Abstract
The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for a gradient-based local NLP solver. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 144 smooth NLP and MINLP problems due to Floudas et al, most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and many constraints. Global solutions to almost all problems are found in a small number of NLP solver calls, often one or two.
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References
Biegler, L.T., I.E. Grossman and A.W. Westerberg (1997) Systematic Methods of Chemical Process Design, Prentice-Hall, Englewood Cliffs, NJ.
Brooke, A., D. Kendrick, A. Meeraus and R. Raman (1992) GAMS: A User's Guide, Boyd and Fraser, Danvers, MA.
Dixon, L. and G.P. Szego (1975) “Towards Global Optimization,” in Proceedings of a Workshop at the University of Cagliari, Italy, North Holland.
Drud, A. (1994) “CONOPT—A Large-Scale GRG-Code,” ORSA Journal on Computing, 6(2):207–216.
Floudas, C. (1995) Nonlinear and Mixed-Integer Optimization, Oxford University Press, New York.
Floudas C.A., P.M. Pardalos, C.S. Adjiman, W.R. Esposito, Z. Gumus, S.T. Harding, J.L. Klepeis, C.A. Meyer and C.A. Schweiger (1999) Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers.
Frontline Systems, Inc. (2000) “Premium Solver Platform User Guide,” 95–96.
Laguna, M. and R. Martí (2000) “Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions,” Working Paper, Department D'Estadistica i Investigacio Operativa, Universitat de Valencia, Burjassot 46100, Spain.
Laguna, M. and R. Martí (2001) “The OptQuest Callable Library” to appear in Optimization Software Class Libraries, Stefan Voß and D. Woodruff, eds., Kluwer Academic Publishers, Boston.
Locatelli, M. and F. Schoen (1999) “Random Linkage: A Family of Acceptance/Rejection Algorithms for Global Optimization,” Math. Programming, 85(2): 379–396.
Murtagh, B.A. and M.A. Saunders (1982) “A Projected Lagrangian Algorithm and Its Implementation for Sparse Nonlinear Constraints,” Mathematical Programming Study, 16: 84–117.
Nash, S.G. “Nonlinear Programming,” OR/MS Today, 36–45.
Nocedal, J., and A. Sofer (1996) Linear and Nonlinear Programming, the McGraw-Hill Companies, Inc.
Nocedal, J., and S. J. Wright (1999) Numerical Optimization, Springer Series in Operations Research.
Rinnooy Kan, A.H.G. and G.T. Timmer (1987) “Stochastic Global Optimization Methods; part I: Clustering Methods”, Mathematical Programming, 37: 27–56.
Rinnooy Kan, A.H.G. and G.T. Timmer (1987) “Stochastic Global Optimization Methods; part II: Multi Level Methods”, Mathematical Programming, 37: 57–78.
Smith, S. and L. Lasdon (1992) “Solving Large Sparse Nonlinear Programs Using GRG,” ORSA Journal on Computing, 4(1): 3–15.
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Ugray, Z., Lasdon, L., Plummer, J.C., Glover, F., Kelly, J., Martí, R. (2005). A Multistart Scatter Search Heuristic for Smooth NLP and MINLP Problems. In: Sharda, R., Voß, S., Rego, C., Alidaee, B. (eds) Metaheuristic Optimization via Memory and Evolution. Operations Research/Computer Science Interfaces Series, vol 30. Springer, Boston, MA. https://doi.org/10.1007/0-387-23667-8_2
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DOI: https://doi.org/10.1007/0-387-23667-8_2
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