The finite-offset common-reflection-surface (FO-CRS) stack method can be used to simulate any common-offset (CO) seismic section by stacking prestack seismic data along the surfaces defined by the paraxial hyperbolic traveltime approximation. In two dimensions, the FO-CRS stacking operator depends on five kinematic wavefield attributes for every time sample of the target CO section. The main problem with this method is identifying a computationally efficient data-driven search strategy for accurately determining the best set of FO-CRS attributes that produce the optimal coherence measure of the seismic signal in the prestack data. Identifying a global optimization algorithm with the best performance is a challenge when solving this optimization problem. This is because the objective function is multimodal and involves a large volume of data, which leads to high computational costs. We introduced a comparative and competitive study through the application of two global optimization algorithms that simultaneously search the FO-CRS attributes from the prestack seismic data, very fast simulated annealing (VFSA) and the differential evolution (DE). By applying this FO-CRS stack to the Marmousi synthetic seismic data set, we have compared the performances of the two optimization algorithms with regard to their efficiency and effectiveness in estimating the five FO-CRS attributes. To analyze the robustness of the two algorithms, we apply them to real land seismic data and show their ability to find the near-optimal attributes and to improve reflection events in noisy data with a very low fold. We reveal that VFSA is efficient in reaching the optimal coherence value with the lowest computational costs, and that DE is effective and reliable in reaching the optimal coherence for determining the best five searched-for attributes. Regardless of the differences, the FO-CRS stack produces enhanced and regularized high-quality CO sections using both global optimization methods.