鲸鱼算法

自编代码

# main.py

import numpy as np
from numpy import random
from copy import deepcopy

from function import fun, new_min, new_max, pdist2, jingyu

sub = np.array([-50, -50, -50, -50, -50, -50, -50, -50, -50, -50])  # 自变量下限
up = np.array([50, 50, 50, 50, 50, 50, 50, 50, 50, 50])  # 自变量上限
opt = -1  # -1为最小化，1为最大化
# 程序为最小化寻优，如果是最大化寻优更改排序部分程序即可
n = len(sub)  # 自变量个数
num = 500 * n  # 种群大小
det = 10 * n + 100  # 迭代次数
k = 1.5 + 0.1 * n  # k为最大环绕圈数
R = 0.1 * pow(n, 2)  # 当鲨鱼进入猎物该范围，则直接对猎物位置进行逼近
Mc = (up - sub) * 0.1  # 猎物行动最大范围
x = np.zeros([num, n])
f = np.zeros(num)

for s in range(num):
    rand_data = random.random(n)
    rand_data = np.array(rand_data)
    x[s, :] = sub + (up - sub) * rand_data
    f[s] = fun(x[s, :])

best_x = np.zeros(n)
best_f = 0
# 以最小化为例
if opt == -1:
    best_f, a = new_min(f)  # 记录历史最优值
    best_x = x[a, :]  # 记录历史最优解
elif opt == 1:
    best_f, a = new_max(f)  # 记录历史最优值
    best_x = x[a, :]  # 记录历史最优解

trace = np.array([deepcopy(best_f)])
xx = np.zeros([num, n])
ff = np.zeros(num)

for ii in range(det):
    # 猎物躲避,蒙特卡洛模拟周围1000次，并选择最佳的点作为下一逃跑点
    d = pdist2(best_x, x)
    d.sort()
    z = np.exp(-d[1] / np.mean(Mc))  # 猎物急躁系数
    z = max(z, 0.1)
    best_t = []
    best_c = []
    yx = []
    dx = []
    for i in range(1000):
        m = []

        for iii in range(n):
            randi = random.randint(1, 3)
            a = pow(-1, randi)
            m.append(a)

        m = np.array(m)
        random_rand = random.random(n)
        xd = best_x + Mc * z * ((det - (ii + 1)) / det) * random_rand * m
        xd = np.maximum(sub, xd)
        xd = np.minimum(up, xd)
        if i < 1:
            dx = deepcopy(xd)  # (det-ii)/det表示随着追捕，猎物可逃窜的范围越来越小
        else:
            dx = np.vstack((dx,xd))  # (det-ii)/det表示随着追捕，猎物可逃窜的范围越来越小
        yx=np.hstack((yx,fun(xd)))

    if opt == -1:
        best_t, a = new_min(yx)  # 选择最佳逃跑点
        best_c = dx[a, :]
        if best_t < best_f:
            best_f = best_t
            best_x = best_c
        else:
            pass
    elif opt == 1:
        best_t, a = new_max(yx)  # 选择最佳逃跑点
        best_c = dx[a, :]
        if best_t > best_f:
            best_f = best_t
            best_x = best_c
        else:
            pass

    # 鲸鱼追捕
    for i in range(num):
        # 更新公式
        if np.sqrt(np.sum((x[i, :] - best_x) ** 2)) <= R:
            rand = random.random()
            xx[i, :] = x[i, :] + rand * (x[i, :] - best_x)
            xx[i, :] = np.maximum(sub, xx[i, :])
            xx[i, :] = np.minimum(up, xx[i, :])
            ff[i] = fun(xx[i, :])
        else:
            xx[i, :] = x[i, :] + np.real(jingyu(x[i, :] - best_x, k))
            xx[i, :] = np.maximum(sub, xx[i, :])
            xx[i, :] = np.minimum(up, xx[i, :])
            ff[i] = fun(xx[i, :])

