Skip to main content
SpringerLink
Log in

Artificial bee colonies for continuous optimization: Experimental analysis and improvements

  • Published:
Swarm Intelligence Aims and scope Submit manuscript

Abstract

The artificial bee colony (ABC) algorithm is a recent class of swarm intelligence algorithms that is loosely inspired by the foraging behavior of honeybee swarms. It was introduced in 2005 using continuous optimization problems as an example application. Similar to what has happened with other swarm intelligence techniques, after the initial proposal, several researchers have studied variants of the original algorithm. Unfortunately, often these variants have been tested under different experimental conditions and different fine-tuning efforts for the algorithm parameters. In this article, we review various variants of the original ABC algorithm and experimentally study nine ABC algorithms under two settings: either using the original parameter settings as proposed by the authors, or using an automatic algorithm configuration tool using a same tuning effort for each algorithm. We also study the effect of adding local search to the ABC algorithms. Our experimental results show that local search can improve considerably the performance of several ABC variants and that it reduces strongly the performance differences between the studied ABC variants. We also show that the best ABC variants are competitive with recent state-of-the-art algorithms on the benchmark set we used, which establishes ABC algorithms as serious competitors in continuous optimization.

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.

Algorithm 1
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. Note that, in analogy to the natural inspiration, in the original literature a food source corresponds to a solution. Here, we present the ABC algorithms using an optimization-oriented nomenclature rather than the original bee-inspired one. The analogy to real bee colonies is discussed in Karaboga (2005), Karaboga and Akay (2009) and Diwold et al. (2011b).

  2. Note that the wrong scaling choice for the number of variables to be modified can be seen as an artifact that is introduced by tuning on training problems of only one single dimension and by the choice of defining the parameter MR as a factor. To avoid this artifact, more advanced possibilities for tuning the scaling behavior of parameters would have to be considered.

  3. An exception is the best-so-far ABC algorithm (Banharnsakun et al. 2011) for which we have observed poor performance. In Sect. 4.2.4, we have shown that this poor behavior is due to specific choices in the algorithm design.

  4. Possible options might be the Black-Box Optimization Benchmarking (BBOB) suite or the benchmark set from the CEC 2005 and 2013 special sessions on real-parameter optimization.

References

  • Abraham, A., Jatoth, R. K., & Rajasekhar, A. (2012). Hybrid differential artificial bee colony algorithm. Journal of Computational and Theoretical Nanoscience, 9(2), 249–257.

    Article  Google Scholar 

  • Akay, B., & Karaboga, D. (2009). Parameter tuning for the artificial bee colony algorithm. In N. T. Nguyen et al. (Eds.), LNCS: Vol. 5796. Proceedings of the international conference on computational collective intelligence (pp. 608–619). Berlin: Springer.

    Google Scholar 

  • Akay, B., & Karaboga, D. (2012). A modified artificial bee colony algorithm for real-parameter optimization. Information Sciences, 192, 120–142.

    Article  Google Scholar 

  • Alam, M. S., Ul Kabir, M. W., & Islam, M. M. (2010). Self-adaptation of mutation step size in artificial bee colony algorithm for continuous function optimization. In Proceedings of international conference on computer and information technology (pp. 69–74). Piscataway: IEEE Press.

    Google Scholar 

  • Alataş, B. (2010). Chaotic bee colony algorithms for global numerical optimization. Expert Systems with Applications, 37(8), 5682–5687.

    Article  Google Scholar 

  • Auger, A., & Hansen, N. (2005). A restart CMA evolution strategy with increasing population size. In Proceedings of IEEE Congress on evolutionary computation (pp. 1769–1776). Piscataway: IEEE Press.

    Google Scholar 

  • Aydın, D., Liao, T., Montes de Oca, M. A., & Stützle, T. (2012). Improving performance via population growth and local search: the case of the artificial bee colony algorithm. In J. K. Hao et al. (Eds.), LNCS: Vol. 7401. Proceedings of the international conference on artificial evolution (pp. 85–96). Berlin: Springer.

