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We investigate the design and planning of translucent optical networks with heterogeneous signal modulation formats. By employing multiple signal modulation formats of different optical reaches in the network, the required number of optical regenerators can be minimized. Hence, the overall network deployment capital cost and operational cost are much reduced. By building auxiliary graphs, a novel integer linear programming (ILP) is formulated to minimize the overall weighted network cost. Also, an effective heuristic is proposed to tackle networks of much larger scales. Numerical simulation studies indicate that our approach can achieve significant savings in overall network costs.