational Research Department.

  • Gautam Appa and Paul Williams are in LSE's Operational Research Department
  • Leonidas Pitsoulis is a former visiting fellow in the Operational Research Department