o código
Nomenclatura geral do código: os seguintes códigos estão em ordem
1、
clear;
clc;
%% A和a的变化图
dim = 1;
Max_iter = 500;
% figure;
for t = 1:Max_iter
origin_a = 2-t*((2)/Max_iter);
if t <= 0.5*Max_iter
a = 1+cos(pi*t/Max_iter);
else
a = cos(pi*(t-0.5*Max_iter)/Max_iter);
end
A = 2*a*rand(1, dim)-a;
plot(t, a, 'r.-', t, origin_a, 'k.-');
hold on;
plot(t, A, 'b.', 'MarkerSize', 16);
hold on;
end
xlabel '迭代次数'; ylabel '参数取值';
legend('提出的a', '原始的a', 'A');
2、
function [fitnessgbest, gbest, BestCost] = ABC(X, N, MaxIt, lb, ub, dim, fobj)
%% 问题设定
VarSize = [1, dim];
%% ABC参数
nPop = N; % 蜂群大小
nOnlooker = nPop; % 侦察蜂个数
L = round(0.6*dim*nPop); % 探索极值限制参数
a = 1; % 加速度系数上限
%% 初始化
% 产生初始种群
for i = 1:nPop
fitness(i) = fobj(X(i, :));
end
[bestfitness, bestindex] = min(fitness);
gbest = X(bestindex, :);
fitnessgbest = bestfitness;
% 丢解计数器
C = zeros(nPop, 1);
% 保存最优函数值的数组
BestCost = zeros(MaxIt, 1);
%% ABC迭代
for it = 1:MaxIt
% 引领蜂
for i = 1:nPop
% 随机选择不等于i的k
K = [1:i-1 i+1:nPop];
k = K(randi([1 numel(K)]));
% 定义加速度系数
phi = a*unifrnd(-1, +1, VarSize);
% 新的蜜蜂位置
newbee_X(i, :) = X(i, :)+phi.*(X(i, :)-X(k, :));
% 边界处理
newbee_X(i, :) = max(newbee_X(i, :), lb);
newbee_X(i, :) = min(newbee_X(i, :), ub);
% 新的蜜蜂函数值
newbee_fitness(i) = fobj(newbee_X(i, :));
% 比较
if newbee_fitness(i) <= fitness(i)
X(i, :) = newbee_X(i, :);
fitness(i) = newbee_fitness(i);
else
C(i) = C(i)+1;
end
end
% 计算适应度值和选择概率
F = zeros(nPop, 1);
MeanCost = mean(fitness);
for i = 1:nPop
% 将函数值转换为适应度
if fitness(i) >= 0
F(i) = 1/(1+fitness(i));
else
F(i) = 1+abs(fitness(i));
end
end
P = F/sum(F);
% 跟随蜂
for m = 1:nOnlooker
% 选择食物源
i = RouletteWheelSelection(P);
% 随机选择不等于i的k
K = [1:i-1 i+1:nPop];
k = K(randi([1 numel(K)]));
% 定义加速度系数
phi = a*unifrnd(-1, +1, VarSize);
% 新的蜜蜂位置
newbee_X(i, :) = X(i, :)+phi.*(X(i, :)-X(k, :));
% 边界处理
newbee_X(i, :) = max(newbee_X(i, :), lb);
newbee_X(i, :) = min(newbee_X(i, :), ub);
% 新的蜜蜂函数值
newbee_fitness(i) = fobj(newbee_X(i, :));
% 比较
if newbee_fitness(i) <= fitness(i)
X(i, :) = newbee_X(i, :);
fitness(i) = newbee_fitness(i);
else
C(i) = C(i) + 1;
end
end
% 侦察蜂
for i = 1:nPop
if C(i) >= L % 超出探索极值参数
maxPos = max(X(i, :));
minPos = min(X(i, :));
for j = 1:numel(X(i, :))
X(i, j) = minPos+rand*(maxPos-minPos);
end
fitness(i) = fobj(X(i, :));
C(i) = 0;
end
end
% 更新每轮最优解
for i = 1:nPop
if fitness(i) <= fitnessgbest
gbest = X(i, :);
fitnessgbest = fitness(i);
end
end
% 保存每轮最优解
BestCost(it) = fitnessgbest;
% 显示迭代信息
disp(['ABC: At iteration ', num2str(it), ' ,the best fitness is ', num2str(BestCost(it))]);
end
% %% 结果显示
% figure;
% % plot(BestCost, 'LineWidth', 2);
% semilogy(BestCost, 'r', 'LineWidth', 2);
% xlabel('Iteration');
% ylabel('Best Cost');
% grid on;
3、
function [fmin, best_pos, Curve] = BOA(X, N, Max_iter, lb, ub, dim, fobj)
%% BOA参数
p = 0.8; % 开关概率
power_exponent = 0.1;
sensory_modality = 0.01;
for i = 1:N
