Skip to main content

Crossover-based artificial bee colony algorithm for constrained optimization problems

Neural Computing and Applications volume 26, pages 1587–1601 (2015)Cite this article

Abstract

Artificial bee colony (ABC) algorithm represents one of the most-studied swarm intelligence algorithms. Since the original ABC has been found to be very effective, today there are a lot of improved variants of ABC algorithm used to solve a wide range of hard optimization problems. This paper describes a novel artificial bee colony algorithm for constrained optimization problems. In the proposed algorithm, five modifications are introduced. Firstly, to improve the exploitation abilities of ABC, two different modified ABC search operators are used in employed and onlooker phases, and crossover operator is used in scout phase instead of random search. Secondly, modifications related to dynamic tolerance for handling equality constraints and improved boundary constraint-handling method are employed. The experimental results, obtained by testing on a set of 24 well-known benchmark functions and four widely used engineering design problems, show that the proposed approach can outperform ABC-based approaches for constrained optimization problems in terms of the quality of the results, robustness and convergence speed. Additionally, it provides better results in most cases compared with other state-of-the-art algorithms.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1

References

  1. Akay B (2013) A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput 13(6):3066–3091

    Article  Google Scholar 

  2. Akay B, Karaboga D (2009) Solving integer programming problems by using artificial bee colony algorithm. In: Serra R, Cucchiara R (eds) AI*IA 2009: emergent perspectives in artificial intelligence, lecture notes in computer science, vol 5883. Springer, Berlin, pp 355–364

    Chapter  Google Scholar 

  3. Akay B, Karaboga D (2012) Artificial bee colony algorithm for large-scale problems and engineering design optimization. J Intell Manuf 23(4):1001–1014

    Article  Google Scholar 

  4. Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192:120–142

    Article  Google Scholar 

  5. Brajevic I, Tuba M (2013) An upgraded artificial bee colony algorithm (ABC) for constrained optimization problems. J Intell Manuf 24(4):729–740

    Article  Google Scholar 

  6. Brajevic I, Tuba M, Subotic M (2011) Performance of the improved artificial bee colony algorithm on standard engineering constrained problems. Int J Math Comput Simul 5(2):135–143

    Google Scholar 

  7. Deb K (2000) An efficient constraint-handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338

    Article  MATH  Google Scholar 

  8. Dhadwal MK, Jung SN, Kim CJ (2014) Advanced particle swarm assisted genetic algorithm for constrained optimization problems. Comput Optim Appl 58(3):781–806

    Article  MathSciNet  MATH  Google Scholar 

  9. Durgun I, Yildiz AR (2012) Structural design optimization of vehicle components using cuckoo search algorithm. Mater Test 54(3):185–188

    Article  Google Scholar 

  10. Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336

    Article  Google Scholar 

  11. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Article  MathSciNet  Google Scholar 

  12. Gao WF, Liu SY, Huang LL (2013a) A novel artificial bee colony algorithm based on modified search equation and orthogonal learning. IEEE Trans Cybern 43(3):1011–1024

    Article  Google Scholar 

  13. Gao WF, Liu SY, Huang LL (2013b) A novel artificial bee colony algorithm with Powell’s method. Appl Soft Comput 13(9):3763–3775

    Article  Google Scholar 

  14. Gao WF, Liu SY, Huang LL (2014a) Enhancing artificial bee colony algorithm using more information-based search equations. Inf Sci 270(20):112–133

    Article  MathSciNet  Google Scholar 

  15. Gao WF, Yen G, Liu SY (2014) A dual-population differential evolution with coevolution for constrained optimization. IEEE Trans Cybern PP(99):1. doi:10.1109/TCYB.2014.2345478

    Google Scholar 

  16. Gong W, Cai Z, Liang D (2014) Engineering optimization by means of an improved constrained differential evolution. Comput Methods Appl Mech Eng 268:884–904

    Article  MathSciNet  MATH  Google Scholar 

  17. Hajela P, Lee J (1996) Constrained genetic search via schema adaptation: an immune network solution. Struct Optim 12(1):11–15

    Article  Google Scholar 

  18. Hamida SB, Schoenauer M (2002) ASCHEA: new results using adaptive segregational constraint handling. In: Proceedings of the congress on evolutionary computation 2002 (CEC’2002), vol 1, pp 884–889

  19. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department

  20. Karaboga D, Akay B (2010) PID controller design by using artificial bee colony, harmony search and the bees algorithms. Proceedings of the institution of mechanical engineers, part I. J Syst Control Eng 224(I7):869–883

