Optimum structural design of spatial truss structures via migration-based imperialist competitive algorithm

Document Type : Article


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


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.


  1. References

    1. S Mirjalili, SM Mirjalili, A Lewis. Grey wolf optimizer, Advances in engineering software, 69, pp. 46-61 (2014). doi:10.1016/j.advengsoft.2013.12.007
    2. A Kaveh. Advances in Metaheuristic Algorithms for Optimal Design of Structures, Springer Nature (2021). doi:10.1007/978-3-030-59392-6
    3. JH Holland. Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, MIT press (1992).
    4. R Storn, K Price. 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. J Kennedy, R Eberhart. Particle swarm optimization. Proceedings of ICNN'95-international conference on neural networks: IEEE. pp. 1942-8 (1995).
    6. M Dorigo, V Maniezzo, A Colorni. 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. OK Erol, I Eksin. 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. S Kirkpatrick, CD Gelatt, MP Vecchi. Optimization by simulated annealing, science, 220(4598), pp. 671-80 (1983). doi:10.1126/science.220.4598.671
    9. A Kaveh, S Talatahari. A novel heuristic optimization method: charged system search, Acta Mechanica, 213(3), pp. 267-89 (2010). doi:10.1007/s00707-009-0270-4
    10. A Kaveh, VR Mahdavi. Colliding bodies optimization: a novel meta-heuristic method, Computers & Structures, 139, pp. 18-27 (2014). doi:10.1016/j.compstruc.2014.04.005
    11. A Kaveh, AD Eslamlou. Metaheuristic optimization algorithms in civil engineering: new applications, Springer Nature (2020). doi:10.1007/978-3-030-45473-9
    12. A Kaveh, F Rajabi. Fuzzy-multi-mode Resource-constrained 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. A Kaveh, F Rajabi, S Mirvalad. Many-objective optimization for construction project scheduling using non-dominated sorting differential evolution algorithm based on reference points, Scientia Iranica. (2021). doi:10.24200/sci.2021.58952.5988
    14. A Kaveh, KB Hamedani, M Kamalinejad. An enhanced Forensic-Based Investigation algorithm and its application to optimal design of frequency-constrained dome structures, Computers & Structures, 256, pp. 106643 (2021). doi:10.1016/j.compstruc.2021.106643
    15. SK Azad, S Aminbakhsh, SS Shaban. Multi-stage guided stochastic search for optimization and standardization of free-form steel double-layer grids. Structures: Elsevier. pp. 678-99 (2021).
    16. A Kaveh, M Kamalinejad, H Arzani, F Barzinpour. New enhanced colliding body optimization algorithm based on a novel strategy for exploration, Journal of Building Engineering, 43, pp. 102553 (2021). doi:10.1016/j.jobe.2021.102553
    17. SK Azad. Monitored convergence curve: a new framework for metaheuristic structural optimization algorithms, Structural and Multidisciplinary Optimization, 60(2), pp. 481-99 (2019). doi:10.1007/s00158-019-02219-5
    18. A Kaveh, RM Moghanni, S Javadi. 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. SK Azad, O Hasançebi. 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. T Ting, X-S Yang, S Cheng, K Huang. 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. M Jafari, E Salajegheh, J Salajegheh. Optimal design of truss structures using a hybrid method based on particle swarm optimizer and cultural algorithm. Structures: Elsevier. pp. 391-405 (2021).
    22. DT Le, D-K Bui, TD Ngo, Q-H Nguyen, H Nguyen-Xuan. A novel hybrid method combining electromagnetism-like mechanism and firefly 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. QX Lieu, DT Do, J Lee. An adaptive hybrid evolutionary firefly 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. S Sharma, AK Saha, G Lohar. Optimization of weight and cost of cantilever retaining wall by a hybrid metaheuristic algorithm, Engineering with Computers, pp. 1-27 (2021). doi:10.12989/gae.2021.24.3.237
    25. S Talatahari, AH Gandomi, X-S Yang, S Deb. 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. A Kaveh, M Ilchi Ghazaan. A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures, Engineering Optimization, 50(2), pp. 235-52 (2018). doi:10.1080/0305215X.2017.1313250
    27. D Simon. Biogeography-based optimization, IEEE transactions on evolutionary computation, 12(6), pp. 702-13 (2008). doi:10.1109/TEVC.2008.919004
    28. E Atashpaz-Gargari, C Lucas. Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. IEEE congress on evolutionary computation: Ieee. pp. 4661-7 (2007).
    29. A Kaveh, T Bakhshpoori. Metaheuristics: outlines, MATLAB codes and examples, Springer (2019). doi:10.1007/978-3-030-04067-3
    30. E-G Talbi. A taxonomy of hybrid metaheuristics, Journal of heuristics, 8(5), pp. 541-64 (2002). doi:10.1023/A:1016540724870
    31. S Jalili, Y Hosseinzadeh, N Taghizadieh. 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. A Kaveh, S Talatahari. 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. M Saka. 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. A Kaveh, M Massoudi. Multi-objective optimization of structures using charged system search, Scientia Iranica, 21(6), pp. 1845-60 (2014).
    35. A Kaveh, A Zaerreza. 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. A Kaveh, H Akbari, SM Hosseini. 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. O Hasançebi, S Çarbaş, E Doğan, F Erdal, M Saka. 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. A Kaveh, S Talatahari. 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. S Talatahari, A Kaveh, R Sheikholeslami. 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. S Talatahari, M Kheirollahi, C Farahmandpour, AH Gandomi. 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. S Jalili, Y Hosseinzadeh. 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), pp. e1495 (2018). doi:10.1002/tal.1495
    43. S Degertekin. 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. M Jafari, E Salajegheh, J Salajegheh. 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. A Kaveh, S Talatahar. A hybrid particle swarm and ant colony optimization for design of truss structures, 9(4), pp. 329-48 (2008).
    46. A Kaveh, P Rahmani, AD Eslamlou. An efficient hybrid approach based on Harris Hawks optimization and imperialist competitive algorithm for structural optimization, Engineering with Computers, pp. 1-29 (2021). doi:10.1007/s00366-020-01258-7
    47. A Kaveh, S Talatahari. 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. A Kaveh, S Talatahari. a discrete big bang-big crunchalgorithm for optimaldesign of skeletal structures, 11(1), pp. 103-22 (2010).
    49. A Mortazavi, V Toğan. 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. A Kaveh, GM Ilchi. a hybrid ecbo and ubs algorithm for optimal design of skeletal structures, 17(7), pp. 918-36 (2016). doi:10.24200/j30.2018.1369