Python优化算法20——精英反向学习与二次插值改进的黏菌算法(ISMA)

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科研里面优化算法都用的多，尤其是各种动物园里面的智能仿生优化算法，但是目前都是MATLAB的代码多，python几乎没有什么包，这次把优化算法系列的代码都从底层手写开始。

需要看以前的优化算法文章可以参考：Python优化算法_阡之尘埃的博客-CSDN博客

算法背景

之前写过黏菌优化算法的文章，现在有很多新的黏菌优化算法，都是进行了一些改进。本次带来的是混沌精英黏菌算法，当然也会和普通的黏菌优化进行对比。

这是文章的摘要：

针对基本黏菌算法（ＳＭＡ）易陷入局部最优值、收敛精度较低和收敛速度较慢的

问题，提出精英反向学习与二次插值改进的黏菌算法（ＩＳＭＡ）。精英反向学习策

略有利于提高黏菌种群多样性和种群质量，提升算法全局寻优性能与收敛精度；利用二次插值生成新的黏菌个

体，并用适应度评估更新全局最优解，有利于增强算法局部开发能力，减少算法收敛时间，使算法跳出局部极值。

通过求解多个单模态、多模态和高维度测试函数进行不同算法之间的对比，结果显示，结合两种策略的ＩＳＭＡ具

有较高的寻优精度、寻优速度和鲁棒性。

文章和理论看看就行，主要是代码。本文都是python实现。文章和代码文件都在文末有获取方式。

代码实现

导入包

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import seaborn as sns
import warnings
import copyplt.rcParams ['font.sans-serif'] ='SimHei'               #显示中文
plt.rcParams ['axes.unicode_minus']=False               #显示负号
warnings.filterwarnings('ignore')
plt.rcParams['font.family'] = 'DejaVu Sans'

只给代码不给使用案例就都是钓鱼的。我这里给出代码，也要给使用案例，先采用一些简单的优化算法常用的测试函数。由于都优化算法需要测试函数，我们先都定义好常见的23个函数：

