Energy landscapes of atomic clusters as black box Optimization benchmarks

Evolutionary Computation

Volumn 20, Issue 4, 2012, Pages 543-573

  Muller C L ^a   Sbalzarini, I F ^a,b  

^a ETH ZURICH   (Switzerland)

^b MAX PLANCK INSTITUTE OF MOLECULAR CELL BIOLOGY AND GENETICS   (Germany)

Author keywords

Atomic cluster; Black box optimization benchmark; CMA ES; Energy landscape; Ground state

Indexed keywords

ATOMIC ARRANGEMENT; ATOMIC CLUSTERS; ATOMIC POSITIONS; BENCHMARK SUITES; BLACK-BOX OPTIMIZATION; CMA-ES; ENERGY LANDSCAPE; ENERGY MINIMIZATION; GENERAL CLASS; GEOMETRY OPTIMIZATION; LENNARD-JONES CLUSTER; NP COMPLETE; OPTIMIZATION PROBLEMS; PACKING PROBLEMS; PAIRWISE DISTANCES; PAIRWISE INTERACTION; PROBLEM INSTANCES;

ATOMS; GROUND STATE; POTENTIAL ENERGY; TOPOLOGY;

ATOMIC BEAMS;

ALGORITHM; ARTICLE; CHEMICAL MODEL; CLUSTER ANALYSIS; METHODOLOGY; QUALITY CONTROL; THERMODYNAMICS;

ALGORITHMS; BENCHMARKING; CLUSTER ANALYSIS; MODELS, CHEMICAL; THERMODYNAMICS;

EID: 84869430878     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/EVCO_a_00086     Document Type: Article

References (61)

