CEC2017基础函数说明Python版本

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CEC2017基础函数说明Python版本

前言

撑得慌,拿来练练手。部分函数没有实现,因为比较麻烦。我这边玩的话,也是直接拿这个玩,因为实际上他们玩的时候因该是加了偏置转换的,像cec2003好像都是没有偏置的。反正都能够说明问题,管你那么多。

Bent Cigar Function

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def F1(self,X):
        Dim = len(X)
        res = X[0]*X[0]
        temp = 0.
        for i in range(2,Dim+1):
            temp+=X[i-1]*X[i-1]
        res+=self.pow(10,6)*temp
        return res
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Sum of Different Power Function

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def F2(self,X):
        res = 0.
        Dim = len(X)
        for i in range(1,Dim+1):
            res+=self.pow(abs(X[i-1]),(i+1))
        return res
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Zakharov Function

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 def F3(self,X):
        part1 = 0.
        part2 = 0.
        for x in X:
            part1+=x*x
            part2+=0.5*x
        res = part1+self.pow(part2,2)+self.pow(part2,4)
        return res
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Rosenbrock’s Function

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    def F4(self,X):
        Dim  = len(X)
        res = 0.
        for i in range(1,Dim):
            res+=100*self.pow((self.pow(X[i-1],2)-X[i]),2)+(X[i-1]-1)+self.pow((X[i]-1),2)
        return res
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Rastrigin’s Function

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 def F5(self,X):
        res = 0.
        for x in X:
            res+=(x*x-10*self.cos(2*self.pi*x)+10)
        return res
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Expanded Schaffer’s F6 Function

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    def __g(self,x1,x2):
        res = 0.5+(self.pow(self.sin(self.sqrt(x1*x1+x2*x2)),2)/self.pow((1+0.001*(x1*x1+x2*x2)),2))
        return res

    def F6(self,X):
        Dim = len(X)
        res = 0.
        for i in range(Dim-1):
            res+=self.__g(X[i],X[i+1])
        res+=self.__g(X[Dim-1],X[0])
        return res
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Lunacek bi-Rastrigin Function

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Non-continuous Rotated Rastrigin’s Function

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    def F8(self,X):

        res = 0.
        for x in X:
            if(abs(x)<0.5):
                y = x
            else:
                y = (round(2*x)/2)
            res+=y*y - 10*(self.cos(2*self.pi*y)) + 10
        return res
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Levy Function

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def F9(self,X):
        Dim = len(X)
        res = self.pow(self.sin(self.pi*(1+(X[0]-1/4))),2)
        part2 = 0.
        for i in range(1,Dim):
            w = (1+(X[i-1]-1/4))
            part2+=self.pow(w,2)*(1+10*self.pow(self.pi*w+1,2))
        w = (1 + (X[Dim - 1] - 1 / 4))
        res+=part2+(self.pow(w-1,2)*(1+self.pow(self.sin(2*self.pi*w),2)))
        return res
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Modified Schwefel’s Function

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High Conditioned Elliptic Function

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def F11(self,X):
        Dim = len(X)
        res = 0.
        for i in range(1,Dim+1):
            res+=self.pow(1000000,(i-1/Dim-1))*X[i-1]*X[i-1]
        return res
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Discus Function

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  def F12(self,X):
        res = 1000000*X[0]*X[0]
        Dim = len(X)
        for i in range(1,Dim):
            res+=X[i]*X[i]
        return res
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Ackley’s Function

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    def F13(self,X):
        Dim = len(X)
        part2 = 0.
        part3 = 0.
        for x in X:
            part2+=x*x
            part3+=self.cos(self.pi*2*x)
        res = -20*self.exp(-0.2*self.sqrt((1/Dim)*part2))-self.exp((1/Dim)*part3)+20+self.e
        return res
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Weierstrass Function

