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.
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References
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.
T.E. Baker and L.S. Lasdon. Successive linear programming at Exxon. Mgmt. Sci., 31 (3): 264, 1985.
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.
R. R. E. de Gaston and M. G. Sofonov. Exact calculation of the multiloop stability margin. Ieee Transactions on Automatic Control, 2: 156, 1988.
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.
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.
C. A. Floudas and A. R. Ciric. Strategies for overcoming uncertainties in heat exchanger network synthesis. Comp. and Chem. Eng., 13 (10): 1133, 1989.
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.
C. A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. theory. CandChE, 14: 1397, 1990.
C. A. Floudas and V. Visweswaran. A primal-relaxed dual global optimization approach. J. Optim. Theory and Appl., 78 (2): 187, 1993.
R. E. Griffith and R. A. Stewart. A nonlinear programming technique for the optimization of continuous processesing systems. Manag. Sci., 7: 379, 1961.
Studies of the Behaviour of Recursion for the Pooling Problem. ACM SIGMAP Bulletin, 25: 19, 1978.
Behaviour of Recursion Model - More Studies. SIGMAP Bulletin, 26: 22, 1979.
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.
W. B. Liu and C. A. Floudas. A Remark on the GOP Algorithm for Global Optimization. J. Global Optim., 3: 519, 1993.
C.D. Maranas and C.A. Floudas. A Global Optimization Approach for Lennard-Jones Microclusters. J. Chem. Phys., 97 (10): 7667, 1992.
C.M. McDonald and C.A. Floudas. A user guide to GLOPEQ. Computer Aided Systems Laboratory, Chemical Engineering Department, Princeton University, NJ, 1994.
C.M. McDonald and C.A. Floudas. Global Optimization for the Phase Stability Problem. AICHE Journal, 41: 1798, 1995.
F. Palacios-Gomez, L.S. Lasdon, and M. Engquist. Nonlinear Optimization by Successive Linear Programming. Mgmt. Sci., 28 (10): 1106, 1982.
A parallel algorithm for constrained concave quadratic global minimization. Mathematical Programming, 42: 421, 1988.
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.
I. Quesada and I. E. Grossmann. Global Optimization Algorithm for Heat Exchanger Networks. IandEC Res., 32: 487, 1993.
H. Sherali and C. H. Tuncbilek. Tight Reformulation-Linearization Technique Representations for Solving Nonconvex Quadratic Programming Problems. Submitted for Publication, 1994.
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.
V. Visweswaran and C. A. Floudas. cGOP: A User’s Guide. Princeton University, Princeton, New Jersey, 1995b.
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Visweswaran, V., Floudas, C.A. (1996). Computational Results for an Efficient Implementation of the GOP Algorithm and Its Variants. In: Grossmann, I.E. (eds) Global Optimization in Engineering Design. Nonconvex Optimization and Its Applications, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5331-8_4
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DOI: https://doi.org/10.1007/978-1-4757-5331-8_4
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