1. Adip, A. B. (2005). NP-hardness of the cluster minimization problem revisited. Journal of Physics A: Mathematical and General, 38(40): 8487, doi: 10.1088/0305-4470/38/40/001
2. Auger, A., and Hansen, N. (2005). A restart CMA evolution strategy with increasing population size. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), Vol. 2, pp. 1769-1776.
3. Barron, C., G ómez, S., and Romero, D. (1996). Archimedean polyhedron structure yields a lower energy atomic cluster. Applied Mathematics Letters, 9(5): 75-78.
4. Born, M., and Oppenheimer, R. (1927). Zur quantentheorie der molekeln. Annalen der Physik, 389(20): 457-484.
5. Call, S. T., Zubarev, D. Y., and Boldyrev, A. I. (2007). Global minimum structure searches via particle swarm optimization. Journal of Computational Chemistry, 28(7): 1177-1186.
6. Catlow, C. R. A., Bromley, S. T., Hamad, S., Mora-Fonz, M., Sokol, A. A., and Woodley, S. M. (2010). Modelling nano-clusters and nucleation. Physical Chemistry Chemical Physics, 12(4): 786-811.
7. Cleri, F., and Rosato, V. (1993). Tight-binding potentials for transition metals and alloys. Physical Review B, 48(1): 22-33.
8. Cohn, H., and Kumar, A. (2009). Algorithmic design of self-assembling structures. Proceedings of the National Academy of Sciences of the United States of America, 106(24): 9570-9575.
9. Cox, G., Berry, R. S., and Johnston, R. L. (2006). Characterizing potential surface topographies through the distribution of saddles and minima. Journal of Physical Chemistry A, 110(40): 11543-11550.
10. Deaven, D., Tit, N., Morris, J., and Ho, K. (1996). Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chemical Physical Letters, 256(1-2): 195-200.
11. Doye, J. (2000). Effect of compression on the global optimization of atomic clusters. Physical Review E, 62(6, Part B): 8753-8761.
12. Doye, J. P. K., Miller, M. A., and Wales, D. J. (1999a). Evolution of the potential energy surface with size for Lennard-Jones clusters. Journal of Chemical Physics, 111(18): 8417-8428.
13. Doye, J. P. K., Miller, M. A., and Wales, D. J. (1999b). The double-funnel energy landscape of the 38-atom Lennard-Jones cluster. Journal of Chemical Physics, 110(14): 6896-6906.
14. Finck, S., Hansen, N., Ros, R., and Auger, A. (2009). Real-parameter black-box optimization bench marking 2009: Presentation of the noiseless functions contents, http://citesecrx.1st.psu.edu-viewdoc-summary?doi=10.1.140.4404
15. Finnis, M. W., and Sinclair, J. E. (1984). A simple empirical N-body potential for transition metals. Philosophical Magazine A, 50(1): 45-55.
16. Hansen, N. (2008). The CMA evolution strategy: A tutorial. Retrieved from http://www.lri.fr/ hansen/cmatutorial.pdf
17. Hansen, N. (2009a). Benchmarking a bi-population CMA-ES on the BBOB-2009 noisy testbed. In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, GECCO'09, pp. 2397-2402.
18. Hansen, N. (2009b). Benchmarking the Nelder-Mead downhill simplex algorithm with many local restarts. In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference, GECCO'09, pp. 2403-2408.
19. Hartke, B. (2004). Application of evolutionary algorithms to global cluster geometry optimization. In R. L. Johnston (Ed.), Applications of Evolutionary Computation in Chemistry, Vol. 110 (pp. 33-53). Berlin: Springer.
20. Hasse, R. W. (1991). Structure and magic numbers of large Lennard-Jones quasicrystals and crystals. Physics Letters A, 161(2): 130-134.
21. Hoare, M. R. (1979). Structure and dynamics of simple microclusters. New York: Wiley.
22. Kunz, R., and Berry, R. (1995). Statistical interpretation of topographies and dynamics of multi dimensional potentials. Journal of Chemical Physics, 103(5): 1904-1912.
23. Leary, R. (2000). Global optimization on funneling landscapes. Journal of Global Optimization, 18(4): 367-383.
24. Lennard-Jones, J. (1924). On the determination of molecular fields, II, From the equation of state of a gas. Proceedings of the Royal Society of London Series A, Containing Papers of a Mathematical and Physical Character, 106(738): 463-477.
25. Li, Z., and Scheraga, H. A. (1987). Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proceedings of the National Academy of Sciences of the United States of America, 84(19): 6611-6615.
26. Meng, G., Arkus, N., Brenner, M. P., and Manoharan, V. N. (2010). The free-energy landscape of clusters of attractive hard spheres. Science, 327(5965): 560-563.
27. Morse, P. (1929). Diatomic molecules according to the wave mechanics, II; Vibrational levels. Physical Review, 34(1): 57-64.
28. Müller, C. L., Baumgartner, B., and Sbalzarini, I. F. (2009). Particle swarm CMA evolution strategy for the optimization of multi-funnel landscapes. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), pp. 2685-2692.
29. M̈uller, C. L., and Sbalzarini, I. F. (2009). A tunable real-world multi-funnel benchmark problem for evolutionary optimization-And why parallel island models might remedy the failure of CMA-ES on it. In International Joint Conference on Computational Intelligence, IJCCI, pp. 248-253.
30. M̈uller, S. D., Schraudolph, N. N., and Koumoutsakos, P. (2003). Evolutionary and gradient-based algorithms for Lennard-Jones cluster optimization. In Proceedings of the 5th Annual Conference on Genetic and Evolutionary Computation, GECCO'03.