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    def F14(self,X):
        kmax = 20;a=0.5;b=3
        Dim = len(X)

        part1 = 0.
        for x in X:
            temp = 0.
            for i in range(kmax+1):
                temp+=self.pow(a,i)*self.cos(2*self.pi*self.pow(b,i)*(x+0.5))
            part1+=temp
        part2 = Dim
        temp=0.
        for i in range(kmax+1):
            temp += self.pow(a, i) * self.cos(2 * self.pi * self.pow(b, i) * 0.5)
        part2*=temp
        res = part1-part2
        return res

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Griewank’s Function

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   def F15(self,X):

        part1 = 0.
        part2 = 1
        Dim = len(X)
        for i in range(1,Dim+1):
            part1+=X[i-1]*X[i-1]/4000
            part2*=self.cos(X[i-1]/self.sqrt(i))
        res = part1-part2 +1
        return res
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Katsuura Function

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def F16(self,X):
        Dim = len(X)
        part1 = 1
        for i in range(1,Dim+1):
            temp=0.
            for j in range(1,33):
                temp+=abs(self.pow(2,j)*X[i-1]-round(self.pow(2,j)*X[i-1]))/2**j
            temp = self.pow(1+i*temp,(10/Dim**1.2))
            part1*=temp
        res = (10/Dim**2)*part1-(10/Dim**2)
        return res
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HappyCat Function

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  def F17(self,X):
        Dim = len(X)
        part1 = 0.
        part2 = 0.

        for x in X:
            part1+=x*x
            part2+=x
        res = self.pow(abs(part1-Dim),0.25)+(0.5*part1+part2)/Dim + 0.5

        return res
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HGBat Function

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    def F18(self,X):
        Dim = len(X)
        part1 = 0.
        part2 = 0.
        for x in X:
            part1+=x*x
            part2+=x
        res = self.pow(abs(self.pow(part1,2)-self.pow(part2,2)),0.5)+(0.5*part1+part2)/Dim + 0.5
        return res

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Schaffer's F7 Function

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    def F20(self,X):
        Dim = len(X)
        part1 = 0.
        for i in range(0,Dim-1):
            s = self.sqrt(X[i]**2+X[i+1]**2)
            part1+=self.sqrt(s)*(self.sin(50.0*s**0.2)+1)
        res = self.pow((1/(Dim-1))*part1,2)
        return res



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完整代码

import math
class Functions(object):
    """
    先实例出对象来,减少new对象的时间,python优化
    """
    pow = math.pow
    cos = math.cos
    sin = math.sin
    pi = math.pi
    exp = math.exp
    sqrt = math.sqrt
    e = math.e
    def F1(self,X):
        Dim = len(X)
        res = X[0]*X[0]
        temp = 0.
        for i in range(2,Dim+1):
            temp+=X[i-1]*X[i-1]
        res+=self.pow(10,6)*temp
        return res
    def F2(self,X):
        res = 0.
        Dim = len(X)
        for i in range(1,Dim+1):
            res+=self.pow(abs(X[i-1]),(i+1))
        return res
    def F3(self,X):
        part1 = 0.
        part2 = 0.
        for x in X:
            part1+=x*x
            part2+=0.5*x
        res = part1+self.pow(part2,2)+self.pow(part2,4)
        return res
    def F4(self,X):
        Dim  = len(X)
        res = 0.
        for i in range(1,Dim):
            res+=100*self.pow((self.pow(X[i-1],2)-X[i]),2)+(X[i-1]-1)+self.pow((X[i]-1),2)
        return res
    def F5(self,X):
        res = 0.
        for x in X:
            res+=(x*x-10*self.cos(2*self.pi*x)+10)
        return res

    def __g(self,x1,x2):
        res = 0.5+(self.pow(self.sin(self.sqrt(x1*x1+x2*x2)),2)/self.pow((1+0.001*(x1*x1+x2*x2)),2))
        return res

    def F6(self,X):
        Dim = len(X)
        res = 0.
        for i in range(Dim-1):
            res+=self.__g(X[i],X[i+1])
        res+=self.__g(X[Dim-1],X[0])
        return res