    Google Scholar 

  21. Karaboga D, Akay B (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031

    Article  Google Scholar 

  22. Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: LNAI 4529: IFSA’07, Springer, Berlin, pp 789–798

  23. Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42(1):21–57

    Article  Google Scholar 

  24. Kashan MH, Nahavandi N, Kashan AH (2012) Disabc: a new artificial bee colony algorithm for binary optimization. Appl Soft Comput 12(1):342–352

    Article  Google Scholar 

  25. Kisi O, Ozkan C, Akay B (2012) Modelling discharge–sediment relationship using neural networks with artificial bee colony algorithm. J Hydrol 428–429:94–103

    Article  Google Scholar 

  26. Kran MS, Işcan H, Gündüz M (2013) The analysis of discrete artificial bee colony algorithm with neighborhood operator on traveling salesman problem. Neural Comput Appl 23(1):9–21

    Article  Google Scholar 

  27. Kukkonen S, Lampinen J (2006) Constrained real-parameter optimization with generalized differential evolution. In: IEEE congress on evolutionary computation 2006 (CEC 2006), pp 207–214

  28. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933

    Article  MATH  Google Scholar 

  29. Li X, Yin M (2014) Self-adaptive constrained artificial bee colony for constrained numerical optimization. Neural Comput Appl 24(3–4):723–734

    Article  MathSciNet  Google Scholar 

  30. Liang J, Runarsson T, Mezura-Montes E, Clerc M, Suganthan P, Coello C, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Technical report, Nanyang Technological University, Singapore

  31. Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10(2):629–640

    Article  Google Scholar 

  32. Liu YF, Liu SY (2013) A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem. Appl Soft Comput 13(3):1459–1463

    Article  Google Scholar 

  33. Melo VVD, Carosio GLC (2012) Evaluating differential evolution with penalty function to solve constrained engineering problems. Expert Syst Appl 39(9):7860–7863

    Article  Google Scholar 

  34. Melo VVD, Carosio GLC (2013) Investigating multi-view differential evolution for solving constrained engineering design problems. Expert Syst Appl 40(9):3370–3377

    Article  Google Scholar 

  35. Mezura-Montes E, Cetina-Domínguez O (2009) Exploring promising regions of the search space with the scout bee in the artificial bee colony for constrained optimization. In: Proceedings of the artificial neural networks in engineering conference (ANNIE2009), ASME Press Series, vol 19, pp 253–260

  36. Mezura-Montes E, Cetina-Domínguez O (2012) Empirical analysis of a modified artificial bee colony for constrained numerical optimization. Appl Math Comput 218(22):10943–10973

    Article  MathSciNet  MATH  Google Scholar 

  37. Mezura-Montes E, Coello Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evolut Comput 1(4):173–194

    Article  Google Scholar 

  38. Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208

    Article  Google Scholar 

  39. Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evolut Comput 4(3):284–294

    Article  Google Scholar 

  40. Runarsson TP, Yao X (2005) Search biases in constrained evolutionary optimization. IEEE Trans Syst Man Cybern Part C Appl Rev 35(2):233–243

    Article  Google Scholar 

  41. Sharma TK, Pant M (2013) Enhancing the food locations in an artificial bee colony algorithm. Soft Comput 17(10):1939–1965

    Article  Google Scholar 

  42. Singh A, Sundar S (2011) An artificial bee colony algorithm for the minimum routing cost spanning tree problem. Soft Comput 15(12):2489–2499

    Article  Google Scholar 

  43. Storn R (1999) System design by constraint adaptation and differential evolution. IEEE Trans Evolut Comput 3(1):22–34

    Article  Google Scholar 

  44. Sun C, Zeng J, Pan J (2011) An improved vector particle swarm optimization for constrained optimization problems. Inf Sci 181(6):1153–1163

    Article  Google Scholar 

  45. Szeto W, Wu Y, Ho SC (2011) An artificial bee colony algorithm for the capacitated vehicle routing problem. Eur J Oper Res 215(1):126–135

    Article  Google Scholar 

  46. Taspinar N, Karaboga D, Yildirim M, Akay B (2011) PAPR reduction using artificial bee colony algorithm in OFDM systems. Turk J Electr Eng Comput Sci 19:47–58

    Google Scholar 

  47. Tsai HC (2014) Integrating the artificial bee colony and bees algorithm to face constrained optimization problems. Inf Sci 258:80–93

    Article  Google Scholar 

  48. Čerpinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv (CSUR) 45(3):1–33

    Google Scholar 

  49. Yang XS (2011a) Metaheuristic optimization: algorithm analysis and open problems. In: Pardalos P, Rebennack S (eds) Experimental algorithms, lecture notes in computer science, vol 6630. Springer, Berlin, pp 21–32

