目标函数
编码方式
本程序采用的是二进制编码精确到小数点后五位，经过计算可知对于 其编码长度为18，对于 其编码长度为15，因此每个基于的长度为33。
参数设置
算法步骤
设计的程序主要分为以下步骤：1、参数设置；2、种群初始化；3、用轮盘赌方法选择其中一半较好的个体作为父代；4、交叉和变异；5、更新最优解；6、对最有个体进行自学习操作；7结果输出。其算法流程图为：
算法结果
由程序输出可知其最终优化结果为38.85029，
输出基因编码为[1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1]。
代码
import numpy as npimport randomimport mathimport copyclass Ind(): def __init__(self): self.fitness = 0 self.x = np.zeros(33) self.place = 0 self.x1 = 0 self.x2 = 0def Cal_fit(x, upper, lower): #计算适应度值函数 Temp1 = 0 for i in range(18): Temp1 += x[i] * math.pow(2, i) Temp2 = 0 for i in range(18, 33, 1): Temp2 += math.pow(2, i - 18) * x[i] x1 = lower[0] + Temp1 * (upper[0] - lower[0])/(math.pow(2, 18) - 1) x2 = lower[1] + Temp2 * (upper[1] - lower[1])/(math.pow(2, 15) - 1) if x1 > upper[0]: x1 = random.uniform(lower[0], upper[0]) if x2 > upper[1]: x2 = random.uniform(lower[1], upper[1]) return 21.5 + x1 * math.sin(4 * math.pi * (x1)) + x2 * math.sin(20 * math.pi * x2)def Init(G, upper, lower, Pop): #初始化函数 for i in range(Pop): for j in range(33): G[i].x[j] = random.randint(0, 1) G[i].fitness = Cal_fit(G[i].x, upper, lower) G[i].place = idef Find_Best(G, Pop): Temp = copy.deepcopy(G[0]) for i in range(1, Pop, 1): if G[i].fitness > Temp.fitness: Temp = copy.deepcopy(G[i]) return Tempdef Selection(G, Gparent, Pop, Ppool): #选择函数 fit_sum = np.zeros(Pop) fit_sum[0] = G[0].fitness for i in range(1, Pop, 1): fit_sum[i] = G[i].fitness + fit_sum[i - 1] fit_sum = fit_sum/fit_sum.max() for i in range(Ppool): rate = random.random() Gparent[i] = copy.deepcopy(G[np.where(fit_sum > rate)[0][0]])def Cross_and_Mutation(Gparent, Gchild, Pc, Pm, upper, lower, Pop, Ppool): #交叉和变异 for i in range(Ppool): place = random.sample([_ for _ in range(Ppool)], 2) parent1 = copy.deepcopy(Gparent[place[0]]) parent2 = copy.deepcopy(Gparent[place[1]]) parent3 = copy.deepcopy(parent2) if random.random() < Pc: num = random.sample([_ for _ in range(1, 32, 1)], 2) num.sort() if random.random() < 0.5: for j in range(num[0], num[1], 1): parent2.x[j] = parent1.x[j] else: for j in range(0, num[0], 1): parent2.x[j] = parent1.x[j] for j in range(num[1], 33, 1): parent2.x[j] = parent1.x[j] num = random.sample([_ for _ in range(1, 32, 1)], 2) num.sort() num.sort() if random.random() < 0.5: for j in range(num[0], num[1], 1): parent1.x[j] = parent3.x[j] else: for j in range(0, num[0], 1): parent1.x[j] = parent3.x[j] for j in range(num[1], 33, 1): parent1.x[j] = parent3.x[j] for j in range(33): if random.random() < Pm: parent1.x[j] = (parent1.x[j] + 1) % 2 if random.random() < Pm: parent2.x[j] = (parent2.x[j] + 1) % 2 parent1.fitness = Cal_fit(parent1.x, upper, lower) parent2.fitness = Cal_fit(parent2.x, upper, lower) Gchild[2 * i] = copy.deepcopy(parent1) Gchild[2 * i + 1] = copy.deepcopy(parent2)def Choose_next(G, Gchild, Gsum, Pop): #选择下一代函数 for i in range(Pop): Gsum[i] = copy.deepcopy(G[i]) Gsum[2 * i + 1] = copy.deepcopy(Gchild[i]) Gsum = sorted(Gsum, key = lambda x: x.fitness, reverse = True) for i in range(Pop): G[i] = copy.deepcopy(Gsum[i]) G[i].place = idef Decode(x): #解码函数 Temp1 = 0 for i in range(18): Temp1 += x[i] * math.pow(2, i) Temp2 = 0 for i in range(18, 33, 1): Temp2 += math.pow(2, i - 18) * x[i] x1 = lower[0] + Temp1 * (upper[0] - lower[0]) / (math.pow(2, 18) - 1) x2 = lower[1] + Temp2 * (upper[1] - lower[1]) / (math.pow(2, 15) - 1) if x1 > upper[0]: x1 = random.uniform(lower[0], upper[0]) if x2 > upper[1]: x2 = random.uniform(lower[1], upper[1]) return x1, x2def Self_Learn(Best, upper, lower, sPm, sLearn): #自学习操作 num = 0 Temp = copy.deepcopy(Best) while True: num += 1 for j in range(33): if random.random() < sPm: Temp.x[j] = (Temp.x[j] + 1)%2 Temp.fitness = Cal_fit(Temp.x, upper, lower) if Temp.fitness > Best.fitness: Best = copy.deepcopy(Temp) num = 0 if num > sLearn: break return Bestif __name__ == '__main__': upper = [12.1, 5.8] lower = [-3, 4.1] Pop = 100 Ppool = 50 G_max = 300 Pc = 0.8 Pm = 0.1 sPm = 0.05 sLearn = 20 G = np.array([Ind() for _ in range(Pop)]) Gparent = np.array([Ind() for _ in range(Ppool)]) Gchild = np.array([Ind() for _ in range(Pop)]) Gsum = np.array([Ind() for _ in range(Pop * 2)]) Init(G, upper, lower, Pop) #初始化 Best = Find_Best(G, Pop) for k in range(G_max): Selection(G, Gparent, Pop, Ppool) #使用轮盘赌方法选择其中50%为父代 Cross_and_Mutation(Gparent, Gchild, Pc, Pm, upper, lower, Pop, Ppool) #交叉和变异生成子代 Choose_next(G, Gchild, Gsum, Pop) #选择出父代和子代中较优秀的个体 Cbest = Find_Best(G, Pop) if Best.fitness < Cbest.fitness: Best = copy.deepcopy(Cbest) #跟新最优解 else: G[Cbest.place] = copy.deepcopy(Best) Best = Self_Learn(Best, upper, lower, sPm, sLearn) print(Best.fitness) x1, x2 = Decode(Best.x) print(Best.x) print([x1, x2])
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