【Matlab】智能优化算法_海洋捕食者算法MPA
1.背景介绍
1.1 布朗运动
1.2 莱维运动
2.数学模型
2.1 MPA配方
2.2 MPA优化场景
2.3 涡流形成与FAD效应
3.文件结构
func_plot.m % 绘图函数
Get_Functions_details.m % 基准的全部信息和实现
initialization.m % 初始化
levy.m % 莱维运动方程
main.m % 主函数
MPA.m % 海洋捕食者算法
4.伪代码
5.详细代码及注释
5.1 func_plot.m
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');
colormap winter
end
5.2 Get_Functions_details.m
function [lb,ub,dim,fobj] = Get_Functions_details(F)
switch F
case 'F1'
fobj = @F1;
lb=-100;
ub=100;
dim=50;
case 'F2'
fobj = @F2;
lb=-10;
ub=10;
dim=50;
case 'F3'
fobj = @F3;
lb=-100;
ub=100;
dim=50;
case 'F4'
fobj = @F4;
lb=-100;
ub=100;
dim=50;
case 'F5'
fobj = @F5;
lb=-30;
ub=30;
dim=50;
case 'F6'
fobj = @F6;
lb=-100;
ub=100;
dim=50;
case 'F7'
fobj = @F7;
lb=-1.28;
ub=1.28;
dim=50;
case 'F8'
fobj = @F8;
lb=-500;
ub=500;
dim=50;
case 'F9'
fobj = @F9;
lb=-5.12;
ub=5.12;
dim=50;
case 'F10'
fobj = @F10;
lb=-32;
ub=32;
dim=50;
case 'F11'
fobj = @F11;
lb=-600;
ub=600;
dim=50;
case 'F12'
fobj = @F12;
lb=-50;
ub=50;
dim=50;
case 'F13'
fobj = @F13;
lb=-50;
ub=50;
dim=50;
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
5.3 initialization.m
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
5.4 levy.m
function [z] = levy(n,m,beta)
num = gamma(1+beta)*sin(pi*beta/2); % used for Numerator
den = gamma((1+beta)/2)*beta*2^((beta-1)/2); % used for Denominator
sigma_u = (num/den)^(1/beta);% Standard deviation
u = random('Normal',0,sigma_u,n,m);
v = random('Normal',0,1,n,m);
z =u./(abs(v).^(1/beta));
end
5.5 main.m
clear all
clc
format long
SearchAgents_no=25; % Number of search agents
Function_name='F23';
Max_iteration=500; % Maximum number of iterations
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);
[Best_score,Best_pos,Convergence_curve]=MPA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);
% function topology
figure('Position',[500 400 700 290])
subplot(1,2,1);
func_plot(Function_name);
title('Function Topology')
xlabel('x_1');
ylabel('x_2');
zlabel([Function_name,'( x_1 , x_2 )'])
% Convergence curve
subplot(1,2,2);
semilogy(Convergence_curve,'Color','r')
title('Objective space')
xlabel('Iteration');
ylabel('Best score obtained so far');
display(['The best solution obtained by MPA is : ', num2str(Best_pos,10)]);
display(['The best optimal value of the objective function found by MPA is : ', num2str(Best_score,10)]);
disp(sprintf('--------------------------------------'));
5.6 MPA.m
function [Top_predator_fit,Top_predator_pos,Convergence_curve]=MPA(SearchAgents_no,Max_iter,lb,ub,dim,fobj)
Top_predator_pos=zeros(1,dim);
Top_predator_fit=inf;
Convergence_curve=zeros(1,Max_iter);
stepsize=zeros(SearchAgents_no,dim);
fitness=inf(SearchAgents_no,1);
Prey=initialization(SearchAgents_no,dim,ub,lb);