    # 引入上一代进行排序,并重新分配角色
    F = np.hstack((np.array([best_f]), f, ff))
    F= np.array(F)
    X = np.vstack(([best_x], x, xx))
    X=np.array(X)
    temp=np.sort(F,axis=-1,kind='stable')
    if opt == -1:
        F, b = temp, np.argsort(F)  # 按小到大排序
    elif opt == 1:
        F, b = temp[::-1], np.argsort(-F)  # 按大到大排序

    X = X[b, :]
    f = F[:num]
    x = X[:num, :]

    if opt == -1:
        best_f, a = new_min(f)  # 记录历史最优值
    elif opt == 1:
        best_f, a = new_max(f)  # 记录历史最优值

    best_x = x[a, :]  # 记录历史最优解
    trace = np.hstack((trace, [best_f]))

print('最优解为：')
print(best_x)
print('最优值为：')
print(float(best_f))

import numpy as np

def new_min(arr):
    min_data = min(arr)
    key = np.argmin(arr)
    
    return min_data, key

import numpy as np

def new_max(arr):
    max_data = max(arr)
    key = np.argmax(arr)
    
    return max_data, key

import numpy as np

def pdist2(best_x, x):
    best_x = np.array(best_x)
    x = np.array(x)
    a = x - best_x
    b = pow(a, 2)
    c = np.sum(b, axis=1)
    d = pow(c, 0.5)

    return d

import copy

import numpy as np
from numpy import random

def jingyu(X, K):
    n = len(X)
    Y = []
    y = np.zeros(n - 1)
    costheta = np.zeros(n - 1)
    theta = np.zeros(n - 1)
    k = np.zeros(n - 1)

    for i in range(n - 1):
        Y = np.append(X[0:i + 1], 0)
        y[i] = np.sqrt(np.sum((X[0:i + 2]) ** 2))
        # 计算角度（圈数）
        costheta[i] = (X[0:i + 2] @ Y) / (np.sqrt(np.sum(X[0:i + 2] ** 2)) * np.sqrt(np.sum(Y ** 2)))

        if np.isnan(costheta[i]) == 1:
            costheta[i] = 1
        if X[i + 1] >= 0:
            theta[i] = np.arccos(costheta[i]) / (2 * np.pi)
        else:
            theta[i] = 2 - np.arccos(costheta[i]) / (2 * np.pi)

        theta[i] = theta[i] * 2 * np.pi
        # 自适应调节k
        if y[i] >= 10:
            k[i] = K * np.exp(-2)
        else:
            k[i] = K * np.exp(-y[i] / 5)

    # 位置更新公式，左包围或右包围
    f = []
    l = 0
    yy = copy.deepcopy(y)
    rand = random.random()

    ttheta = copy.deepcopy(theta)
    l = k[0] * rand
    yy[0] = yy[0] * np.exp(-l)
    ttheta[0] = ttheta[0] + l * 2 * np.pi * (-1) ** (random.randint(1, 3))
    f = [yy[0] * np.cos(ttheta[0]), yy[0] * np.sin(ttheta[0])]
    f = np.array(f)

    if n > 2:
        for j in range(n - 2):
            a = (j + 1) % 2
            if a == 1:
                rand = random.random()
                l = k[j + 1] * rand
                yy[j + 1] = yy[j + 1] * np.exp(-l)
                ttheta[j + 1] = ttheta[j + 1] + l * 2 * np.pi * ((-1) ** (random.randint(1, 3)))
                f = np.concatenate((f * abs(np.cos(ttheta[j + 1])), np.array([yy[j + 1] * np.sin(ttheta[j + 1])])))
            elif a == 0:
                rand = random.random()
                l = k[j + 1] * rand
                yy[j + 1] = yy[j + 1] * np.exp(-l)
                ttheta[j + 1] = ttheta[j + 1] + l * 2 * np.pi * ((-1) ** random.randint(1, 3))
                f = np.concatenate((f * abs(np.sin(ttheta[j + 1])), np.array([yy[j + 1] * np.cos(ttheta[j + 1])])))

