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Performance of genetic algorithms in search for water splitting perovskites

Abstract

We examine the performance of genetic algorithms (GAs) in uncovering solar water light splitters over a space of almost 19,000 perovskite materials. The entire search space was previously calculated using density functional theory to determine solutions that fulfill constraints on stability, band gap, and band edge position. Here, we test over 2500 unique GA implementations in finding these solutions to determine whether GA can avoid the need for brute force search, and thereby enable larger chemical spaces to be screened within a given computational budget. We find that the best GAs tested offer almost a 6 times efficiency gain over random search, and are comparable to the performance of a search based on informed chemical rules. In addition, the GA is almost 10 times as efficient as random search in finding half the solutions within the search space. By employing chemical rules, the performance of the GA can be further improved to approximately 12–17 better than random search. We discuss the effect of population size, selection function, crossover function, mutation rate, fitness function, and elitism on the final result, finding that selection function and elitism are especially important to GA performance. In addition, we determine that parameters that perform well in finding solar water splitters can also be applied to discovering transparent photocorrosion shields. Our results indicate that coupling GAs to high-throughput density functional calculations presents a promising method to rapidly search large chemical spaces for technological materials.

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References

  1. 1.

    Hohenberg P, Kohn W (1964) Phys Rev 136:B864

  2. 2.

    Kohn W, Sham LJ (1965) Phys Rev 140:1133

  3. 3.

    Hautier G, Jain A, Ong SP (2012) J Mater Sci 47:7317. doi:10.1007/s10853-012-6424-0

  4. 4.

    Hafner J, Wolverton C, Ceder G (2006) MRS Bull 31:659

  5. 5.

    Castelli IE, Landis DD, Thygesen KS, Dahl S, Chorkendorff I, Jaramillo TF et al (2012) Energy Environ Sci 5:9034

  6. 6.

    Castelli IE, Olsen T, Datta S, Landis DD, Dahl S, Thygesen KS et al (2012) Energy Environ Sci 5:5814

  7. 7.

    Jain A, Hautier G, Moore CJ, Ong SP, Fischer CC, Mueller T et al (2011) Comput Mater Sci 50:2295

  8. 8.

    Materials Project (2011) http://www.materialsproject.org

  9. 9.

    Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

  10. 10.

    Hautier G, Fischer C, Ehrlacher V, Jain A, Ceder G (2011) Inorg Chem 50:656

  11. 11.

    Hautier G, Fischer CC, Jain A, Mueller T, Ceder G (2010) Chem Mater 22:3762

  12. 12.

    Balachandran PV, Broderick SR, Rajan K (2011) Proc R Soc A 467:2271

  13. 13.

    Franceschetti A, Zunger A (1999) Nature 402:60

  14. 14.

    Kim K, Graf PA, Jones WB (2005) J Comput Phys 208:735

  15. 15.

    Dudiy S, Zunger A (2006) Phys Rev Lett 97:1

  16. 16.

    d’Avezac M, Luo J-W, Chanier T, Zunger A (2012) Phys Rev Lett 108:1

  17. 17.

    Johannesson G, Bligaard T, Ruban A, Skriver H, Norskov JK (2002) Phys Rev Lett 1:255506

  18. 18.

    Graf PA, Kim K, Jones WB, Hart GLW (2005) Appl Phys Lett 87:243111

  19. 19.

    Piquini P, Graf P, Zunger A (2008) Phys Rev Lett 100:1

  20. 20.

    Chakraborti N (2004) Genetic algorithms in materials design and processing. Int Mater Rev 49:246

  21. 21.

    Bhalla A, Guo R, Roy R (2000) Mater Res Innov 4:3

  22. 22.

    Peña MA, Fierro JL (2001) Chem Rev 101:1981

  23. 23.

    Landis DD, Hummelshøj JS, Nestorov S, Greeley J, Dulak M, Bligaard T et al (2012) Comput Sci Eng 14:51

  24. 24.

    Computational Materials Repository (2013) https://cmr.fysik.dtu.dk/cmr/index.php

  25. 25.

    Enkovaara J, Rostgaard C, Mortensen JJ, Chen J, Dułak M, Ferrighi L et al (2010) J Phys Condens Matter 22:253202

  26. 26.

    Mortensen J, Hansen L, Jacobsen K (2005) Phys Rev B 71:1

  27. 27.

    Hammer B, Hansen L, Nørskov J (1999) Phys Rev B 59:7413

  28. 28.

    Kuisma M, Ojanen J, Enkovaara J, Rantala T (2010) Phys Rev B 82:1

  29. 29.

    Gritsenko O, van Leeuwen R, van Lenthe E, Baerends E (1995) Phys Rev A 51:1944

  30. 30.

    Xu Y, Schoonen M (2000) Am Mineral 85:543

  31. 31.

    Butler MA, Ginley DS (1978) J Electrochem Soc 125:228

  32. 32.

    Armiento R, Kozinsky B, Fornari M, Ceder G (2011) Phys Rev B 84:04103

  33. 33.

    Oganov A, Lyakhov A, Valle M (2011) Acc Chem Res 44:227

  34. 34.

