The success of the search for good candidate structures relies on the matching of the surrogate PES with the one of a reference method capable of reproducing the experimental results. Ideally, running the GA with the surrogate should lead to a similar coverage of the configurational space as well as a good match of the relative energetics between structures within an affordable computational cost. We therefore seek to establish here which approximation provides the best compromise between accuracy and computational expenses. However, a quantitative evaluation of the performance of a given fitness function is non-trivial due to the stochastic nature of GAs, in addition to the intractable cost of running multiple benchmark instances with, for example, hybrid DFT. Furthermore, assessing accuracy differences between various methods has been one of the major challenges in computational chemistry for decades. For this reason, we rather test the quality of the different PES approximations on a finite test set of GPGG geometries.