Given a set of cities and distances to travel between each pair of them, the Traveling Salesman Problem (TSP) is to find the shortest tour which visits every city exactly once and returns to the starting city. In some practical cases, the balance between edges in the tour is as important as the total distance. It motivates us to study an equitable version of TSP where the optimal tour satisfies: i) Pareto optimality (i.e. not improvable on all distances simultaneously), ii)fairness (or the balance between edges). In this work, we study a variant of TSP where the ordered weighted averaging (OWA) is used to control both Pareto efficiency and fairness, we call this problem OWATSP. OWA imposes implicitly the balance between edges by Pigou-Dalton transfer principle claiming that a transfer from a richer resource to a poorer one results in a fairer distribution.OWATSP belongs to the class of fair combinatorial optimization considered in [2]. The main challenge of this problem class is the non-linearity of OWA objective. Fortunately, it can be cast to Mixed-Integer Programs (MIPs) by several existing linearization methods [3, 1]. However, the time spent to solve exact formulations increases considerably with the size of instances and might reach hours for small-size ones. To tackle the issue, an iterative algorithm based on Lagrangian relaxation [2] is proposed and verified the efficiency of several fair optimization problems related to matching. In this paper, we focus on algorithms to solve efficiently large-size instances of OWATSP - an NP-hard problem.