    Sastry K, Goldberg D, Kendall G (2005) In: Burke EK, Kendall G (eds) Search methodologies. Springer, New York, p 97

  35. 35.

    Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Reading

  36. 36.

    Perone C (2012) Pyevolve software https://github.com/perone/Pyevolve

  37. 37.

    Perone CS (2009) ACM SIGEVOlution 4:12

  38. 38.

    Konak A, Coit DW, Smith AE (2006) Reliab Eng Syst Saf 91:992

  39. 39.

    Mercer RE (1977) Adaptive search using a reproductive meta-plan. University of Alberta, Edmonton

  40. 40.

    Grefenstette JJ (1986) IEEE Trans Syst Man Cybern 16:122

  41. 41.

    Sastry K, Abbass H, Goldberg D, Johnson DD (2005) In: Proceedings of the 2005 conference on genetic and evolutionary computation, p 671

  42. 42.

    Perry ZA (1984) Experimental study of speciation in ecological niche theory using genetic algorithms. Doctoral Thesis, University of Michigan

  43. 43.

    Mauldin M (1984) In: Proceedings of the national conference on artificial intelligence, Austin, TX, p 247

  44. 44.

    Goldberg DE, Richardson J (1987) In: Proceedings of the second international conference on genetic algorithms, p 41

  45. 45.

    Goldschmidt VM (1926) Naturwissenschaften 14:477

  46. 46.

    Schmuland B (2012) Math Exchange Forum. http://math.stackexchange.com/questions/206798/pul

  47. 47.

    Fisher RA (1925) Math Proc Camb Philos Soc 22:700

  48. 48.

    Rojas I, González J, Pomares H, Merelo JJ, Castillo PA, Romero G (2002) IEEE Trans Syst Man Cybern Part C 32:31

  49. 49.

    Sahai H, Ageel MI (2000) The analysis of variance: fixed, random and mixed models. Birkhäuser, Boston

  50. 50.

    Calle-Vallejo F, Martínez JI, García-Lastra JM, Mogensen M, Rossmeisl J (2010) Angew Chem Int Ed 49:7699

  51. 51.

    Holland J (1968) Hierarchical descriptions of universal spaces and adaptive systems. Technical Report, University of Michigan, Department of Computer and Communication Sciences

  52. 52.

    Berger R, Neaton J (2012) Phys Rev B 86:1

  53. 53.

    Wu Y, Lazic P, Hautier G, Persson K, Ceder G (2013) Energy Environ Sci 6:157

  54. 54.

    Oganov AR, Glass CW (2006) J Chem Phys 124:244704

  55. 55.

    Woodley S (2004) Appl Evol Comput Chem 110:95

  56. 56.

    Bethke AD (1976) Comparison of genetic algorithms and gradient-based optimizers on parallel processors: efficiency of use of processing capacity. Technical Report, University of Michigan, Logic of Computers Group

  57. 57.

    Cantu-Paz E (2000) Efficient and accurate parallel genetic algorithms. Springer, New York

  58. 58.

    Bandow B, Hartke B (2006) J Phys Chem A 23:5809

  59. 59.

    Munter TR, Landis DD, Abild-Pedersen F, Jones G, Wang S, Bligaard T (2009) Comput Sci Discov 2:015006

  60. 60.

    Ortiz C, Eriksson O, Klintenberg M (2009) Comput Mater Sci 44:1042

  61. 61.

    Balamurugan D, Yang W, Beratan DN (2008) J Chem Phys 129:174105

  62. 62.

    von Lilienfeld OA (2009) J Chem Phys 131:164102

  63. 63.

    Wang M, Hu X, Beratan DN, Yang W (2006) J Am Chem Soc 128:3228

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Acknowledgements

We thank Dr. Shahar Keinan, Dr. Yosuke Kanai, Dr. Jeffrey Tilson, and Dr. Robert Fowler for their thoughts and assistance in designing this study. We thank Dr. Byron Schmuland for providing an elegant derivation of the random choosing probability problem via Math Exchange. Geoffroy Hautier acknowledges the F.R.S.- FNRS Belgium for financial support under a ‘‘Chargé de Recherche’’ grant. Anubhav Jain acknowledges funding through the U.S. Government under Contract DE-AC02-05CH11231 and the Luis W. Alvarez Fellowship in Computational Science. Ivano E. Castelli and Karsten W. Jacobsen acknowledge support from the Danish Center for Scientific Computing through grant HDW-1103-06, from the Catalysis for Sustainable Energy (CASE) initiative funded by the Danish Ministry of Science, Technology and Innovation and from the Center for Atomic-scale Materials Design (CAMD) sponsored by the Lundbeck Foundation. This research is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-05CH11231.

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Correspondence to Anubhav Jain.

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Jain, A., Castelli, I.E., Hautier, G. et al. Performance of genetic algorithms in search for water splitting perovskites. J Mater Sci 48, 6519–6534 (2013). https://doi.org/10.1007/s10853-013-7448-9

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Keywords

  • Genetic Algorithm
  • Perovskite
  • Fitness Function
  • Density Functional Theory Computation
  • Random Search