Abstract
Performance comparison of meta-heuristics (MHs) is conducted for truss sizing design. Six traditional truss sizing design problems with mass objective function subject to displacement and stress constraints were employed for performance test. The test problems have two types with and without including buckling constraints. Eighteen self-adaptive MHs from literature are employed to tackle the truss sizing problems. The results from implementing the self-adaptive MHs are compared in terms of convergence rate and consistency. It is found that for the test problem without buckling constraints, the top two optimisers according to the statistical Wilcoxon rank sum tests are Success-History Based Adaptive Differential Evolution with Linear Population Size Reduction (L-SHADE) and Success-History Based Adaptive Differential Evolution (SHADE) while the top two optimiser for the test problems with buckling constraints is L-SHADE and L-SHADE with Eigenvector-Based Crossover and Successful-Parent-Selecting Framework (SPS-L-SHADE-EIG). The buckling constraints are significantly important and should be included to truss design subjected to static loads.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahrari, A. and Atai, A. A. (2013). “Fully stressed design evolution strategy for shape and size optimization of truss structures.” Computers & Structures, Vol. 123, pp. 58–67, DOI: 10.1016/j.compstruc.2013.04.013.
Ahrari, A., Atai, A. A., and Deb, K. (2015). “Simultaneous topology, shape and size optimization of truss structures by fully stressed design based on evolution strategy.” Engineering Optimization, Vol. 47, No. 8, pp. 1063–1084, DOI: 10.1080/0305215X.2014.947972.
Baluja, S. (1994). Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning, In Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning Ed CMU-CS-94-163, t.r. Carnagie Mellon University, Pittsburgh.
Baykasoğlu, A. and Ozsoydan, F. B. (2014). “An improved firefly algorithm for solving dynamic multidimensional knapsack problems.” Expert Systems with Applications, Vol. 41, No. 8, pp. 3712–3725, DOI: 10.1016/j.eswa.2013.11.040.
Beck, A., Ben-Tal, A., and Tetruashvili, L. (2010). “A sequential parametric convex approximation method with applications to nonconvex truss topology design problems.” Journal of Global Optimization, Vol. 47, No. 1, pp. 29–51, DOI: 10.1007/s10898-009-9456-5.
Bekdaş, G., Nigdeli, S. M., and Yang, X.-S. (2015). “Sizing optimization of truss structures using flower pollination algorithm.” Applied Soft Computing, Vol. 37, pp. 322–331, DOI: 10.1016/j.asoc.2015.08.037.
Bekdas, G., Nigdeli, S. M., and Türakin, O. H. (2017a). “Non-Linear programing for sizing optimization of truss structures.” International Journal of Theoretical and Applied Mechanics, Vol. 1, pp. 274–284.
Bekdas, G., Nigdeli, S. M., and Yang, X. S. (2017b). “Size optimization of truss structures employing flower pollination algorithm without grouping structural members.” International Journal of Theoretical and Applied Mechanics, Vol. 1, pp. 269–273.
Brest, J., Greiner, S., Boskovic, B., Mernik, M., and Zumer, V. (2006). “Self-Adapting control parameters in differential evolution: A comparative study on numerical benchmark problems.” Evolutionary Computation, IEEE Transactions on, Vol. 10, No. 6, pp. 646–657, DOI: 10.1109/TEVC.2006.872133.
Bureerat, S. (2011). Improved Population-Based Incremental Learning in Continuous Spaces, In Improved Population-Based Incremental Learning in Continuous Spaces Eds Gaspar-Cunha, A., Takahashi, R., Schaefer, G. & Costa, L. pp. 77–86. Springer Berlin Heidelberg, DOI: 10.1007/978-3-642-20505-7_6.
Bureerat, S. and Pholdee, N. (2015). “Optimal truss sizing using an adaptive differential evolution algorithm.” Journal of Computing in Civil Engineering, 04015019, DOI: 10.1061/(ASCE)CP.1943-5487.0000487#sthash.zn4UhHlF.dpuf.
Camp, C. V. and Farshchin, M. (2014). “Design of space trusses using modified teaching–learning based optimization.” Engineering Structures, Vols. 62–63, pp. 87–97, DOI: 10.1016/j.engstruct.2014.01.020.
Dede, T. and Ayvaz, Y. (2015). “Combined size and shape optimization of structures with a new meta-heuristic algorithm.” Applied Soft Computing, Vol. 28, pp. 250–258, DOI: 10.1016/j.asoc.2014.12.007
Degertekin, S. O. (2012). “Improved harmony search algorithms for sizing optimization of truss structures.” Computers & Structures, Vols. 92–93, pp. 229–241, DOI: 10.1016/j.compstruc.2011.10.022.
Degertekin, S. O. and Hayalioglu, M. S. (2013). “Sizing truss structures using teaching-learning-based optimization.” Computers & Structures, Vol. 119, pp. 177–188, DOI: 10.1016/j.compstruc.2012.12.011.
Degertekin, S. O., Lamberti, L., and Hayalioglu, M. S. (2017). “Heat transfer search algorithm for sizing optimization of truss structures.” Latin American Journal of Solids and Structures, Vol. 14, No. 3, pp. 373–397, DOI: 10.1590/1679-78253297.
Elsayed, S. M., Sarker, R. A., Essam, D. L., and Hamza, N. M. (2014). Testing united multi-operator evolutionary algorithms on the CEC2014 real-parameter numerical optimization, In Testing united multioperator evolutionary algorithms on the CEC2014 real-parameter numerical optimization pp. 1650–1657, DOI: 10.1109/CEC.2014. 6900308.
Flager, F., Adya, A., Haymaker, J., and Fischer, M. (2014). “A bi-level hierarchical method for shape and member sizing optimization of steel truss structures.” Computers & Structures, Vol. 131, pp. 1–11, DOI: 10.1016/j.compstruc.2013.10.004.
García-Martínez, C., Lozano, M., Herrera, F., Molina, D., and Sánchez, A. M. (2008). “Global and local real-coded genetic algorithms based on parent-centric crossover operators.” European Journal of Operational Research, Vol. 185, No. 3, pp. 1088–1113, DOI: 10.1016/j.ejor.2006. 06.043.
Gholizadeh, S. and Barzegar, A. (2012). “Shape optimization of structures for frequency constraints by sequential harmony search algorithm.” Engineering Optimization, Vol. 45, No. 6, pp. 627–646, DOI: 10.1080/0305215X.2012.704028.
Hajela, P. (1990). “Genetic search-An approach to the nonconvex optimization problem.” AIAA Journal, Vol. 28, No. 7, pp. 1205–1210, DOI: 10.2514/3.25195.
Hansen, N., Muller, S. D., and Koumoutsakos, P. (2003). “Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES).” Evol. Comput., Vol. 11, No. 1, pp. 1–18, DOI: 10.1162/106365603321828970.
Hosseini, K., Nodoushan, E. J., Barati, R., and Shahheydari, H. (2016). “Optimal design of labyrinth spillways using meta-heuristic algorithms.” KSCE Journal of Civil Engineering, Vol. 20, No. 1, pp. 468–477, DOI: 10.1007/s12205-015-0462-5.
Husseinzadeh Kashan, A. (2011). “An efficient algorithm for constrained global optimization and application to mechanical engineering design: League Championship Algorithm (LCA).” Computer-Aided Design, Vol. 43, No. 12, pp. 1769–1792, DOI: 10.1016/j.cad.2011. 07.003.
Jia, G., Wang, Y., Cai, Z., and Jin, Y. (2013). “An improved (μ+λ)-constrained differential evolution for constrained optimization.” Information Sciences, Vol. 222, pp. 302–322, DOI: 10.1016/j.ins. 2012.01.017.
Jung, J., Jayakrishnan, R., and Nam, D. (2015). “High coverage pointto-point transit: Hybrid evolutionary approach to local vehicle routing.” KSCE Journal of Civil Engineering, Vol. 19, No. 6, pp. 1882–1891, DOI: 10.1007/s12205-014-0069-2.
Kaveh, A. and Ilchi Ghazaan, M. (2015). “Hybridized optimization algorithms for design of trusses with multiple natural frequency constraints.” Advances in Engineering Software, Vol. 79, pp. 137–147, DOI: 10.1016/j.advengsoft.2014.10.001.
Kaveh, A. and Ilchi Ghazaan, M. (2016). “Optimal design of dome truss structures with dynamic frequency constraints.” Structural and Multidisciplinary Optimization, Vol. 53, No. 3, pp. 605–621, DOI: 10.1007/s00158-015-1357-2.
Kaveh, A. and Javadi, S.M. (2014). “Shape and size optimization of trusses with multiple frequency constraints using harmony search and ray optimizer for enhancing the particle swarm optimization algorithm.” Acta Mechanica, Vol. 225, No. 6, pp. 1595–1605, DOI: 10.1007/s00707-013-1006-z.
