We exploit the permutation creation ability of genetic optimization to find the permutation of one point set that puts it into correspondence with another one. To this end, we provide a genetic algorithm for the 3D shape correspondence problem, which is the main contribution of this article. As another significant contribution, we present an adaptive sampling approach that relocates the matched points based on the currently available correspondence via an alternating optimization. The point sets to be matched are sampled from two isometric (or nearly isometric) shapes. The sparse one-to-one correspondence, i.e., bijection, that we produce is validated both in terms of running time and accuracy in a comprehensive test suite that includes four standard shape benchmarks and state-of-the-art techniques.