    Google Scholar 

  50. Yang XS (2011b) Review of metaheuristics and generalized evolutionary walk algorithm. Int J Bio Inspir Comput 3(2):77–84

    Article  Google Scholar 

  51. Yang XS, Huyck C, Karamanoglu M, Khan N (2013) True global optimality of the pressure vessel design problem: a benchmark for bio-inspired optimisation algorithms. Int J Bio Inspir Comput 5(6):329–335

    Article  Google Scholar 

  52. Yeh WC, Hsieh TJ (2011) Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Comput Oper Res 38(11):1465–1473

    Article  MathSciNet  Google Scholar 

  53. Yildiz AR (2008) Hybrid Taguchi-harmony search algorithm for solving engineering optimization problems. Int J Ind Eng Theory Appl Pract 15(3):286–293

    Google Scholar 

  54. Yildiz AR (2009a) An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry. J Mater Process Technol 209(6):2773–2780

    Article  Google Scholar 

  55. Yildiz AR (2009b) Hybrid immune-simulated annealing algorithm for optimal design and manufacturing. Int J Mater Prod Technol 34(3):217–226

    Article  Google Scholar 

  56. Yildiz AR (2009c) A new design optimization framework based on immune algorithm and Taguchi’s method. Comput Ind 60(8):613–620

    Article  Google Scholar 

  57. Yildiz AR (2009d) A novel hybrid immune algorithm for global optimization in design and manufacturing. Robot Comput Integr Manuf 25(2):261–270

    Article  Google Scholar 

  58. Yildiz AR (2009e) A novel particle swarm optimization approach for product design and manufacturing. Int J Adv Manuf Technol 40(5–6):617–628

    Article  Google Scholar 

  59. Yildiz AR (2012a) A comparative study of population-based optimization algorithms for turning operations. Inf Sci 210:81–88

    Article  MathSciNet  Google Scholar 

  60. Yildiz AR (2012b) A new hybrid particle swarm optimization approach for structural design optimization in automotive industry. Proc Inst Mech Eng Part D J Automob Eng 226(10):1340–1351

    Article  Google Scholar 

  61. Yildiz AR (2013a) Comparison of evolutionary based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26(1):327–333

    Article  Google Scholar 

  62. Yildiz AR (2013b) Cuckoo search algorithm for the selection of optimal machining parameters in milling operations. Int J Adv Manuf Technol 64(1–4):55–61

    Article  Google Scholar 

  63. Yildiz AR (2013c) Hybrid Taguchi-differential evolution algorithm for optimization of multi-pass turning operations. Appl Soft Comput 13(3):1433–1439

    Article  Google Scholar 

  64. Yildiz AR (2013d) A new hybrid bee colony optimization approach for robust optimal design and manufacturing. Appl Soft Comput 13(5):2906–2912

    Article  Google Scholar 

  65. Yildiz AR (2013e) A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations. Appl Soft Comput 13(3):1561–1566

    Article  Google Scholar 

  66. Yildiz AR (2013f) Optimization of cutting parameters in multi-pass turning using artificial bee colony-based approach. Inf Sci 220:399–407

    Article  MathSciNet  Google Scholar 

  67. Yildiz AR, Saitou K (2011) Topology synthesis of multicomponent structural assemblies in continuum domains. ASME J Mech Des 133(1):011008

    Article  Google Scholar 

  68. Yildiz AR, Solanki KN (2012) Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach. Int J Adv Manuf Technol 59(1–4):367–376

    Article  Google Scholar 

  69. Zavala AEM, Aguirre AH, Diharce ERV (2005) Constrained optimization via particle evolutionary swarm optimization algorithm (PESO). In: GECCO ’05 proceedings of the 2005 conference on genetic and evolutionary computation, ACM Press, pp 209–216

  70. Zhu G, Kwong S (2010) Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl Math Comput 217(7):3166–3173

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This research is supported by Ministry of Education and Science of Republic of Serbia, Grant No. III-44006

Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Ivona Brajevic

Authors
  1. Ivona Brajevic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ivona Brajevic.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Brajevic, I. Crossover-based artificial bee colony algorithm for constrained optimization problems. Neural Comput & Applic 26, 1587–1601 (2015). https://doi.org/10.1007/s00521-015-1826-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-1826-y

Keywords

  • Artificial bee colony algorithm
  • Constrained optimization
  • Nature-inspired algorithms
  • Swarm intelligence
  • Exploitation
  • Exploration