Sains Malaysiana 43(8)(2014): 1271-1274

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

Received: 15 June 2013/Accepted: 16 December 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

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*Corresponding author; email: msaraj@scu.ac.ir