fitness(i) = fobj(X(i, :));
end
% 最优解
[fmin, I] = min(fitness);
best_pos = X(I, :);
S = X;
%% 迭代
for t = 1:Max_iter
for i = 1:N
% 计算与目标函数相关的每只蝴蝶的香味
Fnew = fobj(S(i, :));
FP = (sensory_modality*(Fnew^power_exponent));
% 全局或局部搜索
if rand < p
dis = rand * rand * best_pos - X(i, :); % Eq. (2) in paper
S(i, :) = X(i, :)+dis*FP;
else
% 在附近随机找蝴蝶
epsilon = rand;
JK = randperm(N);
dis = epsilon*epsilon*X(JK(1), :)-X(JK(2), :);
S(i, :) = X(i, :)+dis*FP; % Eq. (3) in paper
end
% 边界处理
S(i, :) = simplebounds(S(i, :), lb, ub);
% 新的个体适应度值
Fnew = fobj(S(i, :)); % Fnew represents new fitness values
% If fitness improves (better Xutions found), update then
if Fnew <= fitness(i)
X(i, :) = S(i, :);
fitness(i) = Fnew;
end
% 更新当前全局最优解
if Fnew <= fmin
best_pos = S(i, :);
fmin = Fnew;
end
end
Curve(t) = fmin;
% 更新感觉因子
sensory_modality = sensory_modality_NEW(sensory_modality, Max_iter);
disp(['BOA: At iteration ', num2str(t), ' ,the best fitness is ', num2str(Curve(t))]);
end
% Boundary constraints
function s=simplebounds(s,Lb,Ub)
% Apply the lower bound
ns_tmp=s;
I=ns_tmp<Lb;
ns_tmp(I)=Lb;
% Apply the upper bounds
J=ns_tmp>Ub;
ns_tmp(J)=Ub;
% Update this new move
s=ns_tmp;
end
function y=sensory_modality_NEW(x, Ngen)
y = x+(0.025/(x*Ngen));
end
end
4、
%_________________________________________________________________________%
% Whale Optimization Algorithm (WOA) source codes demo 1.0 %
% %
% Developed in MATLAB R2011b(7.13) %
% %
% Author and programmer: Seyedali Mirjalili %
% %
% e-Mail: ali.mirjalili@gmail.com %
% seyedali.mirjalili@griffithuni.edu.au %
% %
% Homepage: http://www.alimirjalili.com %
% %
% Main paper: S. Mirjalili, A. Lewis %
% The Whale Optimization Algorithm, %
% Advances in Engineering Software , in press, %
% DOI: http://dx.doi.org/10.1016/j.advengsoft.2016.01.008 %
% %
%_________________________________________________________________________%
% This function draw the benchmark functions
function func_plot(func_name)
[lb,ub,dim,fobj]=Get_Functions_details(func_name);
switch func_name
case 'F1'
x=-100:2:100; y=x; %[-100,100]
case 'F2'
x=-100:2:100; y=x; %[-10,10]
case 'F3'
x=-100:2:100; y=x; %[-100,100]
case 'F4'
x=-100:2:100; y=x; %[-100,100]
case 'F5'
x=-200:2:200; y=x; %[-5,5]
case 'F6'
x=-100:2:100; y=x; %[-100,100]
case 'F7'
x=-1:0.03:1; y=x %[-1,1]
case 'F8'
x=-500:10:500;y=x; %[-500,500]
case 'F9'
x=-5:0.1:5; y=x; %[-5,5]
case 'F10'
x=-20:0.5:20; y=x;%[-500,500]
case 'F11'
x=-500:10:500; y=x;%[-0.5,0.5]
case 'F12'
x=-10:0.1:10; y=x;%[-pi,pi]
case 'F13'
x=-5:0.08:5; y=x;%[-3,1]
case 'F14'
x=-100:2:100; y=x;%[-100,100]
case 'F15'
x=-5:0.1:5; y=x;%[-5,5]
case 'F16'
x=-1:0.01:1; y=x;%[-5,5]
case 'F17'
x=-5:0.1:5; y=x;%[-5,5]
case 'F18'
x=-5:0.06:5; y=x;%[-5,5]
case 'F19'
x=-5:0.1:5; y=x;%[-5,5]
case 'F20'
x=-5:0.1:5; y=x;%[-5,5]
case 'F21'
x=-5:0.1:5; y=x;%[-5,5]
case 'F22'
x=-5:0.1:5; y=x;%[-5,5]
case 'F23'
x=-5:0.1:5; y=x;%[-5,5]
end
L=length(x);
f=[];
for i=1:L
for j=1:L
if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0
f(i,j)=fobj([x(i),y(j)]);
end
if strcmp(func_name,'F15')==1
f(i,j)=fobj([x(i),y(j),0,0]);
end
if strcmp(func_name,'F19')==1
f(i,j)=fobj([x(i),y(j),0]);
end
if strcmp(func_name,'F20')==1
f(i,j)=fobj([x(i),y(j),0,0,0,0]);
end
if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1
f(i,j)=fobj([x(i),y(j),0,0]);
end
end
end
surfc(x,y,f,'LineStyle','none');
end
5、
function G = Gconstant(iteration, max_it)
%% 计算引力常数（公式13）
alfa = 30;
G0 = 100;
G = G0*exp(-alfa*iteration/max_it); % 公式28
6、
function [lb,ub,dim,fobj] = Get_Functions_details(F)
switch F
case 'F1'
fobj = @F1;
lb=-100;
ub=100;
dim=30;
case 'F2'
fobj = @F2;
lb=-10;
ub=10;
dim=30;
case 'F3'
fobj = @F3;
lb=-100;
ub=100;
dim=30;
case 'F4'
fobj = @F4;
lb=-100;
ub=100;
dim=30;
case 'F5'
fobj = @F5;
lb=-30;
ub=30;
dim=30;
case 'F6'
fobj = @F6;
lb=-100;
ub=100;
dim=30;
case 'F7'
fobj = @F7;
lb=-1.28;
ub=1.28;
dim=30;
case 'F8'
fobj = @F8;
lb=-500;
ub=500;
dim=30;
case 'F9'
fobj = @F9;
lb=-5.12;
ub=5.12;
dim=30;
case 'F10'
fobj = @F10;
lb=-32;
ub=32;
dim=30;
case 'F11'
fobj = @F11;
lb=-600;
ub=600;
dim=30;
case 'F12'
fobj = @F12;
lb=-50;
ub=50;
dim=30;
case 'F13'
fobj = @F13;
lb=-50;
ub=50;
dim=30;
case 'F14'
fobj = @F14;
lb=-65.536;
ub=65.536;
dim=2;
case 'F15'
fobj = @F15;
lb=-5;
ub=5;
dim=4;
case 'F16'
fobj = @F16;
lb=-5;
ub=5;
dim=2;
case 'F17'
fobj = @F17;
lb=[-5,0];
ub=[10,15];
dim=2;
case 'F18'
fobj = @F18;
lb=-2;
ub=2;
dim=2;
case 'F19'
fobj = @F19;
lb=0;
ub=1;
dim=3;
case 'F20'
fobj = @F20;
lb=0;
ub=1;
dim=6;
case 'F21'
fobj = @F21;
lb=0;
ub=10;
dim=4;
case 'F22'
fobj = @F22;
lb=0;
ub=10;
dim=4;
case 'F23'
fobj = @F23;
lb=0;
ub=10;
dim=4;
end
end
% F1
function o = F1(x)
o=sum(x.^2);
end
% F2
function o = F2(x)
o=sum(abs(x))+prod(abs(x));
end
% F3
function o = F3(x)
dim=size(x,2);
o=0;
for i=1:dim
o=o+sum(x(1:i))^2;
end
end
% F4
function o = F4(x)
o=max(abs(x));
end
% F5
function o = F5(x)
dim=size(x,2);
o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2);
end
% F6
function o = F6(x)
o=sum(abs((x+.5)).^2);
end
% F7
function o = F7(x)
dim=size(x,2);
o=sum([1:dim].*(x.^4))+rand;
end
% F8
function o = F8(x)
o=sum(-x.*sin(sqrt(abs(x))));
end
% F9
function o = F9(x)
dim=size(x,2);
o=sum(x.^2-10*cos(2*pi.*x))+10*dim;
end
% F10
function o = F10(x)
dim=size(x,2);
o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1);
end
% F11
function o = F11(x)
dim=size(x,2);
o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1;
end
% F12
function o = F12(x)
dim=size(x,2);
o=(pi/dim)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dim-1)+1)./4).^2).*...
(1+10.*((sin(pi.*(1+(x(2:dim)+1)./4)))).^2))+((x(dim)+1)/4)^2)+sum(Ufun(x,10,100,4));
end
% F13
function o = F13(x)
dim=size(x,2);
o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+...
