Reliability-Based Design Optimization of Trusses with Linked-Discrete Design Variables using the Improved Firefly Algorithm


  • N. M. Okasha Civil Engineering Department, University of Hail, Hail, Saudi Arabia


In this paper, an approach for conducting a Reliability-Based Design Optimization (RBDO) of truss structures with linked-discrete design variables is proposed. The sections of the truss members are selected from the AISC standard tables and thus the design variables that represent the properties of each section are linked. Latin hypercube sampling is used in the evaluation of the structural reliability. The improved firefly algorithm is used for the optimization solution process. It was found that in order to use the improved firefly algorithm for efficiently solving problems of reliability-based design optimization with linked-discrete design variables; it needs to be modified as proposed in this paper to accelerate its convergence.


Fierfly, RBDO, LHS, truss, linked-discrete


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P. Venkataraman, Applied Optimization with MATLAB Programming, John Wiley & Sons, Inc. Hoboken, NJ, 2009

J. S. Arora, M. W. Huang, C. C. Hsieh, “Methods for Optimization of Nonlinear Problems with Discrete Variables: a Review”, Structural Optimization, Vol. 8, No. 2/3, pp. 69-85, 1994 DOI:

A. Baghlani, M. H. Makiabadi, M. Sarcheshmehpour, “Discrete Optimum Design of Truss Structures by an Improved Firefly Algorithm”, Advances in Structural Engineering, Vol. 17, No. 10, pp. 1517-1530, 2014 DOI:

M. Alapati, “Discrete Optimization of Truss Structure Using Genetic Algorithm”, International Journal of Recent Development in Engineering and Technology, Vol. 3, No. 1, pp. 105-111, 2014

A. H. Gandomi, X. S. Yang, A. H. Alavi, “Mixed Variable Structural Optimization using Firefly Algorithm”, Computers and Structures, Vol. 89, No. 23/24, pp. 2325–2336, 2011 DOI:

S. Mathakari, P. Gardoni, “Reliability-Based Optimal Design of Electrical Transmission Towers Using Multi-Objective Genetic Algorithms”, Computer-Aided Civil and Infrastructure Engineering, Vol. 22, No. 4, pp. 282–292, 2007 DOI:

AISC Manual of Steel Construction, 14th Edition, American Institute of Steel Construction, Chicago, 2011

J. S. Arora, M. W. Huang, “Discrete Structural Optimization with Commercially Available Sections: a Review”, Journal of Structural and Earthquake Engineering, Vol. 13, No. 2, pp. 93-110, 1996

M. W. Huang, J. S. Arora, “Optimal Design of Steel Structures using Standard Sections”, Structural Optimization, Vol. 14, No. 1, pp. 24-37, 1997 DOI:

Y. Aoues, A. Chateauneuf, “Benchmark Study of Numerical Methods for Reliability-Based Design Optimization”, Structural and Multidisciplinary Optimization, Vol. 41, No. 2, pp. 277–294, 2010 DOI:

A. Strauss, T. Zimmermann, D. Lehky, D. Novak, Z. Kersner, “Stochastic Fracture-Mechanical Parameters for the Performance-Based Besign of Concrete Structures”, Structural Concrete, Vol. 15, No. 3, pp. 380-394, 2014 DOI:

N. M. Okasha, D. M. Frangopol, “Efficient Method Based on Optimization and Simulation for the Probabilistic Strength Computation of the Ship Hull”, Journal of Ship Research, Vol. 54, No. 4, pp. 1-13, 2010

N. M. Okasha, D. M. Frangopol, A. Deco, “Integration of Structural Health Monitoring in Life-Cycle Performance Assessment of Ship Structures Under Uncertainty”, Marine Structures, Vol. 3, No. 23, pp. 303-321, 2010 DOI:

K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, Wiley, New York, 2001

X. S. Yang, X. He, “Firefly Algorithm: Recent Advances and Applications”, International Journal of Swarm Intelligence, Vol. 1, No. 1, pp. 36–50, 2013 DOI:

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by Simulated Annealing’, Science, Vol. 220, No. 4598, pp. 671-680, 1983 DOI:

P. Thanedar, G. Vanderplaats, “Survey of Discrete Variable Optimization for Structural Design”, Journal of Structural Engineering, Vol. 121, No. 2, pp. 301–306, 1995 DOI:

K. Deep, K. P. Singh, M. L. Kansal, C. Mohan, “A real coded genetic algorithm for solving integer and mixed integer optimization problems”, Applied Mathematics and Computation, Vol. 212, No. 2, pp. 505–518, 2009 DOI:

J. C. McCormac, S. F. Csernak, Structural Steel Design, 5th Edition. Prentice Hall, Upper Saddle River, NJ, 2012

A. H. Ang, W. H. Tang, Probability Concepts in Engineering Planning and Design: Decision, Risk and Reliability, Volume II, John Wiley and Sons, NY, 1984

J. Farkas, K. Jarmai, Optimum Design of Steel Structures, Springer-Verlag, Berlin Heidelberg, 2013 DOI:

S. Rajeev, C. Krishnamoorthy, “Discrete Optimization of Structures Using Genetic Algorithms”, Journal of Structural Engineering, Vol. 118, No. 5, pp. 1233–1250, 1992 DOI:

R. Nakib, “Deterministic and Reliability-Based Optimization of Truss Bridges”, Computers and Structures, Vol. 65, No. 5, pp. 767-775, 1997 DOI:

MathWorks, Global Optimization Toolbox - User’s Guide, 2015

MathWorks, Optimization ToolboxTM User’s Guide, 2015


How to Cite

N. M. Okasha, “Reliability-Based Design Optimization of Trusses with Linked-Discrete Design Variables using the Improved Firefly Algorithm”, Eng. Technol. Appl. Sci. Res., vol. 6, no. 2, pp. 964–971, Apr. 2016.


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