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Wireless Mesh Networks are a scalable and cost-effective solution for next-generation wireless networking. In the present work, we consider the Round Weighting Problem (RWP) which solves a joint routing and scheduling problem to satisfy a given demand subjected to the multi-access interferences. We propose a multiobjective approach that deals with two objectives. The first one is to balance the load in the routers, increasing the security in case of failure. The second objective is to minimize the communication time. We aim to find the Pareto set of the problem, as it captures the trade-off generated by using these two conflicting objective functions. We make experiments with some networks with different number of gateways. The column generation method is used to solve efficiently the test instances. Our approach finds out the relationship between the objective functions, corresponding to a convex piecewise linear function.