((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4));
end
% F14
function o = F14(x)
aS=[-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];
for j=1:25
bS(j)=sum((x'-aS(:,j)).^6);
end
o=(1/500+sum(1./([1:25]+bS))).^(-1);
end
% F15
function o = F15(x)
aK=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246];
bK=[.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK;
o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);
end
% F16
function o = F16(x)
o=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4);
end
% F17
function o = F17(x)
o=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10;
end
% F18
function o = F18(x)
o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*...
(30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2)));
end
% F19
function o = F19(x)
aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];
pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828];
o=0;
for i=1:4
o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end
% F20
function o = F20(x)
aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14];
cH=[1 1.2 3 3.2];
pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;...
.2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381];
o=0;
for i=1:4
o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end
% F21
function o = F21(x)
aSH=[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=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
o=0;
for i=1:5
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end
% F22
function o = F22(x)
aSH=[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=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
o=0;
for i=1:7
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end
% F23
function o = F23(x)
aSH=[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=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];
o=0;
for i=1:10
o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);
end
end
function o=Ufun(x,a,k,m)
o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));
end
7、
%% This function calculates the accelaration of each agent in gravitational field. eq.7-10,21.
function a = Gfield(M, X, G, Rnorm, Rpower, ElitistCheck, iteration, max_it)
%% 计算了重力场中每个个体的加速度
[N, dim] = size(X);
final_per = 2; % 在上一次迭代中，只有2%的个体对其他个体施加力。
% 总的力计算
if ElitistCheck == 1
kbest = final_per+(1-iteration/max_it)*(100-final_per); % 公式21的kbest
kbest = round(N*kbest/100);
else
kbest = N; % 公式9
end
[Ms, ds] = sort(M, 'descend');
for i = 1:N
E(i, :) = zeros(1, dim);
for ii = 1:kbest
j = ds(ii);
if j ~= i
R = norm(X(i, :)-X(j, :), Rnorm); % 欧几里德距离
for k = 1:dim
E(i, k) = E(i, k)+rand*(M(j))*((X(j, k)-X(i, k))/(R^Rpower+eps));
% 注意，Mp(i)/Mi(i)=1
end
end
end
end
% 加速度
a = E.*G; % 注意，Mp(i)/Mi(i)=1
8、
%% Gravitational Search Algorithm.
function [Fbest, Lbest, Curve] = GSA(X, N, Max_iter, lb, ub, dim, fobj)
%V: 速度.
%a: 加速度.
%M: 质量. Ma=Mp=Mi=M;
%dim: 测试函数的维数.
%N: 种群规模.
%X: 种群位置.
%R: 搜索空间中代理之间的距离.
%[low-up]: 搜索空间的允许范围.
%Rnorm: 公式8中的标准值.
%Rpower: 式7中R的幂.
Rnorm = 2;
ElitistCheck = 1;
Rpower = 1;
% 初始化进化曲线
Curve = zeros(1, Max_iter);
V = zeros(N, dim);
%% 迭代寻优
for iter = 1:Max_iter
for i = 1:N
% 边界处理
Flag4ub = X(i, :) > ub;
Flag4lb = X(i, :) < lb;
X(i, :) = (X(i, :).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
% 计算适应度值
fitness(i) = fobj(X(i, :));
end
% 计算最小的适应度值
[best, best_X]=min(fitness);
if iter == 1
Fbest = best;
Lbest=X(best_X, :);
end
if best < Fbest
Fbest = best;
Lbest=X(best_X, :);
end
