得益于仿生學的研究和發展，群智能優化領域近年來衍生出了多種細化的方法，包括遺傳算法、粒子群優化算法(附代碼)、雜草算法(附代碼)、果蠅算法以及人工魚群算法。其中，李曉磊博士于2003年提出的魚群算法具有避免最優解提前收斂即能夠跳出局部最優解而尋求全局最優解的優點。

0 自然界中的魚群特征

捕食行為：魚向著生存環境中富集度高的地方游去并捕食。

追尾行為：魚A能夠察覺視線范圍內魚B所處的富集度最高，若魚B周圍不太擁擠，那么魚A朝著魚B游去。

聚群行為：魚找到視線范圍內所有的魚，并能夠衡量這些魚的中間位置，如果這個中間位置不是很擁擠，那么魚朝著中間位置游去

隨機行為：魚在當前環境中隨機游動

1 人工魚群算法

1.0 初始化魚群及算法參數

div-----------------解的自變量個數。 e.g: div = 3 --> X = x1, x2, x3

number----------自變量向量?

visual-------------魚群視覺范圍

step---------------魚移動一步的最大步長

try_time----------魚進行捕食行為時搜索周圍環境更優解的次數

delta--------------擁擠程度，[0, 1)，影響追尾和聚群

tag----------------公告牌，記錄每次循環過后，目標函數的最優值

1.1 進入循環，魚群中的魚分別進行如下操作：(偽代碼如下)

捕食行為

def prey()pre_score = fish.func() # 原來fish的目標函數值for(i in 0 : try_time) newfish = new Fish(rnorm(fish.number, sigma)) # 以fish為中心生成新的new_fishif(newfish.func() > pre_score) # 產生了更優解fish = new_fish

追尾行為

def follow()fo = 魚fish視線范圍內所有魚的集合best_fish = fo集合中目標函數值最高的魚if(best_fish周圍擁擠)執行其他操作，如捕食行為、隨機行為elsefish向best_fish移動，最大移動距離為step

聚群行為

def swarm()sw = 魚fish視線范圍內所有魚的集合center_fish = sw的中心位置if(center_fish周圍擁擠)執行其他行為，如隨機操作、捕食操作elsefish向center_fish移動，最大移動step長

