New methods for solving the fractional programming problems

Abstract

 In this paper, two approximation algorithms for solving the fractional programming (FP) problems are presented. The first algorithm is introduced for solving the convex fractional problem based on an objective space cut and bound method. Then, before stating the second algorithm, we propose an algorithm based on the Pascoletti-Serafini secularization approach for solving the bi-objective programming problems. The purpose of this algorithm is to obtain an approximation of the Pareto front that covers the whole Pareto front uniformly. In addition, for testing the quality of the obtained approximation of this algorithm, we use five test problems with a convex, non-convex, continuous and discontinuous Pareto fronts and compare its results with the results of some algorithms, including NC, WC, DE, MOEA/D-DE, NSGA-II and SMS-EAMO algorithms. The computational results confirm the effectiveness of the presented algorithm. Afterwards, we use this bi-objective algorithm for presenting the second algorithm for solving an FP problem in the general case. Some illustrative examples are used to demonstrate the working of the fractional algorithms. In addition, several examples are applied to demonstrate the good performance of the proposed fractional algorithms.