Relaxation Methods for Pure and Mixed Integer Programming Problems

G. A. Gorry, J. F. Shapiro

ISBN 10: 1332278612 / ISBN 13: 9781332278619

Editore: Forgotten Books, 2018

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Print on Demand. This book innovates mathematical procedures for solving integer programming (IP) problems, a fundamental category of optimization problems where variables can only take on whole number values. The techniques refine group theory methods by adjusting coefficients to reduce the complexity of induced finite abelian groups. The approach offers tighter constraints and more precise solutions. The author extends the applicability of group theory in IP by introducing relaxation methods that control group size, a significant obstacle in earlier applications. These methods show promise in resolving practical IP problems, as illustrated by computational experience. The book's significance lies in its contribution to the field of IP, providing a practical framework for solving complex problems with integer variables. Its insights enhance the utility of group theory methods and broaden their applicability in various domains. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Codice articolo 9781332278619_0

Dati bibliografici

• Titolo: Relaxation Methods for Pure and Mixed Integer Programming Problems
• Editore: Forgotten Books
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 1332278612
• ISBN 13: 9781332278619
• Rilegatura: Paperback
• Condizione: New
• Tipo di libro: print-on-demand item
• Cataloghi dei venditori:
  • Algebra

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Riassunto

Excerpt from Relaxation Methods for Pure and Mixed Integer Programming Problems

Computational experience with a group theoretic integer programming (ip) algorithm has been unusually promising; see reference 6. A major irawback, however, of this method in the past has been the size of the finite abelian groups encountered during the computation of certain 1? Problems. In this paper, we show how the difficulty can be overcome by the application of some rather simple number theoretic procedures. Although these procedures cannot be guaranteed to reduce the size of the induced groups, computational experience to date has shown them to be efficacious in practically all cases. The central idea is that a given IP problem can be usefully transformed by dividing all the coefficients of an inequality by a rational divisor greater than 1, and then taking integer parts. Such a transformation of the problem, called a relaxation, has the property that all feasible solutions to the original IP problem are feasible in the transformed or relaxed problem. The idea for this particular relaxation method in IP is originally due to Wolsey The term relaxation is also used by Geoffrion in [3] to describe mathematical programming methods conceived in the same spirit as the ones here.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.