Solving Fractional Programming Problems based on Swarm Intelligence

Subject Areas : Mathematical Optimization

Osama Abdel Raouf ¹ , Ibrahim M. Hezam ²

1 - Operations Research and DSS Department, Menofia University, Shebien El-koum, Menofia , 32511, Egypt
2 - Department of Mathematics and computer, Faculty of Education, Ibb University, Ibb city, Yemen|Operations Research and DSS Department, Menofia University, Shebien El-koum, Menofia , 32511, Egypt

Received: 2020-10-02 Accepted : 2020-10-02 Published : 2014-06-01

Keywords: Swarm intelligence  Particle swarm, optimization  Firefly algorithm  Fractional programming,

Abstract :

This paper presents a new approach to solve Fractional Programming Problems (FPPs) based on two different Swarm Intelligence (SI) algorithms. The two algorithms are: Particle Swarm Optimization, and Firefly Algorithm. The two algorithms are tested using several FPP benchmark examples and two selected industrial applications. The test aims to prove the capability of the SI algorithms to solve any type of FPPs. The solution results employing the SI algorithms are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Swarm Intelligence can be denoted as an effective technique for solving linear or nonlinear, nondifferentiable fractional objective functions. Problems with an optimal solution at a finite point and an unbounded constraint set, can be solved using the proposed approach. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using the two SI algorithms revealed the superiority of the proposed technique among others in computational time. A better accuracy was remarkably observed in the solution results of the industrial application problems.