112
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

An outer approximation based branch and cut algorithm for convex 0-1 MINLP problems

, &
Pages 21-47 | Received 01 Oct 2000, Published online: 31 Jan 2008

References

  • Akrotirianakis , I. and Rustem , B. 1997 . A globally convergent interior point algorithm for non-linear programming , London, UK : Department of Computing, Imperial College . Technical Report 97-14
  • Balas , E. , Ceria , S. and Cornuejols , G. 1993 . A lift-and-project cutting plane algorithm for mixed 0-1 programs . Mathematical Programming , 58 ( 3 ) : 295 – 324 .
  • Balas , E. , Ceria , S. and Cornuejols , G. 1996 . Mixed 0-1 programming by lift-and project in a branch-and-cut framework . Management Science , 42 : 1229 – 1246 .
  • Balas , E. , Ceria , S. , Cornuejols , G. and Natraj , N. 1996 . Gomory cuts revisited . Operations Research Letters , 19 : 1 – 9 .
  • Dakin , R.J. 1986 . A tree search algorithm for mixed integer programming problems . Computer Journal , 8 : 250 – 255 .
  • Duran , M. and Grossmann , I. 1986 . An outer approximation algorithm for a class of MINLP problems . Mathematical Programming , 36 : 307 – 339 .
  • Fletcher , R. 1987 . Practical methods of optimization , UK : John Wiley and Sons .
  • Fletcher , R. and Leyffer , S. 1994 . Solving mixed integer nonlinear programs by outer approximation . Mathematical Programming , 66 : 327 – 350 .
  • Floudas , C. 1995 . Nonlinear and Mixed Integer Optimization , Oxford : Oxford University Press .
  • Gavish , B. , Horsky , D. and Srikanth , K. 1983 . An approach to the optimal positioning of a new product . Management Science , 29 ( 1l ) : 1277 – 1297 .
  • Geoffrion , A.M. 1972 . Generalized benders decomposition . JOTA , 10 ( 4 ) : 237 – 260 .
  • Gomory , R. 1958 . Outline of an algorithm for integer solutions to linear programs . Bulletin of the American Mathematical Society , 64 : 275 – 278 .
  • Gomory , R.E. 1963 . “ An algorithm for integer solutions to linear programs ” . In Recent Advances in Mathematical Programming , Edited by: Graves , L. and Wolfe , P. New York : McGraw-Hill .
  • Grossmann , I. and Kravanja , Z. “ Mixed integer nonlinear programming: A survey of algorithms and applications ” . In Large Scale Optimization with Applications , Edited by: Conn , A.R. , Biegler , L.T. , Coleman , T.F. and Santosa , F.N. New York : Part II: Optimization Design and Control .
  • Jüinger , M. , Reinelt , G. and Thienel , S. 1995 . “ Practical problem solving with cutting plane algorithms in combinatorial optimization ” . In Combinatorial Optimization , Vol. 20 , 111 – 152 . R.I. : DIMACS Series in Discrete Mathematics and Theoretical Computer Science, AMS, Providence .
  • Kocis , G. and Grossmann , I. 1987 . Relaxation strategy for the structural optimization of process flow sheets . Ind. and Eng. Chem. Res. , 26 : 1869 – 1880 .
  • Kocis , G. and Grossmann , I. 1988 . Global optimization of nonconvex MINLP problems in process synthesis . Ind. and Eng. Chem. Res. , 27 ( 8 ) : 1407 – 1421 .
  • Land , A.H. and Doig , A.G. 1960 . An automatic method of solving discrete programming problems . Econornetrica , 28 : 497 – 520 .
  • Leyffer , S. 1993 . Deterministic methods for mixed integer nonlinear programming , Scotland, UK : Department of Mathematics and Computer Science. University of Dundee .
  • Lustig , I.J. , Marsten , R.E. and Shanno , D.F. 1991 . Computational experience with a primal-dual interior point method for linear programming . Linear Algebra and Applications , 152 : 191 – 222 .
  • Nemhauser , G. and Wolsey , L. 1988 . Integer and Combinatorial Optimization , New York : J. Wiley .
  • Padberg , M. and Rinaldi , D. 1991 . A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems , 33 SIAM Review, 33, 6&100
  • Quesada , I. and Grossmann , I.E. 1992 . An LP/NLP based branch and bound algorithm for convex MINLP optimization problems . Computers and Chemical Engineering , 16 ( 10/1I ) : 937 – 947 .
  • Quist , A.J. , van Geemert , R. , Hoogenboom , R. , Illes , J.E. , de Klerk , T. , Roos , C. and Terlaky , T. 1997 . Optimization of a nuclear reactor core reload pattern using nonlinear optimization and search heuristics , Delft, The Netherlands : Department of Operations Research, Delft University of Technology .
  • Stubbs , R.A. and Mehrotra , S. 2000 . A branch and cut method for 0-1 mixed convex programming . Mathematical Programming , 86 ( 3 ) : 515 – 532 .
  • Taha , H. 1975 . Integer Programming: Theory, Applications and Computations , New York : Academic Press .
  • Vanderbei , R.J. and Shanno , D.F. 2000 . An interior point algorithm for nonconvex nonlinear programming . Mathematical Programming , 87 ( 2 ) : 303 – 316 .
  • Viswanathan , C. and Grossmann , I.E. 1990 . A combined penalty function and outer approximation method for MINLP optimization . Computers and Chemical Engineering , 14 ( 769 )
  • Westerlund , T. , Harjunkowski , I. and Isaksson , J. 1998 . Solving a production optimization problem in a paper converting mill with MILP . Computers and Chemical Engineering , 22 : 563 – 570 .
  • Yuan , X. , Zhang , S. , Pibouleau , A. and Domenech , S. 1988 . Une methode d'optimasation non linkare en variables mixtes pour la conception de prockdbs . Recherch Opirationnelle , 22 ( 4 ) : 331 – 346 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.