Document Type : Article

**Authors**

School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran

**Abstract**

This paper presents a new hybrid algorithm generated by combining advantageous features of the Imperialist Competitive Algorithm (ICA) and Biogeography Based Optimization (BBO) to create an effective search technique. Although the ICA performs fairly well in the exploration phase, it is less effective in the exploitation stage. In addition, its convergence speed is problematic in some instances. Meanwhile, the BBO method's migration operator strongly emphasizes local search to focus on promising solutions and finds the optimum solution more precisely. The combination of these two algorithms leads to a robust hybrid algorithm that has both exploratory and exploitative functionalities. The proposed hybrid algorithm is named Migration-Based Imperialist Competitive Algorithm (MBICA). To validate its performance, MBICA is used to optimize a variety of benchmark truss structures. Compared to some other methods, this algorithm converges to better or at least identical solutions by reducing the number of structural analyses. Finally, the results of the standard BBO, ICA, and other recently developed metaheuristic optimization methods are compared with the results of this study.

**Keywords**

References:

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27. Simon, D. "Biogeography-based optimization", IEEE Transactions on Evolutionary Computation, 12(6), pp. 702-13 (2008). DOI: 10.1109/TEVC.2008.919004.

28. Atashpaz-Gargari, E. and Lucas, C. "Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition", IEEE Congress on Evolutionary Computation: Ieee., pp. 4661-7 (2007).

29. Kaveh, A. and Bakhshpoori, T. "Metaheuristics: outlines, MATLAB codes and examples", Springer (2019). DOI: 10.1007/978-3-030-04067-3.

30. Talbi, E.-G. "A taxonomy of hybrid metaheuristics", Journal of Heuristics, 8(5), pp. 541-64 (2002). DOI: 10.1023/A:1016540724870.

31. Jalili, S., Hosseinzadeh, Y., and Taghizadieh, N. "A biogeography-based optimization for optimum discrete design of skeletal structures", Engineering Optimization, 48(9), pp. 1491-514 (2016). DOI: 10.1080/0305215X.2015.1115028.

32. Kaveh, A. and Talatahari, S. "Optimum design of skeletal structures using imperialist competitive algorithm", Computers & Structures, 88(21-22), pp. 1220- 9 (2010). DOI: 10.1016/j.compstruc.2010.06.011.

33. Saka, M. "Optimum design of pin-jointed steel structures with practical applications", Journal of Structural Engineering, 116(10), pp. 2599-620 (1990). DOI: 10.1061/(ASCE)0733-9445(1990)116:10(2599).

34. Kaveh, A. and Massoudi, M. "Multi-objective optimization of structures using charged system search", Scientia Iranica, 21(6), pp. 1845-60 (2014).

35. Kaveh, A. and Zaerreza, A. "Shuffled shepherd optimization method: a new meta-heuristic algorithm", Engineering Computations, 37(7), pp. 2357-89 (2020). DOI: 10.1108/ec-10-2019-0481.

36. Kaveh, A., Akbari, H., and Hosseini, S.M. "Plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems", Engineering Computations, 38(4), pp. 1554-606 (2020). DOI: 10.1108/ec-05-2020-0235.

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40. Talatahari, S., Kaveh, A., and Sheikholeslami, R. "Chaotic imperialist competitive algorithm for optimum design of truss structures", Structural and Multidisciplinary Optimization, 46(3), pp. 355-67 (2012). DOI: 10.1007/s00158-011-0754-4.

41. Talatahari, S., Kheirollahi, M., Farahmandpour, C., et al. "A multi-stage particle swarm for optimum design of truss structures", Neural Computing and Applications, 23(5), pp. 1297-309 (2013). DOI: 10.1007/s00521-012-1072-5.

42. Jalili, S. and Hosseinzadeh, Y. "Design optimization of truss structures with continuous and discrete variables by hybrid of biogeography-based optimization and differential evolution methods", The Structural Design of Tall and Special Buildings, 27(14), p. e1495 (2018). DOI: 10.1002/tal.1495.

43. Degertekin, S. "Improved harmony search algorithms for sizing optimization of truss structures", Computers & Structures, 92, pp. 229-41 (2012). DOI: 10.1016/j.compstruc.2011.10.022.

