Skip to main content
Log in

Performance of genetic algorithms in search for water splitting perovskites

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

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

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Chapter  Google Scholar 

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

    Google Scholar 

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

  37. Perone CS (2009) ACM SIGEVOlution 4:12

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

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

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

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

  45. Goldschmidt VM (1926) Naturwissenschaften 14:477

    Article  CAS  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anubhav Jain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-013-7448-9

Keywords

Navigation