We consider the general problem of generating code for the automated selection of the expected best implementation variants for multiple subcomputations on a heterogeneous multicore system, where the program's control flow between the subcomputations is structured by sequencing and loops. A naive greedy approach as applied in previous works on multi-variant selection code generation would determine the locally best variant for each subcomputation instance but might miss globally better solutions. We present a formalization and a fast algorithm for the global variant selection problem for loop-based programs. We also show that loop unrolling can additionally improve performance, and prove an upper bound of the unroll factor which allows to keep the run-time space overhead for the variant-dispatch data structure low. We evaluate our method in case studies using an ARM big.LITTLE based system and a GPU based system where we consider optimization for both energy and performance.