Editing Automatic label placement (section)

==Local optimization algorithms==
The simplest [[greedy algorithm]] places consecutive labels on the map in positions that result in minimal overlap of labels. Its results are not perfect even for very simple problems, but it is extremely fast.

Slightly more complex algorithms rely on local optimization to reach a local optimum of a placement evaluation function – in each iteration placement of a single label is moved to another position, and if it improves the result, the move is preserved. It performs reasonably well for maps that are not too densely labelled. Slightly more complex variations try moving 2 or more labels at the same time. The algorithm ends after reaching some local optimum.

A simple algorithm – [[simulated annealing]] – yields good results with relatively good performance. It works like local optimization, but it may keep a change even if it worsens the result. The chance of keeping such a change is <math>\exp \frac{-\Delta E}{T}</math>, where <math>\Delta E</math> is the change in the evaluation function, and <math>T</math> is the ''temperature''. The temperature is gradually lowered according to the ''annealing schedule''. When the temperature is high, simulated annealing performs almost random changes to the label placement, being able to escape a [[local optimum]]. Later, when hopefully a very good local optimum has been found, it behaves in a manner similar to local optimization. The main challenges in developing a simulated annealing solution are choosing a good evaluation function and a good annealing schedule. Generally too fast cooling will degrade the solution, and too slow cooling will degrade the performance, but the schedule is usually quite a complex algorithm, with more than just one parameter.

Another class of direct search algorithms are the various [[evolutionary algorithm]]s, e.g. [[genetic algorithm]]s.