Editing Local search (optimization) (section)

{{Short description|Method for problem solving in optimization}}
{{more footnotes|date=May 2015}}

In [[computer science]], '''local search''' is a [[heuristic]] method for solving computationally hard [[Mathematical optimization|optimization]] problems. Local search can be used on problems that can be formulated as finding a solution that maximizes a criterion among a number of [[candidate solution]]s. Local search algorithms move from solution to solution in the space of candidate solutions (the ''search space'') by applying local changes, until a solution deemed optimal is found or a time bound is elapsed.

Local search algorithms are widely applied to numerous hard computational problems, including problems from [[computer science]] (particularly [[artificial intelligence]]), [[mathematics]], [[operations research]], [[engineering]], and [[bioinformatics]]. Examples of local search algorithms are WalkSAT, the [[2-opt|2-opt algorithm for the Traveling Salesman Problem]] and the [[Metropolis–Hastings algorithm]].<ref>{{cite web|url=https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/12LocalSearch.pdf|title=12LocalSearch.key}}</ref> 

While it is sometimes possible to substitute [[gradient descent]] for a local search algorithm, gradient descent is not in the same family: although it is an [[iterative method]] for [[Global optimization|local optimization]], it relies on an [[loss function|objective function’s gradient]] rather than an explicit exploration of the solution space.