Hill climbing
![A convex surface. Hill-climbers are well-suited for optimizing over such surfaces, and will converge to the global maximum.](/Images/godic/202501/18/Hill_climb5954.png")
![A surface with two local maxima. (Only one of them is the global maximum.) If a hill-climber begins in a poor location, it may converge to the lower maximum.](/Images/godic/202501/18/Local_maximum5954.png")
![Despite the many local maxima in this graph, the global maximum can still be found using simulated annealing. Unfortunately, the applicability of simulated annealing is problem-specific because it relies on finding lucky jumps that improve the position. In problems that involve more dimensions, the cost of finding such a jump may increase exponentially with dimensionality. Consequently, there remain many problems for which hill climbers will efficiently find good results while simulated annealing will seemingly run forever without making progress. This depiction shows an extreme case involving only one dimension.](/Images/godic/202501/18/Hill_Climbing_with_Simulated_Annealing5954.gif")
![A ridge](/Images/godic/202501/18/Ridge5954.png")
In computer science, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution. If the change produces a better solution, an incremental change is made to the new solution, repeating until no further improvements can be found.