44. Jafari, M., Salajegheh, E., and Salajegheh, J. "An efficient hybrid of elephant herding optimization and cultural algorithm for optimal design of trusses", Engineering with Computers, 35(3), pp. 781-801 (2019). DOI: 10.1007/s00366-018-0631-5.

45. Kaveh, A. and Talatahar, S. "A hybrid particle swarm and ant colony optimization for design of truss structures", Asian Journal of Civil Engineering, 9(4), pp. 325-344 (2008).

46. Kaveh, A., Rahmani, P., and Eslamlou, A.D. "An efficient hybrid approach based on Harris Hawks optimization and imperialist competitive algorithm for structural optimization", Engineering with Computers, pp. 1-29, Pub Date: 2021-02-03. DOI: 10.1007/s00366- 020-01258-7.

47. Kaveh, A. and Talatahari, S. "A particle swarm ant colony optimization for truss structures with discrete variables", Journal of Constructional Steel Research, 65(8-9), pp. 1558-68 (2009). DOI: 10.1016/j.jcsr.2009.04.021.

48. Kaveh, A. and Talatahari, S. "A discrete big bangbig crunch algorithm for optimal design of skeletal structures", Asian Journal of Civil Engineering, 11(1), pp. 103-123 (2010).

49. Mortazavi, A. and Togan, V. "Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer", Structural and Multidisciplinary Optimization, 54(4), pp. 715-36 (2016). DOI: 10.1007/s00158-016-1449-7.

50. Kaveh, A. and Ilchi, G.M. "A hybrid ecbo and ubs algorithm for optimal design of skeletal structures", Asian Journal of Civil Engineering, 17(7), pp. 918-36 (2016).DOI: 10.24200/j30.2018.1369.

2. Kaveh, A., Advances in Metaheuristic Algorithms for Optimal Design of Structures, Springer Nature (2021). DOI: 10.1007/978-3-030-59392-6.

3. Holland, J.H. "Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence", MIT Press (1992).

4. Storn, R. and Price, H. "Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces", Journal of Global Optimization, 11(4), pp. 341-59 (1997). DOI: 10.1023/A:1008202821328.

5. Kennedy, J. and Eberhart, R. "Particle swarm optimization", Proceedings of ICNN'95-International Conference on Neural Networks: IEEE. pp. 1942-8 (1995).

6. Dorigo, M., Maniezzo, V., and Colorni, A. "Ant system: optimization by a colony of cooperating agents", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(1), pp. 29-41 (1996). DOI: 10.1109/3477.484436.

7. Erol, O.K. and Eksin, I. "A new optimization method: big bang-big crunch", Advances in Engineering Software, 37(2), pp. 106-11 (2006). DOI: 10.1016/j.advengsoft.2005.04.005.

8. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. "Optimization by simulated annealing", Science, 220(4598), pp. 671-80 (1983). DOI: 10.1126/science.220.4598.671.

9. Kaveh, A. and Talatahari, S. "A novel heuristic optimization method: charged system search", Acta Mechanica, 213(3), pp. 267-89 (2010). DOI: 10.1007/s00707-009-0270-4.

10. Kaveh, A. and Mahdavi, V.R. "Colliding bodies optimization: a novel meta-heuristic method", Computers & Structures, 139, pp. 18-27 (2014). DOI: 10.1016/j.compstruc.2014.04.005.

11. Kaveh, A. and Eslamlou, A.D., Metaheuristic Optimization Algorithms in Civil Engineering: New Applications, Springer Nature (2020). DOI: 10.1007/978-3- 030-45473-9.

12. Kaveh, A. and Rajabi, F. "Fuzzy-multi-mode resourceconstrained discrete time-cost-resource optimization in project scheduling using ENSCBO", Periodica Polytechnica Civil Engineering, 66(1), pp. 50-62 (2022). DOI: 10.3311/PPci.19145.

13. Kaveh, A., Rajabi, F., and Mirvalad, S. "Manyobjective optimization for construction project scheduling using non-dominated sorting differential evolution algorithm based on reference points", Scientia Iranica, A, 28(6), pp. 3112-33128 (2021). DOI: 10.24200/sci.2021.58952.5988.

14. Kaveh, A., Hamedani, K.B., and Kamalinejad, M. "An enhanced Forensic-Based Investigation algorithm and its application to optimal design of frequencyconstrained dome structures", Computers & Structures, 256, p. 106643 (2021). DOI: 10.1016/j.compstruc.2021.106643.

