Integrated real-time dynamic routing (IRR) networks provide dynamic routing features for multiple classes-of-service on an integrated transport network. In a previous Journal paper it is shown that IRR networks allow reduced network management costs since with real-time dynamic routing a number of network operations are simplified or eliminated, leading to savings in operations costs and expenses. In this paper a new algorithm is described for the transport design of IRR networks which achieves near-optimal capacity engineering. In particular, a Karmarkar Algorithm optimal solution to the linear programming flow model achieves approximately a 5 to 8 percentage point reduction in network design cost in comparison to the designs of pre-planned dynamic networks solved with heuristic design techniques. The optimization techniques described in this and the previous Journal paper attain significant capital cost reductions and network performance improvements by properly modeling the more efficient operation of IRR networks.