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Volume :32 Issue : 2 2005      Add To Cart                                                                    Download

The optimal path problems in a Bi-attribute network with fractional objective function

Auther : H.M. SOROUSH

Department of Statistics and Operations Research

College of Science, Kuwait University, P.O. Box: 5969, Safat, 13060, Kuwait

e-mail: hsoroush@kuc01.kuniv.edu.kw

 

ABSTRACT

 

Networks are extensively used to model and solve real-world problems in diverse areas such as enginering, manufacturing, communication, transportation, management, business and many others.  An improtant network proble is the problem of finding a path through a multi-attribute network which optimizes a certain objective function of path attributes.  In this paper, we study an optimal path problem in a general bi-attribute network in which the objective function for path evaluation is fractional.  A converging algorithm is presented to find an optimal simple path (i.e. an optimal path which no cycles) through the network when arc attributes are non-negative.  The algorithm is based on a network optimization reformulation of the problem in which a shortest path problem is repeatedly solved in order to get the solution to the proposed optimal path problem.  Our computational experiments demonstrate that the proposed algorithm finds optimal simple paths in specially structured undirected networks in a reasonable amount of time.

 

Keywords: Bi-attribute; fractional/rational function; network; optimal path; optimization

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