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Solving Linear Multi-Objective
Geometric Programming Problems
via Reference Point Approach
(Menyelesaikan
Masalah Linear Berbilang Objektif Geometri Pengaturcaraan melalui
Pendekatan
Titik Rujukan)
F. Bazikar & M. Saraj*
Department of Mathematics, Faculty of
Mathematical Sciences and Computer
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Diserahkan: 15 Jun 2013/Diterima:
16 Disember 2013
Abstract
In
the last few years we have seen a very rapid development on solving generalized
geometric programming (GGP) problems, but so far less works has been devoted to
MOGP due to the inherent difficulty which may arise in solving such problems.
Our aim in this paper was to consider the problem of multi-objective geometric
programming (MOGP) and solve the problem via two-level relaxed linear
programming problem Yuelin et al. (2005) and that is due to
simplicity which occurs through linearization i.e. transforming a GP to LP. In
this approach each of the objective functions in multi-objective geometric
programming is individually linearized using two-level linear relaxed bound
method, which provides a lower bound for the optimal values. Finally our MOGP
is transformed to a multi-objective linear programming problem (MOLP) which is
solved by reference point approach. In the end, a numerical example is given to
investigate the feasibility and effectiveness of the proposed approach.
Keywords: Geometric programming; linearization technique; multi-objective programming;
reference point method
ABSTRAK
Sejak beberapa tahun lepas,
kita telah melihat pembangunan yang sangat pesat dalam masalah penyelesaian am
geometri pengaturcaraan (GGP), tetapi setakat terdapat kurang kajian tentang
MOGP kerana wujud kesukaran yang mungkin timbul dalam menyelesaikan masalah
tersebut. Matlamat kami dalam kertas ini adalah untuk mempertimbangkan masalah
pengaturcaraan pelbagai objektif geometri (MOGP) dan menyelesaikan masalah ini
melalui masalah pengaturcaraan linear santai dua peringkat Yuelin et al. (2005) dan yang adalah kerana kemudahan yang
berlaku melalui pelinearan iaitu transformasi GP ke LP. Dalam pendekatan ini,
setiap satu daripada fungsi objektif dalam pengaturcaraan pelbagai objektif
geometri secara individu adalah dilinearkan menggunakan kaedah terikat santai linear
dua peringkat, yang memberikan sesuatu had lebih rendah bagi nilai yang
optimum. Akhirnya MOGP ini berubah menjadi
sebuah masalah pengaturcaraan linear pelbagai objektif (MOLP) yang diselesaikan
melalui pendekatan titik rujukan. Akhirnya contoh berangka diberikan untuk
mengkaji kemungkinan dan keberkesanan pendekatan yang dicadangkan.
Kata kunci: Kaedah titik rujukan; pelbagai objektif pengaturcaraan; pengaturcaraan geometri; pelinearan teknik
RUJUKAN
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Sahidul, I. 2008. Multi-objective marketing
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238-246.
Shen, P-P., Li, X-A.
& Jiao, H-W. 2008. Accelerating method of global optimization for signomial geometric programming. Journal of Computational and Applied Mathematics 214: 66-77.
Shen, P. & Zhang,
K. 2004. Global optimization of signomial geometric programming using linear relaxation. Applied Mathematics and Computation 150: 99-114.
Qu,
S., Zhang, K. & Wang, F. 2008. A global optimization using linear relaxation for generalized geometric
programming. European Journal of
Operational Research 190: 345-356.
Wu, Y-K. 2008.
Optimizing the geometric programming problem with single-term exponents subject
to max-min fuzzy relational equation constraints. Mathematical and Computer Modelling 47: 352-362.
Yuelin, G., Chengxian,
X., Yanjun, W. & Lianshen,
Z. 2005. A new two-level linear relaxed bound method for geometric programming
problems. Applied Mathematics and
Computation 164: 117-131.
*Pengarang untuk surat-menyurat; email: msaraj@scu.ac.ir
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