Advertisement

Optimization and Engineering

, Volume 20, Issue 1, pp 65–88 | Cite as

Differential evolution with the adaptive penalty method for structural multi-objective optimization

  • Dênis E. C. VargasEmail author
  • Afonso C. C. Lemonge
  • Helio J. C. Barbosa
  • Heder S. Bernardino
Research Article
First Online:
  • 155 Downloads

Abstract

Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance.

Keywords

Structural multi-objective optimization Differential evolution Constraint handling Adaptive penalty method 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The authors thank CNPq (Grants 310778/2013-1 and 306186/2017-9) and FAPEMIG (Grants TEC PPM 528/11, TEC PPM 388/14, and APQ-03414-15).

References

  1. Angelo JS, Bernardino HS, Barbosa HJC (2012) Multi-objective ant colony approaches for structural optimization problems. In: Proceedings of the eleventh international conference on computational structures technology, paper, p 66Google Scholar
  2. Angelo JS, Bernardino HS, Barbosa HJC (2015) Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint. Adv Eng Softw 80:101–115CrossRefGoogle Scholar
  3. Barbosa HJC, Lemonge ACC (2002) An adaptive penalty scheme in genetic algorithms for constrained optimization problems. In: Proceedings of the genetic and evolutionary computation conference on GECCO’02, New York, pp 287–294Google Scholar
  4. Barbosa HJC, Lemonge ACC (2003a) An adaptive penalty scheme for steady-state genetic algorithms. In: Proceedings of the 2003 international conference on genetic and evolutionary computation: parti GECCO’03, pp 718–729Google Scholar
  5. Barbosa HJC, Lemonge ACC (2003b) A new adaptive penalty scheme for genetic algorithms. Inf Sci 156(3–4):215–251MathSciNetCrossRefGoogle Scholar
  6. Barbosa HJC, Lemonge ACC, Borges CCH (2008) A genetic algorithm encoding for cardinality constraints and automatic variable linking in structural optimization. Eng Struct 30(12):3708–3723CrossRefGoogle Scholar
  7. Barbosa HJC, Bernardino HS, Barreto AMS (2010) Using performance profiles to analyze the results of the 2006 CEC constrained optimization competition. In: 2010 IEEE world congress on computational intelligence-WCCI, pp 1–8Google Scholar
  8. Barbosa HJC, Bernardino HS, Angelo JS (2015) Derivative-free techniques for multiobjective structural optimization: a review. Comput Technol Rev 12:27–52.  https://doi.org/10.4203/ctr.12.2 CrossRefGoogle Scholar
  9. Carvalho ECR, Carvalho JPG, Bernardino H, Hallak PH, Lemonge ACC (2016) An adaptive constraint handling technique for particle swarm in constrained optimization problems. In: CIATEC-UPF, p 8Google Scholar
  10. Coello CAC, Lamont GB, Veldhuizen DAV (2007) Evolutionary algorithms for solving multi-objective problems (genetic and evolutionary computation), 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  11. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2(6):182–197CrossRefGoogle Scholar
  12. Dolan ED, More J (2002) Benchmarking optimization software with performance profiles. Math Program 91:201–213MathSciNetCrossRefzbMATHGoogle Scholar
  13. Gellatly RA, Berke L (1971) Optimal structural design. Tech. rep, DTIC DocumentGoogle Scholar
  14. Gong W, Cai Z, Zhu L (2009) An efficient multiobjective differential evolution algorithm for engineering design. Struct Multidiscip Optim 38(2):137–157CrossRefGoogle Scholar
  15. Hasançebi O (2008) Adaptive evolution strategies in structural optimization: enhancing their computational performance with applications to large-scale structures. Comput Struct 86(1):119–132CrossRefGoogle Scholar
  16. Kukkonen S, Lampinen J (2005) GDE3: The third evolution step of generalized differential evolution. In: IEEE congress on evolutionary computation (CEC 2005), IEEE, pp 443–450Google Scholar
  17. Lemonge ACC, Barbosa HJC, Bernardino HS (2015) Variants of an adaptive penalty scheme for steady-state genetic algorithms in engineering optimization. Eng Comput. https://doi.org/10.1108/EC-07-2014-0158
  18. Patnaik SN, Hopkins DA, Coroneos R (1996) Structural optimization with approximate sensitivities. Comput Struct 58(2):407–418CrossRefzbMATHGoogle Scholar
  19. Pholdee N, Bureerat S (2013) Hybridisation of real-code population-based incremental learning and differential evolution for multiobjective design of trusses. Inf Sci 223:136–152MathSciNetCrossRefGoogle Scholar
  20. Rajeev S, Krishnamoorthy CS (1992) Discrete optimization of structures using genetic algorithms. ASCE J Struct Eng 118(5):1233–1250.  https://doi.org/10.1061/(ASCE)0733-9445(1992)118:5(1233) CrossRefGoogle Scholar
  21. Sierra MR, Coello CAC (2005) Improving PSO-based multi-objective optimization using crowding, mutation and epsilon-dominance. In: EMO 2005. Springer, Berlin, pp 505–519Google Scholar
  22. Silva EK, Barbosa HJC, Lemonge ACC (2011) An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optim Eng 12(1–2):31–54MathSciNetzbMATHGoogle Scholar
  23. Silva EK, Augusto DA, Barbosa HJC (2013) Improved surrogate model assisted differential evolution with an infill criterion. In: Proceedings of 10th world congress on structural and multidisciplinary optimization. http://www2.mae.ufl.edu/mdo/Papers/5576.pdf. Accessed 5 Nov 2015.
  24. Storn R, Price K (1995) Differential evolution a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech. Rep. 95-012. University of California, Berkeley, CAGoogle Scholar
  25. Storn R, Price K (1997) Differential evolution a simple and efficient adaptive scheme for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  26. Vargas DEC, Lemonge ACC, Barbosa HJC, Bernardino HS (2016) An algorithm based on differential evolution for structural multiobjective optimization problems with constraints (in portuguese). Rev Int Métodos Num Cálc Diseño Ing 32(2):91–99Google Scholar
  27. Venkayya V (1971) Design of optimum structures. Comput Struct 1(1):265–309CrossRefGoogle Scholar
  28. Xue F, Sanderson A, Graves R (2003) Pareto-based multiobjective differential evolution. Proc Congr Evol Comput (CEC) 2:862–869Google Scholar
  29. Zavala GR, Nebro AJ, Luna F, Coello CAC (2014) A survey of multi-objective metaheuristics applied to structural optimization. Struct Multidiscip Optim 49(4):537–558MathSciNetCrossRefGoogle Scholar
  30. Zeng F, Low MYH, Decraene J, Zhou S, Cai W (2010) Self-adaptive mechanism for multi-objective evolutionary algorithms. In: Proceedings of the international multiconference of engineers and computer scientists 2010, vol 1Google Scholar
  31. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar
  32. Zitzler E, Thiele L, Laumanns M, Fonseca CM, Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117–132CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Dênis E. C. Vargas
    • 1
    Email author
  • Afonso C. C. Lemonge
    • 2
  • Helio J. C. Barbosa
    • 2
    • 3
  • Heder S. Bernardino
    • 2
  1. 1.Instituto Federal de EducaçãoCiência e Tecnologia do Sudeste de Minas GeraisRio PombaBrazil
  2. 2.Universidade Federal de Juiz de ForaJuiz de ForaBrazil
  3. 3.Laboratório Nacional de Computação CientíficaPetrópolisBrazil

Personalised recommendations

Cite article

Buy options