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Original Articles

Branch-and-Bound interval global optimization on shared memory multiprocessors

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Pages 689-701 | Received 29 Sep 2007, Published online: 17 Sep 2008

References

  • Bader , D. A. , Hart , W. E. and Phillips , C. A. 2004 . “ Parallel algorithm design for branch and bound, in Tutorials on Emerging Methodologies and Applications in Operations Research ” . Edited by: Greenberg , H. 1 – 44 . New York : Springer . Chapter 5
  • Benyoub , A. and Daoudi , E. M. 2001 . “ Parallelization of the continuous global optimization problem with inequality constraints by using interval arithmetic, in High-Performance Computing and Networking, Lecture Notes in Computer Science ” . Vol. 2110 , 595 – 599 . Berlin : Springer .
  • Berger , E. D. 2000 . Hoard: a scalable memory allocator for multithreaded applications . SIGPLAN Not , 35 : 117 – 128 .
  • Berner , S. 1996 . Parallel methods for verified global optimization, practice and theory . J. Global Optim , 9 : 1 – 22 .
  • Caprani , O. , Godthaab , B. and Madsen , K. 1993 . Use of a real-valued local minimum in parallel interval global optimization . Inter. Comput , 2 : 71 – 82 .
  • Caprani , O. and Madsen , K. 1998 . An almost embarrasingly parallel interval global optimization method, in Interval ’98 . : 15 – 18 . Nanjing University
  • Casado , L. G. and García , I. Work load balance approaches for branch and bound algorithms on distributed systems . Proceedings of the 7th Euromicro Workshop on Parallel and Distributed Processing . Danvers, MA. pp. 155 – 162 . IEEE Press .
  • Clausen , J. 1996 . “ Parallel search-based methods in optimization, in Applied Parallel Computing Industrial Computation and Optimization ” . In Lecture Notes in Computer Science , Vol. 1184 , 176 – 185 . Berlin : Springer .
  • Correa , R. and Ferreira , A. 1996 . “ Parallel best-first branch and bound in discrete optimization: a framework, in IRREGULAR ’95, Solving Combinatorial Optimization Problems in Parallel Methods and Techniques ” . Edited by: Correa , R. and Pardalos , P. 145 – 170 . Berlin : Springer .
  • Crainic , T. , Cun , B. L. and Roucairol , C. 2006 . “ Parallel branch and bound algorithms, in Parallel Combinatorial Optimization ” . Edited by: Talbi , E. G. 1 – 28 . New Jersey : John Wiley & Sons . Chapter 1
  • Dixon , L. and Szego , G. 1975 . “ Towards Global Optimization, 1 ” . North-Holland, Amsterdam
  • Dorta , I. , Leon , C. and Rodríguez , C. Performance analysis of branch-and-bound skeletons . Proceedings of the 14th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP’06) . Danvers, MA. pp. 75 – 82 . IEEE computer Society .
  • Eriksson , J. and Lindstrom , P. 1995 . A parallel interval method implementation for global optimization using dynamic load balancing . Reliab. Comput , 1 : 77 – 91 .
  • Gendron , B. and Crainic , T. G. 1994 . Parallel branch-and-bound algorithms: Survey and synthesis . Oper. Res , 42 : 1042 – 1066 .
  • Hansen , E. and Walster , G. W. 2003 . “ Global Optimization Using Interval Analysis, Pure and Applied Mathematics ” . Baca Raton, FL : CRC Press .
  • Henriksen , T. and Madsen , K. 1992 . Parallel algorithms for Global Optimization . Inter. Comput , 3 : 88 – 95 .
  • Henriksen , T. and Madsen , K. 1992 . “ Use of a depth-first strategy in parallel Global Optimization ” . In Tech. Rep , Technical University of Denmark . 92-10, Institute for Numerical Analysis
  • Ibraev , S. 2001 . “ A new parallel method for verified global optimization ” . Wuppertal : University of Wuppertal . Ph.D. thesis
  • Kahan , S. and Konecny , P. MAMA!: a memory allocator for multithreaded architectures, in . PPoPP ’06: Proceedings of the eleventh ACM SIGPLAN symposium on Principles and practice of parallel programming . New York. pp. 178 – 186 . ACM Press .
  • Kearfott , R. B. 1996 . “ Rigorous Global Search: Continuous Problems ” . Dordrecht, Holland : Kluwer Academic Publishers .
  • Knizhnik , K. 2006 . Threadalloc . Available at http://www.garret.ru/knizhnik/threadalloc
  • Leclerc , A. 1993 . Parallel interval global optimization and its implementation in C++ . Inter. Comput , 3 : 148 – 163 .
  • Martínez , J. 2006 . Interval parallel global optimization with Charm++ . Lecture Notes Comput. Sci , 3732 : 161 – 168 .
  • Martínez , J. A. 2004 . “ AMIGO: Advanced multidimensional interval analysis global optimization algorithm, in Nonconvex Optimization and Applications Series. Frontiers in Global Optimization ” . Edited by: Floudas , C. and Pardalos , P. Vol. 74 , 313 – 326 . Kluwer Academic Publishers .
  • Moore , R. 1966 . “ Interval Analysis ” . New Jersey, , USA : Prentice-Hall .
  • Moore , R. , Hansen , E. and Leclerc , A. 1992 . “ Rigorous methods for global optimization, in Recent Advances in Global Optimization ” . Edited by: Floudas , C. A. and Pardalos , P. M. 321 – 342 . Princeton, , NJ, USA : Princeton University Press . Princeton series in computer science
  • Neumaier , A. 1990 . “ Interval Methods for Systems of Equations ” . Cambridge : Cambridge University Press .
  • Nichols , B. , Buttlar , D. and Farrell , J. P. 1998 . “ PThreads Programming: A POSIX Standard for Better Multiprocessing ” . Sebastopol, CA : O'Reilly .
  • Pardalos , P. M. , Xue , G. and Panagiotopoulos , P. D. 1996 . “ Parallel algorithms for global optimization problems, in Solving Combinatorial Optimization Problems in Parallel – Methods and Techniques ” . 232 – 247 . Berlin : Springer-Verlag .
  • Ratschek , H. and Rokne , J. 1988 . “ New Computer Methods for Global Optimization ” . Chichester, , England : Ellis Horwood Ltd .
  • Ratz , D. and Csendes , T. 1995 . On the selection of subdivision directions in interval branch and bound methods for global optimization . J. Global Optim , 7 : 183 – 207 .
  • Revol , N. A methodology of parallelization for continuous verified global optimization . Parallel Processing and Applied Mathematics: 4th International conference, PPAM 2001 . Berlin. Lecture Notes in Computer Scienc , Vol. 2328 , pp. 803 – 810 . Springer .
  • Torn , A. A. and Zilinskas , A. 1989 . “ Global Optimization, Lecture Notes in Computer Science ” . Vol. 350 , Berlin : Springer .
  • Walster , G. W. , Hansen , E. R. and Sengupta , S. 1985 . “ Test results for a global optimization algorithm, in Numerical Optimization 1984 ” . Edited by: Boggs , P. T. , Byrd , R. H. and Schnabel , R. B. 272 – 287 . Philadelphia : SIAM .
  • Wiethoff , A. 1998 . “ Verifizierte globale optimierung auf parallelrechnern ” . Karlsruhe : Universitt Karlsruhe . Ph.D. thesis
  • Zabatta , F. and Ying , K. Dynamic thread creation: An asynchronous load balancing scheme for parallel searches . Proceedings of 10th International Conference on Parallel and Distributed Computing and Systems . Anahem, CA. IASTED ACTA Press .

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