Curve(iter) = Fbest;
% 根据公式14-20计算M
[M] = massCalculation(fitness);
% 根据公式13计算引力常数
G = Gconstant(iter, Max_iter);
% 计算根据公式7-10,21计算重力场中的加速度
a = Gfield(M, X, G, Rnorm, Rpower, ElitistCheck, iter, Max_iter);
% 根据公式11-12进行个体的位置移动
[X, V] = move(X, a, V);
disp(['GSA: At iteration ', num2str(iter), ' ,the best fitness is ', num2str(Fbest)]);
end %iter
9、
function [Alpha_score, Alpha_pos, Convergence_curve] = GWO(Positions, N, Max_iter, lb, ub, dim, fobj)
%% 灰狼优化算法
% 初始化alpha, beta和delta_pos
Alpha_pos = zeros(1, dim);
Alpha_score = inf; % 将此更改为-inf以解决最大化问题
Beta_pos = zeros(1,dim);
Beta_score = inf; % 将此更改为-inf以解决最大化问题
Delta_pos = zeros(1,dim);
Delta_score = inf; % 将此更改为-inf以解决最大化问题
% 初始化种群位置
Convergence_curve = zeros(1, Max_iter); % 收敛曲线
l = 0; % 循环计数器
% 主要循环
while l < Max_iter
for i = 1:N
% 边界处理
Flag4ub = Positions(i, :)>ub;
Flag4lb = Positions(i, :)<lb;
Positions(i, :) = (Positions(i, :).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
% Positions(i, :) = max(Positions(i, :), lb);
% Positions(i, :) = min(Positions(i, :), ub);
% 计算每个种群的目标函数
fitness = fobj(Positions(i, :));
% 更新Alpha, Beta和Delta
if fitness < Alpha_score
Alpha_score = fitness; % 更新alpha
Alpha_pos = Positions(i, :);
end
if fitness > Alpha_score && fitness < Beta_score
Beta_score = fitness; % 更新beta
Beta_pos = Positions(i, :);
end
if fitness > Alpha_score && fitness > Beta_score && fitness < Delta_score
Delta_score = fitness; % 更新delta
Delta_pos = Positions(i, :);
end
end
a = 2-l*((2)/Max_iter); % a从2线性减小到0
% 更新包括omegas在内的种群的位置
for i = 1:N
for j = 1:dim
r1 = rand(); % r1是[0,1]中的随机数
r2 = rand(); % r2是[0,1]中的随机数
A1 = 2*a*r1-a; % 公式（4）
C1 = 2*r2; % 公式（5）
D_alpha = abs(C1*Alpha_pos(j)-Positions(i, j)); % 公式（6）-第一部分
X1 = Alpha_pos(j)-A1*D_alpha; % 公式 (7)-第一部分
r1 = rand();
r2 = rand();
A2 = 2*a*r1-a; % 公式（4）
C2 = 2*r2; % 公式（5）
D_beta = abs(C2*Beta_pos(j)-Positions(i, j)); % 公式（6）-第二部分
X2 = Beta_pos(j)-A2*D_beta; % 公式 (7)-第二部分
r1 = rand();
r2 = rand();
A3 = 2*a*r1-a; % 公式 (4)
C3 = 2*r2; % 公式 (5)
D_delta = abs(C3*Delta_pos(j)-Positions(i, j)); % 公式（6）-第三部分
X3 = Delta_pos(j)-A3*D_delta; % 公式 (7)-第三部分
Positions(i, j)=(X1+X2+X3)/3; % 公式 (8)
end
end
l = l+1;
Convergence_curve(l) = Alpha_score;
disp(['GWO: At iteration ', num2str(l), ' ,the best fitness is ', num2str(Alpha_score)]);
end
10、
% This function initialize the first population of search agents
function Positions = initialization(SearchAgents_no, dim, ub, lb)
Boundary_no= size(ub, 2); % numnber of boundaries
% If the boundaries of all variables are equal and user enter a signle
% number for both ub and lb
if Boundary_no==1
Positions = rand(SearchAgents_no, dim).*(ub-lb)+lb;
end
% If each variable has a different lb and ub
if Boundary_no > 1
for i=1:dim
ub_i = ub(i);
lb_i = lb(i);
Positions(:, i) = rand(SearchAgents_no, 1).*(ub_i-lb_i)+lb_i;
end
end
11、
function [M] = massCalculation(fit)
%% 计算每个个体的质量（公式14-20）
Fmax = max(fit);
Fmin = min(fit);
Fmean = mean(fit);
[i, N] = size(fit);
if Fmax == Fmin
M = ones(N, 1);
else
best = Fmin; worst = Fmax; %eq.17-18.
M = (fit-worst)./(best-worst); %eq.15,
end
M=M./sum(M); %eq. 16.
12、
% GSA code v1.1.
% Generated by Esmat Rashedi, 2010.
% " E. Rashedi, H. Nezamabadi-pour and S. Saryazdi,
%揋SA: A Gravitational Search Algorithm�, Information sciences, vol. 179,
%no. 13, pp. 2232-2248, 2009."
%
%This function updates the velocity and position of agents.
function [X,V]=move(X,a,V)
%movement.
[N,dim]=size(X);
V=rand(N,dim).*V+a; %eq. 11.
X=X+V; %eq. 12.
