A Hybrid Particle Swarm Optimization and Genetic Algorithm for Truss Structures with Discrete Variables

Document Type : Research Paper


1 Department of Civil Engineering, Lorestan University, Lorestan, Khorramabad, Iran

2 Department of Civil Engineering, University of Tabriz, Tabriz, Iran


A new hybrid algorithm of Particle Swarm Optimization and Genetic Algorithm (PSOGA) is presented to get the optimum design of truss structures with discrete design variables. The objective function chosen in this paper is the total weight of the truss structure, which depends on upper and lower bounds in the form of stress and displacement limits. The Particle Swarm Optimization basically modeled the social behavior of birds on the basis of the fact that Individual birds exchange information about their position, velocity, fitness, and on the basis that the behavior of the flock is then influenced to increase the probability of migration to other regions with high fitness. One of the problems of PSO is that it is easily trapped at the local point due to its non-uniform movement. The present study uses the mutation, random selection, and reproduction to reach the best genetic algorithm with the operators of natural genetics. Therefore, only identical chromosomes or particles can be converged. In other words, PSO and GA algorithm goes from one point in the search space to another point, interacting with each other. In this way, this helps them to find the optimum design by means of deterministic and probabilistic rules. The present study merged the two algorithms together in order to design several benchmark truss structures, and then the results of the new algorithm compared to those of other evolutionary optimization methods.


Main Subjects

[1] Rajeev, S., Krishnamoorthy, C.S., Discrete optimization of structures suing Genetic Algorithm. Journal of Structural Engineering, 118, 1992, 1233-1250.
[2] Cao, G., Optimized design of framed structures using a genetic algorithm. PhD thesis, The University of Memphis, TN, 1996.
[3] Kennedy, J., Eberhart, R., Particle swarm optimization. Proceedings of IEEE international conference on neural networks. 1995. p. 1942–48.
[4] Lee, K.S., Geem, Z.W., A new structural optimization method based on the harmony search algorithm. Computers & Structures, 82(9–10), 2004, 781–98. 
[5] Dorigo, M., Optimization, learning and natural algorithms. PhD thesis, Dip. Elettronica e Informazione, Politecnico di  Milano, Italy; 1992.
[6] Kaveh, A., Talatahari, S., A novel heuristic optimization method: charged system search. Acta Mechanica, 213, 2010, 267–289.
[7] Erol, O.K., Eksin, I., A new optimization method: big bang–big crunch. Advances in Engineering Software, 37, 2006, 106–11.
[8] Kaveh, A., Talatahari, S., Size optimization of space trusses using big bang–big crunch algorithm. Computers & Structures, 87(17–18), 2009, 1129–40.
[9] Sonmez, M., Artificial bee colony algorithm for optimization of truss structures. Applied Soft Computing, 11(2), 2011, 2406–18.
[10] Li, L.J., Huang, Z.B., Liu, F., Wu, Q.H., A heuristic particle swarm optimizer for optimization of pin connected structures. Computers & Structures, 85(7–8), 2007, 340–9.
[11] Kaveh, A., Talatahari, S., Hybrid Algorithm of Harmony Search, Particle Swarm and Ant Colony for Structural Design Optimization. Computers & Structures, 3, 2009, 642-03450.
[12] Hasancebi, O., Erbatur, F., Layout optimization of trusses using improved GA methodologies. Acta Mechanica, 146, 2001, 87–107.
[13] Camp, C.V., Bichon, B.J., Design of space trusses using ant colony optimization. Journal of Structural Engineering, 130(5), 2004, 741–51.
[14] Camp, C.V., Design of space trusses using big bang–big crunch optimization. Journal of Structural Engineering, 133(7), 2007, 999–1008.
[15] Camp, C.V., Farshchin, M., Design of space trusses using modified teaching–learning based optimization. Engineering Structures, 62–63, 2014, 87–97.
[16] Mahfouz, S.Y., Design optimization of structural steelwork. Ph.D. thesis, Department of Civil and Environmental Engineering, University of Bradford, United Kingdom, 1999.
[17] Barbosa, H.J.C., Lemonge A.C.C., Borges, C.C.H., A genetic algorithm encoding for cardinality constraints and automatic variable linking in structural optimization. Engineering Structures, 30(12), 2008, 3708–23.
[18] Wu, S.J., Chow, P.T., Steady-state genetic algorithms for discrete optimization of trusses. Computers & Structures, 56(6), 1995, 97991.
[19] Lee, K.S., Geem, Z.W., Lee, S.H., Bae, K.W., The harmony search heuristic algorithm for discrete structural optimization. Engineering Optimization, 37(7), 2005, 663:84.
[20] Li, L.J., Huang, Z.B., Liu, F., A heuristic particle swarm optimization method for truss structures with discrete variables. Computers and Structures, 87(78), 2009, 435:43.
[21] Kaveh, A., Talatahari, S., A particle swarm ant colony optimization for truss structures with discrete variables. Journal of Constructional Steel Research, 65, 2009, 1558-1568
[22] Kaveh, A. Talatahari, S., Hybrid Algorithm of Harmony Search, Particle Swarm and Ant Colony for Structural Design Optimization. Studies in Computational Intelligence, 2009, 159-198.
[23] Meshki, H., Joghataie, A., Structural optimization by spherical interpolation of objective function and constraints. Scintia Iranica, 23(2), 2016, 548-557.
[24] Kaveh, A., Ilchi, M., Computer codes for colloding bodies optimization and its enhanced version. International Journal of Optimization in Civil Engineering, 4(3), 2014, 321-339.
[25] Kaveh, A., Ilchi, M., A new meta-heuristic algorithm: Vibrating particles system. Scientia Iranica, 24, 2017, 551-566.
[26] Gandomi, A.H., Alavi, A.H., Krill herd: A new bio-inspired optimization algorithm. Communications in Nonlinear Science and Numerical Simulation, 17, 2012, 4831–4845.
[27] Mirjalili, S., Lewis, A., The whale optimization algorithm. Advance Engineering Software, 95, 2016, 51-67.
[28] Cheng, M-.Y., Prayogo, D., Wu, Y-.W., Marcellinus Lukito, M., A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure. Automation in Construction, 69, 2016, 21-33.
[29] Tuo, S., Yong, L., Deng, F., Li, Y., Lin, Y., Lu, Q., A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for complex high-dimensional optimization problems. Plos One, 12(4), 2017, 10-1371.
[30] Ouyang, H.B., Gao, L.Q., Kong, X.Y., Zou, D.X., Li, S., Teaching-learning based optimization with global crossover for global optimization problems. Applied Mathematics and Computation, 265, 2015, 533–556.
[31] Kaveh, A., Rahami, H., Analysis, design and optimization of structures using force method and genetic algorithm. International Journal for Numerical Methods in Engineering, 65, 2016, 1570-1584.
[32] Sadollah, A., Eskandar, H., Bahreininejad, A., Kim, J.H., Water cycle, mine blast and improved mine blast algorithms for discrete sizing optimization of truss structures. Computers & Structures, 149, 2015, 1-16.
[33] Mortazavi, A., Toğan, V., Nuhoğlu, A., An integrated particle swarm optimizer for optimization of truss structures with discrete variables. Structural Engineering and Mechanics, 61, 2017, 359-370.