'''F1函数'''
def F1(X):Results=np.sum(X**2)return Results'''F2函数'''
def F2(X):Results=np.sum(np.abs(X))+np.prod(np.abs(X))return Results'''F3函数'''
def F3(X):dim=X.shape[0]Results=0for i in range(dim):Results=Results+np.sum(X[0:i+1])**2return Results'''F4函数'''
def F4(X):Results=np.max(np.abs(X))return Results'''F5函数'''
def F5(X):dim=X.shape[0]Results=np.sum(100*(X[1:dim]-(X[0:dim-1]**2))**2+(X[0:dim-1]-1)**2)return Results'''F6函数'''
def F6(X):Results=np.sum(np.abs(X+0.5)**2)return Results'''F7函数'''
def F7(X):dim = X.shape[0]Temp = np.arange(1,dim+1,1)Results=np.sum(Temp*(X**4))+np.random.random()return Results'''F8函数'''
def F8(X):Results=np.sum(-X*np.sin(np.sqrt(np.abs(X))))return Results'''F9函数'''
def F9(X):dim=X.shape[0]Results=np.sum(X**2-10*np.cos(2*np.pi*X))+10*dimreturn Results'''F10函数'''
def F10(X):dim=X.shape[0]Results=-20*np.exp(-0.2*np.sqrt(np.sum(X**2)/dim))-np.exp(np.sum(np.cos(2*np.pi*X))/dim)+20+np.exp(1)return Results'''F11函数'''
def F11(X):dim=X.shape[0]Temp=np.arange(1,dim+1,+1)Results=np.sum(X**2)/4000-np.prod(np.cos(X/np.sqrt(Temp)))+1return Results'''F12函数'''
def Ufun(x,a,k,m):Results=k*((x-a)**m)*(x>a)+k*((-x-a)**m)*(x<-a)return Resultsdef F12(X):dim=X.shape[0]Results=(np.pi/dim)*(10*((np.sin(np.pi*(1+(X[0]+1)/4)))**2)+\np.sum((((X[0:dim-1]+1)/4)**2)*(1+10*((np.sin(np.pi*(1+X[1:dim]+1)/4)))**2)+((X[dim-1]+1)/4)**2))+\np.sum(Ufun(X,10,100,4))return Results'''F13函数'''
def Ufun(x,a,k,m):Results=k*((x-a)**m)*(x>a)+k*((-x-a)**m)*(x<-a)return Resultsdef F13(X):dim=X.shape[0]Results=0.1*((np.sin(3*np.pi*X[0]))**2+np.sum((X[0:dim-1]-1)**2*(1+(np.sin(3*np.pi*X[1:dim]))**2))+\((X[dim-1]-1)**2)*(1+(np.sin(2*np.pi*X[dim-1]))**2))+np.sum(Ufun(X,5,100,4))return Results'''F14函数'''
def F14(X):aS=np.array([[-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32,-32,-16,0,16,32],\[-32,-32,-32,-32,-32,-16,-16,-16,-16,-16,0,0,0,0,0,16,16,16,16,16,32,32,32,32,32]])bS=np.zeros(25)for i in range(25):bS[i]=np.sum((X-aS[:,i])**6)Temp=np.arange(1,26,1)Results=(1/500+np.sum(1/(Temp+bS)))**(-1)return Results'''F15函数'''
def F15(X):aK=np.array([0.1957,0.1947,0.1735,0.16,0.0844,0.0627,0.0456,0.0342,0.0323,0.0235,0.0246])bK=np.array([0.25,0.5,1,2,4,6,8,10,12,14,16])bK=1/bKResults=np.sum((aK-((X[0]*(bK**2+X[1]*bK))/(bK**2+X[2]*bK+X[3])))**2)return Results'''F16函数'''
def F16(X):Results=4*(X[0]**2)-2.1*(X[0]**4)+(X[0]**6)/3+X[0]*X[1]-4*(X[1]**2)+4*(X[1]**4)return Results'''F17函数'''
def F17(X):Results=(X[1]-(X[0]**2)*5.1/(4*(np.pi**2))+(5/np.pi)*X[0]-6)**2+10*(1-1/(8*np.pi))*np.cos(X[0])+10return Results'''F18函数'''
def F18(X):Results=(1+(X[0]+X[1]+1)**2*(19-14*X[0]+3*(X[0]**2)-14*X[1]+6*X[0]*X[1]+3*X[1]**2))*\(30+(2*X[0]-3*X[1])**2*(18-32*X[0]+12*(X[0]**2)+48*X[1]-36*X[0]*X[1]+27*(X[1]**2)))return Results'''F19函数'''
def F19(X):aH=np.array([[3,10,30],[0.1,10,35],[3,10,30],[0.1,10,35]])cH=np.array([1,1.2,3,3.2])pH=np.array([[0.3689,0.117,0.2673],[0.4699,0.4387,0.747],[0.1091,0.8732,0.5547],[0.03815,0.5743,0.8828]])Results=0for i in range(4):Results=Results-cH[i]*np.exp(-(np.sum(aH[i,:]*((X-pH[i,:]))**2)))return Results'''F20函数'''
def F20(X):aH=np.array([[10,3,17,3.5,1.7,8],[0.05,10,17,0.1,8,14],[3,3.5,1.7,10,17,8],[17,8,0.05,10,0.1,14]])cH=np.array([1,1.2,3,3.2])pH=np.array([[0.1312,0.1696,0.5569,0.0124,0.8283,0.5886],[0.2329,0.4135,0.8307,0.3736,0.1004,0.9991],\[0.2348,0.1415,0.3522,0.2883,0.3047,0.6650],[0.4047,0.8828,0.8732,0.5743,0.1091,0.0381]])Results=0for i in range(4):Results=Results-cH[i]*np.exp(-(np.sum(aH[i,:]*((X-pH[i,:]))**2)))return Results'''F21函数'''
def F21(X):aSH=np.array([[4,4,4,4],[1,1,1,1],[8,8,8,8],[6,6,6,6],[3,7,3,7],\[2,9,2,9],[5,5,3,3],[8,1,8,1],[6,2,6,2],[7,3.6,7,3.6]])cSH=np.array([0.1,0.2,0.2,0.4,0.4,0.6,0.3,0.7,0.5,0.5])Results=0for i in range(5):Results=Results-(np.dot((X-aSH[i,:]),(X-aSH[i,:]).T)+cSH[i])**(-1)return Results'''F22函数'''
def F22(X):aSH=np.array([[4,4,4,4],[1,1,1,1],[8,8,8,8],[6,6,6,6],[3,7,3,7],\[2,9,2,9],[5,5,3,3],[8,1,8,1],[6,2,6,2],[7,3.6,7,3.6]])cSH=np.array([0.1,0.2,0.2,0.4,0.4,0.6,0.3,0.7,0.5,0.5])Results=0for i in range(7):Results=Results-(np.dot((X-aSH[i,:]),(X-aSH[i,:]).T)+cSH[i])**(-1)return Results'''F23函数'''
def F23(X):aSH=np.array([[4,4,4,4],[1,1,1,1],[8,8,8,8],[6,6,6,6],[3,7,3,7],\[2,9,2,9],[5,5,3,3],[8,1,8,1],[6,2,6,2],[7,3.6,7,3.6]])cSH=np.array([0.1,0.2,0.2,0.4,0.4,0.6,0.3,0.7,0.5,0.5])Results=0for i in range(10):Results=Results-(np.dot((X-aSH[i,:]),(X-aSH[i,:]).T)+cSH[i])**(-1)return Results