    Google Scholar 

  • Balaprakash, P., Birattari, M., & Stützle, T. (2007). Improvement strategies for the F-race algorithm: sampling design and iterative refinement. In T. Bartz-Beielstein et al. (Eds.), Hybrid metaheuristics, LNCS (Vol. 4771, pp. 108–122). Berlin: Springer.

    Chapter  Google Scholar 

  • Banharnsakun, A., Achalakul, T., & Sirinaovakul, B. (2011). The best-so-far selection in artificial bee colony algorithm. Applied Soft Computing, 11(2), 2888–2901.

    Article  Google Scholar 

  • Birattari, M. (2009). Tuning metaheuristics: a machine learning perspective. Studies in computational intelligence: Vol. 197. Berlin: Springer.

    Book  Google Scholar 

  • Birattari, M., Stützle, T., Paquete, L., & Varrentrapp, K. (2002). A racing algorithm for configuring metaheuristics. In Proceedings of the genetic and evolutionary computation conference (pp. 11–18). San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Birattari, M., Yuan, Z., Balaprakash, P., & Stützle, T. (2010). F-race and iterated f-race: an overview. In T. Bartz-Beielstein et al. (Eds.), Experimental methods for the analysis of optimization algorithms (pp. 311–336). Berlin: Springer.

    Chapter  Google Scholar 

  • Diwold, K., Aderhold, A., Scheidler, A., & Middendorf, M. (2011a). Performance evaluation of artificial bee colony optimization and new selection schemes. Memetic Computing, 3(3), 149–162.

    Article  Google Scholar 

  • Diwold, K., Beekman, M., & Middendorf, M. (2011b). Honeybee optimisation-an overview and a new bee inspired optimisation scheme. In B. K. Panigrahi et al. (Eds.), Handbook of swarm intelligence-concepts, principles and application, adaptation, learning, and optimization (Vol. 8, pp. 295–328). Berlin: Springer.

    Google Scholar 

  • El-Abd, M. (2011a). A hybrid ABC-SPSO algorithm for continuous function optimization. In Proceedings of IEEE symposium on swarm intelligence (pp. 1–6). Piscataway: IEEE Press.

    Google Scholar 

  • El-Abd, M. (2011b). Opposition-based artificial bee colony algorithm. In Proceedings of the genetic and evolutionary computation conference (pp. 109–116). New York: ACM.

    Google Scholar 

  • Eshelman, L. J., & Schaffer, J. D. (1993). Real-coded genetic algorithms and interval-schemata. In D. L. Whitley (Ed.), Foundation of genetic algorithms 2 (pp. 187–202). San Mateo: Morgan Kaufmann.

    Google Scholar 

  • Fister, I., Fister, I. Jr., Brest, J., & Zumer, V. (2012). Memetic artificial bee colony algorithm for large-scale global optimization. In Proceedings of IEEE Congress on evolutionary computation (pp. 1–8). Piscataway: IEEE Press.

    Google Scholar 

  • Gao, W., & Liu, S. (2011). Improved artificial bee colony algorithm for global optimization. Information Processing Letters, 111(17), 871–882.

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, W., Liu, S., & Huang, L. (2012). A global best artificial bee colony algorithm for global optimization. Journal of Computational and Applied Mathematics, 236(11), 2741–2753.

    Article  MathSciNet  MATH  Google Scholar 

  • Guo, P., Cheng, W., & Liang, J. (2011). Global artificial bee colony search algorithm for numerical function optimization. In Proceedings of international conference on natural computation (Vol. 3, pp. 1280–1283). Piscataway: IEEE Press.

    Google Scholar 

  • Herrera, F., Lozano, M., & Molina, D. (2010). Test suite for the special issue of Soft Computing on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. http://sci2s.ugr.es/eamhco/.

  • Hoos, H. H., & Stützle, T. (2005). Stochastic local search—foundations and applications. San Francisco: Morgan Kaufmann.

    MATH  Google Scholar 

  • Kang, F., Li, J., & Ma, Z. (2011). Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions. Information Sciences, 181(16), 3508–3531.

    Article  MathSciNet  MATH  Google Scholar 

  • Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization (Technical Report TR06). Computer Engineering Department, Erciyes University, Kayseri, Turkey.