31. Nelder, J. A., and Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4): 308-313.
32. Northby, J. (1987). Structure and binding of Lennard-Jones clusters: 13 ≤ N ≤ 147. Journal of Chemical Physics, 87(10): 6166-6177.
33. Osada, R., Funkhouser, T., Chazelle, B., and Dobkin, D. (2002). Shape distributions. ACM Transactions on Graphics, 21(4): 807-832.
34. Rechtsman, M. C., Stillinger, F. H., and Torquato, S. (2005). Optimized interactions for targeted self-assembly: Application to a honeycomb lattice. Physical Review Letters, 95(22): 228301.
35. Rechtsman, M. C., Stillinger, F. H., and Torquato, S. (2006a). Designed interaction potentials via inverse methods for self-assembly. Physical Review E, 73 1: 011406.
36. Rechtsman, M. C., Stillinger, F. H., and Torquato, S. (2006b). Self-assembly of the simple cubic lattice with an isotropic potential. Physical Review E, 74(2): 021404.
37. Rechtsman, M. C., Stillinger, F. H., and Torquato, S. (2007). Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions. Physical Review E, 75(3): 031403.
38. Sloane, N., Hardin, R., Duff, T., and Conway, J. (1995). Minimal-energy clusters of hard spheres. Discrete and Computational Geometry, 14(1): 237-259.
39. Sloane, N. J. A., Hardin, R. H., Duff, T. S., and Conway, J. H. (1997). The sphere packing cluster database. Information Sciences Research, AT&T Shannon Lab, Florham Park, New Jersey. Retrieved from http://www2.research.att.com/njas/cluster/index.html
40. Sloane, N. J. A., Hardin, R. H., and Smith, W. D. (2000). Spherical codes: Nice arrangements of points on a sphere in various dimensions. Information Sciences Research, AT&T Shannon Lab, Florham Park, New Jersey. Retrieved from http://www2.research.att.com/ njas/packings/
41. Smit, S., and Eiben, A. (2010). Beating the "world champion" evolutionary algorithm via REVAC tuning. In Proceedings of the 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1-8.
42. Steinhardt, P. J., Nelson, D. R., and Ronchetti, M. (1983). Bond-orientational order in liquids and glasses. Physical Review B, 28(2): 784-805.
43. Stillinger, F. H., and Weber, T. A. (1984). Packing structures and transitions in liquids and solids. Science, 225(4666): 983-989.
44. Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y.-P., Auger, A., and Tiwari, S. (2005). Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore (Tech. Rep. 2009005).
45. Sutton, A. P., and Chen, J. (1990). Long-range Finnis-Sinclair potentials. Philosophical Magazine Letters, 61(3): 139-146.
46. Thomson, J. J. (1904). On the structure of the atom: An investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; With application of the results to the theory of atomic structure. Philosophical Magazine, 7(39): 237-265.
47. Torquato, S. (2009). Inverse optimization techniques for targeted self-assembly. Soft Matter, 5(6): 1157-1173.
48. Van Hoyweghen, C., and Naudts, B. (2000). Symmetry in the search space. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2000), Vol. 2, pp. 1072-1078.
49. Van Hoyweghen, C., Naudts, B., and Goldberg, D. (2002). Spin-flip symmetry and synchronization. Evolutionary Computation, 10(4): 317-344.
50. Wales, D. (2004). Energy landscapes: Applications to clusters, biomolecules and glasses. Cambridge, UK: Cambridge University Press.
51. Wales, D. J. (2005). Energy landscapes and properties of biomolecules. Physical Biology, 2(4): S86-S93.
52. Wales, D. J., and Doye, J. P. K. (1997). Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. Journal of Physical Chemistry A, 101(28): 5111-5116.
53. Wales, D. J., Doye, J. P. K., Dullweber, A., Hodges, M. P., Naumkin, F. Y., Calvo, F., Hernández-Rojas, J., and Middleton, T. F. (2009). The Cambridge cluster database. Retrieved from http://www-wales.ch.cam.ac.uk/CCD.html
54. Wales, D. J., and Scheraga, H. (1999). Review: Chemistry-Global optimization of clusters, crystals, and biomolecules. Science, 285(5432): 1368-1372.
55. Weber, T. A., and Stillinger, F. H. (1985). Interactions, local order, and atomic-rearrangement kinetics in amorphous nickel-phosphorous alloys. Physical Review B, 32(8): 5402-5411.
56. Weisstein, E. W. (2010). Wigner 3j-Symbol. From MathWorld-A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/Wigner3j-Symbol.html
57. Whitley, D. (2010). Personal communication. Chair, Department of Computer Science, Colorado State University, Fort Collins.
58. Wille, L. (1987). Minimum-energy configurations of atomic clusters: New results obtained by simulated annealing. Chemical Physics Letters, 133(5): 405-410.
59. Wille, L. T., and Vennik, J. (1985). Computational complexity of the ground-state determination of atomic clusters. Journal of Physics A: Mathematical and General, 18(8): L419.
60. Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proceedings of the Sixth International Congress on Genetics, pp. 356-366.
61. Wu, C. W., and Verma, D. (2008). A sensor placement algorithm for redundant covering based on Riesz energy minimization. In International Symposium on Circuits and Systems, ISCAS, pp. 2074-2077.