In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

The sum of a fractional program is a nonconvex optimization problem in the field of fractional programming and it is difficult to solve. The development of research is restricted to single objective sums of fractional problems only. The branch and bound methods/algorithms are developed in the literature for this problem as a single objective problem. The theoretical and algorithmic development ...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

We deal with a class of generalized fractional programming problems having a polyhedral feasible region and as objective the ratio of an affine function and the power p > 0 of an affine one. We aim to propose simplex-like sequential methods for finding the global maximum points. As the objective function may have local maximum points not global, we analyze the theoretical properties of the prob...

This paper presents fuzzy goal programming approach for bilevel linear fractional programming problem with a single decision maker at the upper level and a single decision maker at the lower level. Here, each level has single objective function, which are fractional in nature and the system constraints are linear functions. In the proposed approach, we first construct fractional membership func...

We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is fractional, it can be replaced by a piece-wise linear convex function. Numerical experiments show that our formulation has significantly good performance for ...

We consider a fractional 0-1 programming problem arising in manufacturing. The problem consists in clustering of machines together with parts processed on these machines into manufacturing cells so that intra-cell processing of parts is maximized and inter-cell movement is minimized. This problem is called Cell Formation Problem (CFP) and it is an NP-hard optimization problem with Boolean varia...

DNA sequencing enables the discovery of new genes in high-throughput, low-cost experiments. Conversely, gene function is determined by low-throughput, high-cost experiments. This inverse relationship for these two types of data is a major impediment in meeting one of the major scientific challenges of our time—the understanding of genomes. This mismatch in throughput is illustrated by consideri...