**heuristics**to get a best approximation of the optimal solution.

Metaheuristics can be used to produce solutions to mathematical problems under conditions of limited computational capacity. Hill climbing is a metaheuristic that can be used to find local optima by iteratively improving an arbitrary solution to a problem but it is not guaranteed to produce a global optima.

The hill climbing metaheuristic can be used for example to optimize a solution to the traveling salesman problem by first finding a basic feasible solution and then switching the order in which certain nodes are visited as long as that switch improves the solution. There are various other metaheuristics such as tabu search that can be used to solve mathematical optimization problems.

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