A Hybrid Direction Method for Linear Fractional Programming

  • Mohammed Amin Hakmi LaMOS research unit, Modeling and Optimization of Systems, University of Bejaia
  • Mohand Bentobache Laboratory of Pure and Applied Mathematics, University of Laghouat https://orcid.org/0000-0003-3028-5118
  • Mohand Ouamer Bibi LaMOS research Unit, Modeling and Opimization of Systems, University of Bejaia
Keywords: Linear Fractional Programming, Simplex Method, Adaptive Method, Hybrid Direction, Bounded Variables, Numerical Experiments

Abstract

In this article, we propose a new method for solving Linear Fractional Programming (LFP) problems with bounded variables. The proposed algorithm passes from a support feasible solution to a better one following the feasible direction proposed in [K. Djeloud, M. Bentobache and M. O. Bibi, A new method with hybrid direction for linear programming, Concurrency and Computation, Practice and Experience 33 (1), 2021]. Optimality and suboptimality criteria which allow to stop the algorithm when an optimal or suboptimal solution is achieved were stated and proved. Then, a new method called a Hybrid Direction Method (HDM) is described and a numerical example is given for illustration purpose. In order to compare our method to the classical approaches, we develop an implementation with the Matlab programming language. The obtained numerical results on solving 120 randomly generated LFP test problems show that HDM with long step rule is competitive with the primal simplex method and the interior-points method implemented in Matlab.
Published
2025-01-02
How to Cite
Hakmi, M. A., Bentobache, M., & Bibi, M. O. (2025). A Hybrid Direction Method for Linear Fractional Programming. Statistics, Optimization & Information Computing, 13(3), 922-947. https://doi.org/10.19139/soic-2310-5070-2245
Section
Research Articles