13、
function [Leader_score, Leader_pos, Curve] = MSWOA(X, N, Max_iter, lb, ub, dim, fobj)
%% MSWOA参数
limit = 10;
p = sobolset(dim);
% 计算适应度值
for i = 1:N
X(i, :) = p(i, :).*(ub-lb)+lb;
fitness(i) = fobj(X(i, :));
end
% 初始化领导者的位置和适应度值
[bestfitness, bestindex] = min(fitness);
Leader_pos = X(bestindex, :);
Leader_score = bestfitness;
% 初始化进化曲线
Curve = zeros(1, Max_iter);
t = 0; % 迭代次数计数器
count = 0;
%% 迭代寻优
while t < Max_iter
% 计数超过limit阈值
if count > limit
% 对最优个体进行柯西变异
X_new = Leader_pos.*(1+trnd(1, 1, dim));
% 更新
fit = fobj(X_new);
if fit < Leader_score
Leader_pos = X_new;
Leader_score = fit;
X(bestindex, :) = X_new;
fitness(i) = fit;
end
end
% a=2-t*((2)/Max_iter); % 式（2.3）中，a从2线性减小到0
% 非线性时变因子
if t <= 0.5*Max_iter
a = 1+cos(pi*t/Max_iter);
else
a = cos(pi*(t-0.5*Max_iter)/Max_iter);
end
% 自适应权值
w = 2/pi*tan(t/Max_iter);
a2=-1+t*((-1)/Max_iter); % a2从-1到-2线性递减，用以计算公式（3.12）中的t
% 更新种群位置
for i = 1:N
r1 = rand(); % r1是[0,1]中的随机数
r2 = rand(); % r2是[0,1]中的随机数
A = 2*a*r1-a; % 公式(2.3)
C = 2*r2; % 公式(2.4)
b = 1; % 公式(2.5)里的参数
l = (a2-1)*rand+1; % 公式(2.5)里的参数
p = rand(); % 公式(2.6)里的p
for j = 1:dim
if p < 0.5
if abs(A) >= 1
%% 随机性学习策略
% 随机选择不等于i的k
K = [1:i-1 i+1:N];
k = K(randi([1 numel(K)]));
% 学习产生新个体
if fitness(k) < fitness(i)
X_new = X(i, :)+rand*(X(i, :)-X(k, :));
else
X_new = X(i, :)+rand*(X(k, :)-X(i, :));
end
% 判断随机学习产生的新个体是否优于当前个体
fit = fobj(X_new);
if fit < fitness(i)
X(i, :) = X_new;
fitness(i) = fit;
end
% 更新个体位置
rand_leader_index = floor(N*rand()+1);
X_rand = X(rand_leader_index, :);
D_X_rand = abs(C*X_rand(j)-X(i,j)); % 公式(2.7)
X(i, j) = w*X_rand(j)-A*D_X_rand; % 公式(2.8)
elseif abs(A) < 1
D_Leader = abs(C*Leader_pos(j)-X(i, j)); % 公式(2.1)
X(i, j) = w*Leader_pos(j)-A*D_Leader; % 公式(2.2)
end
else
distance2Leader = abs(Leader_pos(j)-X(i, j));
% 公式(2.5)
X(i, j) = distance2Leader*exp(b.*l).*cos(l.*2*pi)+(1-w)*Leader_pos(j);
end
end
end
for i = 1:N
% 边界处理
Flag4ub = X(i, :) > ub;
Flag4lb = X(i, :) < lb;
X(i, :) = (X(i, :).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
% 计算适应度
fitness(i) = fobj(X(i, :));
end
% 记录上一次的最优解
Last_Leader_score = Leader_score;
% 初始化领导者的位置和适应度值
[bestfitness, bestindex] = min(fitness);
if bestfitness < Leader_score
Leader_pos = X(bestindex, :);
Leader_score = bestfitness;
end
if Leader_score == Last_Leader_score
count = count+1; % 无变化计数加1
else
count = 0; % 有变化计数赋为0
end
t = t+1;
Curve(t) = Leader_score;
disp(['MSWOA: At iteration ', num2str(t), ' ,the best fitness is ', num2str(Leader_score)]);
end
14、
function [fitnessgbest, gbest, zz] = PSO(X, N, maxgen, lb, ub, dim, fobj)
%% 参数初始化
c1 = 2; % 社会认知参数
c2 = 2; % 自我认知参数
Vmax = 2; % 最大速度
Vmin = -2; % 最小速度
ub = 100; % 位置最大值
lb = -100; % 位置最小值
Wmax = 0.8; Wmin = 0.2;
V = rand(N, dim).*(Vmax-Vmin)+Vmin;
for i = 1:N
fitness(i) = fobj(X(i, :));
end
%%
[bestfitness, bestindex] = min(fitness);
gbest = X(bestindex, :); % 群体最优极值
zbest = X; % 个体最优极值
fitnessgbest = bestfitness; % 种群最优适应度值
