聊一聊人工智能中的常用搜索策略

  人工智能中的搜索策略大体分为两种：无信息搜索和有信息搜索。无信息搜索是指我们不知道接下来要搜索的状态哪一个更加接近目标的搜索策略，因此也常被成为盲目搜索；而有信息搜索则是用启发函数f（n）来衡量哪一个状态更加接近目标状态，并优先对该状态进行搜索，因此与无信息搜索相比往往能够更加高效得解决问题。
  要衡量一个搜索策略的好坏，我们需要从四个方面对其进行判断：完备性、时间复杂度、空间复杂度和最优性。因此以下通过这四个方面来比较常见搜索策略之间的优劣。

无信息搜索策略

宽度优先搜索（BFS）

  首先扩展根节点，然后扩展根节点的所有后继，接着再扩展它们的后继，从而一层一层的对节点进行扩展。BFS是一个简单的搜索策略，在搜索过程中会对所有状态进行遍历，因此它是完备的；假设搜索树每个节点有b个后继，深度为d，则时间复杂度和空间复杂度均为O(bd)；最后考虑最优性，因为我们总会在最浅那一层找到目标状态，因此当且仅当每一步的代价都一致的时候，BFS可以得到最优解。

一致代价搜索

  在BFS的基础上，一致代价搜索不在扩展深度最浅的节点，而是通过比较路径消耗g（n），并选择当前代价最小的节点进行扩展，因此可以保证无论每一步代价是否一致，都能够找到最优解。

深度优先搜索（DFS）

  DFS扩展根节点的一个后继，然后扩展它的一个后继，直到到达搜索树的最深层，那里的节点没有后继，于是DFS回溯到上一层，扩展另外一个未被扩展的节点。在有限状态空间中，DFS是完备的，因为它可以把所有空间遍历一遍；而在无限空间中，DFS则有可能会进入深度无限的分支，因此是不完备的。DFS的时间复杂度为为O(bd)，而空间复杂度仅为O（d），因为我们只需要保存当前分支的状态，因此空间复杂度远远好于BFS。然而DFS并不能保证找到最优解。

深度受限搜索

  深度受限搜索设定一个最大深度dmax，当搜索深度大于dmax的时候立即回溯，从而避免了在无穷状态空间中陷入深度无限的分支。

迭代加深的深度有限搜索

  迭代加深的深度有限搜索也设定一个最大深度dmax，开始我们把dmax设为1，然后进行深度受限搜索，如果么有找到答案，则让dmax加一，并再次进行深度有限搜索，以此类推直到找到目标。这样既可以避免陷入深度无限的分支，同时还可以找到深度最浅的目标解，从而在每一步代价一致的时候找到最优解，再加上其优越的空间复杂度，因此常常作为首选的无信息搜索策略。

有信息搜索

贪婪最佳优先搜索

贪婪最佳优先搜索总是扩展距离目标最近的节点，其启发函数f（n）=h（n）其中:

f（n）=节点n到目标节点的最小代价路径的估计值

贪婪最佳优先搜索的最大问题是它往往不能找到最优解。

A*

为了找到最优解，A*算法对一个节点的评估结合了h（n）和g（n）从开始节点到节点n的路径代价，即f（n）=g（n）+h（n）

f（n）=经过节点n的最小代价解的估计代价

因为A*搜索总是搜索f（n）最小的点，因此它总能找到最优解。

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