Solving Fractional Programming Problems based on Swarm Intelligence

Authors

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

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.

Keywords