fitnesszbest = fitness; % 个体最优适应度值
%% 初始结果显示
disp(['初始位置：' , num2str(gbest)]);
disp(['初始函数值：', num2str(fitnessgbest)]);
%% 迭代寻优
for i = 1:maxgen
W = Wmax-((Wmax-Wmin)/maxgen)*i;
for j=1:N
% 速度更新
V(j, :) = W*V(j, :) + c1*rand*(zbest(j, :) - X(j, :)) + c2*rand*(gbest - X(j, :));
V(j,find(V(j,:)>Vmax)) = Vmax;
V(j,find(V(j,:)<Vmin)) = Vmin;
% 种群更新
X(j,:) = X(j,:) + V(j,:);
X(j,find(X(j,:)>ub)) = ub;
X(j,find(X(j,:)<lb)) = lb;
% 适应度值更新
fitness(j) = fobj(X(j,:));
end
%% 个体和群体极值更新
for j = 1:N
% 个体最优更新
if fitness(j) < fitnesszbest(j)
zbest(j,:) = X(j,:);
fitnesszbest(j) = fitness(j);
end
% 群体最优更新
if fitness(j) < fitnessgbest
gbest = X(j,:);
fitnessgbest = fitness(j);
end
end
%% 每一代群体最优值存入zz数组
zz(i) = fitnessgbest;
disp(['PSO: At iteration ', num2str(i), ' ,the best fitness is ', num2str(zz(i))]);
end
% %% 最终结果显示
% disp(['最终位置：' , num2str(gbest)]);
% disp(['最终函数值：', num2str(zz(end))]);
% %% 绘图
% figure;
% plot(zz, 'r', 'lineWidth', 2); % 画出迭代图
% xlabel('迭代次数', 'fontsize', 12);
% ylabel('目标函数值', 'fontsize', 12);
15、
function i = RouletteWheelSelection(P)
r = rand;
C = cumsum(P);
i = find(r <= C, 1, 'first');
end
16、
function [Leader_score, Leader_pos, Curve] = WOA(Positions, N, Max_iter, lb, ub, dim, fobj)
%% The Whale Optimization Algorithm
% 计算适应度值
for i = 1:N
fitness(i) = fobj(Positions(i, :));
end
% 初始化领导者的位置和适应度值
[bestfitness, bestindex] = min(fitness);
Leader_pos = Positions(bestindex, :);
Leader_score = bestfitness;
% 初始化进化曲线
Curve = zeros(1, Max_iter);
t = 0; % 迭代次数计数器
%% 迭代寻优
while t < Max_iter
a=2-t*((2)/Max_iter); % 式（2.3）中，a从2线性减小到0
a2=-1+t*((-1)/Max_iter); % a2从-1到-2线性递减，用以计算公式（3.12）中的t
% 更新种群位置
for i = 1:N
r1 = rand(); % r1是[0,1]中的随机数
r2 = rand(); % r2是[0,1]中的随机数
A = 2*a*r1-a; % 公式(2.3)
C = 2*r2; % 公式(2.4)
b = 1; % 公式(2.5)里的参数
l = (a2-1)*rand+1; % 公式(2.5)里的参数
p = rand(); % 公式(2.6)里的p
for j = 1:dim
if p < 0.5
if abs(A) >= 1
rand_leader_index = floor(N*rand()+1);
X_rand = Positions(rand_leader_index, :);
D_X_rand = abs(C*X_rand(j)-Positions(i,j)); % 公式(2.7)
Positions(i, j) = X_rand(j)-A*D_X_rand; % 公式(2.8)
elseif abs(A) < 1
D_Leader = abs(C*Leader_pos(j)-Positions(i, j)); % 公式(2.1)
Positions(i, j) = Leader_pos(j)-A*D_Leader; % 公式(2.2)
end
else
distance2Leader = abs(Leader_pos(j)-Positions(i, j));
% 公式(2.5)
Positions(i, j) = distance2Leader*exp(b.*l).*cos(l.*2*pi)+Leader_pos(j);
end
end
end
for i = 1:N
% 边界处理
Flag4ub = Positions(i, :) > ub;
Flag4lb = Positions(i, :) < lb;
Positions(i, :) = (Positions(i, :).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
% 计算适应度
fitness(i) = fobj(Positions(i, :));
end
% 初始化领导者的位置和适应度值
[bestfitness, bestindex] = min(fitness);
if bestfitness < Leader_score
Leader_pos = Positions(bestindex, :);
Leader_score = bestfitness;
end
t = t+1;
Curve(t) = Leader_score;
disp(['WOA: At iteration ', num2str(t), ' ,the best fitness is ', num2str(Leader_score)]);
end
17、
%% 清除环境变量
clear
clc
