A Fuzzy Programming Technique for Solving Multi-objective Structural Problem

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Samir Deya 1,* Tapan Kumar Roy 2

1. Department of Mathematics, Asansol Engineering College, Asansol-713305, West Bengal, India

2. Department of Mathematics, Indian Institute of Engineering Science and Technology, Howrah-711103, West Bengal, India.

* Corresponding author.

DOI: https://doi.org/10.5815/ijem.2014.05.03

Received: 10 Sep. 2014 / Revised: 8 Oct. 2014 / Accepted: 21 Nov. 2014 / Published: 29 Dec. 2014

Index Terms

Structural Optimization, Fuzzy Optimization, Generalized fuzzy number


This paper proposes a new fuzzy multi-objective optimization approach to solve a multi-objective nonlinear programming problem in context of a structural design. We have been developed a multi-objective structural problem of a planar truss structural model in fuzzy environment. Here, the objectives are (i) to minimize weight of the structure and (ii) to minimize the vertical deflection at loading point. In this model, the design variables are the cross-section of the truss members and the constraints are the stresses in members. This approach is used to solve the structural model under uncertainty based on different operator. A numerical illustration is given to support our approach.

Cite This Paper

Samir Deya, Tapan Kumar Roy,"A Fuzzy Programming Technique for Solving Multi-objective Structural Problem", IJEM, vol.4, no.5, pp.24-42, 2014. DOI: 10.5815/ijem.2014.05.03


[1]Wang,G.Y.,Wang, W.Q., " Fuzzy optimum design of structure." Engineering Optimization 1985; 8: 291-300.

[2]L. A. Zadeh, Fuzzy set, Information and Control 1965; 8(3): 338-353.

[3]R.E. Bellman and L.A. Zadeh, "Decision-making in a fuzzy environment," Management Science 1970; 17(4): B141-B164.

[4]Zimmermann, H.J., "fuzzy linear programming with several objective function" Fuzzy sets and systems 1978; 1: 45-55.

[5]Xu, C. "Fuzzy optimization of structures by the two-phase method", Computer and Structure 1989; 31(4): 575–580.

[6]Yeh, Y.C, and Hsu, D.S. "Structural optimization with fuzzy parameters". Computer and Structure 1990; 37(6): 917–924.

[7]Rao, S.S., "Description and optimum Design of Fuzzy Mathematical Systems", Journal of Mechanisms, Transmissions, and Automation in Design 1987; 109: 126-132.

[8]Shih,C. J. and Lee, H. W. "Level-cut Approaches of First and Second Kind for Unique Solution Design in Fuzzy Engineering Optimization Problems", Tamkang Journal of Science and Engineering 2004; 7( 3): 189-198.

[9]Shih, C.J., Chi, C.C. and Hsiao, J.H. "Alternative -level-cuts methods for optimum structural design with fuzzy resources", Computers and Structures 2003; 81:2579–2587.

[10]Perez, R.E. and Behdinan, K.: Particle swarm approach for structural design optimization, Computers & Structures 2007; 85 (19-20):1579-1588.

[11]Kaveh, A., Rahami, H., "Nonlinear Analysis and Optimal Design of Structures via Force Method and Genetic Algorithm," Computers and Structures 2006; 84:770-778.

[12]Kaveh, A, Talatahari S. "An improved ant colony optimization for the design of planar steel frames." Eng Struct 2010; 32(3):864–873.

[13]Kaveh, A., Talatahari, S., "Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures". Computers and Structures 2009; 87(56):267–283.

[14]Kaveh, A., Khayatazad, M., "Ray optimization for size and shape optimization of truss structures". Computers and Structures 2013; 117:82–94.

[15]Dede T, Bekirog .lu S, Ayvaz Y. "Weight minimization of trusses with genetic algorithm". Appl Soft Comput 2011; 11(2):2565–2575.

[16]Luh GC, Lin CY. "Optimal design of truss-structures using particle swarm optimization." Computers and Structures 2011; 89(2324):2221–2232.

[17]Sonmez M. "Discrete optimum design of truss structures using artificial bee colony algorithm". Struct Multidiscip Optimiz 2011; 43(1):85–97.

[18]G. Bortolan, R. Degani, A review of some methods for ranking fuzzy numbers, Fuzzy Sets and systems 1985;15: 1–19.

[19]C.H. Hsieh, S.H. Chen, "Similarity of generalized fuzzy numbers with graded mean integration representation," in: Proc. 8th Int. fuzzy Syst. Association World Congress, Taipei,Taiwan, Republic of China, 1999 ;2: 551–555.

[20]T.S. Liou, M.J.J. Wang, "Ranking fuzzy numbers with integral value," Fuzzy Sets and Systems 1992; 50: 247–255.

[21]S.H. Chen, "Operations on fuzzy numbers with function principal," Tamkang Journal of Management Science 1985; 6 (1): 13–25.

[22]S.H. Chen, "Ranking generalized fuzzy number with graded mean integration," Proceedings of 8th International Fuzzy System Association World Congress, Taipei, Taiwan, Republic of China 1999;2:899–902.