  • Karaboga, D., & Akay, B. (2009). A survey: algorithms simulating bee swarm intelligence. Artificial Intelligence Review, 31(1–4), 61–85.

    Article  Google Scholar 

  • Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39(3), 459–471.

    Article  MathSciNet  MATH  Google Scholar 

  • Karaboga, D., & Basturk, B. (2008). On the performance of artificial bee colony (ABC) algorithm. Applied Soft Computing, 8(1), 687–697.

    Article  Google Scholar 

  • KhudaBukhsh, A. R., Xu, L., Hoos, H. H., & Leyton-Brown, K. (2009). SATenstein: automatically building local search SAT solvers from components. In Proceedings of international joint conferences on artificial intelligence (pp. 517–524). Menlo Park: AAAI Press.

    Google Scholar 

  • LaTorre, A., Muelas, S., & Peña, J. M. (2011). A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test. Soft Computing, 15(11), 2187–2199.

    Article  Google Scholar 

  • Lee, W. P., & Cai, W. T. (2011). A novel artificial bee colony algorithm with diversity strategy. In Proceedings of international conference on natural computation (Vol. 3, pp. 1441–1444). Piscataway: IEEE Press.

    Google Scholar 

  • Liao, T., Montes de Oca, M. A., Aydin, D., Stützle, T., & Dorigo, M. (2011). An incremental ant colony algorithm with local search for continuous optimization. In Proceedings of the genetic and evolutionary computation conference (pp. 125–132). New York: ACM.

    Google Scholar 

  • Liao, T., Aydın, D., & Stützle, T. (2013). Artificial bee colonies for continuous optimization: Experimental analysis and improvements. http://iridia.ulb.ac.be/supp/IridiaSupp2013-002.

  • López-Ibáñez, M., & Stützle, T. (2012). The automatic design of multi-objective ant colony optimization algorithms. IEEE Transactions on Evolutionary Computation, 16(6), 861–875.

    Article  Google Scholar 

  • López-Ibáñez, M., Dubois-Lacoste, J., Stützle, T., & Birattari, M. (2011). The irace package, iterated race for automatic algorithm configuration (Technical Report TR/IRIDIA/2011-004). IRIDIA, Université Libre de Bruxelles, Belgium.

  • Lozano, M., Molina, D., & Herrera, F. (2011). Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems. Soft Computing, 15(11), 2085–2087.

    Article  Google Scholar 

  • Ming, H., Baohui, J., & Xu, L. (2010). An improved bee evolutionary genetic algorithm. In Proceedings of IEEE international conference on intelligent computing and intelligent systems (Vol. 1, pp. 372–374). Piscataway: IEEE Press.

    Google Scholar 

  • Molina, D., Lozano, M., García-Martínez, C., & Herrera, F. (2010). Memetic algorithms for continuous optimisation based on local search chains. Evolutionary Computation, 18(1), 27–63.

    Article  Google Scholar 

  • Molina, D., Lozano, M., Sánchez, A., & Herrera, F. (2011). Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains. Soft Computing, 15(11), 2201–2220.

    Article  Google Scholar 

  • Montes de Oca, M. A. (2011). Incremental social learning in swarm intelligence systems. Ph.D. Thesis, Université Libre de Bruxelles, Brussels, Belgium.

  • Montes de Oca, M. A., Aydin, D., & Stützle, T. (2011). An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Computing, 15(11), 2233–2255.

    Article  Google Scholar 

  • Powell, M. J. D. (1964). An efficient method for finding the minimum of a function of several variables without calculating derivatives. Computer Journal, 7(2), 155–162.

    Article  MathSciNet  MATH  Google Scholar 

  • Rajasekhar, A., Abraham, A., & Pant, M. (2011). Levy mutated artificial bee colony algorithm for global optimization. In Proceedings of IEEE international conference on systems, man, and cybernetics (pp. 655–662). Piscataway: IEEE Press.

    Google Scholar 

  • Rechenberg, I. (1973). Evolutionsstrategie: optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart: Frommann-Holzboog.