Kaveh, A. and Khayatazad, M. (2013). “Ray optimization for size and shape optimization of truss structures.” Computers & Structures, Vol. 117, pp. 82–94, DOI: 10.1016/j.compstruc.2012.12.010
Kaveh, A. and Mahdavi, V. R. (2015). “A hybrid CBO–PSO algorithm for optimal design of truss structures with dynamic constraints.” Applied Soft Computing, Vol. 34, pp. 260–273, DOI: 10.1016/j.asoc.2015.05.010.
Kaveh, A. and Talatahari, S. (2009). “Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures.” Computers and Structures, Vol. 87, Issues 5–6, pp. 267–283, DOI: 10.1016/j.compstruc.2009.01.003.
Kaveh, A. and Talatahari, S. (2010). “A novel heuristic optimization method: Charged system search.” Acta Mechanica, Vol. 213, No. 3, pp. 267–289, DOI: 10.1007/s00707-009-0270-4.
Kaveh, A. and Zolghadr, A. (2012). “Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability.” Computers & Structures, Vols. 102–103, pp. 14–27, DOI: 10.1016/j.compstruc.2012.03.016.
Kaveh, A. and Zolghadr, A. (2014). “Enhanced bat algorithm for optimal design of skeletal structure.” Asian Journal of Civil Engineering (Building and Housing), Vol. 15, pp. 179–212.
Kaveh, A., Bakhshpoori, T., and Afshari, E. (2014). “An efficient hybrid particle swarm and swallow swarm optimization algorithm.” Computers & Structures, Vol. 143, pp. 40–59, DOI: 10.1016/j.compstruc.2014. 07.012.
Kaveh, A., Sheikholeslami, R., Talatahari, S., and Keshvari-Ilkhichi, M. (2014). “Chaotic swarming of particles: A new method for size optimization of truss structures.” Advances in Engineering Software, Vol. 67, pp. 136–147, DOI: 10.1016/j.advengsoft.2013.09.006.
Khatibinia, M. and Yazdani, H. (2017). “Accelerated multi-gravitational search algorithm for size optimization of truss structures.” Swarm and Evolutionary Computation, in press, DOI: 10.1016/j.swevo.2017.07.001.
Lei, C., Hai-lin, L., Chaoda, P., and Shengli, X. (2015). “An improved covariance matrix leaning and searching preference algorithm for solving CEC 2015 benchmark problems.” In An improved covariance matrix leaning and searching preference algorithm for solving CEC 2015 benchmark problems, pp. 1041–1045, DOI: 10.1109/CEC. 2015.7257004.
Lei, C., Hai-lin, L., Zhe, Z., and Shengli, X. (2014). “An evolutionary algorithm based on Covariance Matrix Leaning and Searching Preference for solving CEC 2014 benchmark problems.” In An evolutionary algorithm based on Covariance Matrix Leaning and Searching Preference for solving CEC 2014 benchmark problems, pp. 2672–2677, DOI: 10.1109/CEC.2014.6900594.
Li, J.-P. (2014). “Truss topology optimization using an improved species-conserving genetic algorithm.” Engineering Optimization, Vol. 47, No. 1, pp. 107–128, DOI: 10.1080/0305215X.2013.875165
Liang, J. J., Qin, A. K., Suganthan, P. N., and Baskar, S. (2006). “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions.” IEEE Transactions on Evolutionary Computation, Vol. 10, No. 3, pp. 281–295, DOI: 10.1109/TEVC.2005.857610.
Mallipeddi, R., Suganthan, P. N., Pan, Q. K., and Tasgetiren, M. F. (2011). “Differential evolution algorithm with ensemble of parameters and mutation strategies.” Applied Soft Computing, Vol. 11, No. 2, pp. 1679–1696, DOI: 10.1016/j.asoc.2010.04.024.
Meng, T. and Pan, Q.-K. (2017). “An improved fruit fly optimization algorithm for solving the multidimensional knapsack problem.” Applied Soft Computing, Vol. 50, pp. 79–93, DOI: 10.1016/j.asoc.2016.11.023.
Miguel, L. F. F. and Fadel Miguel, L. F. (2012). “Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms.” Expert Systems with Applications, Vol. 39, No. 10, pp. 9458–9467, DOI: 10.1016/j.eswa. 2012.02.113.
