An algorithm for enumerating all nondominated vectors of multiple objective integer linear programs is presented. The method tests different regions where candidates can be found using an auxiliary binary problem for tracking the regions already explored. An experimental comparision with our previous efforts shows the method has relatively good time performance.
Mots-clés : integer programming, multiple objective programming, parametric programming
@article{RO_2008__42_3_371_0, author = {Sylva, John and Crema, Alejandro}, title = {Enumerating the set of non-dominated vectors in multiple objective integer linear programming}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {371--387}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/ro:2008018}, mrnumber = {2444493}, zbl = {1153.90511}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro:2008018/} }
TY - JOUR AU - Sylva, John AU - Crema, Alejandro TI - Enumerating the set of non-dominated vectors in multiple objective integer linear programming JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2008 SP - 371 EP - 387 VL - 42 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2008018/ DO - 10.1051/ro:2008018 LA - en ID - RO_2008__42_3_371_0 ER -
%0 Journal Article %A Sylva, John %A Crema, Alejandro %T Enumerating the set of non-dominated vectors in multiple objective integer linear programming %J RAIRO - Operations Research - Recherche Opérationnelle %D 2008 %P 371-387 %V 42 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2008018/ %R 10.1051/ro:2008018 %G en %F RO_2008__42_3_371_0
Sylva, John; Crema, Alejandro. Enumerating the set of non-dominated vectors in multiple objective integer linear programming. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 371-387. doi : 10.1051/ro:2008018. http://archive.numdam.org/articles/10.1051/ro:2008018/
[2] Linear multiple objective programs with zero-one variables. Math. Program. 13 (1977) 121-139. | MR | Zbl
,[3] Multicriteria integer programming: An overview of different algorithmic approaches, in Multicriteria Analysis, edited by J. Climaco, Springer-Verlag, Berlin, 1997, pp. 248-258. | Zbl
, and ,[4] COIN-OR, Computational infrastructure for operations research home page, http://www.coin-or.org/, Acceso 26/03/2006.
[5] An interactive algorithm for integer programming. Eur. J. Oper. Res. 68 (1993) 344-351. | Zbl
, and ,[6] An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. Eur. J. Oper. Res. 169 (2006) 932-942. | MR | Zbl
, and ,[7] Zero-one programming with multiple criteria. Eur. J. Oper. Res. 26 (1986) 83-95. | MR | Zbl
,[8] The design of multiactivity multifacility systems. Eur. J. Oper. Res. 12 (1983) 95-104. | Zbl
,[9] Multiple criteria optimization-theory, computation and application, John Wiley and Sons, (1986). | MR | Zbl
,[10] A method for finding the set of nondominated vectors for multiple objective integer linear programs. Asia-Pacific J. Oper. Res. 158 (2004) 46-55. | MR | Zbl
and ,[11] 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. | MR | Zbl
and ,[12] A survey of techniques for finding efficient solutions to multi-objective integer linear programming. Asia-Pacific J. Oper. Res. 3 (1986) 95-108. | Zbl
and ,[13] A recursive algorithm for multiobjective combinatorial optimization problems with q criteria. Tech. report, Institut für Mathematik, Technische Universität Graz, (2003).
,[14] Multi-objective combinatorial optimization problems: A survey. J. Multi-Criteria Decision Anal. 3 (1994), 83-104. | Zbl
and ,Cité par Sources :