    f = f.T
    return f

import numpy as np

def fun(data_list):
    arr = np.array(data_list)
    f = sum(pow(arr, 2))

    return f

结果

摘录代码

鲸鱼优化算法（WOA）（学习）_轨迹跟踪杨的博客-CSDN博客_鲸鱼优化算法

%参数初始化，初始时主要设置代理数量和最大迭代次数即可，其他算法相关的参数因为和当前迭代次数相关，需要在迭代中设置。
clc;clear;
dim=2;%变量的维数
SearchAgents_no=30; % 搜索代理数量,种群中个体个数
Max_iteration=500; % 最大迭代次数
ub=15;%上限
lb=-15;%下限
%种群初始化。随机初始化所有代理各个维度上的位置值，需要保证在取值范围内。
Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;
Leader_score = fobj(Positions(1,:));
for t=1:Max_iteration
    fit(t)=Leader_score;
    %(评估种群中每个代理的目标值，如有某个代理由于当前最优解，则将其设为最优解。)
    for i=1:size(Positions,1)
    % 计算每个代理的目标值
    fitness=fobj(Positions(i,:));
    % 更新最优解
        if fitness < Leader_score % 如果是最大化问题，这里就是">"
        Leader_score=fitness; 
        Leader_pos=Positions(i,:);
        end
    end
    
    
    %(设置和迭代次数相关的算法参数。)
    a=2-t*((2)/Max_iteration); % 等式（3）中a随迭代次数从2线性下降至0 
    %a2从-1线性下降至-2，计算l时会用到
    a2=-1+t*((-1)/Max_iteration);
 
    
    % Update the Position of search agents（对每个代理的每一维度进行位置更新）
    for i=1:size(Positions,1)
        r1=rand(); % r1为[0,1]之间的随机数
        r2=rand(); % r2为[0,1]之间的随机数
 
        A=2*a*r1-a;  % 等式（3）
        C=2*r2;      % 等式（4）
 
        b=1;               %  等式（5）中的常数b
        l=(a2-1)*rand+1;   %  等式（5）中的随机数l
        p = rand();        %  等式（6）中的概率p
        for j=1:size(Positions,2)
            if p<0.5   
                if abs(A)>=1
                rand_leader_index = floor(SearchAgents_no*rand()+1);
                X_rand = Positions(rand_leader_index, :);
                D_X_rand=abs(C*X_rand(j)-Positions(i,j)); % 等式（7）
                Positions(i,j)=X_rand(j)-A*D_X_rand;      % 等式（8）
 
                elseif abs(A)<1
                D_Leader=abs(C*Leader_pos(j)-Positions(i,j)); % 等式（1）
                Positions(i,j)=Leader_pos(j)-A*D_Leader;      % 等式（2）
                end
            elseif p>=0.5
 
                distance2Leader=abs(Leader_pos(j)-Positions(i,j));
                % 等式（5）
                Positions(i,j)=distance2Leader*exp(b.*l).*cos(l.*2*pi)+Leader_pos(j);
            end
        end
    end
 
end
k=1:1:500;
plot(k,fit,'r');

function y=fobj(x)
 
 y=2*x(1)^2+x(2)^2-x(1)*x(2)-10*x(1)-4*x(2)+60;
  
end

鲸鱼优化算法Python实现 - 代码先锋网 (codeleading.com)

import numpy as np
import random
import math
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

'''优化函数'''


# y = x^2, 用户可以自己定义其他函数
def fun(X):
    output = sum(np.square(X))
    return output


''' 种群初始化函数 '''


def initial(pop, dim, ub, lb):
    X = np.zeros([pop, dim])
    for i in range(pop):
        for j in range(dim):
            X[i, j] = random.random() * (ub[j] - lb[j]) + lb[j]

    return X, lb, ub


'''边界检查函数'''


def BorderCheck(X, ub, lb, pop, dim):
    for i in range(pop):
        for j in range(dim):
            if X[i, j] > ub[j]:
                X[i, j] = ub[j]
            elif X[i, j] < lb[j]:
                X[i, j] = lb[j]
    return X