隨機行為

def rand()以當前fish位置為中心，隨機向四周移動，每個維度上最多移動step長

2 python實現過程

import math import matplotlib.pyplot as plt import numpymy_flag = 1 # my_flag == 0 計算第一個函數最大值 # my_flag == 1 計算第二個函數最大值class fish:def __init__(self, div, number, visual, step, try_time, delta):# 初始化self.div = divself.number = numberself.visual = visualself.step = stepself.try_time = try_timeself.delta = deltadef distance(self, f):# 計算self魚和f魚之間的距離ll = len(self.number)res = 0.0for i in range(ll):res = res + (self.number[i] - f.number[i]) * (self.number[i] - f.number[i])return math.sqrt(res)def func(self, flag):# 計算魚在當前位置的函數ll = len(self.number)if flag == 0:res = 0for i in range(ll):res = res + self.number[i] * self.number[i]return 500-reselse:res = 0mul = 1for i in range(ll):res = res + math.fabs(self.number[i])mul = mul * math.fabs(self.number[i])return 500-(res + mul)def prey(self):# 捕食操作pre = self.func(my_flag)for i in range(self.try_time):rand = numpy.random.randint(-99, 99, self.div) / 100 * self.visualfor j in range(self.div):self.number[j] = self.number[j] + rand[j]cur = self.func(my_flag)if cur > pre:# 捕食成功# print('原始分數：' + str(pre) + '新分數：' + str(cur) + '捕食成功！！')return curelse:# 捕食失敗for j in range(self.div):self.number[j] = self.number[j] - rand[j]# print("捕食失敗！")return predef swarm(self, fishes):# 聚群行為：向視覺內魚群中心前進stepclose_swarm = find_close_swarm(fishes, self)center_f = center_fish(close_swarm)n = len(close_swarm) - 1if n != 0 and (center_f.func(my_flag) / n > self.delta * self.func(my_flag)):# print("聚群運動")for i in range(self.div):self.number[i] = self.number[i] + self.step * center_f.number[i]return self.func(my_flag)else:# print("隨機運動")return self.rand()def rand(self):for i in range(self.div):self.number[i] = self.number[i] + self.step * numpy.random.uniform(-1, 1, 1)def follow(self, fishes):# 追尾行為：向著視覺內魚群中目標函數值最優的魚前進stepclose_swarm = find_close_swarm(fishes, self)best_f = best_fish(close_swarm)n = len(close_swarm) - 1if n != 0 and (best_f.func(my_flag) / n > self.delta * self.func(my_flag)):# 向前移動# print("向前移動")for i in range(self.div):self.number[i] = self.number[i] + self.step * (best_f.number[i] - self.number[i])return self.func(my_flag)else:# 隨機運動# print("隨機運動")return self.rand()def find_close_swarm(fishes, fish_):# 在種群fishes中查找fish_視覺范圍內的魚# 輸入為fishes，是一個list型變量 和一個fish對象# 輸出為一個fish listres = []for fi in fishes:if fish_.distance(fi) < fish_.visual:res.append(fi)return resdef center_fish(fishes):# 計算當前種群的中心位置，并將其中心位置記為certer_fish以完成聚群操作# 輸入為fishes，是一個list型變量# 輸出為一個fish對象ll = len(fishes)if ll == 0 or ll == 1:return Noneres = fish(fishes[0].div, fishes[0].number, fishes[0].visual, fishes[0].step, fishes[0].try_time, fishes[0].delta)for i in range(fishes[0].div):res.number[i] = 0for i in range(ll):for j in range(res.div):res.number[j] = res.number[j] + fishes[i].number[j]return resdef best_fish(fishes):# 計算當前種群最優個體的位置，并將其返回用于追尾操作# 輸入為fishes，是一個list型變量# 輸出為一個fish對象ll = len(fishes)if ll == 0 or ll == 1:return Noneindex = -1max = 0for i in range(ll):if index == -1 or max < fishes[i].func(my_flag):index = imax = fishes[i].func(my_flag)return fishes[index]def main(): # 主函數fishes = []div = 3 # xi中i的大小，e.g. div == 3 --> x1, x2, x3fish_num = 50 # 魚群個體數目gmax = 100 # 循環最大次數tag = 0 # 公告牌visual = 1step = 0.2try_time = 10delta = 0.3list_of_fishes = []# 初始化魚群for i in range(fish_num):num = numpy.random.uniform(10, 20, div)fi = fish(div, num, visual, step, try_time, delta)fishes.append(fi)for i in range(fish_num):list_of_fishes.append([])for g in range(gmax):for i in range(fish_num):if fishes[i].func(my_flag) > tag:tag = fishes[i].func(my_flag)# print(g, tag)for i in range(fish_num):if g >= 50:list_of_fishes[i].append(fishes[i].func(my_flag))for i in range(fish_num):if tag == fishes[i].func(my_flag):fishes[i].prey()continuetmp = numpy.random.randint(0, 3, 1)if tmp == 0:fishes[i].swarm(fishes)elif tmp == 1:fishes[i].follow(fishes)else:fishes[i].prey()print(tag)x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]# print(x)for i in range(fish_num):# print(list_of_fishes[i][49] < 0.5)if math.fabs(list_of_fishes[i][49] - 500) < 20:plt.plot(x, list_of_fishes[i], color='orangered', marker='o', linestyle='-', label='A')else:plt.plot(x, list_of_fishes[i], color='green', marker='*', linestyle=':', label='C')plt.ylim(20, 50)plt.ylim(-500, 500)plt.xlabel("Loop_time") # X軸標簽plt.ylabel("Value") # Y軸標簽plt.show()if __name__ == '__main__':main()

3 結果展示

目標函數為F(X) = 500 - x1^2 - x2 ^ 2 - x3 ^2

最優解為F(0, 0, 0) = 500 (最大值)

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附：

其他群智能優化算法：
粒子群優化算法(附代碼)https://blog.csdn.net/cccddduil/article/details/123671197?spm=1001.2014.3001.5501

雜草算法(附代碼)https://blog.csdn.net/cccddduil/article/details/124843486?spm=1001.2014.3001.5502

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