2016五一联赛B题：基于PSO的带等式及不等是约束的多元优化问题求解思路及程序代码
本程序是针对2016年第十三届五一联赛B题的求解。为了解决等式约束这一问题，采用了分段罚函数与PSO（自适应权重调节）算法相结合的方式来解决问题中的优化问题。约束条件：1.各公司新的能源分配方案使能耗相较原来下降5%
2.各公司新方案的能源分配数量相较原始能源分配尽量变动较小
目标：各公司在新方案下的产值综合相较去年应增加8%以上，越大越好。
然而可以看到我们的求解并未比8%大多少，这主要是由于我们的约束条件2所导致。如果没有这条限制，我们可以将能量多数集中在单位能耗极高的一两家公司，从而使产值综合较原始产值能加几十甚至上百倍！
下面是程序（由于我上一次直接粘贴代码出现很多错误的符号，这一次我同时给出代码的图片，方便大家阅读复制）：
主程序：
clc;
clear all;
close all;
tic
% warning off;
%% 参数设置
c1=1.49445;
c2=1.49455;
maxgen=50000;%迭代次数
sizepop=100;%种群规模
%速度范围
Vmax=10;
Vmin=-10;
%粒子空间维数
par_num=2725;
%p空间范围
Popmax=inf;
Popmin=0;
%读取数据
global data;
data=xlsread('Data.xls');
pop=xlsread('time_10000.xlsx');%初次优化后的近似解
%%
%共有两个粒子群，第一个粒子群求解完成后，第二个粒子群求解
%% 初始化种群
for i=1:sizepop
V(i,:)=rands(1,par_num);%粒子群1速度
fitness(i)=fun_pso1(pop(i,:));%%计算适应度
end
=APSO_Fun(pop,V,fitness,maxgen,sizepop,par_num,c1,c2,1.2,0.6,Vmax,Vmin,Popmax,Popmin)
%% 结果
num=0;
for i=1:par_num
if(zbest(i)==0)
num=num+1;
end
end
num
max(zbest)
max(data(:,4))
Lirunlv=sum(zbest(1,:)'.*(data(:,2)./data(:,4)))/sum(data(:,2))
Nenghaobi=sum(zbest(1,:))/sum(data(:,4))
plot(yy);
toc
优化函数APSO：
function =APSO_Fun(pop,V,fitness,maxgen,sizepop,par_num,c1,c2,wmax,wmin,Vmax,Vmin,Popmax,Popmin)
% pop: The primitive solution
% V: The particle velocity
% fitness: fitness
% maxgen: iterations
% sizepop: The number of particle swarm
% par_num:dimensionality
%
global data;
%% 找到最好的适应度
=max(fitness);%查询粒子群1的最佳适应度
zbest=pop(bestindex,:);%粒子群1全局最佳解
gbest=pop;%粒子群1个体最佳解
fitnessgbest=fitness;%粒子群1个体最佳适应度
fitnesszbest=bestfitness;%粒子群1全局最佳适应度
%% 迭代寻优
for i=1:maxgen
favg=sum(fitness)/sizepop;
fmin=min(fitness);
for j=1:sizepop
if fitness(j)<favg
w=wmin+(fitness(j)-fmin)*(wmax-wmin)/(favg-fmin);
else
w=wmax;
end
%更新速度
V(j,:)=w*V(j,:)+c1*rand*(gbest(j,:)-pop(j,:))+c2*rand*(zbest-pop(j,:));
V(j,find(V(j,:)>Vmax))=Vmax;
V(j,find(V(j,:)<Vmin))=Vmin;
%更新路径
pop(j,:)=pop(j,:)+V(j,:);
pop(j,find(pop(j,:)<Popmin))=Popmin;
%自适应变异
if rand>0.8
k=ceil(par_num*rand);
pop(j,k)=rand;
end
%适应度
fitness(j)=fun_pso1(pop(j,:));
%个体最优更新
if fitness(j)>fitnessgbest(j)
gbest(j,:)=pop(j,:);
fitnessgbest(j)=fitness(j);
end
%群体最优解
if fitness(j)>fitnesszbest;
zbest=pop(j,:);
fitnesszbest=fitness(j);
end
end
yy(i)=fitnesszbest;
%满足一定条件时，跳出循环并终止
a1=sum(zbest(1,:)'./data(:,4).*data(:,2))/sum(data(:,2))-1.08
a2=abs(sum(zbest(1,:))/sum(data(:,4)-0.95))
if(a1>0 && a2<1e-3)
break;
end
end
end
目标函数fun_pso1：
function y1=fun_pso1(x)
global data;
k=sum(x(1,:))/sum(data(:,4));
k=abs(k-0.95);%k为罚函数k越小越好
if k<1e-4
k=0;
else if k<1e-3
k=1;
else if k<1e-2
k=1e3;
else
k=1e4;
end
end
end
q=abs(abs(x(1,:)'-data(:,4))./data(:,4));
for i=1:length(q)
if(q(i)<0.1)
q(i)=q(i);
else if(q(i)<0.9)
q(i)=5*q(i);
else
q(i)=20*q(i);
end
end
end
q=sum(q);
p=sum(x(1,:)'.*(data(:,2)./data(:,4)))/sum(data(:,2))-1.08;%越大于1.08越好
if(p<0)
p=-1e4;
end
a=100;
b=1;
c=1;
y1=a*p-b*k-c*q;
注：data位于处理之后的原始数据，time_10000.slxs为近似解
程序运行结果如下图：
各公司能源分配如下：
33.5965343392910
300.628196324124
130.062274121335
42.7229876626742
755.324032310245
480.091617102128
75.7189577007960
127.726380815518
132.804903183349
3550.94149903030
0
666.150325416320
120.888840993557
0
190.406544613823
385.972482515892
183.708967691615
0
0
136.560505384536
75.9784929429717
374.927409765619
353.918050444746
165.441569314121
793.730348950821
0
0
89.2545198042397
176.983924371456
30.1626791123244
172.857642153534
260.674519106137
588.326676365994
23641.9522245734
37.4398695219377
543.573499399719
1278.39370646571
92.9177593213669
430.250540233213
201.459452761768
502.060116214768
0
270.314449837472
78.7379633450238
3364.66422042628
1082.75420884452
35.1349831987058
1061.80307438565
308.356656591317
1222.28871636944
78.6577851221104
0
0
374.148788063405
107.731005514660
20.7851038294637
651.347573824327
276.799661792494
3672.25904751341
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26.2982089250107
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34.5598557078038
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0
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1304.96780552733
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467.193972575924
77.5428585407070
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359.721308556742
282.789013261231
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E:\数学建模\五一数学建模联赛\B题资料\程序主.jpgE:\数学建模\五一数学建模联赛\B题资料\程序函数1.jpgE:\数学建模\五一数学建模联赛\B题资料\程序函数2.jpgE:\数学建模\五一数学建模联赛\B题资料\目标函数.jpg
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