Solving Large MINLPs on Computational Grids

We consider the solution of Mixed Integer Nonlinear Programming (MINLP) problems by a parallel implementation of nonlinear branch-and-bound on a computational grid or meta-computer. Computational experience on a set of large MINLPs is reported which indicates that this approach is efficient for the solution of these problems.

[1]  I. Maros,et al.  An outer approximation based branch and cut algorithm for convex 0-1 MINLP problems , 2001 .

[2]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[3]  A. Land,et al.  An Automatic Method for Solving Discrete Programming Problems , 1960, 50 Years of Integer Programming.

[4]  John E. Mitchell,et al.  An improved branch and bound algorithm for mixed integer nonlinear programs , 1994, Comput. Oper. Res..

[5]  Sven Leyffer,et al.  Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming , 2001, Comput. Optim. Appl..

[6]  Miron Livny,et al.  Interfacing Condor and PVM to harness the cycles of workstation clusters , 1996, Future Gener. Comput. Syst..

[7]  Jonathan Eckstein,et al.  Parallel Branch-and-Bound Algorithms for General Mixed Integer Programming on the CM-5 , 1994, SIAM J. Optim..

[8]  A. J. Quist.  Application of Mathematical Optimization Techniques to Nuclear Reactor Reload Pattern Design , 2000 .

[9]  Ignacio E. Grossmann,et al.  Mixed-Integer Nonlinear Programming: A Survey of Algorithms and Applications , 1997 .

[10]  Christodoulos A. Floudas,et al.  Distributed Branch and Bound Algorithms for Global Optimization , 1999 .

[11]  Nikolaos V. Sahinidis,et al.  BARON: A general purpose global optimization software package , 1996, J. Glob. Optim..

[12]  Nicholas I. M. Gould,et al.  Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming , 2002, SIAM J. Optim..

[13]  Qun Chen,et al.  FATCOP 2.0: Advanced Features in an Opportunistic Mixed Integer Programming Solver , 2001, Ann. Oper. Res..

[14]  Sanjay Mehrotra,et al.  A branch-and-cut method for 0-1 mixed convex programming , 1999, Math. Program..

[15]  John Wilson.  Model Solving in Mathematical Programming , 1993 .

[16]  A. M. Geoffrion.  Generalized Benders decomposition , 1972 .

[17]  Joseph F. Pekny,et al.  A parallel branch and bound algorithm for solving large asymmetric traveling salesman problems , 1992, Math. Program..

[18]  V. A. Roshchin,et al.  Models and methods of solution of quadratic integer programming problems , 1987 .

[19]  Per S. Laursen.  Simple Approches to Parallel Branch and Bound , 1993, Parallel Comput..

[20]  Qun Chen,et al.  FATCOP: A Fault Tolerant Condor-PVM Mixed Integer Programming Solver , 2000, SIAM J. Optim..

[21]  Jeff T. Linderoth,et al.  Solving large quadratic assignment problems on computational grids , 2002, Math. Program..

[22]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[23]  Omprakash K. Gupta,et al.  Branch and Bound Experiments in Convex Nonlinear Integer Programming , 1985 .

[24]  I. Grossmann,et al.  Cyclic scheduling of continuous parallel‐process units with decaying performance , 1998 .

[25]  Stephen J. Wright,et al.  Decomposition Algorithms for Stochastic Programming on a Computational Grid , 2001, Comput. Optim. Appl..

[26]  Ignacio E. Grossmann,et al.  An outer-approximation algorithm for a class of mixed-integer nonlinear programs , 1986, Math. Program..

[27]  Iiro Harjunkoski,et al.  Different transformations for solving non-convex trim-loss problems by MINLP , 1998, Eur. J. Oper. Res..

[28]  T. Westerlund,et al.  An extended cutting plane method for solving convex MINLP problems , 1995 .

[29]  Martin W. P. Savelsbergh,et al.  A Computational Study of Search Strategies for Mixed Integer Programming , 1999, INFORMS J. Comput..

[30]  Jeff T. Linderoth,et al.  An enabling framework for master-worker applications on the Computational Grid , 2000, Proceedings the Ninth International Symposium on High-Performance Distributed Computing.

[31]  Per S. Laursen.  Can Parallel Branch and Bound without Communication Be Effective? , 1994, SIAM J. Optim..