Abstract
In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see http://www.optimization-online.org/DB_HTML/2005/02/1056.html). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.
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Ball, K.D., Berry, R.S., Kunz, R.E., Li, F.-Y., Proykova, A., Wales, D.J.: From topographies to dynamics on multidimensional potential energy surfaces of atomic clusters. Science 271, 963–966 (1996)
Braier, P.A., Berry, R.S., Wales, D.J.: How the range of pair interactions governs features of multidimensional potentials. J. Chem. Phys. 93(12), 8745–8756 (1990)
Cvijovic, D., Klinowski, J.: Taboo search: an approach to the multiple minima problem. Science 267, 664–666 (1995)
Doye, J.P.K., Leary, R.H.: Locatelli M.. Schoen, F., The global optimization of Morse clusters by potential transformations. INFORMS J. Comput. 16, 371–379 (2004)
Doye, J.P.K., Wales, D.J.: The effect of range of the potential on the structure and stability of simple liquids: from clusters to bulk, from sodium to C60. J. Phys. B 29, 4859–4894 (1996)
Doye, J.P.K., Wales, D.J.: The structure and stability of atomic liquids: from clusters to bulk. Science 271, 484–487 (1996)
Doye, J.P.K., Wales, D.J.: Structural consequences of the range of the interatomic potential: a menagerie of clusters. J. Chem. Soc. Faraday Trans. 93, 4233 (1997)
Doye, J.P.K., Wales, D.J.: On the thermodynamics of global optimization. Phys. Rev. Lett. 80, 1357–1360 (1998)
Floudas, C.A., Jongen, H.Th.: Global optimization: local minima and transition points. J. Glob. Optim. 32, 409–415 (2005)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Dordrecht (1997)
Grosso, A., Locatelli, M., Schoen, F.: A population based approach for hard global optimization problems based on dissimilarity measures. Math. Program., in press. Available at http://www.optimization-online.org/DB_HTML/2005/02/1056.html
Hartke, B.: Global cluster geometry optimization by a phenotype algorithm with niches: location of elusive minima and low-order scaling with cluster size. J. Comput. Chem. 20, 1752 (1999)
Leary, R.H.: Global optimization on funneling landscapes. J. Glob. Optim. 18, 367–383 (2000)
Lee, I., Lee, H., Lee, J.: Unbiased global optimization of Lennard-Jones clusters for N≤201 using the conformational space annealing method. Phys. Rev. Lett. 91(8) (2003) 080201/1–4
Locatelli, M.: On the multilevel structure of global optimization problems. Comput. Optim. Appl. 30, 5–22 (2005)
Miller, M.A., Doye, J.P.K., Wales, D.J.: Structural relaxation in Morse clusters: energy landscapes. J. Chem. Phys. 110, 328 (1999)
Miller, M.A., Doye, J.P.K., Wales, D.J.: Structural relaxation in atomic clusters: master equation dynamics. Phys. Rev. E 60, 3701 (1999)
Pullan, W.J.: An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: 2≤N≤372. J. Comput. Chem. 26(9), 899–906 (2005)
Pullan, W.J.: Personal communication
Schwefel, H.P.: Numerical Optimization of Computer Models. Wiley, Chichester (1981)
Törn, A., Žilinskas, A. Global Optimization. Lecture Notes in Computer Sciences. Springer, Berlin (1989)
Wales, D.J.: A microscopic basis for the global appearance of energy landscapes. Science 293, 2067–2070 (2001)
Wales, D.J.: Energy Landscapes with Applications to Clusters, Biomolecules and Glasses. Cambridge University Press, Cambridge (2003)
Wales, D.J., Doye, J.P.K.: Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116, (1997)
Wood, G.R., Zabinsky, Z.B., Kristinsdottir, B.P.: Hesitant adaptive search: the distribution of the number of iterations to convergence. Math. Program. 89, 479–486 (2001)
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Grosso, A., Locatelli, M. & Schoen, F. An experimental analysis of a population based approach for global optimization. Comput Optim Appl 38, 351–370 (2007). https://doi.org/10.1007/s10589-007-9026-z
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DOI: https://doi.org/10.1007/s10589-007-9026-z