'''计算适应度函数'''


def CaculateFitness(X, fun):
    pop = X.shape[0]
    fitness = np.zeros([pop, 1])
    for i in range(pop):
        fitness[i] = fun(X[i, :])
    return fitness


'''适应度排序'''


def SortFitness(Fit):
    fitness = np.sort(Fit, axis=0)
    index = np.argsort(Fit, axis=0)
    return fitness, index


'''根据适应度对位置进行排序'''


def SortPosition(X, index):
    Xnew = np.zeros(X.shape)
    for i in range(X.shape[0]):
        Xnew[i, :] = X[index[i], :]
    return Xnew


'''鲸鱼优化算法'''


def WOA(pop, dim, lb, ub, Max_iter, fun):
    X, lb, ub = initial(pop, dim, ub, lb)  # 初始化种群
    fitness = CaculateFitness(X, fun)  # 计算适应度值
    fitness, sortIndex = SortFitness(fitness)  # 对适应度值排序
    X = SortPosition(X, sortIndex)  # 种群排序
    GbestScore = fitness[0]
    GbestPositon = np.zeros([1,dim])
    GbestPositon[0,:] = X[0, :]
    Curve = np.zeros([MaxIter, 1])
    for t in range(MaxIter):
        Leader = X[0, :]  # 领头鲸鱼
        a = 2 - t * (2 / MaxIter)  # 线性下降权重2 - 0
        a2 = -1 + t * (-1 / MaxIter)  # 线性下降权重-1 - -2
        for i in range(pop):
            r1 = random.random()
            r2 = random.random()

            A = 2 * a * r1 - a
            C = 2 * r2
            b = 1
            l = (a2 - 1) * random.random() + 1

            for j in range(dim):

                p = random.random()
                if p < 0.5:
                    if np.abs(A) >= 1:
                        rand_leader_index = min(int(np.floor(pop * random.random() + 1)), pop - 1)
                        X_rand = X[rand_leader_index, :]
                        D_X_rand = np.abs(C * X_rand[j] - X[i, j])
                        X[i, j] = X_rand[j] - A * D_X_rand
                    elif np.abs(A) < 1:
                        D_Leader = np.abs(C * Leader[j] - X[i, j])
                        X[i, j] = Leader[j] - A * D_Leader
                elif p >= 0.5:
                    distance2Leader = np.abs(Leader[j] - X[i, j])
                    X[i, j] = distance2Leader * np.exp(b * l) * np.cos(l * 2 * math.pi) + Leader[j]

        X = BorderCheck(X, ub, lb, pop, dim)  # 边界检测
        fitness = CaculateFitness(X, fun)  # 计算适应度值
        fitness, sortIndex = SortFitness(fitness)  # 对适应度值排序
        X = SortPosition(X, sortIndex)  # 种群排序
        if fitness[0] <= GbestScore:  # 更新全局最优
            GbestScore = fitness[0]
            GbestPositon[0,:] = X[0, :]
        Curve[t] = GbestScore

    return GbestScore, GbestPositon, Curve


'''主函数 '''
# 设置参数
pop = 50  # 种群数量
MaxIter = 1000  # 最大迭代次数
dim = 30  # 维度
lb = -100 * np.ones([dim, 1])  # 下边界
ub = 100 * np.ones([dim, 1])  # 上边界

GbestScore, GbestPositon, Curve = WOA(pop, dim, lb, ub, MaxIter, fun)
print('最优适应度值：', GbestScore)
print('最优解：', GbestPositon)

# 绘制适应度曲线
plt.figure(1)
plt.plot(Curve, 'r-', linewidth=2)
plt.xlabel('Iteration', fontsize='medium')
plt.ylabel("Fitness", fontsize='medium')
plt.grid()
plt.title('WOA', fontsize='large')

