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This paper optimizes timing and power consumption of mixed-radix Ling adders with the physical area constraints using an integer linear programming formulation. Each cell in the prefix network is flexible to have different radix and size, and Ling carries are incorporated. Optimal solutions are obtained by solving the proposed formulation. The experiments show that the produced optimal structures have a large power saving compared with traditional designs. The ASIC implementation results are superior to those produced by Synopsys Module Compiler.