ژاله شیرین نژاد - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
منصور سراج - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
سارا شکراللهی - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
فاطمه کیانی - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

This study proposes a method for solving mixed integer multi-objective fractional signomial geometric programming (MIMOFSGP) problems. A few methods have been applied in the recent past to convert a fractional signomial objective function into a non-fractional signomial objective function to find the optimal solution by use of some common mathematical programming techniques. In this paper, at first a multi-objective fractional signomial programming is converted into a non-fractional multi-objective signomial programming problem by a new convenient reformulation strategy. A convex relaxation is used to reach global solution and then fuzzy programming technique is applied to find the optimal compromise solution. A mixed integer compromise optimal solution of the convex programming problem can finally be found by use of nonlinear branch and bound algorithm. Then ۰n using the Spacial branch and bound algorithm, we find a solution that has the shortest distance from the solution of original problem. Finally two illustrative examples are included to demonstrate the correctness and efficiency of the proposed strategy and compare the results with the other solutions obtained by the other methods.

Multi-objective programming, geometric programming, fractional programming, Mixed integer programming, Spatial branch and bound algorithm