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In this paper, we formulate an optimization problem for the design of light-tree based logical topology in wavelength division multiplexing (WDM) networks. The problem is comprised of two parts: (1) multicast routing and wavelength assignment of light-trees, and (2) the design of light-tree based logical topology for multicast streams. In the first part, we use mixed integer linear programming (MILP) to solve the optimal routing and wavelength assignment problem of light-trees with an end-to-end delay bound, and obtain the optimal placement of power splitters and wavelength converters. The numerical results show that networks with just a few power splitters and wavelength converters can efficiently carry multicast data. In the second part, we extend the above formulation to design the logical topology based on light-trees for multicast streams. In our approach, a light-tree can carry data of multiple multicast streams, and data of a multicast stream may traverse multiple light-trees to reach a receiver. The numerical results show that our approach use network resources more efficiently, as compared to the approach with a separate light-tree for a multicast stream and to the approach of transporting multicast streams over lightpath based logical networks.