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There is often no unique version of a program that provides the best performance in all circumstances. Compilers should rely on an adaptive runtime decision to choose which optimizing and parallelizing transformations will lead to the best performance in any execution context. We present a new adaptive framework solving two drawbacks of existing methods: it is effective since the very first execution, and it handles slight variations of input data shape and size. In our proposal, different code versions of parallel loop nests are statically generated by the compiler. At install time, each version is profiled in different execution contexts. At runtime, the execution time of each code version is predicted using the profiling results, the current input data shape and the number of available processor cores. The predicted best version is then run. Our framework handles several versions of possibly tiled parallel loops, using the polytope model for both the profiling and the dynamic selection phases. We show on several benchmark programs that our runtime system selects one of the most efficient version with a very low runtime overhead. This quick and efficient selection leads to speedups compared to the usage of a unique version in every execution context.