Mortazavi, A. and Toğan, V. (2017). “Sizing and layout design of truss structures under dynamic and static constraints with an integrated particle swarm optimization algorithm.” Applied Soft Computing, Vol. 51, pp. 239–252, DOI: 10.1016/j.asoc.2016.11.032.
Muthiah-Nakarajan, V. and Noel, M. M. (2016). “Galactic Swarm Optimization: A new global optimization metaheuristic inspired by galactic motion.” Applied Soft Computing, Vol. 38, pp. 771–787, DOI: 10.1016/j.asoc.2015.10.034.
Nariman, N. A. (2016). “Aerodynamic stability parameters optimization and global sensitivity analysis for a cable stayed Bridge.” KSCE Journal of Civil Engineering, pp. 1–16, DOI: 10.1007/s12205-016-0962-y.
Noilublao, N. and Bureerat, S. (2011). “Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms.” Computers & Structures, Vol. 89, Nos. 23–24, pp. 2531–2538, DOI: 10.1016/j.compstruc. 2011.08.010.
Noilublao, N. and Bureerat, S. (2013). “Simultaneous topology, shape, and sizing optimisation of plane trusses with adaptive ground finite elements using MOEAs.” Mathematical Problems in Engineering, Vol. 2013, Article ID 838102, 9 pages, DOI: 10.1155/2013/838102.
Pholdee, N. and Bureerat, S. (2013). “Hybridisation of real-code population-based incremental learning and differential evolution for multiobjective design of trusses.” Information Sciences, Vol. 223, pp. 136–152, DOI: 10.1016/j.ins.2012.10.008.
Pholdee, N. and Bureerat, S. (2014a). “Hybrid real-code populationbased incremental learning and approximate gradients for multiobjective truss design. Engineering Optimization, Vol. 46, No. 8, pp. 1032–1051, DOI: 10.1080/0305215X.2013.823194.
Pholdee, N. and Bureerat, S. (2014b). “Comparative performance of meta-heuristic algorithms for mass minimisation of trusses with dynamic constraints.” Advances in Engineering Software, Vol. 75, pp. 1–13, DOI: 10.1016/j.advengsoft.2014.04.005.
Qin, A. K., Huang, V. L., and Suganthan, P. N. (2009). “Differential evolution algorithm with strategy adaptation for global numerical optimization.” IEEE Transactions on Evolutionary Computation, Vol. 13, No. 2, pp. 398–417, DOI: 10.1109/TEVC.2008.927706.
Rao, R. V., Savsani, V. J., and Vakharia, D. P. (2011). “Teaching–learningbased optimization: A novel method for constrained mechanical design optimization problems.” Computer-Aided Design, Vol. 43, No. 3, pp. 303–315, DOI: 10.1016/j.cad.2010.12.015.
Rashedi, E., Nezamabadi-pour, H., and Saryazdi, S. (2009). “GSA: A Gravitational Search Algorithm.” Information Sciences, Vol. 179, No. 13, pp. 2232–2248, DOI: 10.1016/j.ins.2009.03.004.
Richardson, J., Adriaenssens, S., Bouillard, P., and Filomeno Coelho, R. (2012). “Multiobjective topology optimization of truss structures with kinematic stability repair.” Structural and Multidisciplinary Optimization, Vol. 46, No. 4, pp. 513–532, DOI: 10.1007/s00158-012-0777-5.
Richardson, J.N., Coelho, R. F., and Adriaenssens, S. (2016). “A unified stochastic framework for robust topology optimization of continuum and truss-like structures.” Engineering Optimization, Vol. 48, No. 2, pp. 334–350, DOI: 10.1080/0305215X.2015.1011152.
Sallam, K. M., Sarker, R. A., Essam, D. L., and Elsayed, S. M. (2015). “Neurodynamic differential evolution algorithm and solving CEC2015 competition problems.” In Neurodynamic differential evolution algorithm and solving CEC2015 competition problems, pp. 1033–1040, DOI: 10.1109/CEC.2015.7257003.
Sheikholeslami, R., Khalili, B. G., Sadollah, A., and Kim, J. (2016). “Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy.” KSCE Journal of Civil Engineering, Vol. 20, No. 6, pp. 2428–2438, DOI: 10.1007/s12205-015-1163-9.
Shu-Mei, G., Tsai, J. S. H., Chin-Chang, Y., and Pang-Han, H. (2015). “A self-optimization approach for L-SHADE incorporated with eigenvector-based crossover and successful-parent-selecting framework on CEC 2015 benchmark set.” Evolutionary Computation (CEC), 2015 IEEE Congress on, pp. 1003–1010, DOI: 10.1109/CEC.2015. 7256999.