把他们的参数设置都用字典装起来

#维度，搜索区间下界，搜索区间上界，最优值
Funobject = {'F1': F1,'F2': F2,'F3': F3,'F4': F4,'F5': F5,'F6': F6,'F7': F7,'F8': F8,'F9': F9,'F10': F10,'F11': F11,'F12': F12,'F13': F13,'F14': F14,'F15': F15,'F16': F16,'F17': F17,'F18': F18,'F19': F19,'F20': F20,'F21': F21,'F22': F22,'F23': F23}
Funobject.keys()Fundim={'F1': [30,-100,100],'F2': [30,-10,10],'F3': [30,-100,100],'F4': [30,-10,10],'F5': [30,-30,30],'F6': [30,-100,100],'F7': [30,-1.28,1.28],'F8': [30,-500,500],'F9':[30,-5.12,5.12],'F10': [30,-32,32],'F11': [30,-600,600],'F12': [30,-50,50],'F13': [30,-50,50],'F14': [2,-65,65],'F15':[4,-5,5],'F16': [2,-5,5],'F17':[2,-5,5],'F18': [2,-2,2],'F19': [3,0,1],'F20': [6,0,1],'F21':[4,0,10],'F22': [4,0,10],'F23': [4,0,10]}

Fundim字典里面装的是对应这个函数的，维度，搜索区间下界，搜索区间上界。这样写好方便我们去遍历测试所有的函数。

精英反向与二次插值改进的黏菌算法

终于到了算法的主代码阶段了，这里还会给出普通的黏菌优化算法的代码。

import numpy as np
import random
import math
import copy''' 精英反向策略种群初始化函数 '''def initial(pop, dim, ub, lb,fun):X = np.zeros([pop, dim])Xback = np.zeros([pop, dim])index = np.zeros(pop)for i in range(pop):for j in range(dim):X[i, j] = random.random()*(ub[j] - lb[j]) + lb[j]Xback[i,j]=ub[j]+lb[j]-X[i,j]if fun(Xback[i,:])<fun(X[i,:]):X[i,:]=copy.copy(Xback[i,:])else:index[i]=1 # 原始解更优，则该解为精英解ubJ = np.max(X,axis=0)lbJ = np.min(X,axis=0)for i in range(pop):if index[i]==0: #更新精英反向解X[i,:]=np.random.random()*(ubJ[j]+lbJ[j])-X[i,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'''改进黏菌优化算法'''def ISMA(pop, dim, lb, ub, MaxIter, fun):z = 0.03  # 位置更新参数X, lb, ub = initial(pop, dim, ub, lb,fun)  # 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 = copy.copy(fitness[0])GbestPositon = copy.copy(X[0, :])Curve = np.zeros([MaxIter, 1])W = np.zeros([pop, dim])  # 权重W矩阵for t in range(MaxIter):worstFitness = fitness[-1]bestFitness = fitness[0]S = bestFitness-worstFitness + 10E-8  # 当前最优适应度于最差适应度的差值，10E-8为极小值，避免分母为0；for i in range(pop):if i < pop/2:  # 适应度排前一半的W计算W[i, :] = 1+np.random.random([1, dim]) * \np.log10((bestFitness-fitness[i])/(S)+1)else:  # 适应度排后一半的W计算W[i, :] = 1-np.random.random([1, dim]) * \np.log10((bestFitness-fitness[i])/(S)+1)# 惯性因子a,btt = -(t/MaxIter)+1if tt != -1 and tt != 1:a = math.atanh(tt)else:a = 1b = 1-t/MaxIter# 位置更新for i in range(pop):if np.random.random() < z:X[i, :] = (ub.T-lb.T)*np.random.random([1, dim])+lb.Telse:p = np.tanh(abs(fitness[i]-GbestScore))vb = 2*a*np.random.random([1, dim])-avc = 2*b*np.random.random([1, dim])-bfor j in range(dim):r = np.random.random()A = np.random.randint(pop)B = np.random.randint(pop)if r < p:X[i, j] = GbestPositon[j] + \vb[0, j]*(W[i, j]*X[A, j]-X[B, j])else:X[i, j] = vc[0, j]*X[i, 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 = copy.copy(fitness[0])GbestPositon = copy.copy(X[0, :])# 改进点：进行二次插值# 随机选择两个个体indexR1 = np.random.randint(pop)indexR2 = np.random.randint(pop)XX=copy.deepcopy(X[indexR1,:])Y = copy.deepcopy(X[indexR2,:])Z = copy.deepcopy(GbestPositon)Fx = fitness[indexR1]Fy=fitness[indexR2]Fz=GbestScoreTemp = np.zeros([1,dim])Temp[0,:]=((Z**2-Y**2)*Fx+(XX**2-Z**2)*Fy+(Y**2-XX**2)*Fz)/(2*((Z-Y)*Fx+(XX-Z)*Fy+(Y-XX)*Fz))for j in range(dim):if Temp[0,j]>ub[j]:Temp[0,j]=ub[j]if Temp[0,j]<lb[j]:Temp[0,j]=lb[j]fTemp = fun(Temp[0,:])if fTemp<GbestScore:GbestScore=fTempfitness[0]=fTempX[0,:]=copy.copy(Temp[0,:])GbestPositon = copy.copy(Temp[0,:])Curve[t] = GbestScorereturn GbestScore, GbestPositon, Curve

普通黏菌优化(SMA)：

''' 种群初始化函数 '''
def initial_SMA(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_SMA(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_SMA(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_SMA(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_SMA(X,index):Xnew = np.zeros(X.shape)for i in range(X.shape[0]):Xnew[i,:] = X[index[i],:]return Xnew'''黏菌优化算法'''
def SMA(pop,dim,lb,ub,MaxIter,fun):z = 0.03 #位置更新参数X,lb,ub = initial_SMA(pop, dim, ub, lb) #初始化种群fitness = CaculateFitness_SMA(X,fun) #计算适应度值fitness,sortIndex = SortFitness_SMA(fitness) #对适应度值排序X = SortPosition_SMA(X,sortIndex) #种群排序GbestScore = copy.copy(fitness[0])GbestPositon = copy.copy(X[0,:])Curve = np.zeros([MaxIter,1])W = np.zeros([pop,dim]) #权重W矩阵for t in range(MaxIter):worstFitness = fitness[-1]bestFitness = fitness[0]S=bestFitness-worstFitness+ 10E-8 #当前最优适应度于最差适应度的差值，10E-8为极小值，避免分母为0；for i in range(pop):if i<pop/2: #适应度排前一半的W计算W[i,:]= 1+np.random.random([1,dim])*np.log10((bestFitness-fitness[i])/(S)+1)else:#适应度排后一半的W计算W[i,:]= 1-np.random.random([1,dim])*np.log10((bestFitness-fitness[i])/(S)+1)#惯性因子a,btt = -(t/MaxIter)+1if tt!=-1 and tt!=1:a = math.atanh(tt)else:a = 1b = 1-t/MaxIter#位置更新for i in range(pop):if np.random.random()<z:X[i,:] = (ub.T-lb.T)*np.random.random([1,dim])+lb.Telse:p = np.tanh(abs(fitness[i]-GbestScore))vb = 2*a*np.random.random([1,dim])-avc = 2*b*np.random.random([1,dim])-bfor j in range(dim):r = np.random.random()A = np.random.randint(pop)B = np.random.randint(pop)if r<p:X[i,j] = GbestPositon[j] + vb[0,j]*(W[i,j]*X[A,j]-X[B,j])else:X[i,j] = vc[0,j]*X[i,j]X = BorderCheck_SMA(X,ub,lb,pop,dim) #边界检测       fitness = CaculateFitness_SMA(X,fun) #计算适应度值fitness,sortIndex = SortFitness_SMA(fitness) #对适应度值排序X = SortPosition_SMA(X,sortIndex) #种群排序if(fitness[0]<=GbestScore): #更新全局最优GbestScore = copy.copy(fitness[0])GbestPositon = copy.copy(X[0,:])Curve[t] = GbestScorereturn GbestScore,GbestPositon,Curve

