Skip to main content
SpringerLink
Log in

Multiobjective firefly algorithm for continuous optimization

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Cagnina LC, Esquivel SC, Coello CA (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32:319–326

    MATH  Google Scholar 

  2. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  3. Leifsson L, Koziel S (2010) Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction. J Comput Sci 1:98–106

    Article  Google Scholar 

  4. Farina M, Deb K, Amota P (2004) Dynamic multiobjective optimization problems: test cases, approximations, and applications. IEEE Trans Evol Comput 8:425–442

    Article  Google Scholar 

  5. Coello CAC (1999) An updated survey of evolutionary multiobjective optimization techniques: state of the art and future trends. In: Proceedings of 1999 congress on evolutionary computation. CEC99. doi:10.1109/CEC.1999.781901

  6. Deb K (1999) Evolutionary algorithms for multi-criterion optimization in engineering design. In: Evolutionary algorithms in engineering and computer science. Wiley, New York, pp 135–161

  7. Geem ZW (2009) Music-inspired harmony search algorithm: theory and applications. Springer, Berlin

    Book  Google Scholar 

  8. Talbi E-G (2009) Metaheuristics: from design to implementation. Wiley, New York

    MATH  Google Scholar 

  9. Yang XS (2008) Nature-inspired metaheuristic algorithms. Luniver Press, Beckington

    Google Scholar 

  10. Yang XS (2010) Engineering optimisation: an introduction with metaheuristic applications. Wiley, New York

    Book  Google Scholar 

  11. Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications, SAGA 2009, LNCS, vol 5792, pp 169–178

  12. Gong WY, Cai ZH, Zhu L (2009) An effective multiobjective differential evolution algorithm for engineering design. Struct Multidisc Optim 38:137–157

    Article  Google Scholar 

  13. Abbass HA, Sarker R (2002) The Pareto differential evolution algorithm. Int J Artif Intell Tools 11(4):531–552

    Article  Google Scholar 

  14. Banks A, Vincent J, Anyakoha C (2008) A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Nat Comput 7:109–124

    Article  MathSciNet  MATH  Google Scholar 

  15. Konak A, Coit DW, Smith AE (2006) Multiobjective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91:992–1007

    Article  Google Scholar 

  16. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Article  Google Scholar 

  17. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. Piscataway, NJ, pp 1942–1948

  18. Osyczka A, Kundu S (1995) A genetic algorithm-based multicriteria optimization method. In: Proceedings of 1st world congress structural and multidisciplinary . Optim, pp 909–914

  19. Reyes-Sierra M, Coello CAC (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308

    MathSciNet  Google Scholar 

  20. Zhang QF, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11:712–731

    Article  Google Scholar 

  21. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of 1st International Conference. Genetic Algorithms, pp 93–100

  22. Robič T, Filipič B (2005) DEMO: differential evolution for multiobjective optimization. In: Coello Coello CA et al (eds) EMO 2005, LNCS, vol 3410, pp 520–533

  23. Xue F (2004) Multi-objective differential evolution: theory and applications, PhD thesis, Rensselaer Polytechnic Institute

  24. Horng M-H, Jiang TW (2010) The codebook design of image vector quantization based on the firefly algorithm. In: Computational collective intelligence, technologies and applications. LNCS, vol 6423, pp 438–447

  25. Apostolopoulos T, Vlachos A (2011) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Combin. doi:10.1155/2011/523806 http://www.hindawi.com/journals/ijct/2011/523806

  26. Gandomi AH, Yang X, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89:2325–2336

    Article  Google Scholar 

  27. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-inspired Comput 2(2):78–84

    Article  Google Scholar 

  28. Yang XS, Deb S (2010) Engineering optimization by cuckoo search. Int J Math Model Numer Optim 1:330–343

    MATH  Google Scholar 

  29. Erfani T, Utyuzhnikov S (2011) Directed search domain: a method for even generation of Pareto frontier in multiobjective optimization. Eng Optim 43(5):467–484

    Article  MathSciNet  Google Scholar 

  30. Gujarathi AM, Babu BV (2009) Improved strategies of multi-objective differential evolution (MODE) for multi-objective optimization. In: Proceedings of 4th Indian international conference on artificial intelligence (IICAI-09) December 16–18

  31. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidisc Optim 26:369–395

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhang QF, Zhou AM, Zhao SZ, Suganthan PN, Liu W, Tiwari S (2009) Multiobjective optimization test instances for the CEC 2009 special session and competition, Technical Report CES-487, University of Essex, UK

  33. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Evol Comput 3:257–271

    Article  Google Scholar 

  34. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195

    Article  Google Scholar 

  35. Zhang LB, Zhou CG, Liu XH, Ma ZQ, Liang YC (2003) Solving multi objective optimization problems using particle swarm optimization. In: Proceedings of the 2003 congress evolutionary computation (CEC’2003), vol 4. IEEE Press, Australia, pp 2400–2405

  36. Li H, Zhang QF (2009) Multiobjective optimization problems with complicated Paroto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 13:284–302

    Article  Google Scholar 

  37. Deb K, Pratap A, Agarwal S, Mayarivan T (2002) A fast and elitist multiobjective algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197

    Article  Google Scholar 

  38. Babu BV, Gujarathi AM (2007) Multi-objective differential evolution (MODE) for optimization of supply chain planning and management. In: IEEE congress on evolutionary computation, (CEC 2007), pp 2732–2739

  39. Pham DT, Ghanbarzadeh A (2007) Multi-objective optimisation using the bees algorithm. In: 3rd international virtual conference on intelligent production machines and systems (IPROMS 2007) Whittles, Dunbeath, Scotland

  40. Madavan NK (2002) Multiobjective optimization using a pareto differential evolution approach. In: Congress on evolutionary computation (CEC’2002), vol 2, pp 1145–1150

  41. Gandomi AH, Yang X (2010) Benchmark problems in structural engineering. In: Koziel S, Yang XS (eds) Computational optimization, methods and algorithms, SCI, vol 356. Springer, Berlin, pp 259–281

  42. Kim JT, Oh JW, Lee IW (1997) Multiobjective optimization of steel box girder brige. In: Proceedings 7th KAIST-NTU-KU trilateral seminar/workshop on civil engineering Kyoto

  43. Rangaiah G (2008) Multi-objective optimization: techniques and applications in chemical engineering. World Scientific Publishing, USA

    Book  Google Scholar 

  44. Ray L, Liew KM (2002) A swarm metaphor for multiobjective design optimization. Eng Optim 34(2):141–153

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    Xin-She Yang

Authors
  1. Xin-She Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin-She Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, XS. Multiobjective firefly algorithm for continuous optimization. Engineering with Computers 29, 175–184 (2013). https://doi.org/10.1007/s00366-012-0254-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-012-0254-1

Keywords

Search

Navigation