Multicast routing technology is important in new distributed computing such as video broadcast, video conferencing, CSCW. In this paper, a shared tree routing protocol based on distributed Genetic Algorithms (GAs) is presented, including building and dynamic maintenance of multicast routing tree in package exchange network. Computing of delay bounded Steiner Tree is also presented. With this algorithm, a dynamic constructed multicast routing tree which has a near optimal network cost under the delay bound constraint can be constructed real time. As a result, how to build and maintain a rooting tree is resolved.