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A method for optimizing over the integer efficient set
1. | USTHB - Faculty of Mathematics - Operations Research Department, Bp 32 El Alia, BEZ, Algiers, 16121, Algeria |
2. | UMONS, Faculté Polytechnique, 9 Rue Houdain-Mons, Mons 7000, Belgium |
References:
[1] |
M. Abbas and D. Chaabane, An algorithm for solving multiple objective integer linear programming problem, RAIRO Operations Research, 36 (2002), 351-364.
doi: 10.1051/ro:2003006. |
[2] |
M. Abbas and D. Chaabane, Optimizing a linear function over an integer efficient set, European Journal of Operational Research, 174 (2006), 1140-1161.
doi: 10.1016/j.ejor.2005.02.072. |
[3] |
H. P. Benson, Existence of efficient solutions for vector maximization problems, Journal of Optimization Theory and Appl, 26 (1978), 569-580.
doi: 10.1007/BF00933152. |
[4] |
H. P. Benson and S. Sayin, Optimization over the efficient set: Four special cases, Journal of Optimization Theory and Appl., 80 (1994), 3-18.
doi: 10.1007/BF02196590. |
[5] |
V. J. Bowman, On the relationship of the Tchebytcheff norm and the efficient frontier of multiple-criteria objectives, Lecture Notes in Economics and Mathematical Systems, 130 (1976), 76-85. |
[6] |
Chaabane Djamal, "Contribution à l'Optimisation Multicritère en Variables Discrètes," Ph.D thesis, UMONS, Polytechnic Faculty of Mons, Belgium, 2007. |
[7] |
A. Crema and J. Sylva, A method for finding the set of non-dominated vectors for multiple objective integer linear programs, European Journal of Operational Research, 158 (2004), 46-55.
doi: 10.1016/S0377-2217(03)00255-8. |
[8] |
G. B. Dantzig, On a linear programming combinatorial approach to the traveling salesman problem, Operations Research, 7 (1959), 58-66.
doi: 10.1287/opre.7.1.58. |
[9] |
J. G. Ecker and J. H. Song, Optimizing a linear function over an efficient set, Journal of Optimization Theory and Applications, 83 (1994), 541-563.
doi: 10.1007/BF02207641. |
[10] |
A. M. Geoffrion, Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22 (1968), 618-630.
doi: 10.1016/0022-247X(68)90201-1. |
[11] |
R. Gupta and R. Malhotra, Multi-criteria integer linear programming problem, Cahiers du CERO, 34 (1992), 51-68. |
[12] |
M. J. Jorge, An algorithm for optimizing a linear function over an integer efficient set, European Journal of Operational Research, 195 (2009), 98-103.
doi: 10.1016/j.ejor.2008.02.005. |
[13] |
J. N. Karaivanova and S. C. Narula, An interactive procedure for multiple objective integer linear programming problems, European Journal of Operational Research, 68 (1993), 344-351.
doi: 10.1016/0377-2217(93)90190-X. |
[14] |
D. Klein and E. Hannan, An algorithm for multiple objective integer linear programming problem, European Journal of Operational Research, 9 (1982), 378-385.
doi: 10.1016/0377-2217(82)90182-5. |
[15] |
N. C. Nguyen, "An Algorithm for Optimizing a Linear Function Over the Integer Efficient Set," Konrad-Zuse-Zentrum fur Informationstechnik Berlin, 1992. |
[16] |
J. Philip, Algorithms for the vector maximization problem, Mathematical Programming, 2 (1972), 207-229.
doi: 10.1007/BF01584543. |
[17] |
J. Sylva and A. Crema, A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs, European Journal of Operational Reserach, 180 (2007), 1011-1027.
doi: 10.1016/j.ejor.2006.02.049. |
[18] |
Ta Van Tu, Optimization over the efficient set of a parametric multiple objective linear programming problem, European Journal of Operational Reserach, 122 (2000), 570-583.
doi: 10.1016/S0377-2217(99)00095-8. |
[19] |
J. Teghem and P. Kunsch, A survey of techniques for finding efficient solutions to multiobjective integer linear programming, Asia Pacific Journal of Operations Research, 3 (1986), 95-108. |
[20] |
D. J. White, The maximization of a function over the efficient set via a penalty function approach, European Journal of Operational Research, 94 (1996), 143-153.
