Routing has always been of immense importance in communication networks due to its impact on the network performance. The significance of scalable and adaptive routing has sky-rocked during the last decade as a consequence of the ever increasing demand for Internet and mobile communications. A routing algorithm selects one or more paths over which devices communicate with each other. In this paper, a new Multiobjective Particle Swarm Optimization (MOPSO) algorithm, with a new velocity equation, for the solution of the Multiobjective Multicast Routing Problem is proposed and tested. A number of variants of the proposed algorithm with global and local exploration abilities are presented and compared with each other. In order to estimate the quality of the methodology, experiments are conducted using classic Euclidean Traveling Salesman Problem benchmark instances taken from the TSP library, modified suitably for the selected problem. The preliminary results indicate the efficiency of the proposed method.