Structural and Multidisciplinary Optimization

, Volume 43, Issue 1, pp 85–97 | Cite as

Discrete optimum design of truss structures using artificial bee colony algorithm

  • Mustafa Sonmez
Research Paper


Over the past few years, swarm intelligence based optimization techniques such as ant colony optimization and particle swarm optimization have received considerable attention from engineering researchers and practitioners. These algorithms have been used in the solution of various engineering problems. Recently, a relatively new swarm based optimization algorithm called the Artificial Bee Colony (ABC) algorithm has begun to attract interest from researchers to solve optimization problems. The aim of this study is to present an optimization algorithm based on the ABC algorithm for the discrete optimum design of truss structures. The ABC algorithm is a meta-heuristic optimization technique that mimics the process of food foraging of honeybees. Originally the ABC algorithm was developed for continuous function optimization problems. This paper describes the modifications made to the ABC algorithm in order to solve discrete optimization problems and to improve the algorithm’s performance. In order to demonstrate the effectiveness of the modified algorithm, four structural problems with up to 582 truss members and 29 design variables were solved and the results were compared with those obtained using other well-known meta-heuristic search techniques. The results demonstrate that the ABC algorithm is very effective and robust for the discrete optimization designs of truss structural problems.


Artificial bee colony Discrete optimization Space truss C# programming 



Grateful thanks to Prof. Mehmet Polat Saka and Prof. Oguzhan Hasançebi–Middle East Technical University, Ankara, Turkey for providing additional information concerning Example 4.


  1. AISC, American Institute of Steel Construction (1999) Manual of steel construction: load and resistance factor design, 2nd end, vol I. Chicago, ILGoogle Scholar
  2. Arora JS (2002) Methods for discrete variable structural optimization. In: Burns SA (ed) Recent advances in optimal structural design. Technical committee on optimal structural design. ASCE, Reston, VA, pp 1–35Google Scholar
  3. Bonabeau E, Dorigo M, Theraulaz G (1999) Swarm intelligence: from natural to artificial systems. Oxford University Press, New YorkzbMATHGoogle Scholar
  4. Camp CV, Bichon BJ (2004) Design of space trusses using ant colony optimization. J Struct Eng, ASCE 130:741–751CrossRefGoogle Scholar
  5. Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: Proceeding of ECAL91- European conference on artificial life. Paris, France, Elsevier Pub, pp 134–142Google Scholar
  6. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4): 311–338zbMATHCrossRefGoogle Scholar
  7. Erbatur F, Hasancebi O, Tutuncu I, Kılıc H (2000) Optimum design of planar and space structures with genetic algorithms. Comput Struct 75:209–224CrossRefGoogle Scholar
  8. Hasancebi O, Çarbaş S, Doğan E, Erdal F, Saka MP (2009) Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures. Comput Struct 87:284–302CrossRefGoogle Scholar
  9. Honey Bee Biology (2010) Texas A&M University. Accessed 2 June 2010
  10. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report, TR06, Erciyes UniversityGoogle Scholar
  11. Karaboga D (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915CrossRefGoogle Scholar
  12. Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: LNCS: advances in soft computing: foundations of fuzzy logic and soft computing, vol 4529/2007. Springer, IFSA, pp 789–798CrossRefGoogle Scholar
  13. Karaboga D, Basturk B (2008) On the performance of artificial bee Colony (ABC). Applied Soft Computing 8:687–697CrossRefGoogle Scholar
  14. Karaboga D, Basturk B (2009) A survey: algorithms simulating bee swarm intelligence. Artif Intell Rev 31:61–85. doi: 10.1007/s10462-009-9127-4 CrossRefGoogle Scholar
  15. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, vol 4. IEEE Press, pp 1942–1948Google Scholar
  16. Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Kaufmann, San FranciscoGoogle Scholar
  17. Kripka M (2004) Discrete optimization of trusses by simulated annealing. J Braz Soc Mech Sci Eng XXVI:170–173Google Scholar
  18. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798CrossRefGoogle Scholar
  19. Lemmens N, Jong S, Tuyls K, Nowe A (2007) A bee algorithm for multi-agent systems: recruitment and navigation combined. In: Proceeding of ALAG 2007, an AAMAS’07 workshop. Honolulu, HawaiiGoogle Scholar
  20. Li LJ, Huang ZB, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87:435–444CrossRefGoogle Scholar
  21. Ministry of Agriculture and Lands of British Colombia (2010) Apiary fact sheets. Accessed 2 June 2010
  22. Moradi S, Fatahi L, Raz P (2009) Finite element model updating using bees algorithm. Struc Multidisc Optim 42(2). doi: 10.1007/s00158-010-0492-z
  23. Pham DT, Granbarzadeh A, Koç E, Otri S, Rahim S, Zaidi M (2006a) The bee algorithm – a novel tool for complex optimization problems. In: Innovation production machines and system virtual conference. Accessed 2 June 2010
  24. Pham DT, Koç E, Granbarzadeh A, Otri S (2006b) Optimization of the weight of multi-layered perceptrons using the bees algorithm. In: Cagıl G, Kubat C, Oztemel E (eds) Procedings of 5th international symposium of intelligence manufacturing systems, IMS 2006. Sakarya, TurkeyGoogle Scholar
  25. Rajeev S, Krishnamoorthy CS (1992) Discrete optimization of structures using genetic algorithms. J Struct Eng, ASCE 118(5):1233–1251CrossRefGoogle Scholar
  26. Teodorovic D (2009) Bee colony optimization (BCO). In: Lim CP et al (eds) Innovations in swarm intelligence, SCI 248. Springer, Heidelberg, pp 39–60CrossRefGoogle Scholar
  27. Teodorovic D, Orco MD (2005) Bee colony optimization-a comparative learning approach to computer transportation problems. In: Advanced or an IA methods in transportation, pp 51–60Google Scholar
  28. Yang X (2005) Engineering optimization via nature-inspired virtual bee algorithms. In: Mira J, Alvarez JR (eds) IWINAC 2005. LNCS, vol 3562. Springer-Verlag Berlin, Heidelberg, pp 317–323Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Civil Engineering, School of EngineeringAksaray UniversityAksarayTurkey

Personalised recommendations