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Distributed Decomposition-Based Approaches in Global Optimization

  • I. P. Androulakis
  • V. Visweswaran
  • C. A. Floudas
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

Recent advances in the theory of deterministic global optimization have resulted in the development of very efficient algorithmic procedures for identifying the global minimum of certain classes of nonconvex optimization problems. The advent of powerful multiprocessor machines combined with such developments make it possible to tackle with substantial efficiency otherwise intractable global optimization problems. In this paper, we will discuss implementation issues and computational results associated with the distributed implementation of the decomposition-based global optimization algorithm, GOP, [5], [6]. The NP-complete character of the global optimization problem, translated into extremely high computational requirements, had made it difficult to address problems of large size.The parallel implementation made it possible to successfully tackle the increased computational requirements in in order to identify the global minimum in computationally realistic times. The key computational bottlnecks are identified and properly addressed. Finaly, results on an Intel-Paragon machine are presented for large scale Indefinite Quadratic Programming problems, with up to 350 quadratic variables, and Blending-Pooling Problems, with up to 12 components and 30 qualities.

Keywords

Global optimization bilinear programming blending pooling indefinite quadratic optimization 

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References

  1. 1.
    F. A. Al-Khayyal . Jointly Constrained Bilinear Programs and Related Problems: An Overview. Computers in Mathematical Applications, 19: 53–62, 1990.Google Scholar
  2. 2.
    A. Ben-Tal, G. Eiger, and V. Gershovitz. Global Minimization by Reducing the Duality Gap. Mathematical Programming, 63: 193–212, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    C. A. Floudas and P. M Pardalos. Recent Advances in Global Optimization. Princeton Series in Computer Science. Princeton University Press, Princeton, New Jersey, 1992.Google Scholar
  4. 4.
    R. Horst and P.M. Pardalos. Handbook of Global Optimization: Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, 1994.Google Scholar
  5. 5.
    C. A. Floudas and V. Visweswaran. A Primal-Relaxed Dual Global Optimization Approach. J. Opt. Th. Appl., 78 (2): 187–225, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    C. A. Floudas and V. Visweswaran. A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs: I. Theory. Comp. chem. Eng., 14: 1397–1417, 1990.CrossRefGoogle Scholar
  7. 7.
    Tuy H., Thieu. T.V;, and N.Q. Thai. A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set. Math. Of Oper. Res., 10 (3): 498–514, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    E. R. Hansen. Global Optimization using Interval Analysis: The One-Dimensional Case. J. Opt. Th. Appl., 29: 331, 1979.zbMATHCrossRefGoogle Scholar
  9. 9.
    P. Hansen, B. Jaumard, and S-H. Lu. Global Optimization of Univariate Lipschitz Functions: I. Survey and Properties. Mathematical Programming, 55 (3): 251–272, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    R. Horst, N. V. Thoai, and J. De Vries. A New Simplicial Cover Technique in Constrained Global Optimization. J. Global. Opt., 2: 1–19, 1992.zbMATHCrossRefGoogle Scholar
  11. 11.
    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by Simulated Annealing. Science, 220: 671, 1983.MathSciNetCrossRefGoogle Scholar
  12. 12.
    P.M. Pardalos and J.B. Rosen. Global optimization approach to the linear complementarity problem. SIAM J. Sci. Stat. Computing, 9 (2): 341–353, 1988.MathSciNetCrossRefGoogle Scholar
  13. 13.
    A. H. G. Rinnooy-Kan and G. T. Timmer. Stochastic Global Optimization Methods. Part I: Clustering Methods. Mathematical Programming, 39: 27, 1987.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    H. Sherali and C. H. Tuncbilek. A Global Optimization Algorithm for Polynomial Programming Problems Using a Reformulation-Linearization Technique. J. Global. Opt., 2: 101–112, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    H. Tuy. A general deterministic approach to global optimization via d.c. programming. In J. Hiriart- Urruty, editor, FERMAT Days 1985: Mathematics for Optimization, pages 273–303. Elsevier Sci. Publishers, 1985.Google Scholar
  16. 16.
    V. Visweswaran and C. A. Floudas. New Properties and Computational Improvement of the GOP Algorithm For Problems With Quadratic Objective Function and Constraints. J. Global Opt., 3(3):439–462, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    V. Visweswaran and C.A. Floudas. A Global Optimization Algorithm (GOP) for Certain Classes of NonconvexNLPs: II. Application of Theory and Test Problems. Comp. & Chem. Eng., 14: 1419–1434, 1990.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • I. P. Androulakis
    • 1
  • V. Visweswaran
    • 1
  • C. A. Floudas
    • 1
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

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