Many new multicast applications emerging from the Internet, such as TV over the Internet, Radio over the Internet, Video Streaming multi-point, etc., need the following resource requirements: bandwidth consumption, end-to-end delay, packet loss ratio, etc. It is therefore necessary to formulate a proposal to specify and provide for these kinds of applications the resources necessary for them to function well. In this thesis, we propose a multi-objective traffic engineering scheme using different distribution trees to multicast several flows. In this case, we are using the multipath approach to every egress node to obtain the multitree approach and of this way to create several multicast tree. Moreover, our proposal solves the traffic split ratio for multiple trees. The proposed approach can be applied in Multiprotocol Label Switching (MPLS) networks by allowing explicit routes in multicast events to be established. In the first instance, the aim is to combine the following weighting objectives into a single aggregated metric: the maximum link utilization, the hop count, the total bandwidth consumption, and the total end-to-end-delay. We have formulated this multi-objective function (MHDB-S model) and the results obtained using a solver show that several weighting objectives are decreased and the maximum link utilization is minimized. The problem is NP-hard, therefore, an algorithm is proposed for optimizing the different objectives. The behavior we get using this algorithm is similar to what we get with the solver. Normally, during multicast transmission the egress node can leave and enter of the tree and for this reason in this thesis we propose a multi-objective traffic engineering scheme using different distribution trees for multicast groups (i.e. in which egress nodes can change during the connection's lifetime). If a multicast tree is recomputed from scratch, it may consume a considerable amount of CPU time and all communication using the multicast tree will be temporarily interrupted. To alleviate these drawbacks we propose an optimization model (dynamic model MHDB-D) that uses a previously computed multicast tree (static model MHDB-S) adding new egress nodes. Using the weighted sum method to solve the analytical model is not necessarily correct, because is possible to have a non-convex space solution and some solutions cannot be found. In addition, other kinds of objectives were found in different research works. For the above reasons, a new model called GMM is proposed and to find a solution to this problem a new algorithm using a Multi- Objective Evolutionary Algorithm (MOEA) is proposed too. This algorithm is inspired by the Strength Pareto Evolutionary Algorithm (SPEA). To give a solution to the dynamic case with this generalized model a dynamic GMM model is proposed and a computational solutions using Breadth First Search (BFS) probabilistic is also proposed to give a solution to the dynamic case in multicast. Finally, in order to evaluate our proposed optimiation scheme, we performed the necessary simulations and tests. The main contributions of this thesis are the taxonomy, the optimization model and the formulation of the multi-objective function in static and dynamic multicast transmission (MHDB-S and MHDB-D), as well as the different algorithms proposed to give computational solutions to this problem. Finally, the generalized model with several functions found in different research works in static and dynamic multicast transmission (GMM and Dynamic GMM), as well as the different algorithms proposed to give computational solutions using MOEA and BFS probabilistic.