其实优化算法差不多都是这个流程，边界函数，适应度函数排序，然后寻优过程等等。

两个算法都放入字典，后面批量化测试。

OPT_algorithms = {'SMA':SMA,'ISMA':ISMA}
OPT_algorithms.keys()

简单使用

我们选择F12来测试，先看看F12函数三维的情况：

'''F12绘图函数'''
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3Ddef F12Plot():fig = plt.figure(1) #定义figureax = Axes3D(fig) #将figure变为3dx1=np.arange(-50,50,1) #定义x1，范围为[-50,50],间隔为1x2=np.arange(-50,50,1) #定义x2，范围为[-50,50],间隔为1X1,X2=np.meshgrid(x1,x2) #生成网格nSize = x1.shape[0]Z=np.zeros([nSize,nSize])for i in range(nSize):for j in range(nSize):X=[X1[i,j],X2[i,j]] #构造F12输入X=np.array(X) #将格式由list转换为arrayZ[i,j]=F12(X)  #计算F12的值#绘制3D曲面# rstride:行之间的跨度  cstride:列之间的跨度# rstride:行之间的跨度  cstride:列之间的跨度# cmap参数可以控制三维曲面的颜色组合ax.plot_surface(X1, X2, Z, rstride = 1, cstride = 1, cmap = plt.get_cmap('rainbow'))ax.contour(X1, X2, Z, zdir='z', offset=0)#绘制等高线ax.set_xlabel('X1')#x轴说明ax.set_ylabel('X2')#y轴说明ax.set_zlabel('Z')#z轴说明ax.set_title('F12_space')plt.show()F12Plot()

然后我们使用优化算法来寻优，自定义好所有的参数：

#设置参数
pop = 30 #种群数量
MaxIter = 200#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
#选择适应度函数
fobj = F12
#原始算法
GbestScore,GbestPositon,Curve = ISMA(pop,dim,lb,ub,MaxIter,fobj) 
#改进算法print('------原始算法结果--------------')
print('最优适应度值：',GbestScore)
print('最优解：',GbestPositon)

其实f12测试函数的最小值是0。所以可以看到这个算法几乎达到了最优，效果看起来还行。

自己使用解决实际问题的时候只需要替换fobj这个目标函数的参数就可以了。

这个函数就如同上面所有的自定义的测试函数一样，你只需要定义输入的x，经过1系列实际问题的计算逻辑，返回的适应度值就可以。

绘制适应度曲线

#绘制适应度曲线
plt.figure(figsize=(6,2.7),dpi=128)
plt.semilogy(Curve,'b-',linewidth=2)
plt.xlabel('Iteration',fontsize='medium')
plt.ylabel("Fitness",fontsize='medium')
plt.grid()
plt.title('ISMA',fontsize='large')
plt.legend(['ISMA'], loc='upper right')
plt.show()

我这里是对数轴，但是也收敛了，200轮左右最小值。

其实看到这里差不多就可以去把这个优化算法的函数拿去使用了，演示结束了，但是由于我们这里还需要对它的性能做一些测试，我们会把它在所有的测试函数上都跑一遍，这个时间可能是有点久的。

所有函数都测试一下

准备存储评价结果的数据框

functions = list(Funobject.keys())
algorithms = list(OPT_algorithms.keys())
columns = ['Mean', 'Std', 'Best', 'Worth']
index = pd.MultiIndex.from_product([functions, algorithms], names=['function_name', 'Algorithm_name'])
df_eval = pd.DataFrame(index=index, columns=columns)
df_eval.head()

