The phrase "wreaks havoc on" is typically used to describe a situation in which something causes widespread damage, chaos or destruction. Antonyms for this phrase include terms related to calmness, such as "soothes," "eases," "calms," "heals," or "restores." Alternatively, antonyms could be related to positivity or productivity, such as "benefits," "improves," "constructs," "grows," or "prospers." In other contexts, antonyms could be related to orderliness or efficiency, such as "organizes," "streamlines," "optimizes," "improves," or "systematizes.