Analysis and Optimization of Truss Structures, Constrained ‎Handling using Genetic Algorithm

Document Type : Research Paper


1 Department of Mechanical Engineering, National Institute of Technology Durgapur, West Bengal, India

2 Department of Mechanical Engineering, University of Aveiro, Aveiro, Portugal


In this study, an attempt is made to minimize the weight of Howe roof and ten member-6 Node trusses, separately. Two constraints, maximum allowable deflection and maximum allowable member stresses have been considered. For the first truss, permissible deflection is not known from the literature; therefore, it is determined using the exhaustive search method. Once magnitudes of the constraints are identified, member cross-sectional areas are varied to get the optimal weight. Both the exhaustive search method and the genetic algorithm have been implemented for this purpose. During the optimization, members tending to form a string may be eliminated from the structure. Doing this, we could further reduce the weights of the trusses and even less than the minimum available in the literature. The second truss is an indeterminate structure, and Maxwell Betti reciprocal theorem is applied to calculate the member forces. Also, further reduction of members is made for this truss, keeping in mind that the truss becomes determinate with the decrease in the member(s).


Main Subjects

[1] Schmit, L.A., Miura, H., A new structural analysis/synthesis capability-ACCESS 1, AIAA Journal, 14(5), 1976, 661–671.
[2] Rizzi, P., Optimization of multi-constrained structures based on optimality criteria, Proc. of the 17th Structures, Structural Dynamics and Materials Conference, King of Prussia, PA, USA, 1976.
[3] Ringertz, U.T., On topology optimization of trusses, Engineering Optimization, 9(3), 1985, 209-218.
[4] Lee, K.S., Geem, Z.W., A new structural optimization method based on the harmony search algorithm, Computers and Structures, 82, 2004, 781–798.
[5] 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, 663–684.
[6] Camp, CV, Design of space trusses using big bang-big crunch optimization, Journal of Structural Engineering, 133(7), 2007, 999–1008.
[7] Kaveh, A., Shojaee, S., Optimal design of skeletal structures using ant colony optimization, International Journal for Numerical Methods in Engineering, 70, 2007, 563–581.
[8] Luh, G.C., Lin, C. Y., Optimal design of truss structures using ant algorithm, Structural and Multidisciplinary Optimization, 36, 2008, 365–379.  
[9] Wu, C.-Y., Tseng, K.-Y., Truss structure optimization using adaptive multi-population differential evolution, Structural and Multidisciplinary Optimization, 42, 2010, 575–590.
[10] Faramarzi, A., Afshar, M.H., Application of cellular automata to size and topology optimization of truss structures, Scientia Iranica, 19(3), 2012, 373–380.
[11] Li, L.J., Huang, Z.B., Liu, F., Wu, Q.H., A heuristic particle swarm optimizer for optimization of pin-connected structures, Computers and Structures, 85, 2007, 340–349.
[12] Li, L.J., Huang, Z.B., Liu, F., A heuristic particle swarm optimization method for truss structures with discrete variables, Computers and Structures, 87, 2009, 435–443.
[13] Kaveh, A., Bakhshpoori, T., Afshari, E., An efficient hybrid particle swarm and swallow swarm optimization algorithm, Computers and Structures, 143, 2014, 40–59.
[14] Kaveh, A., Bakhshpoori, T., A new meta-heuristic for continuous structural optimization: water evaporation optimization, Structural and Multidisciplinary Optimization, 54, 2016, 23–43.
[15] Fenton, M., McNally, C., Byrne, J., Hemberg, E., McDermott, J., O'Neill, M., Automatic innovative truss design using grammatical evolution, Automation in Construction, 39, 2014, 59–69.
[16] Assimi, H., Jamali, A., Zadeh, N. N., Sizing and topology optimization of truss structures using genetic programming, Swarm and Evolutionary Computation, 37, 2017, 90-103.
[17] Rajeev, S., Krishnamoorthy, CS, Discrete optimization of structures using genetic algorithms, Journal of Structural Engineering, 118(5), 1992, 1233–1250.
[18] Hajela, P., Lee, E. Lin, C.Y., Genetic algorithms in structural topology optimization, in M. Bledsoe, C. Soares (Eds.), Topology Design of Structures, NATO ASI Series, 1993, 117-133.
[19] Coello, C.A.C., Rudnick, M., Christiansen, A.D., Using genetic algorithm for the optimal design of trusses, Tools with Artificial Intelligence, 1994, 88–94.
[20] Erbatur, F., Hasancebi, O., Tutuncu, I., Kılıc, H., Optimal design of planar and space structures with a genetic algorithm, Computers and Structures, 75, 2000, 209–224.
[21] Deb, K., Gulati, S., Design of truss-structures for minimum weight using genetic algorithms, Finite Elements in Analysis and Design, 37, 2001, 447–465.
[22] Togan, V., Daloglu, A.T., An improved genetic algorithm with initial population strategy and self-adaptive member groupings, Computers and Structures, 86, 2008, 1204–1218.
[23] Talaslioglu, T., A new genetic algorithm methodology for design optimization of truss structures: bi-population-based genetic algorithm with enhanced interval search, Modelling and Simulation in Engineering, 2009, Article ID 615162.
[24] Dede, T., Bekiroglu, S., Ayvaz, Y., Weight minimization of trusses with a genetic algorithm, Applied Soft Computing, 11, 2011, 2565–2575.
[25] Moradi, A., Nafchi, A. M., Ghanbarzadeh, A., Multi-objective optimization of truss structures using Bees Algorithm, Scientia Iranica, 22(5), 2015, 1789-1800.
[26] Kaveh, A., Ghazaan, M.I., A new meta-heuristic algorithm: vibrating particles system, Scientia Iranica, 24(2), 2017, 551-566.
[27] Shakya, A., Nanakorn, P., Petprakob, W., A ground-structure-based representation with an element-removal algorithm for truss topology optimization, Structural and Multidisciplinary Optimization, 58, 2018, 657–675.
[28] Lieu, Q. X., Do, D.T.T. ,Lee, J., An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints, Computers and Structures, 95, 2018, 99-112.
[29] Parekh, T.D., Parmar, D., Yatitank, Analysis of Howe Roof Truss using Different Rise and Span, International Journal of Engineering Trends and Technology, 47(3), 2017, 146-147.