Acoustic holography offers the ability to generate designed acoustic fields, enhancing the versatility of acoustic micromanipulation. However, the quality of the generated holograms depends on the nature of the iterative algorithm that is utilized, where the iterative angular spectrum approach (IASA) has been the standard method to date. Here, we introduce a novel approach that categorically improves IASA performance, where we apply the principles of simulated annealing for the generation of high-quality acoustic holograms. We utilize this to realize significant improvements in hologram quality via simulations, fabricated holograms, experimental particle patterning, and high-resolution 2D hydrophone scans. Comparing holograms produced from IASA and/or simulated annealing, we demonstrate that the use of simulated annealing in acoustic holography results in sharper reconstructions and improved hologram outputs across a range of evaluation metrics.