一、简介

模拟退火算法介绍\ \ \ \ \ 3 模拟退火算法的参数\ 模拟退火是一种优化算法，它本身是不能独立存在的，需要有一个应用场合，其中温度就是模拟退火需要优化的参数，如果它应用到了聚类分析中，那么就是说聚类分析中有某个或者某几个参数需要优化，而这个参数，或者参数集就是温度所代表的。它可以是某项指标，某项关联度，某个距离等等。

二、源代码

``` %% %

clc; clear; close all;

%% Problem Definition

model=SelectModel(); % Select Model of the Problem

model.eta=0.1;

CostFunction=@(q) MyCost(q,model); % Cost Function

%% SA Parameters

MaxIt=500; % Maximum Number of Iterations

MaxIt2=80; % Maximum Number of Inner Iterations

T0=100; % Initial Temperature

alpha=0.98; % Temperature Damping Rate

%% Initialization

% Create Initial Solution x.Position=CreateRandomSolution(model); [x.Cost, x.Sol]=CostFunction(x.Position);

% Update Best Solution Ever Found BestSol=x;

% Array to Hold Best Cost Values BestCost=zeros(MaxIt,1);

% Set Initial Temperature T=T0;

%% SA Main Loop

for it=1:MaxIt for it2=1:MaxIt2

% Create Neighborxnew.Position=CreateNeighbor(x.Position);[xnew.Cost, xnew.Sol]=CostFunction(xnew.Position);if xnew.Cost<=x.Cost% xnew is better, so it is acceptedx=xnew;else% xnew is not better, so it is accepted conditionallydelta=xnew.Cost-x.Cost;p=exp(-delta/T);if rand<=px=xnew;endend% Update Best Solutionif x.Cost<=BestSol.CostBestSol=x;endend% Store Best Cost
BestCost(it)=BestSol.Cost;% Display Iteration Information
if BestSol.Sol.IsFeasibleFLAG=' *';
elseFLAG='';
end
disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it)) FLAG]);% Reduce Temperature
T=alpha*T;% Plot Solution
figure(1);
PlotSolution(BestSol.Sol,model);
pause(0.01);

end %

function model=CreateRandomModel(I,J)

rmin=10;
rmax=25;
r=randi([rmin rmax],1,I);TotalDemand=sum(r);
cmean=TotalDemand/J;
cmin=round(cmean);
cmax=round(1.25*cmean);
c=randi([cmin cmax],1,J);xmin=0;
xmax=200;ymin=0;
ymax=100;x=randi([xmin xmax],1,I);
y=randi([ymin ymax],1,I);alpha_x=0.1;
xm=(xmin+xmax)/2;
dx=xmax-xmin;
x0min=round(xm-alpha_x*dx);
x0max=round(xm+alpha_x*dx);alpha_y=0.1;
ym=(ymin+ymax)/2;
dy=ymax-ymin;
y0min=round(ym-alpha_y*dy);
y0max=round(ym+alpha_y*dy);x0=randi([x0min x0max]);
y0=randi([y0min y0max]);d=zeros(I,I);
d0=zeros(1,I);
for i=1:Ifor i2=i+1:Id(i,i2)=sqrt((x(i)-x(i2))^2+(y(i)-y(i2))^2);d(i2,i)=d(i,i2);endd0(i)=sqrt((x(i)-x0)^2+(y(i)-y0)^2);
endeta=0.5;model.I=I;
model.J=J;
model.r=r;
model.c=c;
model.xmin=xmin;
model.xmax=xmax;
model.ymin=ymin;
model.ymax=ymax;
model.x=x;
model.y=y;
model.x0=x0;
model.y0=y0;
model.d=d;
model.d0=d0;
model.eta=eta;

end %

function qnew=CreateNeighbor(q)

m=randi([1 3]);switch mcase 1% Do Swapqnew=Swap(q);case 2% Do Reversionqnew=Reversion(q);case 3% Do Insertionqnew=Insertion(q);
end

end

function qnew=Swap(q)

n=numel(q);i=randsample(n,2);
i1=i(1);
i2=i(2);qnew=q;
qnew([i1 i2])=q([i2 i1]);

end

function qnew=Reversion(q)

n=numel(q);i=randsample(n,2);
i1=min(i(1),i(2));
i2=max(i(1),i(2));qnew=q;
qnew(i1:i2)=q(i2:-1:i1);

end

function qnew=Insertion(q)

n=numel(q);i=randsample(n,2);
i1=i(1);
i2=i(2);if i1<i2qnew=[q(1:i1-1) q(i1+1:i2) q(i1) q(i2+1:end)];
elseqnew=[q(1:i2) q(i1) q(i2+1:i1-1) q(i1+1:end)];
end

end ```

三、运行结果

\ \

四、备注

版本：2014a