Comparison of deterministic and stochastic approaches to global optimization

International Transactions in Operational Research

Volumn 12, Issue 3, 2005, Pages 263-285

  Liberti, Leo ^a   Kucherenko, Sergei ^b  

^a POLITECNICO DI MILANO   (Italy)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Bilinear programming; Convex envelope; Global optimization; Low discrepancy sequences; Multi level single linkage; Spatial branch and bound

Indexed keywords

EID: 84870288128     PISSN: 09696016     EISSN: 14753995     Source Type: Journal    
DOI: 10.1111/j.1475-3995.2005.00503.x     Document Type: Article

References (36)

1. Adhya, N., Tawarmalani, M., Sahinidis, N., 1999. A Lagrangian approach to the pooling problem. Industrial and Engineering Chemistry Research, 38, 1956-1972.DOI: 10.1021/ie980666q
2. Adjiman, C., 1998. Global optimization techniques for process systems engineering. PhD Thesis, Princeton University.
3. Adjiman, C., Dallwig, S., Floudas, C., Neumaier, A., 1998. A global optimization method, αBB, for general twice-differentiable constrained NLPs: I. Theoretical advances. Computers & Chemical Engineering, 22, 9, 1137-1158.DOI: 10.1016/S0098-1354(98)00027-1
4. Berkelaar, M., Eikland, K., Notebaert, P., 2004. lpsolve, http://groups.yahoo.com/group/lp_solve
5. Blake, A., 1989. Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 2-12.
6. Boender, C.G.E., 1984. The generalized multinomial distribution: a Bayesian analysis and applications. PhD Thesis, Erasmus Universiteit, Rotterdam and Centrum voor Wiskunde en Informatica, Amsterdam.
7. Decker, A., Aarts, E., 1991. Global optimization and simulated annealing. Mathematical Programming, 50, 367-393.DOI: 10.1007/BF01594945
8. Dixon, L., Gomulka, J., Szego, G., 1975. Towards a global optimization technique. InDixon, L., Szego, G.(eds) Towards Global Optimization. North-Holland, Amsterdam, pp.29-54.
9. Epperly, T., Pistikopoulos, E., 1997. A reduced space branch and bound algorithm for global optimization. Journal of Global Optimization, 11, 287-311.DOI: 10.1023/A: 1008212418949
10. Floudas, C., Pardalos, P., Adjiman, C., Esposito, W., Gumus, Z., Harding, S., Klepeis, J., Meyer, C., Schweiger, C., 1999. Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, Dordrecht.
11. Foulds, L., Haughland, D., Jornsten, K., 1992. A bilinear approach to the pooling problem. Optimization, 24, 165-180.
12. Gill, P., 1999. User’s Guide for SNOPT 5.3. Systems Optimization Laboratory, Department of EESOR, Stanford University, California.
13. Kucherenko, S., Sytsko, Yu., 2005. Application of deterministic low-discrepancy sequences to nonlinear global optimization problems. Computational Optimization and Applications(accepted for publication).
14. Lavor, C., Liberti, L., Maculan, N., 2005. Computational experience with the molecular distance geometry problem. InPintér, J.(ed.) Global Optimization: Selected Case Studies. Kluwer, Dordrecht.
15. Liberti, L., 2004. Reduction constraints for the global optimization of NLPs. International Transactions in Operations Research, 11, 1, 34-41.
16. Liberti, L., 2005. Linearity embedded in nonconvex programs. Journal of Global Optimization(accepted for publication).
17. Liberti, L., Pantelides, C., 2003. Convex envelopes of monomials of odd degree. Journal of Global Optimization, 25, 157-168.DOI: 10.1023/A: 1021924706467
18. Liberti, L., Pantelides, C.C., 2005. An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms. Journal of Global Optimization(submitted).
19. Liberti, L., Tsiakis, P., Keeping, B., Pantelides, C., 2001. oo. Centre for Process Systems Engineering, Chemical Engineering Department, Imperial College, London, UK, v. 1.24.
20. Liberti, L., Maculan, N., Kucherenko, S., 2005. The kissing number problem: a new result from global optimization. Electronic Notes in Discrete Mathematics, 17.
21. Locatelli, M., 2003. A note on the Griewank test function. Journal of Global Optimization, 25, 169-174.DOI: 10.1023/A: 1021956306041
22. McCormick, G., 1976. Computability of global solutions to factorable nonconvex programs: part I - convex underestimating problems. Mathematical Programming, 10, 146-175.
23. Numerical Algorithms Group2002. NAG Library, http://www.nag.co.uk
24. Rinnooy-Kan, A.H.G., Timmer, G.T., 1987a. Stochastic global optimization methods; part I: clustering methods. Mathematical Programming, 39, 27-56.
25. Rinnooy-Kan, A.H.G., Timmer, G.T., 1987b. Stochastic global optimization methods; part II: multilevel methods. Mathematical Programming, 39, 57-78.
26. Schaffler, S., 1994. Unconstrained global optimization using stochastic integral equations. Technical Report, Technische Universität München, Institut für Angewandte Mathematik und Statistik.
27. Schoen, F., 2002. Two-phase methods for global optimization. InPardalos, P., Romeijn, E.(eds) Handbook of Global Optimization 2: Heuristic Approaches, Vol. 2. Kluwer Academic Publishers, Dordrecht, pp.151-177.
28. Smith, E., 1996. On the optimal design of continuous processes. PhD Thesis, Imperial College of Science, Technology and Medicine, University of London.
29. Smith, E., Pantelides, C., 1997. Global optimisation of nonconvex MINLPs. Computers and Chemical Engineering, 21, S791-S796.
30. Smith, E., Pantelides, C., 1999. A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Computers and Chemical Engineering, 23, 457-478.DOI: 10.1016/S0098-1354(98)00286-5
31. Sobol’, I., 1967. On the distribution of points in a cube and the approximate evaluation of integrals. Computational Mathematics and Mathematical Physics, 7, 86-112.DOI: 10.1016/0041-5553(67)90144-9
32. Sobol’, I., 1998. On quasi-Monte Carlo integrations. Mathematics and Computers in Simulation, 47, 103-112.DOI: 10.1016/S0378-4754(98)00096-2
33. Törn, A., Žilinskas, A., 1989. Global Optimization. Springer-Verlag, Berlin.
34. Törn, A., Ali, M., Vjitanen, S., 1999. Stochastic global optimization, problem classes and solution techniques. Journal of Global Optimization, 14, 437-447.DOI: 10.1023/A: 1008395408187
35. Visweswaran, V., Floudas, C., 1996. New formulations and branching strategies for the gop algorithm. InGrossmann, I.E.(ed.) Global Optimization in Engineering Design. Kluwer Academic Publishers, Dordrecht.
36. Zabinsky, Z.B., 1998. Stochastic methods for practical global optimization. Journal of Global Optimization, 13, 433-444.DOI: 10.1023/A: 1008350230239