# 绘制搜索空间
fig = plt.figure(2)
ax = Axes3D(fig)
X = np.arange(-4, 4, 0.25)
Y = np.arange(-4, 4, 0.25)
X, Y = np.meshgrid(X, Y)
Z = X ** 2 + Y ** 2
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='rainbow')
plt.show()

鲸鱼优化数学原理及Python实现 - 知乎 (zhihu.com)

0. 初始化

import numpy as np
import matplotlib.pyplot as plt

1. 样本点生成模块

def sampleGeneartor():
    X = np.arange(0, 5, 0.01)
    Y = X**3 - 4*X**2 + 1*X - 3
    e = np.random.normal(0, 2, 500)
    Y = Y + e
    plt.scatter(X, Y, 0.5)
    return X, Y

2. WOA优化算法模块

class woa():
    #初始化
    def __init__(self, X_train, Y_train, LB=np.array([-5, -5, -5, -5]),\
                 UB= np.array([5, 5, 5, 5]), dim=4, b=1, whale_num=20, max_iter=500):
        self.X_train = X_train
        self.Y_train = Y_train
        self.LB = LB
        self.UB = UB
        self.dim = dim
        self.whale_num = whale_num
        self.max_iter = max_iter
        self.b = b
        #Initialize the locations of whale
        self.X = np.random.uniform(0, 1, (whale_num, dim))*(UB - LB) + LB
        self.gBest_score = np.inf
        self.gBest_curve = np.zeros(max_iter)
        self.gBest_X = np.zeros(dim) 
    
    #适应度函数  
    def fitFunc(self, input):
        a = input[0]; b = input[1]; c = input[2]; d = input[3]
        Y_Hat = a*self.X_train**3 + b*self.X_train**2 + c*self.X_train + d 
        fitFunc = np.sum((Y_Hat - self.Y_train)**2)/np.shape(Y_Hat)[0]
        return fitFunc   
        
    #优化模块  
    def opt(self):
        t = 0
        while t < self.max_iter:
            for i in range(self.whale_num):
                self.X[i, :] = np.clip(self.X[i, :], self.LB, self.UB) #Check boundries
                fitness = self.fitFunc(self.X[i, :])
                # Update the gBest_score and gBest_X
                if fitness < self.gBest_score:
                    self.gBest_score = fitness
                    self.gBest_X = self.X[i, :].copy()
            
            a = 2*(self.max_iter - t)/self.max_iter
            #Update the location of whales
            for i in range(self.whale_num):
                p = np.random.uniform()
                R1 = np.random.uniform()
                R2 = np.random.uniform()
                A = 2*a*R1 - a
                C = 2*R2
                l = 2*np.random.uniform() - 1
                
                if p >= 0.5:
                    D = abs(self.gBest_X - self.X[i, :])
                    self.X[i, :] = D*np.exp(self.b*l)*np.cos(2*np.pi*l)+self.gBest_X
                else:
                    if abs(A) < 1:
                        D = abs(C*self.gBest_X - self.X[i, :])
                        self.X[i, :] = self.gBest_X - A*D
                    else:
                        rand_index = np.random.randint(low=0, high=self.whale_num)
                        X_rand = self.X[rand_index, :]
                        D = abs(C*X_rand - self.X[i, :])
                        self.X[i, :] = X_rand - A*D
        
            self.gBest_curve[t] = self.gBest_score       
            if (t%100 == 0) :
                print('At iteration: ' + str(t))  
            t+=1 
        return self.gBest_curve, self.gBest_X

4. 主程序

# main
'''
main function
'''
X, Y = sampleGeneartor()
fitnessCurve, para = woa(X, Y, dim=4, whale_num=60, max_iter=2000).opt()
yPre = para[0]*X**3 + para[1]*X**2 + para[2]*X + para[3] 
plt.scatter(X, yPre, 0.5)

plt.figure()
plt.plot(fitnessCurve, linewidth='0.5')
plt.show()