索引和列名称都建好了，现在就是一个个跑，把值放进去就行了。

准备存储迭代图的数据框

df_Curve=pd.DataFrame(columns=index)
df_Curve

自定义训练函数

#定义训练函数
def train_fun(fobj_name=None,opt_algo_name=None, pop=30,MaxIter=200,Iter=30,show_fit=False):fundim=Fundim[fobj_name]  ; fobj=Funobject[fobj_name]dim=fundim[0]lb = fundim[1]*np.ones([dim, 1]) ; ub = fundim[2]*np.ones([dim, 1])opt_algo=OPT_algorithms[opt_algo_name]GbestScore_one=np.zeros([Iter])GbestPositon_one=np.zeros([Iter,dim])Curve_one=np.zeros([Iter,MaxIter])for i in range(Iter):GbestScore_one[i],GbestPositon_one[i,:],Curve_oneT =opt_algo(pop,dim,lb,ub,MaxIter,fobj)Curve_one[i,:]=Curve_oneT.Toneal_Mean=np.mean(GbestScore_one) #计算平均适应度值oneal_Std=np.std(GbestScore_one)#计算标准差oneal_Best=np.min(GbestScore_one)#计算最优值oneal_Worst=np.max(GbestScore_one)#计算最差值oneal_MeanCurve=Curve_one.mean(axis=0) #求平均适应度曲线#储存结果df_eval.loc[(fobj_name, opt_algo_name), :] = [oneal_Mean,oneal_Std, oneal_Best,oneal_Worst]df_Curve.loc[:,(fobj_name,opt_algo_name)]=oneal_MeanCurve#df_Curve[df_Curve.columns[(fobj_name,opt_algo_name)]] = oneal_MeanCurveif show_fit:print(f'{fobj_name}函数的{opt_algo_name}算法的平均适应度值是{oneal_Mean}，标准差{oneal_Std}，最优值{oneal_Best}，最差值{oneal_Worst}')

训练测试

#设置参数
pop = 30#种群数量
MaxIter = 100 #代次数
Iter = 30 #运行次数

计算，遍历所有的测试函数

#所有函数，所有算法全部一次性计算
for fobj_name in list(Funobject.keys()):for opt_algo_name in OPT_algorithms.keys():try:train_fun(fobj_name=fobj_name,opt_algo_name=opt_algo_name, pop=pop,MaxIter=MaxIter,Iter=Iter)print(f'{fobj_name}的{opt_algo_name}算法完成')except Exception as e: # 使用 except 来捕获错误print(f'{fobj_name}的{opt_algo_name}算法报错了：{e}') # 打印错误信息

查看计算出来的评价指标

df_eval

由于这里大部分的测试函数最优值都是零，我们可以看到。两个算法在寻优的最优值情况都是差不多的，其中isma会比sma的最优值都稍微小一点。所以说两者的效果是差不多的，isma会稍微好一点点。

同样在f5这个最优值为零的函数上，两者都没有寻到最优，也就是说他可能还是没有跳出局部最优的这种情况。sma有的缺陷，isma可能还是存在，但是整体而言的话，从最优值的情况下来看，它的效果确实还稍微好一点点，例如f6和f8的最优值都稍微更小了一些。

画出迭代图

评价一个优化算法肯定不能只从最优的情况来看，还要看他训练轮数寻优收敛的时间轮数，来综合评价。

colors = ['darkorange', 'limegreen', 'lightpink', 'deeppink', 'red', 'cornflowerblue', 'grey']
markers = ['^', 'D', 'o', '*', 'X', 'p', 's']def plot_log_line(df_plot, fobj_name, step=10, save=False):plt.figure(figsize=(6, 3), dpi=128)for column, color, marker in zip(df_plot.columns, colors, markers):plt.semilogy(df_plot.index[::step], df_plot[column][::step].to_numpy(), color=color, marker=marker, label=column, markersize=4, alpha=0.7)plt.xlabel('Iterations')plt.ylabel('f')plt.legend(loc='best', fontsize=8)if save:plt.savefig(f'./图片/{fobj_name}不同迭代图.png', bbox_inches='tight')plt.show()# 使用示例
# plot_log_line(your_dataframe, 'example_plot')
for fobj_name in df_Curve.columns.get_level_values(0).unique():df1=df_Curve[fobj_name]print(f'{fobj_name}的不同算法效果对比：')plot_log_line(df1,fobj_name,5,False)   #保存图片-True