Finding the Efficiency Status and Efficient Projection in Multiobjective Linear Fractional Programming: A Linear Programming Technique

S Morteza Mirdehghan,Hassan Rostamzadeh

doi:10.1155/2016/9175371

Abstract

Multiobjective linear fractional programming (MOLFP) problems are the important problems with special structures in multiobjective optimization. In the MOLFP problems, the objective functions are linear fractional functions and the constraints are linear; that is, the feasible set is a polyhedron. In this paper, we suggest a method to identify the efficiency status of the feasible solutions of an MOLFP problem. By the proposed method, an efficient projection on the efficient space for an inefficient solution is obtained. The proposed problems are constructed in linear programming structures.

Highlights

Multiobjective programming (MOP) is a well-known research field in optimization and operations research
Many of events and problems are modeled as multiobjective programming problems
Because of the special structure of the multiobjective linear fractional programming (MOLFP) problems, in this paper we suggest a linear programming technique to find the efficiency status of a feasible solution of an MOLFP problem, and if it is not efficient, we project it on the efficient space of the MOLFP problem

Summary

Introduction

Multiobjective programming (MOP) is a well-known research field in optimization and operations research. The multiobjective optimization problems have several objective functions and a set of feasible solutions. A linear fractional programming (LFP) problem includes a polyhedron as the feasible set and a fractional objective function whose numerator and denominator are affine functions. At first, we propose an approach which identifies the efficiency status of an arbitrary feasible solution of an MOLFP problem. We propose an approach which identifies the efficiency status of an arbitrary feasible solution and finds an efficient projection of an arbitrary feasible solution In these two approaches, we construct linear programming problems regarding the MOLFP problem.

Preliminaries

The Proposed Approaches

Examples

Conclusion