doi: 10.1016/0377-2217(95)00184-0. |
[21] |
Y. Yamamoto, Optimization over the efficient set, overview, Journal of Global Optimization, 22 (2002), 285-317. |
show all references
References:
[1] |
M. Abbas and D. Chaabane, An algorithm for solving multiple objective integer linear programming problem, RAIRO Operations Research, 36 (2002), 351-364.
doi: 10.1051/ro:2003006. |
[2] |
M. Abbas and D. Chaabane, Optimizing a linear function over an integer efficient set, European Journal of Operational Research, 174 (2006), 1140-1161.
doi: 10.1016/j.ejor.2005.02.072. |
[3] |
H. P. Benson, Existence of efficient solutions for vector maximization problems, Journal of Optimization Theory and Appl, 26 (1978), 569-580.
doi: 10.1007/BF00933152. |
[4] |
H. P. Benson and S. Sayin, Optimization over the efficient set: Four special cases, Journal of Optimization Theory and Appl., 80 (1994), 3-18.
doi: 10.1007/BF02196590. |
[5] |
V. J. Bowman, On the relationship of the Tchebytcheff norm and the efficient frontier of multiple-criteria objectives, Lecture Notes in Economics and Mathematical Systems, 130 (1976), 76-85. |
[6] |
Chaabane Djamal, "Contribution à l'Optimisation Multicritère en Variables Discrètes," Ph.D thesis, UMONS, Polytechnic Faculty of Mons, Belgium, 2007. |
[7] |
A. Crema and J. Sylva, A method for finding the set of non-dominated vectors for multiple objective integer linear programs, European Journal of Operational Research, 158 (2004), 46-55.
doi: 10.1016/S0377-2217(03)00255-8. |
[8] |
G. B. Dantzig, On a linear programming combinatorial approach to the traveling salesman problem, Operations Research, 7 (1959), 58-66.
doi: 10.1287/opre.7.1.58. |
[9] |
J. G. Ecker and J. H. Song, Optimizing a linear function over an efficient set, Journal of Optimization Theory and Applications, 83 (1994), 541-563.
doi: 10.1007/BF02207641. |
[10] |
A. M. Geoffrion, Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22 (1968), 618-630.
doi: 10.1016/0022-247X(68)90201-1. |
[11] |
R. Gupta and R. Malhotra, Multi-criteria integer linear programming problem, Cahiers du CERO, 34 (1992), 51-68. |
[12] |
M. J. Jorge, An algorithm for optimizing a linear function over an integer efficient set, European Journal of Operational Research, 195 (2009), 98-103.
doi: 10.1016/j.ejor.2008.02.005. |
[13] |
J. N. Karaivanova and S. C. Narula, An interactive procedure for multiple objective integer linear programming problems, European Journal of Operational Research, 68 (1993), 344-351.
doi: 10.1016/0377-2217(93)90190-X. |
[14] |
D. Klein and E. Hannan, An algorithm for multiple objective integer linear programming problem, European Journal of Operational Research, 9 (1982), 378-385.
doi: 10.1016/0377-2217(82)90182-5. |
[15] |
N. C. Nguyen, "An Algorithm for Optimizing a Linear Function Over the Integer Efficient Set," Konrad-Zuse-Zentrum fur Informationstechnik Berlin, 1992. |
[16] |
J. Philip, Algorithms for the vector maximization problem, Mathematical Programming, 2 (1972), 207-229.
doi: 10.1007/BF01584543. |
[17] |
J. Sylva and A. Crema, A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs, European Journal of Operational Reserach, 180 (2007), 1011-1027.
doi: 10.1016/j.ejor.2006.02.049. |
[18] |
Ta Van Tu, Optimization over the efficient set of a parametric multiple objective linear programming problem, European Journal of Operational Reserach, 122 (2000), 570-583.
doi: 10.1016/S0377-2217(99)00095-8. |
[19] |
J. Teghem and P. Kunsch, A survey of techniques for finding efficient solutions to multiobjective integer linear programming, Asia Pacific Journal of Operations Research, 3 (1986), 95-108. |
[20] |
D. J. White, The maximization of a function over the efficient set via a penalty function approach, European Journal of Operational Research, 94 (1996), 143-153.
doi: 10.1016/0377-2217(95)00184-0. |
[21] |
Y. Yamamoto, Optimization over the efficient set, overview, Journal of Global Optimization, 22 (2002), 285-317. |
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