    Google Scholar 

  • Rosenbrock, H. H. (1960). An automatic method for finding the greatest or least value of a function. Computer Journal, 3(3), 175–184.

    Article  MathSciNet  Google Scholar 

  • Sharma, T., & Pant, M. (2012). Enhancing scout bee movements in artificial bee colony algorithm. In Proceedings of the international conference on soft computing for problem solving, advances in intelligent and soft computing (Vol. 130, pp. 601–610). India: Springer.

    Google Scholar 

  • Sharma, T., Pant, M., & Bhardwaj, T. (2011). PSO ingrained artificial bee colony algorithm for solving continuous optimization problems. In Proceedings of international conference on computer applications and industrial electronics (pp. 108–112). Piscataway: IEEE Press.

    Google Scholar 

  • Smit, S. K., & Eiben, A. E. (2010). Beating the ‘world champion’ evolutionary algorithm via REVAC tuning. In Proceedings of IEEE Congress on evolutionary computation (pp. 1–8). Piscataway: IEEE Press.

    Google Scholar 

  • Stern, R., & Price, K. (1997). Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.

    Article  MathSciNet  Google Scholar 

  • Tseng, L. Y., & Chen, C. (2008). Multiple trajectory search for large scale global optimization. In Proceedings of IEEE Congress on evolutionary computation (pp. 3052–3059). Piscataway: IEEE Press.

    Google Scholar 

  • Wu, B., & Sh, F. (2011). Improved artificial bee colony algorithm with chaos. In Y. Yu et al. (Eds.), Communications in computer and information science: Vol. 158. Computer science for environmental engineering and EcoInformatics (pp. 51–56). Berlin: Springer.

    Chapter  Google Scholar 

  • Yan, X., Zhu, Y., & Zou, W. (2011). A hybrid artificial bee colony algorithm for numerical function optimization. In Proceedings of international conference on hybrid intelligent systems (pp. 127–132). Piscataway: IEEE Press.

    Google Scholar 

  • Zhong, Y., Lin, J., Ning, J., & Lin, X. (2011). Hybrid artificial bee colony algorithm with chemotaxis behavior of bacterial foraging optimization algorithm. In Proceedings of international conference on natural computation (Vol. 2, pp. 1171–1174). Piscataway: IEEE Press.

    Google Scholar 

  • Zhu, G., & Kwong, S. (2010). Gbest-guided artificial bee colony algorithm for numerical function optimization. Applied Mathematics and Computation, 217(7), 3166–3173.

    Article  MathSciNet  MATH  Google Scholar 

  • Zou, W., Zhu, Y., Chen, H., & Zhu, Z. (2010). Cooperative approaches to artificial bee colony algorithm. In Proceedings of international conference on computer application and system modeling (Vol. 9, pp. 44–48). Piscataway: IEEE Press.

    Google Scholar 

Download references

Acknowledgements

The research leading to the results presented in this paper has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 246939. This work was also supported by the META-X project, an Action de Recherche Concertée funded by the Scientific Research Directorate of the French Community of Belgium. Thomas Stützle acknowledges support from the Belgian F.R.S.-FNRS, of which he is a Research Associate. Tianjun Liao acknowledges a fellowship from the China Scholarship Council. We also acknowledge the detailed comments by the editor and the referees that helped to improve considerably the paper.

Author information

Authors and Affiliations

  1. IRIDIA, CoDE, Université Libre de Bruxelles (ULB), Brussels, Belgium

    Tianjun Liao & Thomas Stützle

  2. Computer Engineering Dept., Dumlupinar University, 43000, Kütahya, Turkey

    Doğan Aydın

Authors
  1. Tianjun Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Doğan Aydın
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Stützle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Stützle.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

11721_2013_88_MOESM1_ESM.pdf

Online supplementary material to artificial bee colonies for continuous optimization: experimental analysis and improvements (PDF 224 kB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liao, T., Aydın, D. & Stützle, T. Artificial bee colonies for continuous optimization: Experimental analysis and improvements. Swarm Intell 7, 327–356 (2013). https://doi.org/10.1007/s11721-013-0088-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11721-013-0088-5

Keywords

Search

Navigation