In the future Internet, multimedia applications will be strongly present. When a group of users is concerned by the same traffic flow, the multicast communication can decrease considerably the network bandwidth utilization. The major part of this kind of multicast communication needs quality of service (QoS) specification. Often, the QoS is given as a set of QoS criteria and the computation of feasible or optimal routes corresponds to a multi-constrained optimization. Finding the multicast graph respecting the defined QoS requirements and minimizing network resources is a NP-complete optimization task. Exhaustive search algorithms are not supported in real networks. Greedy algorithms was proposed to find good multicast sub-graphs. The local decisions of greedy algorithms can lead to solutions which can be ameliorated. To improve greedy algorithm solution, we propose, first, ICRA algorithm which is an enhanced version of the well known Mamcra algorithm but is also limited. As Meta-heuristics are good candidates to find better solutions using a controlled execution time, we propose, secondly, Taboo-QMR algorithm which is a Taboo Search based algorithm to reduce the multicast sub-graph computed by the first step of the algorithm Mamcra. Simulations of all approaches are run based on random graphs and show that the application of Taboo-QMR algorithm presents a tangible enhancement in almost 32 per cent of the cases.