Structural Design Optimization using Parameterized P-norm Based Geometric Programming Technique
||International Journal of Computer & Organization Trends (IJCOT)||
|© 2016 by IJCOT Journal|
|Volume - 6 Issue - 2
|Year of Publication : 2016|
|Authors : : Mridula Sarkar, Samir Dey, Tapan Kumar Roy|
|DOI : 10.14445/22492593/IJCOT-V33P308|
Mridula Sarkar, Samir Dey, Tapan Kumar Roy"Structural Design Optimization using Parameterized P-norm Based Geometric Programming Technique", International Journal of Computer & organization Trends (IJCOT), V6(2):34-43 Mar - Apr 2016, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.
Abstract In this paper we will make an approach to solve single objective structural model using parameterized p-norm based fuzzy Geometric Programming technique. A structural design model in fuzzy environment has been developed. Here pnorm based generalised triangular fuzzy number (GTFN) is considered as fuzzy parameter so that the decision maker can take advantage of no-exact parameter. Generalised triangular p-norm is discussed with their basic properties and some special cases. In this structural model formulation, the objective function is the weight of the truss; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of our proposed optimization approach. The test problem includes a two-bar planar truss subjected to a single load condition. This approximation approach is used to solve this single-objective structural optimization model. The model is illustrated with numerical examples.
 Zadeh.L.A.. „?Fuzzy Sets??, Information and Control,vol.8 ,pp. 338-353, 1965.
 Zimmermann,H.J „?Fuzzy linear programming with several objective function „?Fuzzy sets and systems,vol.1,pp.45- 55,Jan 1978.
 Wang,G.Y.,Wang,W.Q.,??Fuzzy optimum design of structure??Engineering Optimization,vol. 8,pp. 291- 300,1985.
 Rao, S.S., “Description and optimum Design of Fuzzy Mathematical Systems”,Journal of Mechanisms, Transmissions, and Automation in Design, vol. 109,pp.126- 132, Mar1987.
 Yeh, Y.C, and Hsu, D.S. “Structural optimization with fuzzy parameters”.Computer and Structure, vol. 37,pp. 917–924, 1990.
 Xu, C. “Fuzzy optimization of structures by the two-phase method”,Computer and Structure, vol.31, pp.575–580,Dec 1989.
 Shih,C.J, 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,vol.7,pp. 189-198,Sep 2004.
 Shih,C.J.,Chi,C.C. and Hsiao,J.H. “Alternative -level-cuts methods for optimum structural design withfuzzy resources”, Computers and Structures ,vol.81, pp.2579–2587,Nov 2003.
 R.J.Duffin, E.L.Peterson and C.M.zener, Geometric Programming theory and Applications, Wiley, New York, 1967.
 C.Zener, “Engineering Design by Geometric Programming Wiley, 1971.
 C.S.Beightler,D.T.Phillips.,Applied Geometric Programming, Wiley, New York 1976.
 B.Y.Cao??Solution and theory of question for a kind of fuzzy positive genetic programme,Proc,2nd IFSA Congress,Tokyo, pp.205-208, july 1987.
 Ojha,A.K., Das,A.K.,??Geometric Programming Problem with Coefficients and exponents associated with binary numbers,Int.J.Comput.Sci.,vol.7,pp.49-55,Feb 2010.
 Liu,S.T., “Posynomial Geometric Programming with interval exponent and coefficients??, Eur.J.Oper.Res.,vol.186,pp.17- 27,Apr 2008.
 Dey,S.,Roy,T.K.,?? Truss Design Optimization Using Fuzzy Geometric Programming in Parametric Form??,Journal of computational science,vol.4,400-415,Jan 2014.
 S Islam,T.K.roy, “ A fuzzy EOQ model with flexibility and reliability consideration and demand dependent unit production cost a space constraint: A fuzzy geometric programming approach”, Applied Mathematics and computation, vol.176, pp.531-544,May2006.
 Dey,S.,Roy,T.K.,”Optimized Solution of two-bar truss design using intuitionistic optimization technique.??,I.J.Information Engineering and Electronic Bussiness,vol.4,pp.45-51,Aug 2014.
 Prabha, S, Krishna. Devi,S.,Deepa,S., “An efficient algorithm to obtain the optimal solution for fuzzy transportation problems”, International journal of computer and organization trends,vol.4,pp.32-39,Jan 2014.
Generalized Triangular Fuzzy Number, p-norm, Geometric Programming, Single Objective Optimization, Structural Optimization.