In the domain of computer-aided drug design, achieving precise and accurate estimates of ligand-protein binding is paramount in the context of screening extensive drug libraries and performing ligand optimization. A fundamental aspect of the SILCS (site identification by ligand competitive saturation) methodology lies in the generation of comprehensive 3D free-energy functional group affinity maps (FragMaps), encompassing the entirety of the target molecule structure. These FragMaps offer an intricate landscape of functional group affinities across the protein, bilayer, or RNA, acting as the basis for subsequent SILCS-Monte Carlo (MC) simulations wherein ligands are docked to the target molecule. To augment the efficiency and breadth of ligand sampling capabilities, we implemented an improved SILCS-MC methodology. By harnessing the parallel computing capability of GPUs, our approach facilitates concurrent calculations over multiple ligands and binding sites, markedly enhancing the computational efficiency. Moreover, the integration of a genetic algorithm (GA) with MC allows us to employ an evolutionary approach to perform ligand sampling, assuring enhanced convergence characteristics. In addition, the potential utility of parallel tempering (PT) to improve sampling was investigated. Implementation of SILCS-MC on GPU architecture is shown to accelerate the speed of SILCS-MC calculations by over 2-orders of magnitude. Use of GA and PT yield improvements over Markov-chain MC, increasing the precision of the resultant docked orientations and binding free energies, though the extent of improvements is relatively small. Accordingly, significant improvements in speed are obtained through the GPU implementation with minor improvements in the precision of the docking obtained via the tested GA and PT algorithms.