Abstract
In this paper the problem of determining the atomic cluster configurations that minimize the Lennard-Jones potential energy is approached. Traditional studies are oriented to improve the quality of the solution and practically do not present statistical information to support the efficiency of the reported solution methods. Without this type of evidence the effectiveness of these methods might highly be dependent only on the capacity of the available computing resources. In this work it is proposed to incorporate statistical information on the performance of the solution methods. An advantage of this approach is that when the performance tests are standardized and statistically supported, we can take advantage of efficient solution methods that have been tested only in conditions of modest computing resources. An experimental study of the problem is presented in which the generated statistical information is used to identify two potential areas to improve the performance of the evaluated method.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hoare M.: H. Structure and Dynamics of Simple Microclusters: Advances in Chemical Physics. No 40, pp. 49–135 (1979)
D. Romero, C. Barrón, S. Gómez,: A Genetic Algorithm for Lennard-Jones Atomic Clusters. Applied Mathematics Letters, pp. 85–90 (1998)
D. Romero, C. Barrón, S. Gómez,: The optimal geometry of Lennard-Jones clusters:148–309. Computer Physics Communications 123, pp. 87–96 (1999)
Barr, R.S., Golden, B.L., Kelly, J., Steward, W.R., Resende, M.: Guidelines for Designing and Reporting on Computational Experiments with Heuristic Methods. Proceedings of International Conference on Metaheuristics for Optimization. Kluwer Publishing, Norwell, MA, pp. 1–17 (2001)
Johnson, D.S., McGeoch, L.A.: Experimental Analysis of Heuristics for the STSP. In: Gutin, G., Punnen, A. (eds.): The Traveling Salesman Problem and its Variations. Kluwer Academic Publishers, Dordrecht, pp. 369–443 (2002)
McGeoch, C.: Analyzing Algorithms by Simulation: Variance Reduction Techniques and Simulation Speedups. ACM Computer Survey. Vol. 24 No. 2, pp. 1995–212 (1992)
McGeoch, C.: Experimental Analysis of Algorithms. In: Pardalos, P.M., Romeijn, H.E. (eds.): Handbook of Global Optimization, Vol. 2, pp. 489–513 (2002)
Moret, B.M.E.: “Toward a Discipline of Experimental Algorithmics”. In: Goldwasser, M.H., Johnson, D.S., McGeoch, C. (eds.): Data Structures, Near Neighbor Searches, and Methodology: Fifth and Sixth DIMACS Implementation Challenges, Series DIMACS, Vol. 5, pp. 197–214 (2003)
Fraire H.: Una metodología para el diseño de la fragmentación y ubicación en grandes bases de datos distribuidas. PhD Thesis. CENIDET, Cuernavaca, México (2005)
X. Shao, Y. Xiang, H. Jiang, W. Cai,: An efficient method based on lattice construction and the genetic algorithm for optimization of large Lennard-Jones clusters. J. Phys. Chem. A. 108, pp. 3586–3592 (2004)
X. Shao, Y. Xiang, L. Cheng, W. Cai,: Structural distribution of Lennard-Jones clusters containing 562 to 1000 atoms. J. Phys. Chem. A. 108, pp. 9516–9520 (2004)
X. Shao, Y. Xiang, W. Cai,: Structural transition from icosahedra to decahedra of large Lennard-Jones clusters. J. Phys. Chem. A.109, pp. 5193–5197 (2005)
Coleman, T.F., Y. Li,: An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds. SIAM Journal on Optimization. Vol. 6, pp. 418–445 (1996)
Coleman, T.F., Y. Li: On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds. Mathematical Programming, Vol. 67, No. 2, pp. 189–224 (1994)
Xue, G.L., Maier, R.S., Rosen, J.B.: A discrete-continuous algorithm for molecular energy minimization. IEEE Computer Society Press, pp. 778–786 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Fraire Huacuja, H.J., Vargas, D.R., Valdez, G.C., Camacho Andrade, C.A., Valdez, G.C., Martínez Flores, J.A. (2007). Experimental Analysis for the Lennard-Jones Problem Solution. In: Corchado, E., Corchado, J.M., Abraham, A. (eds) Innovations in Hybrid Intelligent Systems. Advances in Soft Computing, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74972-1_32
Download citation
DOI: https://doi.org/10.1007/978-3-540-74972-1_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74971-4
Online ISBN: 978-3-540-74972-1
eBook Packages: EngineeringEngineering (R0)