Stolpe, M. and Svanberg, K. (2001). “On the trajectories of the epsilonrelaxation approach for stress-constrained truss topology optimization.” Structural and Multidisciplinary Optimization, Vol. 21, No. 2, pp. 140–151, DOI: 10.1007/s001580050178.
Talaei, A. S., Nasrollahi, A., and Ghayekhloo, M. (2016). “An automated approach for optimal design of prestressed concrete slabs using PSOHS.” KSCE Journal of Civil Engineering, pp. 1–10, DOI: 10.1007/s12205-016-1126-9, DOI: 10.1007/s12205-016-1126-9.
Tan, Y. and Zhu, Y. (2010). Fireworks Algorithm for Optimization, In Fireworks Algorithm for Optimization Eds Tan, Y., Shi, Y. & Tan, K. pp. 355–364. Springer Berlin Heidelberg.
Tanabe, R. and Fukunaga, A. (2013). “Evaluating the performance of SHADE on CEC 2013 benchmark problems.” Evolutionary Computation (CEC), 2013 IEEE Congress on, pp. 1952–1959, DOI: 10.1109/CEC.2013.6557798.
Tanabe, R. and Fukunaga, A. S. (2014). “Improving the search performance of SHADE using linear population size reduction.” Evolutionary Computation (CEC), 2014 IEEE Congress on, pp. 1658–1665, DOI: 10.1109/CEC.2014.6900380.
Teh, Y. S. and Rangaiah, G. P. (2003). “Tabu search for global optimization of continuous functions with application to phase equilibrium calculations.” Computers & Chemical Engineering, Vol. 27, No. 11, pp. 1665–1679, DOI: 10.1016/S0098-1354(03)00134-0.
Wang, Y., Cai, Z., and Zhang, Q. (2012). “Enhancing the search ability of differential evolution through orthogonal crossover.” Information Sciences, Vol. 185, No. 1, pp. 153–177, DOI: 10.1016/j.ins.2011.09.001.
Yang, B., Zhang, Q., and Li, H. (2015). “Solving truss topological optimization with discrete design variables via swarm intelligence.” KSCE Journal of Civil Engineering, Vol. 19, No. 4, pp. 952–963, DOI: 10.1007/s12205-015-0501-2.
Yang, B., Zhang, Q., and Zhou, Z. (2015). “Solving truss topological optimization via Swarm Intelligence.” KSCE Journal of Civil Engineering, Vol. 19, No. 7, pp. 1962–1972, DOI: 10.1007/s12205-015-0218-2.
Yang, X.-S. and Deb, S. (2010). “Engineering optimisation by cuckoo search.” International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 1, No. 4, pp. 330–343, DOI: 10.1504/IJMMNO.2010.03543.
Yang, X. S., and Hossein Gandomi, A. (2012). “Bat algorithm: a novel approach for global engineering optimization.” Engineering Computations, Vol. 29, No. 5, pp. 464–483, DOI: 10.1108/02644401211235834.
Yong, W. and Zixing, C. (2012). “Combining multiobjective optimization with differential evolution to solve constrained optimization problems.” IEEE Transactions on Evolutionary Computation, Vol. 16, No. 1, pp. 117–134, DOI: 10.1109/TEVC.2010.2093582.
Yong, W., Zixing, C., and Qingfu, Z. (2011). “Differential evolution with composite trial vector generation strategies and control parameters.” IEEE Transactions On Evolutionary Computation, Vol. 15, No. 1, pp. 55–66, DOI: 10.1109/TEVC.2010.2087271.
Zhang, J. and Sanderson, A.C. (2009). “JADE: Adaptive differential evolution with optional external archive.” IEEE Transactions on Evolutionary Computation, Vol. 13, No. 5, pp. 945–958, DOI: 10.1109/TEVC.2009.2014613.
Zhao, H., Zhao, M., and Zhu, C. (2016). “Reliability-based optimization of geotechnical engineering using the artificial bee colony algorithm.” KSCE Journal of Civil Engineering, Vol. 20, No. 5, pp. 1728–1736, DOI: 10.1007/s12205-015-0117-6.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pholdee, N., Bureerat, S. A Comparative Study of Eighteen Self-adaptive Metaheuristic Algorithms for Truss Sizing Optimisation. KSCE J Civ Eng 22, 2982–2993 (2018). https://doi.org/10.1007/s12205-017-0095-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-017-0095-y