Abstract
In this paper we consider global optimization algorithms based on multiple local searches for the Molecular Distance Geometry Problem (MDGP). Three distinct approaches (Multistart, Monotonic Basin Hopping, Population Basin Hopping) are presented and for each of them a computational analysis is performed. The results are also compared with those of two other approaches in the literature, the DGSOL approach (Moré, Wu in J. Glob. Optim. 15:219–234, 1999) and a SDP based approach (Biswas et al. in An SDP based approach for anchor-free 3D graph realization, Technical Report, Operations Research, Stanford University, 2005).
Similar content being viewed by others
References
Biswas, P., Liang, T.-C., Toh, K.-C., Ye, Y.: An SDP based approach for anchor-free 3D graph realization. Technical Report, Operations Research, Stanford University, Stanford, CA (2005).
Crippen, G., Havel, T.: Distance Geometry and Molecular Conformation. Wiley, New York (1988)
Dong, Q., Wu, Z.: A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data. J. Glob. Optim. 26, 321–333 (2003)
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)
Grosso, A., Locatelli, M., Schoen, F.: A population based approach for hard global optimization problems based on dissimilarity measures. Math. Program. 110, 373–404 (2007)
Grosso, A., Locatelli, M., Schoen, F.: An experimental analysis of population based approach for global optimization. Comput. Optim. Appl. DOI: 10.1007/s10589-007-9026-z (2007)
Hendrickson, B.A.: The molecular problem: determining conformation from pairwise distances. Ph. D. Thesis, Cornell University (1991)
Leary, R.H.: Global optima of Lennard-Jones clusters. J. Glob. Optim. 11, 35–53 (1997)
Leary, R.H.: Global optimization on funneling landscapes. J. Glob. Optim. 18, 367–383 (2000)
Locatelli, M., Schoen, F.: Efficient algorithms for large scale global optimization: Lennard-Jones clusters. Comput. Optim. Appl. 26, 173–190 (2006)
Locatelli, M.: On the multilevel structure of global optimization problems. Comput. Optim. Appl. 30, 5–22 (2005)
Moré, J., Wu, Z.: Global continuation for distance geometry problems. SIAM J. Optim 7, 814–836 (1997)
Moré, J., Wu, Z.: Distance geometry optimization for protein structures. J. Glob. Optim. 15, 219–234 (1999)
Saxe, J.B.: Embeddability of graphs in k-space is strongly NP-hard. In: 17th Allerton Conference in Communication, Control and Computing, pp. 480–489 (1979)
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)
Williams, G.A., Dugan, J.M., Altman, R.B.: Constrained global optimization for estimating molecular structure from atomic distances. J. Comput. Biol. 8, 523–547 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grosso, A., Locatelli, M. & Schoen, F. Solving molecular distance geometry problems by global optimization algorithms. Comput Optim Appl 43, 23–37 (2009). https://doi.org/10.1007/s10589-007-9127-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10589-007-9127-8