人工智能中的局部搜索算法

Posted 2020-09-23 张玉宝

  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 state
    current_state = initial_state
    loop do
        next_state = the highest neighbor
        if (next_state is higher than current_state)
           current_state = next_state
        else
           return 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 state

    current_state = initial_state
    for t = 1 to infinite do
        T = schedule(t)
        if T = 0 then
            return current_state
        next_state = a randomly selected neighbor
        E = next_state.height - current_state.height
        if E > 0 then
            current_state = next_state
        else 
            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 state
    inputs: population, a set of individuals
            fitness， a function that measures fitness of an individual
    
    repeat
        new_population = empty_set
        for i = 1 to sizeof(population) do
            x = RandomSelect(population, fitness)
            y = RandomSelect(population, fitness)
            new_individual = Reproduce(x, y)
            if (a probability) then
                new_individual = Mutate(new_individual)
            add new_individual to new_population
    until some individuals are fit enough or time has elapsed
    return the best individual in the population
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function Reproduce(x, y) returns a new individual
    inputs: x, y, the parents of the new individual
    
    length = Length(x)
    mutation_point = RandomSelectIn(1, length)
    new_individual = Sub(x, 1, mutation_point)
                     + Sub(y, mutation_point, length)
    return new_individual