Python演化计算基准函数详解

基准函数是测试演化计算算法性能的函数集，由于大部分基准函数集都是c/c++编写，python编写的基准函数比较少，因此本文实现了13个常用基准函数的python版。

基准函数定义

代码实现

benchmark.py

import numpy as np
import copy
"""
author : robin_hua
update time : 2021.10.14
version : 1.0
"""
class sphere:
    def __init__(self, x):
        self.x = x
    def getvalue(self):
        res = np.sum(self.x**2)
        return res
class schwefel2_22:
    def __init__(self, x):
        self.x = x
    def getvalue(self):
        res = np.sum(np.abs(self.x)) + np.prod(np.abs(self.x))
        return res
class noise:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        res = np.sum(np.arange(1, d + 1) * self.x ** 4) + np.random.random()
        return res
class schwefel2_21:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        res = np.max(np.abs(self.x))
        return res
class step:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        res = np.sum(int(self.x + 0.5) ** 2)
        return res
class rosenbrock:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        res = np.sum(np.abs(100*(self.x[1:] - self.x[:-1]**2)**2 + (1 - self.x[:-1])**2))
        return res
class schwefel:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        res = 418.9829*d - np.sum(self.x * np.sin(np.sqrt(np.abs(self.x))))
        return res
class rastrigin:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        res = 10 * d + np.sum(self.x ** 2 - 10 * np.cos(2 * np.pi * self.x))
        return res
class ackley:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        res = - 20 * np.exp(-0.2 * np.sqrt(np.mean(self.x ** 2)))
        res = res - np.exp(np.mean(np.cos(2 * np.pi * self.x))) + 20 + np.exp(1)
        return res
class griewank:
    def __init__(self,x):
        self.x = x
    def getvalue(self):
        d = self.x.shape[0]
        i = np.arange(1, d + 1)
        res = 1 + np.sum(self.x ** 2) / 4000 - np.prod(np.cos(self.x / np.sqrt(i)))
        return res
class generalized_penalized:
    def __init__(self,x):
        self.x = x
    def u(self,a,k,m):
        temp = copy.deepcopy(self.x)
        temp[-a <= temp.any() <= a] = 0
        temp[temp > a] = k*(temp[temp > a]-a)**m
        temp[temp < -a] = k * (-temp[temp < -a] - a) ** m
        """
        temp = np.zeros_like(self.x)
        d = self.x.shape[0]
        for i in range(d):
            if self.x[i]>a:
                temp[i] = k*(self.x[i]-a)**m
            elif self.x[i]<-a:
                temp[i] = k * (-self.x[i] - a) ** m
            else:
                pass
        """
        return temp
    def getvalue(self):
        d = self.x.shape[0]
        y = 1+1/4*(self.x+1)
        res = np.pi/d*(10*np.sin(np.pi*y[0])**2+np.sum((y[:-1]-1)**2*(1+10*np.sin(np.pi*y[1:])**2))+(y[-1]-1)**2)+np.sum(self.u(10,100,4))
        return res
def benchmark_func(x,func_num):
    func = func_list[func_num]
    res = func(x)
    return res
func_list = [sphere,schwefel2_22,noise,schwefel2_21,step,rosenbrock,schwefel,rastrigin,ackley,griewank,generalized_penalized]

调用方法

输入为向量x和函数编号func_num

import benchmark
import numpy as np
vector = np.random.random(30)
value = benchmark.benchmark_func(x=vector,func_num=0).getvalue()

总结

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