Neural Computing and Applications

, Volume 22, Issue 6, pp 1239–1255 | Cite as

Bat algorithm for constrained optimization tasks

  • Amir Hossein GandomiEmail author
  • Xin-She Yang
  • Amir Hossein Alavi
  • Siamak Talatahari
Original Article


In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.


Bat algorithm Constraint optimization Metaheuristic algorithm 



The authors gratefully acknowledge the work and help of Engineer Parvin Arjmandi (The University of Akron).


  1. 1.
    Yang X-S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, BristolGoogle Scholar
  2. 2.
    Arora JS (1989) Introduction to optimum design. McGraw-Hill, New YorkGoogle Scholar
  3. 3.
    Talbi E (2009) Metaheuristics: from design to implementation. Wiley, HobokenzbMATHGoogle Scholar
  4. 4.
    Yang X-S (2009) Harmony search as a metaheuristic algorithm. In: Geem ZW (ed) Music-inspired harmony search: theory and applications. Springer, New York, pp 1–14Google Scholar
  5. 5.
    Gandomi AH, Yang XS, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Akhtar S, Tai K, Ray T (2002) A socio-behavioral simulation model for engineering design optimization. Eng Optim 34(4):341–354CrossRefGoogle Scholar
  7. 7.
    Gandomi AH, Alavi AH (2012) Krill Herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul. doi: 10.1016/j.cnsns.2012.05.010
  8. 8.
    Lee KS, Geem ZW (2004) A new meta-heuristic algorithm for continues engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933CrossRefGoogle Scholar
  9. 9.
    Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483Google Scholar
  10. 10.
    Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289zbMATHCrossRefGoogle Scholar
  11. 11.
    Gandomi AH, Yang XS, Alavi AH (2012) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Eng Comput, in press. doi: 10.1007/s00366-011-0241-y
  12. 12.
    Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al. (eds) Nature inspired cooperative strategies for optimization (NISCO 2010). Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74Google Scholar
  13. 13.
    Altringham JD (1996) Bats: biology and behavior. Oxford University Press, OxfordGoogle Scholar
  14. 14.
    Richardson P (2008) Bats. Natural History Museum, LondonGoogle Scholar
  15. 15.
    Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes. Springer, BerlinzbMATHCrossRefGoogle Scholar
  16. 16.
    Michalewicz Z, Schoenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4(1):1–32CrossRefGoogle Scholar
  17. 17.
    Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294CrossRefGoogle Scholar
  18. 18.
    Hedar A, Fukushima M (2006) Derivative-free filter simulated annealing method for constrained continuous global optimization. J Glob Optim 35:521–549MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Amirjanov A (2006) The development of a changing range genetic algorithm. Comput Methods Appl Mech Eng 195:c2495–c2508MathSciNetCrossRefGoogle Scholar
  20. 20.
    Aragon VS, Esquivel SC, Coello CCA (2010) A modified version of a T-cell algorithm for constrained optimization problems. Int J Numer Methods Eng 84:351–378zbMATHGoogle Scholar
  21. 21.
    Becerra RL, Coello CAC (2006) Cultured differential evolution for constrained optimization. Comput Methods Appl Mech Eng 195(33–36):4303–4322zbMATHCrossRefGoogle Scholar
  22. 22.
    Bernardino HS, Barbosa HJC, Lemonge ACC (2006) Constraints handling in genetic algorithms via artificial immune systems. In: Genetic and evolutionary computation-GECCO 2006, genetic and evolutionary computation conference-Late Breaking Paper, Seattle, WA, USAGoogle Scholar
  23. 23.
    Cabrera JCF, Coello CAC (2007) Handling constraints in particle swarm optimization using a small population size. In: Alexander Gelbukh, Angel Fernando Kuri Morales (eds) MICAI 2007: advances in artificial intelligence, 6th international conference on artificial intelligence, lecture notes in artificial intelligence, vol 4827. Springer, Aguascalientes, Mexico, pp 41–51Google Scholar
  24. 24.
    Cortes NC, Trejo-Perez D, Coello CAC (2005) Handling constraints in global optimization using artificial immune system. In: Artificial immune systems, fourth international conference, ICARIS 2005, Banff, Canada. Lecture notes in computer science, vol 3627. Springer, Berlin, pp 234–247Google Scholar
  25. 25.
    Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44CrossRefGoogle Scholar
  26. 26.
    Montes EM, Coello CAC (2003) A simple multimembered evolution strategy to solve constrained optimization problems, Technical Report EVOCINV-04-2003, Evolutionary Computation Group at CINVESTAV, Secci′on de Computaci′on, Departamento de Ingenierıa El′ectrica, CINVESTAV-IPN, Mexico DF, MexicoGoogle Scholar
  27. 27.
    Tessema B, Yen G (2006) A self adaptive penalty function based algorithm for constrained optimization. In: Proceedings 2006 IEEE congress on evolutionary computation, pp 246–253Google Scholar
