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Solution of a fractional combinatorial optimization problem by mixed integer programming

Published online by Cambridge University Press:  12 October 2006

Alain Billionnet  and
Karima Djebali
Alain Billionnet
Affiliation:
CEDRIC-IIE, 18 allée Jean Rostand, 91025 Evry Cedex, France;
Karima Djebali
Affiliation:
CEDRIC-IIE, 18 allée Jean Rostand, 91025 Evry Cedex, France;
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Abstract

Fractionnal mathematical programs appear in numerous operations research, computer science and economic domains. We consider in this paper the problem of maximizing the sum of 0–1 hyperbolic ratios (SRH). In contrast to the single ratio problem, there has been little work inthe literature concerning this problem. We propose two mixed-integer linear programming formulations of SRH and develop two different strategies to solve them. The first one consists in using directly a general-purpose mixed-integer programming solver. The second one is based on a specialized branch and bound algorithm that reformulates more precisely the problem at every node of search tree. We also propose a heuristic method and we exploit the obtained solution in order to improve the first strategy. We present computational experiments that allow to compare the different approaches.

Keywords

Optimisation combinatoire fractionnairesomme de ratios hyperboliquesprogrammation linéaire en variables mixtesbranch-and-boundexpérimentation.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 2: ROADEF 03 , April 2006 , pp. 97 - 111
Copyright
© EDP Sciences, 2006

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