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Enumerating the Set of Non-dominated Vectors in Multiple Objective Integer LinearProgramming

Published online by Cambridge University Press:  20 August 2008

John Sylva  and
Alejandro Crema
John Sylva
Affiliation:
Departamento de Matemáticas Aplicadas, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas, Venezuela; jsylva@cantv.net
Alejandro Crema
Affiliation:
Escuela de Computación, Facultad de Ciencias,Universidad Central de Venezuela, Apartado 47002, Caracas 1041-A, Venezuela; acrema@kuaimare.ciens.ucv.ve
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Abstract

An algorithm for enumerating all nondominated vectors of multiple objectiveinteger linear programs is presented. The method tests different regionswhere candidates can be found using an auxiliary binary problem for trackingthe regions already explored. An experimental comparision with our previousefforts shows the method has relatively good time performance.

Keywords

Integer ProgrammingMultiple Objective ProgrammingParametricProgramming.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 3 , July 2008 , pp. 371 - 387
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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References

Alves, M.J. and J.o Clímaco, An interactive reference point approach for multiobjective mixed-integer programming using branch and bound. Eur. J. Oper. Res. 124 (2000) 478–494. CrossRef
Bitran, G.R., Linear multiple objective programs with zero-one variables. Math. Program. 13 (1977) 121–139. CrossRef
J. Climaco, C. Ferreira and M.E. Captivo, Multicriteria integer programming: An overview of different algorithmic approaches, in Multicriteria Analysis, edited by J. Climaco, Springer-Verlag, Berlin, 1997, pp. 248–258.
COIN-OR, Computational infrastructure for operations research home page, http://www.coin-or.org/, Acceso 26/03/2006.
Karaivanova, J., Narula, S. and Vassilev, V., An interactive algorithm for integer programming. Eur. J. Oper. Res. 68 (1993) 344–351. CrossRef
Laumanns, M., Thiele, L. and Zitzler, E., An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. Eur. J. Oper. Res. 169 (2006) 932–942. CrossRef
Rasmussen, L.M., Zero-one programming with multiple criteria. Eur. J. Oper. Res. 26 (1986) 83–95. CrossRef
R.M. Soland, The design of multiactivity multifacility systems. Eur. J. Oper. Res. 12 (1983) 95–104.
R.E. Steuer, Multiple criteria optimization-theory, computation and application, John Wiley and Sons, (1986).
J. Sylva and A. Crema, A method for finding the set of nondominated vectors for multiple objective integer linear programs. Asia-Pacific J. Oper. Res. 158 (2004) 46–55.
J. Sylva and A. Crema, A method for finding well-dispersed subsets of nondominated vectors for multiple objective mixed integer linear programs. Eur. J. Oper. Res. 180 (2007) 1011–1027.
J. Teghem and P.L. Kunsch, A survey of techniques for finding efficient solutions to multi-objective integer linear programming. Asia-Pacific J. Oper. Res. 3 (1986) 95–108.
D. Tenfelde-Podehl, A recursive algorithm for multiobjective combinatorial optimization problems with q criteria. Tech. report, Institut für Mathematik, Technische Universität Graz, (2003).
E.L. Ulungu and J. Teghem, Multi-objective combinatorial optimization problems: A survey. J. Multi-Criteria Decision Anal. 3 (1994), 83–104.