  28. 28.
    Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4):424–435CrossRefGoogle Scholar
  29. 29.
    Zhua W, Ali MM (2009) Solving nonlinearly constrained global optimization problem via an auxiliary function method. J Comput Appl Math 230:491–503MathSciNetCrossRefGoogle Scholar
  30. 30.
    Barbosa HJC, Lemonge ACC (2002) An adaptive penalty scheme in genetic algorithms for constrained optimization problems. In: Langdon WB, Cantu-Paz E, Mathias K, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke E, Jonoska N (eds) Proceedings of the genetic and evolutionary computation conference (GECCO’2002). Morgan Kaufmann, San Francisco, pp 287–294Google Scholar
  31. 31.
    Bernardino HS, Barbosa HJC, Lemonge ACC (2007) A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: 2007 IEEE congress on evolutionary computation (CEC 2007), Singapore. IEEE Press, New York, pp 646–653Google Scholar
  32. 32.
    Bernardino HS, Barbosa HJC, Lemonge ACC, Fonseca LG (2008) A new hybrid AIS-GA for constrained optimization problems in mechanical engineering. In: 2008 congress on evolutionary computation (CEC’2008), Hong Kong. IEEE Service Center, Piscataway, pp 1455–1462Google Scholar
  33. 33.
    Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32:319–326zbMATHGoogle Scholar
  34. 34.
    Cai J, Thierauf G (1997) Evolution strategies in engineering optimization. Eng Optim 29(1):177–199CrossRefGoogle Scholar
  35. 35.
    Cao YJ, Wu QH. Mechanical design optimization by mixed variable evolutionary programming, In Proc 1997 Int Conf on Evolutionary Computation, Indianapolis; 1997, p. 443–446.Google Scholar
  36. 36.
    Coello CAC (1999) Self-adaptive penalties for GA based optimization. Proc Congr Evol Comput 1:573–580Google Scholar
  37. 37.
    Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127CrossRefGoogle Scholar
  38. 38.
    Coello CAC (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Environ Syst 17:319–346CrossRefGoogle Scholar
  39. 39.
    Coello CAC (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203CrossRefGoogle Scholar
  40. 40.
    Coello CAC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRefGoogle Scholar
  41. 41.
    Coello CAC, Cortés NC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRefGoogle Scholar
  42. 42.
    Coello CAC, Montes EM (2001) Use of dominance-based tournament selection to handle constraints in genetic algorithms, In Intelligent Engineering Systems through Artificial Neural Networks (ANNIE2001), Vol. 11, ASME Press, St. Louis, Missouri, pp 177–182.Google Scholar
  43. 43.
    Deb K, Gene AS (1997) A robust optimal design technique for mechanical component design. Evolutionary Algorithms in Engineering Applications, Springer, pp 497–514.Google Scholar
  44. 44.
    Dos Santos Coelho L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683Google Scholar
  45. 45.
    Fu J, Fenton RG, Cleghorn WL (1991) A mixed integer discrete continuous programming method and its application to engineering design optimization. Eng Optim 17:263–280CrossRefGoogle Scholar
  46. 46.
    Hadj-Alouane AB, Bean JC (1997) A genetic algorithm for the multiple-choice integer program. Oper Res 45:92–101MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    He Q, Wang L (2006) An effective co-evolutionary particle swarm optimization for engineering optimization problems. Eng Appl Artif Intell 20:89–99CrossRefGoogle Scholar
  48. 48.
    He S, Prempain E, Wu QH (2004) An improved particle swarm optimizer for mechanical design optimization problems. Eng Optim 36(5):585–605MathSciNetCrossRefGoogle Scholar
  49. 49.
    Homaifar A, Lai SHY, Qi X (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–254CrossRefGoogle Scholar
  50. 50.
    Hu X, Eberhart RC, Shi Y (2003) Engineering optimization with particle swarm. In: Proc 2003 IEEE swarm intelligence symposium, pp 53–57Google Scholar
  51. 51.
    Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Joines J, Houck C (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Fogel D (ed) Proc first IEEE conf on evolutionary computation, Orlando, Florida. IEEE Press, pp 579–584Google Scholar
  53. 53.
    Kannan BK, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des Trans 116:318–320Google Scholar
  54. 54.
    Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59:703–736zbMATHCrossRefGoogle Scholar
  55. 55.
    Li HL, Chang CT (1998) An approximate approach of global optimization for polynomial programming problems. Eur J Oper Res 107(3):625–632MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Li HL, Chou CT (1994) A global approach for nonlinear mixed discrete programming in design optimization. Eng Optim 22:109–122CrossRefGoogle Scholar
  57. 57.
    Litinetski VV, Abramzon BM (1998) Mars—a multistart adaptive random search method for global constrained optimization in engineering applications. Eng Optim 30(2):125–154CrossRefGoogle Scholar
