遗传算法的简单实现(1):求解函数最大值

刚刚了解了一点遗传算法的原理,参照了网上的一篇入门教程自己实现了一下。

参数和操作：染色体(表示方法)，染色体长度,变异率,交叉率,最大的总群个体数,评估函数,目标函数(在这里与评估函数一致)。

对函数

搜索最大值。

实现思路:将染色体表示为x,y的值(以bit的形式来表示),进行选择，交叉,变异。同时为了保证解具有较好的全局性,我们每次都选择最好的一个解来替代下一代的最差的一个解,同时提高变异率增加多样性。

变异手段就是对某一个bit进行取反,随着变异率的提高,每一代最差个体的情况曲线变得比较稳定。

交叉手段就是对某两个互异的染色体交换部分。

class Person:    def __init__(self,attr,chrom_size,interval):        self.attr = attr        self.interval = interval        self.chrom_size = chrom_size        self.fitness = self.evaluate(self.map_into(attr[0]),self.map_into(attr[1]))    def map_into(self,x):        d = self.interval[1] - self.interval[0]        n = float (2 ** self.chrom_size -1)        return (self.interval[0] + x * d / n)    def evaluate(self,x,y):# to compute the fitness        n = lambda x, y: math.sin (math.sqrt (x*x + y*y)) ** 2 - 0.5        d = lambda x, y: (1 + 0.001 * (x*x + y*y)) ** 2        func = lambda x, y: 0.5 - n (x, y)/d (x, y)        return func (x, y)import randomimport mathclass Population:    def __init__(self,max_num,capacity,mutation_rate,cross_rate,chrom_size):        self.current_generation = []        self.next_generation = []        self.max_generations = max_num        self.size = capacity        self.mutation_rate = mutation_rate        self.cross_rate = cross_rate        self.chrom_size = chrom_size        self.interval = (-10,10)        self.select_prob = []        self.best = None        size = 2**self.chrom_size - 1        for i in range(capacity):            x,y = random.randint(0,size),random.randint(0,size)            one = Person((x,y),self.chrom_size,self.interval)            self.current_generation.append(one)    def generate_selectprob(self):        prob = 0        self.select_prob = []        total = sum(p.fitness for p in self.current_generation)        for each in self.current_generation:            prob += each.fitness/total            self.select_prob.append(prob)    def select(self):        t = random.random()        i = next(i for i,p in enumerate(self.select_prob) if t < p)        return self.current_generation[i]    def cross(self,chrom1,chrom2):        #now:swap only one part         # to do:swap several part of chroms        p = random.random()        if chrom1!=chrom2 and p < self.cross_rate:            pos = random.randint(0,self.chrom_size-1)            mask1,mask2 = (2**self.chrom_size-1)<<pos,2**pos-1            t1,t2 = chrom1&mask1,chrom2&mask1            r1,r2 = chrom1&mask2,chrom2&mask2            chrom1,chrom2 = t1+r2,t2+r1        return chrom1,chrom2    def mutate(self,chrom):        p = random.random()        if p<self.mutation_rate:            pos =  random.randint(1,self.chrom_size)            mask1 = 1<<(pos-1)            chrom = chrom^mask1        return chrom    def evolve(self):        self.generate_selectprob()        num = 0        while num < self.size:            #cross            indv1,indv2 = self.select(),self.select()            indv1_x,indv2_x = self.cross(indv1.attr[0],indv2.attr[0])            indv1_y,indv2_y = self.cross(indv1.attr[1],indv2.attr[1])            #mutation            tmp = [indv1_x,indv1_y,indv2_x,indv2_y]            [indv1_x,indv1_y,indv2_x,indv2_y] = [self.mutate(u) for u in tmp]            one = Person((indv1_x,indv1_y),self.chrom_size,self.interval)            two =  Person((indv2_x,indv2_y),self.chrom_size,self.interval)            self.next_generation.append(one)            self.next_generation.append(two)            num+=2        self.current_generation = self.next_generation        self.next_generation = []    def run (self):        for i in range (self.max_generations):            self.evolve()            _,_,self.best = max((p.fitness,i,p) for i,p in enumerate(self.current_generation))            worest,i = min((p.fitness,i) for i,p in enumerate(self.current_generation))            self.current_generation[i] = self.best            print(self.best.fitness,mean(p.fitness for p in self.current_generation),worest)population = Population(150,50,0.3,0.8,50)ans = population.run()

当我们将搜索空间变大的时候,可以发现找到最优解的情况在变得不稳定,很容易就收敛到局部的最优解,这时候除了增加变异率,最有效的办法就是扩大种群的数量。

结果展示:三元组分别是最优解,平均,最差: