Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primal-dual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is assumed in different form, and then the said formulation is equivalent to single or multi-objective entropy maximization trip distribution problem. We use fuzzy mathematical programming method to show this equivalent problem formulation. The present article we use the concept of multi-objective trip distribution problem.