Using Fuzzy Numbers in Network Design Optimization Problems

The fluctuations that have taken place in the worldwide economy over the past few years make it difficult to estimate the costs of the equipment that have to be used in order to design a telecommunications network. The literature is replete with prescriptive integer programming models for various network design problems that do not take into account the problems inherent vagueness due to equipment costs. This paper considers the real-world wavelength division multiplexing (WDM) network design problem. The vagueness that appears in this problem is assumed and handled by means of fuzzy-set-based methodologies. A fuzzy integer linear programming model is then proposed to be used as an auxiliary model to solve the former problem. With the purpose to obtain cost-effective network designs, this model is then solved using Cplex, which is a commercial high-performance optimization engine.

[1]  H.-J. Zimmermann Fuzzy set theory , 2010 .

[2]  Byeong Gi Lee,et al.  Integrated Broadband Networks: Tcp/Ip, Atm, Sdh/Sonet, and Wdm/Optics , 2001 .

[3]  José L. Verdegay Fuzzy Sets Based Heuristics for Optimization , 2010 .

[4]  Wang Zheng-xiao Supply chain multiobjective optimization based on fuzzy cooperative game , 2009 .

[5]  S. Chanas Fuzzy programming in multiobjective linear programming - a parametric approach , 1989 .

[6]  Adam Kasperski,et al.  Choosing robust solutions in discrete optimization problems with fuzzy costs , 2009, Fuzzy Sets Syst..

[7]  J. M. Cadenas,et al.  A PRIMER ON FUZZY OPTIMIZATION MODELS AND METHODS , 2006 .

[8]  James M. Keller,et al.  Modeling Human Activity From Voxel Person Using Fuzzy Logic , 2009, IEEE Transactions on Fuzzy Systems.

[9]  John M. Wilson,et al.  Fuzzy extensions to Integer Programming models of cell-formation problems in machine scheduling , 2009, Ann. Oper. Res..

[10]  Mahdieh Allahviranloo,et al.  Investment optimization on port's development by fuzzy integer programming , 2008, Eur. J. Oper. Res..

[11]  Belén Melián-Batista,et al.  Fuzzy Optimization Models for the Design of WDM Networks , 2008, IEEE Transactions on Fuzzy Systems.

[12]  Francisco Herrera,et al.  Boolean programming problems with fuzzy constraints , 1993 .

[13]  James J. Buckley,et al.  Fuzzy Integer Programming , 2007 .

[14]  Hans-Jürgen Zimmermann,et al.  Fuzzy mathematical programming , 1983, Comput. Oper. Res..

[15]  Ziyou Gao,et al.  Train Timetable Problem on a Single-Line Railway With Fuzzy Passenger Demand , 2009, IEEE Transactions on Fuzzy Systems.

[16]  M. Vila,et al.  Relating different approaches to solve linear programming problems with imprecise costs , 1990 .

[17]  Raul Poler Escoto,et al.  Fuzzy optimization for supply chain planning under supply, demand and process uncertainties , 2009, Fuzzy Sets Syst..