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In this paper, we present a novel methodology based on Mixed Integer Linear Programming (MILP) for obtaining the complete design tradeoff curve of heterogeneous adders. For each optimal design point of the tradeoff curve, our approach determines both the number of subadders, the architecture of each subadder and the bit width of each subadder. In order to reduce the number of binary variables in the formulation of the MILP, we introduce a new modeling of non-convex curves. Comparisons using five different adder architectures implemented in a standard cells 65nm CMOS technology are shown. Experimental results reveal that the proposed design space exploration methodology is better, when compared with the best published work, up to 11.73 times and 2.16 times in average in terms of CPU time.