Implementations of special ordered sets in MP software

作者: Wilhelm Hummeltenberg

DOI: 10.1016/0377-2217(84)90002-X

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摘要: Abstract Special ordered sets (SOS) have been introduced as a practical device for efficiently handling special classes of nonconvex optimization problems. They are now implemented in most commercial codes mathematical programming (MP software). The paper gives survey possible applications multiple choice restrictions, conditional discrete variables, discontinuous variables and piecewise linear functions, global separable problems, alternative right-hand sides, overlapping the solution quadratic Alternative problem formulations discussed. Since not defined uniquely modelling facilities depend on definition orderedset code. demonstrates superiority SOS to application binary if they treated judiciously.

参考文章(15)
E.M.L. Beale, Branch and Bound Methods for Mathematical Programming Systems Annals of discrete mathematics. ,vol. 5, pp. 201- 219 ,(1979) , 10.1016/S0167-5060(08)70351-0
A. Land, S. Powell, Computer Codes for Problems of Integer Programming Annals of discrete mathematics. ,vol. 5, pp. 221- 269 ,(1979) , 10.1016/S0167-5060(08)70352-2
Andris A. Zoltners, Prabhakant Sinha, Integer Programming Models for Sales Resource Allocation Management Science. ,vol. 26, pp. 242- 260 ,(1980) , 10.1287/MNSC.26.3.242
J. -M. Gauthier, G. Ribière, Experiments in mixed-integer linear programming using pseudo-costs Mathematical Programming. ,vol. 12, pp. 26- 47 ,(1977) , 10.1007/BF01593767
R. J. Dakin, A tree-search algorithm for mixed integer programming problems The Computer Journal. ,vol. 8, pp. 250- 255 ,(1965) , 10.1093/COMJNL/8.3.250
R. Kipp Martin, Dennis J. Sweeney, An ideal column algorithm for integer programs with special ordered sets of variables Mathematical Programming. ,vol. 26, pp. 48- 63 ,(1983) , 10.1007/BF02591892