15. Azad, S.K., Aminbakhsh, S., and Shaban, S.S. "Multistage guided stochastic search for optimization and standardization of free-form steel double-layer grids", Structures: Elsevier. pp. 678-99 (2021).

16. Kaveh, A., Kamalinejad, M., Arzani, H., et al. "New enhanced colliding body optimization algorithm based on a novel strategy for exploration", Journal of Building Engineering, 43, p. 102553 (2021). DOI: 10.1016/j.jobe.2021.102553.

17. Azad, S.K. "Monitored convergence curve: a new framework for metaheuristic structural optimization algorithms, structural and multidisciplinary optimization", Structural and Multidisciplinary Optimization, 60(2), pp. 481-99 (2019). DOI: 10.1007/s00158-019- 02219-5.

18. Kaveh, A., Moghanni, R.M., and Javadi, S. "Chaotic optimization algorithm for performance-based optimization design of composite moment frames", Engineering with Computers, pp. 1-13 (2021). DOI: 10.1007/s00366-020-01244-z.

19. Azad, S.K. and Hasancebi, O. "Upper bound strategy for metaheuristic based design optimization of steel frames", Advances in Engineering Software, 57, pp. 19-32 (2013). DOI: 10.1016/j.istruc.2021.07.068.

20. Ting, T., Yang, X.-S., Cheng, S., et al. "Hybrid metaheuristic algorithms: past, present, and future", Recent Advances in Swarm Intelligence and Evolutionary Computation, pp. 71-83 (2015). DOI: 10.1007/978- 3-319-13826-8 4.

21. Jafari, M., Salajegheh, E., and Salajegheh, J. "Optimal design of truss structures using a hybrid method based on particle swarm optimizer and cultural algorithm", Structures: Elsevier. pp. 391-405 (2021).

22. Le, D.T., Bui, D.-K., Ngo, T.D., et al. "A novel hybrid method combining electromagnetism-like mechanism and fire y algorithms for constrained design optimization of discrete truss structures", Computers & Structures, 212, pp. 20-42 (2019).

DOI: 10.1016/j.compstruc.2018.10.017.

23. Lieu, Q.X., Do, D.T., and Lee, J. "An adaptive hybrid evolutionary fire y algorithm for shape and size optimization of truss structures with frequency constraints", Computers & Structures, 195, pp. 99- 112 (2018). DOI: 10.1016/j.compstruc.2017.06.016.

24. Sharma, S., Saha, A.K., and Lohar, G. "Optimization of weight and cost of cantilever retaining wall by a hybrid metaheuristic algorithm", Engineering with Computers, pp. 1-27 (Aug. 2022). DOI: 10.12989/gae.2021.24.3.237.

25. Talatahari, S., Gandomi, A.H., Yang, X.-S., et al. "Optimum design of frame structures using the eagle strategy with differential evolution", Engineering Structures, 91, pp. 16-25 (2015). DOI: 10.1016/j.engstruct.2015.02.026.

26. Kaveh, A. and Ilchi Ghazaan, M. "A new hybrid metaheuristic algorithm for optimal design of large-scale dome structures", Engineering Optimization, 50(2), pp. 235-52 (2018). DOI: 10.1080/0305215X.2017.1313250.

27. Simon, D. "Biogeography-based optimization", IEEE Transactions on Evolutionary Computation, 12(6), pp. 702-13 (2008). DOI: 10.1109/TEVC.2008.919004.

28. Atashpaz-Gargari, E. and Lucas, C. "Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition", IEEE Congress on Evolutionary Computation: Ieee., pp. 4661-7 (2007).

29. Kaveh, A. and Bakhshpoori, T. "Metaheuristics: outlines, MATLAB codes and examples", Springer (2019). DOI: 10.1007/978-3-030-04067-3.

30. Talbi, E.-G. "A taxonomy of hybrid metaheuristics", Journal of Heuristics, 8(5), pp. 541-64 (2002). DOI: 10.1023/A:1016540724870.

31. Jalili, S., Hosseinzadeh, Y., and Taghizadieh, N. "A biogeography-based optimization for optimum discrete design of skeletal structures", Engineering Optimization, 48(9), pp. 1491-514 (2016). DOI: 10.1080/0305215X.2015.1115028.

32. Kaveh, A. and Talatahari, S. "Optimum design of skeletal structures using imperialist competitive algorithm", Computers & Structures, 88(21-22), pp. 1220- 9 (2010). DOI: 10.1016/j.compstruc.2010.06.011.

