Computational Results for an Efficient Implementation of the GOP Algorithm and Its Variants

  • V. Visweswaran
  • C. A. Floudas
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 9)

Abstract

Recently, Floudas and Visweswaran (1990, 1993) proposed a global optimization algorithm (GOP) for the solution of a large class of nonconvex problems through a series of primal and relaxed dual subproblems that provide upper and lower bounds on the global solution. Visweswaran and Floudas (1995a) proposed a reformulation of the algorithm in the framework of a branch and bound approach that allows for an easier implementation. They also proposed an implicit enumeration of all the nodes in the resulting branch and bound tree using a mixed integer linear (MILP) formulation, and a linear branching scheme that reduces the number of subproblems from exponential to linear. In this paper, a complete implementation of the new versions of the GOP algorithm, as well as detailed computational results of applying the algorithm to various classes of nonconvex optimization problems is presented. The problems considered including pooling and blending problems, problems with separation and heat exchanger networks, robust stability analysis with real parameter uncertainty, and concave and indefinite quadratic problems of medium size.

Keywords

Rosen 

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References

  1. [1]
    I. P. Androulakis, V. Visweswaran, and C. A. Floudas. Distributed Decomposition-Based Approaches in Global Optimization. In Proceedings of State of the Art in Global Optimization: Computational Methods and Applications (Eds. C.A. Floudas and P.M. Pardalos),Kluwer Academic Series on Nonconvex Optimization and Its Applications, 1995. To Appear.Google Scholar
  2. [2]
    T.E. Baker and L.S. Lasdon. Successive linear programming at Exxon. Mgmt. Sci., 31 (3): 264, 1985.MATHCrossRefGoogle Scholar
  3. [3]
    A. Ben-Tal and V. Gershovitz. Computational Methods for the Solution of the Pooling/Blending Problem. Technical report, Technion-Israel Institute of Technology, Haifa, Israel, 1992.Google Scholar
  4. [4]
    R. R. E. de Gaston and M. G. Sofonov. Exact calculation of the multiloop stability margin. Ieee Transactions on Automatic Control, 2: 156, 1988.CrossRefGoogle Scholar
  5. [5]
    C. A. Floudas and A. Aggarwal. A decomposition strategy for global optimum search in the pooling problem. ORSA Journal on Computing, 2 (3): 225, 1990.MATHCrossRefGoogle Scholar
  6. [6]
    C. A. Floudas, A. Aggarwal, and A. R. Ciric. Global optimum search for nonconvex NLP and MINLP problems. C and ChE, 13 (10): 1117, 1989.Google Scholar
  7. [7]
    C. A. Floudas and A. R. Ciric. Strategies for overcoming uncertainties in heat exchanger network synthesis. Comp. and Chem. Eng., 13 (10): 1133, 1989.CrossRefGoogle Scholar
  8. [8]
    C. A. Floudas and P. M. Pardalos. A Collection of Test Problems for Constrained Global Optimization Algorithms, volume 455 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 1990.Google Scholar
  9. [9]
    C. A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. theory. CandChE, 14: 1397, 1990.Google Scholar
  10. [10]
    C. A. Floudas and V. Visweswaran. A primal-relaxed dual global optimization approach. J. Optim. Theory and Appl., 78 (2): 187, 1993.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    R. E. Griffith and R. A. Stewart. A nonlinear programming technique for the optimization of continuous processesing systems. Manag. Sci., 7: 379, 1961.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Studies of the Behaviour of Recursion for the Pooling Problem. ACM SIGMAP Bulletin, 25: 19, 1978.Google Scholar
  13. [13]
    Behaviour of Recursion Model - More Studies. SIGMAP Bulletin, 26: 22, 1979.Google Scholar
  14. [14]
    L.S. Lasdon, A.D. Waren, S. Sarkar, and F. Palacios-Gomez. Solving the Pooling Problem Using Generalized Reduced Gradient and Successive Linear Programming Algorithms. ACM SIGMAP Bulletin, 27: 9, 1979.CrossRefGoogle Scholar
  15. [15]
    W. B. Liu and C. A. Floudas. A Remark on the GOP Algorithm for Global Optimization. J. Global Optim., 3: 519, 1993.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    C.D. Maranas and C.A. Floudas. A Global Optimization Approach for Lennard-Jones Microclusters. J. Chem. Phys., 97 (10): 7667, 1992.CrossRefGoogle Scholar
  17. [17]
    C.M. McDonald and C.A. Floudas. A user guide to GLOPEQ. Computer Aided Systems Laboratory, Chemical Engineering Department, Princeton University, NJ, 1994.Google Scholar
  18. [18]
    C.M. McDonald and C.A. Floudas. Global Optimization for the Phase Stability Problem. AICHE Journal, 41: 1798, 1995.CrossRefGoogle Scholar
  19. [19]
    F. Palacios-Gomez, L.S. Lasdon, and M. Engquist. Nonlinear Optimization by Successive Linear Programming. Mgmt. Sci., 28 (10): 1106, 1982.MATHCrossRefGoogle Scholar
  20. [20]
    A parallel algorithm for constrained concave quadratic global minimization. Mathematical Programming, 42: 421, 1988.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Polycarpos Psarris and C. A. Floudas. Robust Stability Analysis of Linear and Nonlinear Systems with Real Parameter Uncertainty. Journal of Robust and Nonlinear Control,1994. Accepted for publication.Google Scholar
  22. [22]
    I. Quesada and I. E. Grossmann. Global Optimization Algorithm for Heat Exchanger Networks. IandEC Res., 32: 487, 1993.Google Scholar
  23. [23]
    H. Sherali and C. H. Tuncbilek. Tight Reformulation-Linearization Technique Representations for Solving Nonconvex Quadratic Programming Problems. Submitted for Publication, 1994.Google Scholar
  24. [24]
    V. Visweswaran and C. A. Floudas. New Formulations and Branching Strategies for the GOP Algorithm In Global Optimization in Engineering Design, (Ed.) I. E. Grossmann, Kluwer Book Series in Nonconvex Optimization and Its Applications, Chapter 3, 1995a.Google Scholar
  25. [25]
    V. Visweswaran and C. A. Floudas. cGOP: A User’s Guide. Princeton University, Princeton, New Jersey, 1995b.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • V. Visweswaran
    • 1
  • C. A. Floudas
    • 2
  1. 1.Mobil Research and Development CorporationPrincetonUSA
  2. 2.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

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