Multi-Objective Optimization as a Tool for Material Design

  • Zahed AllahyariEmail author
  • Artem R. Oganov
Living reference work entry


In this chapter, we explain the concept of Pareto optimality and Pareto dominance and use these concepts in solving multi-objective (MO) optimization problems. Then, we discuss a few different MO optimization methods and show how MO optimization can be used as a tool for designing new materials. A simple Pareto-based MO optimization method is examined on a few practical case studies to assess how efficient is this method in optimizing double-objective problems.



We thank the Russian Science Foundation (grant 16-13-10459) and the “5 top 100” program of MIPT for the financial support.


  1. Ashby MF (2011) Materials selection in mechanical design. Butterworth-Heinemann, BurlingtonGoogle Scholar
  2. Blöchl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979. Scholar
  3. Chen X-Q, Niu H, Li D, Li Y (2011) Modeling hardness of polycrystalline materials and bulk metallic glasses. Intermetallics 19:1275–1281. Scholar
  4. Corne D, Jerram N, Knowles JD et al (2001) PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the genetic and evoluationary computation conference, pp 283–290. doi: citeulike-article-id:8133801Google Scholar
  5. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197. Scholar
  6. Kolmogorov AN, Shah S, Margine ER et al (2010) New superconducting and semiconducting Fe-B compounds predicted with an Ab Initio evolutionary search. Phys Rev Lett 105:217003. Scholar
  7. Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186. Scholar
  8. Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758–1775. Scholar
  9. Kvashnin AG, Oganov AR, Samtsevich AI, Allahyari Z (2017) Computational search for novel hard chromium-based materials. J Phys Chem Lett 8:755–764. Scholar
  10. Liang Y, Yuan X, Fu Z et al (2012) An unusual variation of stability and hardness in molybdenum borides. Appl Phys Lett 101:1–6. Scholar
  11. Lyakhov AO, Oganov AR (2011) Evolutionary search for superhard materials: methodology and applications to forms of carbon and TiO 2. Phys Rev B 84:92103. Scholar
  12. Lyakhov AO, Oganov AR, Stokes HT, Zhu Q (2013) New developments in evolutionary structure prediction algorithm USPEX. Comput Phys Commun 184:1172–1182. Scholar
  13. Ngatchou P, Zarei A, El-Sharkawi A (2005) Pareto multi objective optimization. In: Proceeding of the 13th international conference on, intelligent systems application to power syststems, pp 84–91.
  14. Núñez-Valdez M, Allahyari Z, Fan T, Oganov AR (2016) Efficient technique for computational design of thermoelectric materials. Comput Phys Commun 222:152–157. Scholar
  15. Oganov AR, Glass CW (2006) Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J Chem Phys 124:244704. Scholar
  16. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. Scholar
  17. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: 1st International conference on genetic algorithms, pp 93–100Google Scholar
  18. Spear KE, Liao PK (1988) The B−Mo (Boron-Molybdenum) system. Bull Alloy Phase Diagr 9:457–466. Scholar
  19. Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248. Scholar
  20. Van Der Geest AG, Kolmogorov AN (2014) CALPHAD: computer coupling of phase diagrams and thermochemistry stability of 41 metal – boron systems at 0 GPa and 30 GPa from fi rst principles. 46:184–204. Scholar
  21. Yu S, Huang B, Jia X et al (2016) Exploring the real ground-state structures of molybdenum dinitride. J Phys Chem C 120:11060–11067. Scholar
  22. Zhang M, Wang HH, Wang HH et al (2010) Structural modifications and mechanical properties of molybdenum borides from first principles. J Phys Chem C 114:6722–6725. Scholar
  23. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3:257–271. Scholar
  24. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. Evolutionary methods for design optimzation and control with applications to industrial problem, pp 95–100.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Materials science and EngineeringSkolkovo Institute of Science and TechnologyMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.International Center for Materials DesignNorthwestern Polytechnical UniversityXi’anChina

Section editors and affiliations

  • Cai-Zhuang Wang
    • 1
  • Christopher M. Wolverton
    • 2
  1. 1.Ames Laboratory and Department of Physics and AstronomyIowa State UniversityAmesUSA
  2. 2.Northwestern UniversityEvanstonUSA

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