Editing Simulated annealing (section)

===Barrier avoidance===
When choosing the candidate generator {{code| neighbor ()}} one must also try to reduce the number of "deep" local minima—states (or sets of connected states) that have much lower energy than all its neighboring states. Such "closed [[catchment]] basins" of the energy function may trap the simulated annealing algorithm with high probability (roughly proportional to the number of states in the basin) and for a very long time (roughly exponential on the energy difference between the surrounding states and the bottom of the basin).

As a rule, it is impossible to design a candidate generator that will satisfy this goal and also prioritize candidates with similar energy. On the other hand, one can often vastly improve the efficiency of simulated annealing by relatively simple changes to the generator. In the traveling salesman problem, for instance, it is not hard to exhibit two tours <math>A</math>, <math>B</math>, with nearly equal lengths, such that (1) <math>A</math> is optimal, (2) every sequence of city-pair swaps that converts <math>A</math> to <math>B</math> goes through tours that are much longer than both, and (3) <math>A</math> can be transformed into <math>B</math> by flipping (reversing the order of) a set of consecutive cities. In this example, <math>A</math> and <math>B</math> lie in different "deep basins" if the generator performs only random pair-swaps; but they will be in the same basin if the generator performs random segment-flips.