A new efficient approach to tackle multi objective linear fractional problem with flexible constraints

Abstract

<p style='text-indent:20px;'>Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization due to the fact that more than one objective must be taken into consideration by the decision maker. For this class of optimization problems, we deal with the concept of efficient solutions. The set of efficient solutions could be an infinite set especially when the objectives are in conflict. In this paper, we present a new methodology to address the MOLFPP with flexible constraints i.e. the constraints with fuzzy right hand sides. In the method, firstly, the concept of the <inline-formula><tex-math id="M1">\begin{document}$ \alpha- $\end{document}</tex-math></inline-formula>cuts and ranking of fuzzy numbers are utilized to transform the original problem into the MOLFPP with fixed right hand sides. Secondly, a new MOLFPP is constructed based on the membership functions of the objectives. Afterward this new problem is changed into a single objective programming problem using the weighted sum approach. Finally, the global optimal solution of this single objective programming is obtained by taking into account a finite number of linear programming problems (LPPs). It is proven that the obtained solution is efficient for the main problem. Numerical examples are given to illustrate the method and comparisons are made to show the accuracy.</p>