Fractional programming through genetic algorithm

Abstract

This paper intends to demonstrate use of Genetic Algorithm for solving fractional programming and which can be extended for DEA. Genetic Algorithm is one of the non-traditional algorithms for solving optimization problems. The multivariable fraction may have multiple optimum points. Genetic algorithm does not run the risk of getting trapped into the local minimum or maximum. The traditional optimization algorithms have difficulty in computing the derivatives and second order partial derivatives for fractional form. Though there are numerical algorithms but they become computationally intensive. The issues of discontinuity seriously affect traditional algorithms. The genetic algorithm may not be very efficient but a generalized way to find optimal points of multivariate fractional function. Two short and simple experiments have been conducted to illustrate the positions. In the second illustration effect of crossover position on the gain of objective function has been studied.