%% 参数设置
N = 30; % 种群规模
Function_name = 'F4'; % 从F1到F23的测试函数的名称（本文中的表1、2、3）
Max_iteration = 500; % 最大迭代次数
% 加载所选基准函数的详细信息
[lb, ub, dim, fobj] = Get_Functions_details(Function_name);
% 初始化种群位置
X = initialization(N, dim, ub, lb);
[MSWOA_Best_score, MSWOA_Best_pos, MSWOA_Curve] = MSWOA(X, N, Max_iteration, lb, ub, dim, fobj);
[WOA_Best_score, WOA_Best_pos, WOA_Curve] = WOA(X, N, Max_iteration, lb, ub, dim, fobj);
[BOA_Best_score, BOA_Best_pos, BOA_Curve] = BOA(X, N, Max_iteration, lb, ub, dim, fobj);
[GWO_Best_score, GWO_Best_pos, GWO_Curve] = GWO(X, N, Max_iteration, lb, ub, dim, fobj);
[GSA_Best_score, GSA_Best_pos, GSA_Curve] = GSA(X, N, Max_iteration, lb, ub, dim, fobj);
[PSO_Best_score, PSO_Best_pos, PSO_Curve] = PSO(X, N, Max_iteration, lb, ub, dim, fobj);
[ABC_Best_score, ABC_Best_pos, ABC_Curve] = ABC(X, N, Max_iteration, lb, ub, dim, fobj);
%% 画图
% 1、画出所选基准函数的三维立体图形
figure;
func_plot(Function_name);
title(Function_name)
xlabel('x_1');
ylabel('x_2');
zlabel([Function_name,'( x_1 , x_2 )'])
% 2、画出目标函数值变化曲线图
figure;
t = 1:Max_iteration;
plot(t, MSWOA_Curve, 'r^-', t, WOA_Curve, 'ko-', t, BOA_Curve, 'bd-', t, GWO_Curve, 'cs-', ...
t, GSA_Curve, 'mp-', t, PSO_Curve, 'k*-', t, ABC_Curve, 'gh-', ...
'linewidth', 1.5, 'MarkerSize', 8, 'MarkerIndices', 1:50:Max_iteration);
title(Function_name)
xlabel('迭代次数');
ylabel('适应度值');
axis fill
grid on
box on
legend('MSWOA', 'WOA', 'BOA', 'GWO', 'GSA', 'PSO', 'ABC');
% h1 = axes('position', [0.4 0.3 0.2 0.3]);
% axis(h1);
% s = t(1:50);
% plot(h1, s, MSWOA_Curve(s), 'r^-', s, WOA_Curve(s), 'ko-', s, BOA_Curve(s), 'bd-', s, GWO_Curve(s), 'cs-', ...
% s, GSA_Curve(s), 'mp-', s, PSO_Curve(s), 'k*-', s, ABC_Curve(s), 'gh-', ...
% 'linewidth', 1, 'MarkerSize', 6, 'MarkerIndices', 1:10:50);
%% 显示结果
disp(['MSWOA得到的最佳位置为 : ', num2str(MSWOA_Best_pos)]);
disp(['MSWOA得到的目标函数的最佳值为 : ', num2str(MSWOA_Best_score)]);
disp(['WOA得到的最佳位置为 : ', num2str(WOA_Best_pos)]);
disp(['WOA得到的目标函数的最佳值为 : ', num2str(WOA_Best_score)]);
disp(['BOA得到的最佳位置为 : ', num2str(BOA_Best_pos)]);
disp(['BOA得到的目标函数的最佳值为 : ', num2str(BOA_Best_score)]);
disp(['GWO得到的最佳位置为 : ', num2str(GWO_Best_pos)]);
disp(['GWO得到的目标函数的最佳值为 : ', num2str(GWO_Best_score)]);
disp(['GSA得到的最佳位置为 : ', num2str(GSA_Best_pos)]);
disp(['GSA得到的目标函数的最佳值为 : ', num2str(GSA_Best_score)]);
disp(['PSO得到的最佳位置为 : ', num2str(PSO_Best_pos)]);
disp(['PSO得到的目标函数的最佳值为 : ', num2str(PSO_Best_score)]);
disp(['ABC得到的最佳位置为 : ', num2str(ABC_Best_pos)]);
disp(['ABC得到的目标函数的最佳值为 : ', num2str(ABC_Best_score)]);
18、
clc;
clear;
%% 随机序列和Sobol序列对比
dim = 30; % 维度
N = 500;
% Sobol序列
p = sobolset(dim);
for i = 1:N
X(i, :) = p(i, :);
end
figure;
plot(X(:, 1), X(:, 2), 'b.', 'MarkerSize', 16);
xlabel '个体第一维度数值'; ylabel '个体第二维度数值';
title 'Sobol序列生成散点图';
% 随机序列
Y = rand(N, dim);
figure;
plot(Y(:, 1), Y(:, 2), 'b.', 'MarkerSize', 16);
xlabel '个体第一维度数值'; ylabel '个体第二维度数值';
title '随机生成个体散点图';
resultado
