Fundamentally, the specific difficulties in ab initio structure determination of practical heterogeneous catalysts have the same origin as the experimental ones: Complex composition and surface irregularity, that hinder the inference of reasonable structures. Accordingly, to study the interplay between the adsorbates and support necessitates the exploration of a vast conformational space including positioning of the support atoms, with minimal assumptions. This task is best achieved through global search algorithms. In particular, the genetic algorithm (GA) has been a powerful tool due to its capability of escaping the local minima by stochastic operations, thus being applied to exploring molecular clusters as well as supported heterogeneous catalysts. To be more relevant, a separate treatment between a rigid cluster with restricted conformation rules and more flexible treatment of adsorbates for structure determination of silver nanoclusters has been proposed, resulting in novel structures due to GA's capacity of sampling distant points in the potential energy surface. This method of structure determination has not been applied to a complex system such as the heterogeneous ZN catalyst and requires a zealous approach to tuning the algorithm towards new finds, with the limited certainties available. The current study delivers a framework for finding a population of stable structures that can provide quantitative data about elusive molecular systems.