【Python】新鲜出炉的海洋捕食者算法Python版本

2020年发表的海洋捕食者算法《Marine Predators Algorithm: A nature-inspired metaheuristic》。

作者只在原论文中给出了MATLAB代码，网上也没有Python版本，我自己用Python重写了MATLAB代码。

"""
    2020海洋捕食者算法
"""
import numpy as np
import random
import math

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]  # 均匀分布随机初始化

    return X, lb, ub


# 将超过边界的直接用边界值赋值
def BorderCheckForOne(x, ub, lb, pop, dim):
    if x > ub[0]:
        x = ub[0]
    elif x < lb[0]:
        x = lb[0]
    return x

def levy(n, m, beta):
    num = math.gamma(1+beta)*math.sin(math.pi*beta/2)
    den = math.gamma((1+beta)/2) * beta * 2**((beta-1)/2)
    sigma_u = (num/den)**(1/beta)
    u = np.random.normal(0,sigma_u,(n,m))
    v = np.random.normal(0,1,(n,m))

    return u/(np.abs(v)**(1/beta)) ## ^的用法好像有错


def MPA(pop, dim, lb, ub, MaxIter, fun):
    Top_predator_pos = np.zeros(dim)  #或者np.zeros([1,dim])
    Top_predator_fit = float("inf")

    Convergence_curve = np.zeros(MaxIter)
    stepsize = np.zeros([pop, dim])  # pop×dim
    fitness = np.inf * np.ones([pop, 1])   # pop×1

    # 初始化种群
    X, lb, ub = initial(pop, dim, ub, lb)

    Xmin = lb[0] * np.ones([pop, dim])
    Xmax = ub[0] * np.ones([pop, dim])

    Iter = 0
    FADs = 0.2
    P = 0.5

    while Iter < MaxIter:

        # =================== 对上一轮的进行复盘 ============
        for i in range(0, pop):
            # 1.边界检测
            for j in range(0, dim):
                X[i, j] = BorderCheckForOne(X[i, j], ub, lb, pop, dim)

            # 2.计算每个鲨鱼的适应度值
            fitness[i, 0] = fun(X[i, :])
            if fitness[i, 0] < Top_predator_fit:  # 23个基准函数都是越小越好
                Top_predator_fit = fitness[i, 0].copy()
                Top_predator_pos = X[i, :].copy()

        # =================== Memory saving ===============
        if Iter == 0:
            fit_old = fitness.copy()
            X_old = X.copy()

        for i in range(pop):
            if fit_old[i, 0] < fitness[i, 0]:
                fitness[i, 0] = fit_old[i, 0].copy()  # 如果上一轮的位置更好，还是用上一轮的
                X[i, :] = X_old[i, :].copy()

        fit_old = fitness.copy()
        X_old = X.copy()

        # =================== Levy=======
        Elite = np.ones([pop, 1]) * Top_predator_pos
        CF = (1-Iter/MaxIter)**(2*Iter/MaxIter)

        RL=0.05*levy(pop, dim, 1.5)  # levy返回一个pop×dim的矩阵
        RB = np.random.randn(pop, dim)  # 满足正态分布的pop×dim大小矩阵

        # ===============遍历每个个体==============
        for i in range(pop):
            for j in range(dim):
                R = random.random()
                # ================公式12============
                if Iter < MaxIter/3:
                    stepsize[i, j] = RB[i, j] * ( Elite[i, j]-RB[i, j]*X[i, j] )
                    X[i, j] = X[i, j] + P*R*stepsize[i, j]
                # ===============公式13 和 14=======
                elif Iter>MaxIter/3 and Iter < 2*MaxIter/3:
                    if i > pop/2:
                        stepsize[i, j] = RB[i, j] * (RB[i, j]*Elite[i, j]-X[i, j])
                        X[i, j] = Elite[i, j] + P*CF*stepsize[i, j]
                    else:
                        stepsize[i, j] = RL[i, j] * (Elite[i, j]-RL[i, j]*X[i, j])
                        X[i, j] = X[i, j] + P * R *stepsize[i, j]
                # ==============公式15==============
                else:
                    stepsize[i, j] = RL[i, j]*( RL[i, j]*Elite[i, j]-X[i, j])
                    X[i, j] = Elite[i, j] + P*CF*stepsize[i, j]

        # =================== 对上一轮的进行复盘 ============
        for i in range(0, pop):
            # 1.边界检测
            for j in range(0, dim):
                X[i, j] = BorderCheckForOne(X[i, j], ub, lb, pop, dim)

            # 2.计算每个鲨鱼的适应度值
            fitness[i, 0] = fun(X[i, :])
            if fitness[i, 0] < Top_predator_fit:  # 23个基准函数都是越小越好
                Top_predator_fit = fitness[i, 0].copy()
                Top_predator_pos = X[i, :].copy()

        # =================== Memory saving ===============
        if Iter == 0:
            fit_old = fitness.copy()
            X_old = X.copy()

        for i in range(pop):
            if fit_old[i, 0] < fitness[i, 0]:
                fitness[i, 0] = fit_old[i, 0].copy()  # 如果上一轮的位置更好，还是用上一轮的
                X[i, :] = X_old[i, :].copy()

        fit_old = fitness.copy()
        X_old = X.copy()

        # =====================对整体进行一个更新（公式16）=====
        if random.random() < FADs:
            U = (np.random.rand(pop, dim) < FADs)
            X = X + CF*np.multiply(Xmin + np.multiply(np.random.rand(pop, dim), (Xmax-Xmin)), U)
        else:
            r = random.random()
            stepsize = (FADs*(1-r)+r) * (X[random.sample(range(0, pop), pop),:] - X[random.sample(range(0, pop), pop),:])
            X = X + stepsize

        Iter = Iter+1
        if Iter!=MaxIter:
            Convergence_curve[Iter] = Top_predator_fit

    return Top_predator_fit, Top_predator_pos, Convergence_curve

在23个基准函数上跑了一遍，验证得代码正确

fun 1 ---- 4 轮的平均值: 1.590879014464718e-22
fun 2 ---- 4 轮的平均值: 3.1015801972813803e-13
fun 3 ---- 4 轮的平均值: 2.1687101928786233e-05
fun 4 ---- 4 轮的平均值: 2.738516688049143e-09
fun 5 ---- 4 轮的平均值: 24.3651022631242
fun 6 ---- 4 轮的平均值: 1.5518969799868655e-08
fun 7 ---- 4 轮的平均值: 0.0007603777498045276
fun 8 ---- 4 轮的平均值: -9759.428902632117
fun 9 ---- 4 轮的平均值: 0.0
fun 10 ---- 4 轮的平均值: 1.1923795284474181e-12
fun 11 ---- 4 轮的平均值: 0.0
fun 12 ---- 4 轮的平均值: 9.427489581332269e-10
fun 13 ---- 4 轮的平均值: 2.018121184109257e-08
fun 14 ---- 4 轮的平均值: 0.9980038377944498
fun 15 ---- 4 轮的平均值: 0.00030748598780886593
fun 16 ---- 4 轮的平均值: -1.0316284534898776
fun 17 ---- 4 轮的平均值: 0.39788735772973816
fun 18 ---- 4 轮的平均值: 2.999999999999924
fun 19 ---- 4 轮的平均值: -3.862782147820756
fun 20 ---- 4 轮的平均值: -3.3219951715813822
fun 21 ---- 4 轮的平均值: -10.153199679022137
fun 22 ---- 4 轮的平均值: -10.40294056677283
fun 23 ---- 4 轮的平均值: -10.53640981666291
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