    def __A(self, alpha,Dim,i):
        res = self.pow(alpha,(i-1/Dim-1))
        return res


    def F8(self,X):

        res = 0.
        for x in X:
            if(abs(x)<0.5):
                y = x
            else:
                y = (round(2*x)/2)
            res+=y*y - 10*(self.cos(2*self.pi*y)) + 10
        return res
    def F9(self,X):
        Dim = len(X)
        res = self.pow(self.sin(self.pi*(1+(X[0]-1/4))),2)
        part2 = 0.
        for i in range(1,Dim):
            w = (1+(X[i-1]-1/4))
            part2+=self.pow(w,2)*(1+10*self.pow(self.pi*w+1,2))
        w = (1 + (X[Dim - 1] - 1 / 4))
        res+=part2+(self.pow(w-1,2)*(1+self.pow(self.sin(2*self.pi*w),2)))
        return res
    def F11(self,X):
        Dim = len(X)
        res = 0.
        for i in range(1,Dim+1):
            res+=self.pow(1000000,(i-1/Dim-1))*X[i-1]*X[i-1]
        return res

    def F12(self,X):
        res = 1000000*X[0]*X[0]
        Dim = len(X)
        for i in range(1,Dim):
            res+=X[i]*X[i]
        return res

    def F13(self,X):
        Dim = len(X)
        part2 = 0.
        part3 = 0.
        for x in X:
            part2+=x*x
            part3+=self.cos(self.pi*2*x)
        res = -20*self.exp(-0.2*self.sqrt((1/Dim)*part2))-self.exp((1/Dim)*part3)+20+self.e
        return res

    def F14(self,X):
        kmax = 20;a=0.5;b=3
        Dim = len(X)

        part1 = 0.
        for x in X:
            temp = 0.
            for i in range(kmax+1):
                temp+=self.pow(a,i)*self.cos(2*self.pi*self.pow(b,i)*(x+0.5))
            part1+=temp
        part2 = Dim
        temp=0.
        for i in range(kmax+1):
            temp += self.pow(a, i) * self.cos(2 * self.pi * self.pow(b, i) * 0.5)
        part2*=temp
        res = part1-part2
        return res

    def F15(self,X):

        part1 = 0.
        part2 = 1
        Dim = len(X)
        for i in range(1,Dim+1):
            part1+=X[i-1]*X[i-1]/4000
            part2*=self.cos(X[i-1]/self.sqrt(i))
        res = part1-part2 +1
        return res

    def F16(self,X):
        Dim = len(X)
        part1 = 1
        for i in range(1,Dim+1):
            temp=0.
            for j in range(1,33):
                temp+=abs(self.pow(2,j)*X[i-1]-round(self.pow(2,j)*X[i-1]))/2**j
            temp = self.pow(1+i*temp,(10/Dim**1.2))
            part1*=temp
        res = (10/Dim**2)*part1-(10/Dim**2)
        return res

    def F17(self,X):
        Dim = len(X)
        part1 = 0.
        part2 = 0.

        for x in X:
            part1+=x*x
            part2+=x
        res = self.pow(abs(part1-Dim),0.25)+(0.5*part1+part2)/Dim + 0.5

        return res

    def F18(self,X):
        Dim = len(X)
        part1 = 0.
        part2 = 0.
        for x in X:
            part1+=x*x
            part2+=x
        res = self.pow(abs(self.pow(part1,2)-self.pow(part2,2)),0.5)+(0.5*part1+part2)/Dim + 0.5
        return res

    def F20(self,X):
        Dim = len(X)
        part1 = 0.
        for i in range(0,Dim-1):
            s = self.sqrt(X[i]**2+X[i+1]**2)
            part1+=self.sqrt(s)*(self.sin(50.0*s**0.2)+1)
        res = self.pow((1/(Dim-1))*part1,2)
        return res


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