在局部搜索算法中，我们不再关心从初始节点到目标节点之间的路径，而是考虑从当前节点出发，移动到它的邻近状态，直到到达合理的目标状态。相比于前面所说的无信息搜索算法和有信息搜索算法，局部搜索算法往往能以常数的空间复杂度（不用保存路径）在很大甚至无限的状态空间中找到合理解。

爬山法

爬山法不断向值增加的方向移动，直到到达顶峰。

function HillClimbing(problem) returns a local maximum statecurrent_state = initial_stateloop donext_state = the highest neighborif (next_state is higher than current_state)current_state = next_stateelsereturn current_state

爬山法的问题在于它只能保证到达局部最大值，却不能保证到达全局最大值。

比如我们从C点出发，那么我们会停在局部最大值A点，因此没办法到达全局最大值B点。

模拟退火算法

  模拟退火算法与爬山法类似，只是我们不再一味地往值增加的方向移动，而是以一定的几率容许往值减小的方向移动，从而使得我们有可能从局部最大值A点走出来，并到达全局最大值B点。
  只所以叫做模拟退火，是因为一开始这个几率相对较高，而随着时间的增加，这个几率则像温度一样慢慢减小。

function SimulatedAnnealing () returns a solution statecurrent_state = initial_statefor t = 1 to infinite doT = schedule(t)if T = 0 thenreturn current_statenext_state = a randomly selected neighborE = next_state.height - current_state.heightif E > 0 thencurrent_state = next_stateelse current_state = next_state with probability e^(E/T)

遗传算法

  遗传算法模拟生物中的遗传过程，从初始种群开始，迭代进行一系列杂交和变异直到获得合适的种群，并从中挑选出最佳个体。

function GeneticAlgorithm(population, fitin) returns a solution stateinputs: population, a set of individualsfitness， a function that measures fitness of an individualrepeatnew_population = empty_setfor i = 1 to sizeof(population) dox = RandomSelect(population, fitness)y = RandomSelect(population, fitness)new_individual = Reproduce(x, y)if (a probability) thennew_individual = Mutate(new_individual)add new_individual to new_populationuntil some individuals are fit enough or time has elapsedreturn the best individual in the population
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function Reproduce(x, y) returns a new individualinputs: x, y, the parents of the new individuallength = Length(x)mutation_point = RandomSelectIn(1, length)new_individual = Sub(x, 1, mutation_point)+ Sub(y, mutation_point, length)return new_individual