Xmin=repmat(ones(1,dim).*lb,SearchAgents_no,1);
Xmax=repmat(ones(1,dim).*ub,SearchAgents_no,1);
Iter=0;
FADs=0.2;
P=0.5;
while Iter<Max_iter
%------------------- Detecting top predator -----------------
for i=1:size(Prey,1)
Flag4ub=Prey(i,:)>ub;
Flag4lb=Prey(i,:)<lb;
Prey(i,:)=(Prey(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
fitness(i,1)=fobj(Prey(i,:));
if fitness(i,1)<Top_predator_fit
Top_predator_fit=fitness(i,1);
Top_predator_pos=Prey(i,:);
end
end
%------------------- Marine Memory saving -------------------
if Iter==0
fit_old=fitness; Prey_old=Prey;
end
Inx=(fit_old<fitness);
Indx=repmat(Inx,1,dim);
Prey=Indx.*Prey_old+~Indx.*Prey;
fitness=Inx.*fit_old+~Inx.*fitness;
fit_old=fitness; Prey_old=Prey;
%------------------------------------------------------------
Elite=repmat(Top_predator_pos,SearchAgents_no,1); %(Eq. 10)
CF=(1-Iter/Max_iter)^(2*Iter/Max_iter);
RL=0.05*levy(SearchAgents_no,dim,1.5); %Levy random number vector
RB=randn(SearchAgents_no,dim); %Brownian random number vector
for i=1:size(Prey,1)
for j=1:size(Prey,2)
R=rand();
%------------------ Phase 1 (Eq.12) -------------------
if Iter<Max_iter/3
stepsize(i,j)=RB(i,j)*(Elite(i,j)-RB(i,j)*Prey(i,j));
Prey(i,j)=Prey(i,j)+P*R*stepsize(i,j);
%--------------- Phase 2 (Eqs. 13 & 14)----------------
elseif Iter>Max_iter/3 && Iter<2*Max_iter/3
if i>size(Prey,1)/2
stepsize(i,j)=RB(i,j)*(RB(i,j)*Elite(i,j)-Prey(i,j));
Prey(i,j)=Elite(i,j)+P*CF*stepsize(i,j);
else
stepsize(i,j)=RL(i,j)*(Elite(i,j)-RL(i,j)*Prey(i,j));
Prey(i,j)=Prey(i,j)+P*R*stepsize(i,j);
end
%----------------- Phase 3 (Eq. 15)-------------------
else
stepsize(i,j)=RL(i,j)*(RL(i,j)*Elite(i,j)-Prey(i,j));
Prey(i,j)=Elite(i,j)+P*CF*stepsize(i,j);
end
end
end
%------------------ Detecting top predator ------------------
for i=1:size(Prey,1)
Flag4ub=Prey(i,:)>ub;
Flag4lb=Prey(i,:)<lb;
Prey(i,:)=(Prey(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
fitness(i,1)=fobj(Prey(i,:));
if fitness(i,1)<Top_predator_fit
Top_predator_fit=fitness(i,1);
Top_predator_pos=Prey(i,:);
end
end
%---------------------- Marine Memory saving ----------------
if Iter==0
fit_old=fitness; Prey_old=Prey;
end
Inx=(fit_old<fitness);
Indx=repmat(Inx,1,dim);
Prey=Indx.*Prey_old+~Indx.*Prey;
fitness=Inx.*fit_old+~Inx.*fitness;
fit_old=fitness; Prey_old=Prey;
%---------- Eddy formation and FADs� effect (Eq 16) -----------
if rand()<FADs
U=rand(SearchAgents_no,dim)<FADs;
Prey=Prey+CF*((Xmin+rand(SearchAgents_no,dim).*(Xmax-Xmin)).*U);
else
r=rand(); Rs=size(Prey,1);
stepsize=(FADs*(1-r)+r)*(Prey(randperm(Rs),:)-Prey(randperm(Rs),:));
Prey=Prey+stepsize;
end
Iter=Iter+1;
Convergence_curve(Iter)=Top_predator_fit;
end
6.运行结果
7.参考文献
