更改

===城市的邻居The neighbours of a state===

===城市的邻居 The neighbours of a state===

Optimization of a solution involves evaluating the neighbours of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the [[travelling salesman problem]] each state is typically defined as a [[permutation]] of the cities to be visited, and its neighbours are the set of permutations produced by reversing the order of any two successive cities. The well-defined way in which the states are altered to produce neighbouring states is called a "move", and different moves give different sets of neighbouring 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).

Optimization of a solution involves evaluating the neighbours of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the [[travelling salesman problem]] each state is typically defined as a [[permutation]] of the cities to be visited, and its neighbours are the set of permutations produced by reversing the order of any two successive cities. The well-defined way in which the states are altered to produce neighbouring states is called a "move", and different moves give different sets of neighbouring 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).

===接受概率Acceptance probabilities===

===接受概率 Acceptance probabilities===

The probability of making the [[state transition|transition]] from the current state <math>s</math> to a candidate new state <math>s'</math> is specified by an ''acceptance probability function'' <math>P(e, e', T)</math>, that depends on the energies <math>e = E(s)</math> and <math>e' = E(s')</math> of the two states, and on a global time-varying parameter <math>T</math> called the ''temperature''.  States with a smaller energy are better than those with a greater energy.  The probability function <math>P</math> must be positive even when <math>e'</math> is greater than <math>e</math>.  This feature prevents the method from becoming stuck at a local minimum that is worse than the global one.

The probability of making the [[state transition|transition]] from the current state <math>s</math> to a candidate new state <math>s'</math> is specified by an ''acceptance probability function'' <math>P(e, e', T)</math>, that depends on the energies <math>e = E(s)</math> and <math>e' = E(s')</math> of the two states, and on a global time-varying parameter <math>T</math> called the ''temperature''.  States with a smaller energy are better than those with a greater energy.  The probability function <math>P</math> must be positive even when <math>e'</math> is greater than <math>e</math>.  This feature prevents the method from becoming stuck at a local minimum that is worse than the global one.

对于任何给定的有限问题，随着退火时间表的扩展，模拟退火算法终止于全局最优解的概率接近1。然而，因为确保取得大概率成功所需的时间通常超过完全搜索解决方案空间所需的时间，所以这一理论结果并不是特别有用，

对于任何给定的有限问题，随着退火时间表的扩展，模拟退火算法终止于全局最优解的概率接近1。然而，因为确保取得大概率成功所需的时间通常超过完全搜索解决方案空间所需的时间，所以这一理论结果并不是特别有用，

==伪代码Pseudocode==

==伪代码Pseudocode==