A fuzzy based branch and bound approach for multi-objective linear fractional (MOLF) optimization problems

Abstract

In the present study, a new fuzzy based branch-bound approach is attempted for solving multi-objective linear fractional (MOLF) optimization problems. The original MOLF optimization problem is converted into equivalent fuzzy multi-objective linear fractional (FMOLF) optimization problem. Then branch and bound techniques is applied on FMOLF optimization problem. The feasible space of FMOLF optimization problem is bounded by triangular simplex space. The weak duality theorem is used to generate the bound for each partition and feasibility conditions are applied to neglect one of the partition in each step. After finite number of steps, a fuzzy efficient (Pareto-optimal) solution is obtained for FMOLF optimization problem which is also efficient (Pareto-optimal) solution of the original MOLF optimization problem. Some theoretical validations are also established for the proposed approach on FMOLF optimization problem. For the efficiency of proposed approach, it has been performed on two numerical applications. The method is coded in Matlab (2016). The results are compared with earlier reported methods.