Editing Simulated annealing (section)

===The neighbors of a state===
Optimization of a solution involves evaluating the neighbors of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the [[traveling salesman problem]] each state is typically defined as a [[permutation]] of the cities to be visited, and the neighbors of any state are the set of permutations produced by swapping any two of these cities. The well-defined way in which the states are altered to produce neighboring states is called a "move", and different moves give different sets of neighboring states. These moves usually result in minimal alterations of the last state, in an attempt to progressively improve the solution through iteratively improving its parts (such as the city connections in the traveling salesman problem). It is even better to reverse the order of an interval of cities. This is a smaller move since swapping two cities can be achieved by twice reversing an interval. 

Simple [[heuristic]]s like [[hill climbing]], which move by finding better neighbor after better neighbor and stop when they have reached a solution which has no neighbors that are better solutions, cannot guarantee to lead to any of the existing better solutions{{snd}} their outcome may easily be just a [[local optimum]], while the actual best solution would be a [[global optimum]] that could be different. [[Metaheuristic]]s use the neighbors of a solution as a way to explore the solution space, and although they prefer better neighbors, they also accept worse neighbors in order to avoid getting stuck in local optima; they can find the global optimum if run for a long enough amount of time.