# Solving Fractional Geometric Programming Problems via Relaxation approach

• Mansour Saraj Shahid Chamran University of Ahvaz
Keywords: Fractional programming, Geometric Programming, Linearization technique

### Abstract

In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach.

### References

G. Yuelin,X.Chengxian,W.Yanjun and Z.Lianshen, A new two-level linear relaxed bound method for geometric programming problems, Applied Mathematics and Computation 164 (2005) 117-131.
Wu ,Yan-Kuen ,Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints, Mathematical and Computer Modelling 47 (2008) 352-362.
Islam and Sahidul, Multi-objective marketing planning inventory model :A geometric programming approach, Applied Mathematics and Computation 205 (2008) 238-246.
Li ,Yiming and Ying -Chien Chen, Temperature -aware flooplanning via geometric programming, Mathematical and Computer Modelling 51 (2010) 927-934.
Liu and Shiang-Tai, A geometric programming approach to profit maximization, Applied Mathematics and Computation 182 (2006) .
Shaojian Qu , Kecun Zhang and Fusheng Wang , A global optimization using linear relaxation for generalized geometric programming, European Journal of Operational Research 190 (2008) 345-356.
Charnes,A.and W.W.Cooper, Management models and industrial applications of linear programming, John wiley, New York, 1961.
F. Bazikar and M. Saraj, Solving linear multi-objective geometric programming problems via reference point approach, Sains Malaysiana 43 (8) (2014) 1271-1274.
S.B. SINHA, A. BISWAS and M.P. BISWAL,Geometric programming problems with negative degrees of difficulty,European Journal of Operational Research 28 (1987) 101-103.
Ching-Ter Chang,On the posynomial fractional programming problems,European Journal of Operational Research 143 (2002) 42-52.
Shaojian Qu , Kecun Zhang, Fusheng Wang,A global optimization using linear relaxation for generalized geometric programming,European Journal of Operational Research 190 (2008) 345–356.
G.S.Mahapatra.T.K.Mandal,Posynomial Parametric Geometric Programming with Interval Valued Coefficient,J Optim Theory Appl (2012)154:120-132.
Shiang-Tai Liu , Posynomial geometric programming with parametric uncertainty,European Journal of Operational Research 168 (2006) 345 -353.
A.K.Ojha and K.K.Biswal, Multi objective geometric programming problem with Epsilon - constraint method , Applied mathematical modelling.38(2014)747-758
Jung-Fa Tsi,Ming-hua-Lin and Yi-Chaung Hu,On generalized geometric programming problems with non-positive variables,Europian journal of operation research 178(2007)10-19.
A.K jha and A.K. Das, Multi objective geometric programming problem being cost coefficient as contineous function with mean method, journal of computing(2010)
Published
2018-12-30
How to Cite
Saraj, M. (2018). Solving Fractional Geometric Programming Problems via Relaxation approach. MathLAB Journal, 1(3), 370-383. Retrieved from http://purkh.com/index.php/mathlab/article/view/187
Issue
Section
Research Articles