  58. 58.
    Michalewicz Z, Attia N (1994) Evolutionary optimization of constrained problems. In: Proceedings of the 3rd annual conf on evolutionary programming. World Scientific, pp 98–108Google Scholar
  59. 59.
    Montes EM, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Montes EM, Ocaña BH (2008) Bacterial foraging for engineering design problems: preliminary results. In: Proceedings of the 4th Mexican congress on evolutionary computation (COMCEV’2008), pp 33–38, CIMAT, México, Oct 2008Google Scholar
  61. 61.
    Montes EM, Coello CAC, Velázquez-Reyes J, Muñoz-Dávila L (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567–589MathSciNetCrossRefGoogle Scholar
  62. 62.
    Parsopoulos KE, Vrahatis MN (2005) Unified particle swarm optimization for solving constrained engineering optimization problems. In: Lecture notes in computer science (LNCS), vol 3612, pp 582–591Google Scholar
  63. 63.
    Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396CrossRefGoogle Scholar
  64. 64.
    Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: Proc ASME design technology conf, Kissimine, FL, pp 95–105Google Scholar
  65. 65.
    Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. ASME J Mech Des 112(2):223–229CrossRefGoogle Scholar
  66. 66.
    Shih CJ, Lai TK (1995) Mixed-discrete fuzzy programming for nonlinear engineering optimization. Eng Optim 23(3):187–199CrossRefGoogle Scholar
  67. 67.
    Tsai JF, Li HL, Hu NZ (2002) Global optimization for signomial discrete programming problems in engineering design. Eng Optim 34(6):613–622CrossRefGoogle Scholar
  68. 68.
    Wu SJ, Chow PT (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim 24:137–159CrossRefGoogle Scholar
  69. 69.
    Yun YS (2005) Study on Adaptive hybrid genetic algorithm and its applications to engineering design problems. Waseda University, MSc ThesisGoogle Scholar
  70. 70.
    Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36:3880–3886CrossRefGoogle Scholar
  71. 71.
    Zhang C, Wang HP (1993) Mixed-discrete nonlinear optimization with simulated annealing. Eng Optim 17(3):263–280Google Scholar
  72. 72.
    Leite JPB, Topping BHV (1998) Improved genetic operators for structural engineering optimization. Adv Eng Softw 29(7–9):529–562CrossRefGoogle Scholar
  73. 73.
    Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338zbMATHCrossRefGoogle Scholar
  74. 74.
    Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015CrossRefGoogle Scholar
  75. 75.
    Atiqullah Mir M, Rao SS (2000) Simulated annealing and parallel processing: an implementation for constrained global design optimization. Eng Optim 32(5):659–685Google Scholar
  76. 76.
    Liu J-L (2005) Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems. Eng Optim 37(5):499–519MathSciNetCrossRefGoogle Scholar
  77. 77.
    Hwang S-F, He R-S (2006) A hybrid real-parameter genetic algorithm for function optimization. Adv Eng Inform 20:7–21CrossRefGoogle Scholar
  78. 78.
    Zhang J, Liang C, Huang Y, Wu J, Yang S (2009) An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. Appl Math Comput 211:392–416MathSciNetzbMATHCrossRefGoogle Scholar
  79. 79.
    Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336CrossRefGoogle Scholar
  80. 80.
    Siddall JN (1972) Analytical decision-making in engineering design. Prentice-Hall, Englewood CliffsGoogle Scholar
  81. 81.
    Ragsdell KM, Phillips DT (1976) Optimal design of a class of welded structures using geometric programming. ASME J Eng Ind 98(3):1021–1025CrossRefGoogle Scholar
  82. 82.
    Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074CrossRefGoogle Scholar
  83. 83.
    Belegundu AD (1982) A study of mathematical programming methods for structural optimization. Department of Civil and Environmental Engineering, University of Iowa, IowaGoogle Scholar
  84. 84.
    Coello CAC, Becerra RL (2004) Efficient evolutionary through the use of a cultural algorithm. Eng Optim 36:219–236CrossRefGoogle Scholar
  85. 85.
    Hsu YL, Liu TC (2007) Developing a fuzzy proportional-derivative controller optimization engine for engineering design optimization problems. Eng Optim 39(6):679–700MathSciNetCrossRefGoogle Scholar
  86. 86.
    Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33(3):735–748CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Amir Hossein Gandomi
    • 1
    Email author
  • Xin-She Yang
    • 2
  • Amir Hossein Alavi
    • 3
  • Siamak Talatahari
    • 4
  1. 1.Young Researchers Club, Central Tehran Branch, Islamic Azad UniversityTehranIran
  2. 2.Mathematics and Scientific Computing, National Physical LaboratoryTeddingtonUK
  3. 3.Young Researchers Club, Mashhad Branch, Islamic Azad UniversityMashhadIran
  4. 4.Marand Faculty of Engineering, University of TabrizTabrizIran

Personalised recommendations