33. Saka, M. "Optimum design of pin-jointed steel structures with practical applications", Journal of Structural Engineering, 116(10), pp. 2599-620 (1990). DOI: 10.1061/(ASCE)0733-9445(1990)116:10(2599).

34. Kaveh, A. and Massoudi, M. "Multi-objective optimization of structures using charged system search", Scientia Iranica, 21(6), pp. 1845-60 (2014).

35. Kaveh, A. and Zaerreza, A. "Shuffled shepherd optimization method: a new meta-heuristic algorithm", Engineering Computations, 37(7), pp. 2357-89 (2020). DOI: 10.1108/ec-10-2019-0481.

36. Kaveh, A., Akbari, H., and Hosseini, S.M. "Plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems", Engineering Computations, 38(4), pp. 1554-606 (2020). DOI: 10.1108/ec-05-2020-0235.

37. Hasancebi, O., C arbas, S., Dogan, E., et al. "Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures", Computers & Structures, 87(5-6), pp. 284-302 (2009). DOI: 10.1016/j.compstruc.2009.01.002.

38. Manual of steel construction. Allowable stress design. Chicago, Illinois, USA. 9th Ed, American Institute of Steel Construction (AISC) (1989).

39. Kaveh, A. and Talatahari, S. "Size optimization of space trusses using big bang-big crunch algorithm", Computers & Structures, 87(17-18), pp. 1129-40 (2009). DOI: 10.1016/j.compstruc.2009.04.011.

40. Talatahari, S., Kaveh, A., and Sheikholeslami, R. "Chaotic imperialist competitive algorithm for optimum design of truss structures", Structural and Multidisciplinary Optimization, 46(3), pp. 355-67 (2012). DOI: 10.1007/s00158-011-0754-4.

41. Talatahari, S., Kheirollahi, M., Farahmandpour, C., et al. "A multi-stage particle swarm for optimum design of truss structures", Neural Computing and Applications, 23(5), pp. 1297-309 (2013). DOI: 10.1007/s00521-012-1072-5.

42. Jalili, S. and Hosseinzadeh, Y. "Design optimization of truss structures with continuous and discrete variables by hybrid of biogeography-based optimization and differential evolution methods", The Structural Design of Tall and Special Buildings, 27(14), p. e1495 (2018). DOI: 10.1002/tal.1495.

43. Degertekin, S. "Improved harmony search algorithms for sizing optimization of truss structures", Computers & Structures, 92, pp. 229-41 (2012). DOI: 10.1016/j.compstruc.2011.10.022.

44. Jafari, M., Salajegheh, E., and Salajegheh, J. "An efficient hybrid of elephant herding optimization and cultural algorithm for optimal design of trusses", Engineering with Computers, 35(3), pp. 781-801 (2019). DOI: 10.1007/s00366-018-0631-5.

45. Kaveh, A. and Talatahar, S. "A hybrid particle swarm and ant colony optimization for design of truss structures", Asian Journal of Civil Engineering, 9(4), pp. 325-344 (2008).

46. Kaveh, A., Rahmani, P., and Eslamlou, A.D. "An efficient hybrid approach based on Harris Hawks optimization and imperialist competitive algorithm for structural optimization", Engineering with Computers, pp. 1-29, Pub Date: 2021-02-03. DOI: 10.1007/s00366- 020-01258-7.

47. Kaveh, A. and Talatahari, S. "A particle swarm ant colony optimization for truss structures with discrete variables", Journal of Constructional Steel Research, 65(8-9), pp. 1558-68 (2009). DOI: 10.1016/j.jcsr.2009.04.021.

48. Kaveh, A. and Talatahari, S. "A discrete big bangbig crunch algorithm for optimal design of skeletal structures", Asian Journal of Civil Engineering, 11(1), pp. 103-123 (2010).

49. Mortazavi, A. and Togan, V. "Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer", Structural and Multidisciplinary Optimization, 54(4), pp. 715-36 (2016). DOI: 10.1007/s00158-016-1449-7.

50. Kaveh, A. and Ilchi, G.M. "A hybrid ecbo and ubs algorithm for optimal design of skeletal structures", Asian Journal of Civil Engineering, 17(7), pp. 918-36 (2016).DOI: 10.24200/j30.2018.1369.

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