MATLAB基于问题的整数线性规划

这几天做题遇到了较为复杂的规划问题，在想能不能用MATLAB实现像LINGO那样的偏向用户输入的编写方法，而非MATLAB矩阵式的，最终实现了基于问题的求解代码。

$$\begin{equation} A = \begin{bmatrix} a & b \\ c & c \end{bmatrix} \end{equation}$$ $$\begin{equation}\ \begin{array}{c} \begin{aligned} \max \quad \mathrm{E} = \frac{Q-F-T}{F+T} \times 100 \% \\ \end{aligned} \\ \begin{aligned} s \cdot t\left\{\begin{array}{l} \frac{\sum_{i = 1}^{8} b_{i} \cdot x_{i}}{L} \leq 2.28 \\ m_{i} \leq x_{i} \leq M_{i} \\ \sum_{i = 1}^{11} x_{i} \cdot r_{i} \geq 0.7069 \cdot \theta \quad 0 \quad 0<\theta \leq 1,2, \cdots 11 \\ x_{i} \text { 为整数 } \quad i = 1,2, \cdots 11 \end{array}\right. \end{aligned} \end{array} \end{equation}$$

代码

主文件

%重新设计建筑规划方案中各房型的最低套数约束;
m=[50;50;50;150;100;150;50;100;50;50;50];
%重新设计建筑规划方案中各房型的最高套数约束;
MM=[450;500;300;500;550;350;450;250;350;400;250];
%各房型的房型面积;
b=[77;98;117;145;156;167;178;126;103;129;133];
%参筹者对各种房型的满意比例;
r=[0.4;0.6;0.5;0.6;0.7;0.8;0.9;0.6;0.2;0.3;0.4];

v = 1;
jieguo = [];
taoshu = [];
for i = 0:10
    v = 1 - 0.01*i;
    x = optimvar('x',11,'LowerBound', 0, 'Type','integer');
    % prob = optimproblem('Objective', sum(r) .* x ./ sum(x) );
     prob = optimproblem('ObjectiveSense', 'max', 'Objective', qiujie(x) ); 
     t1 = sum(r .* x) ./ sum(x);
    con1 = [
        m <= x
        x <= MM
        0.7069 * v <= t1
        sum(x(1:8).*b(1:8))./102077.6 - sum(x(9:11).*b(9:11))./102077.6 <= 2.28
    ];
    prob.Constraints.con1 = con1;
    [sol,fvl] = solve(prob);
    jieguo(i+1) = fvl;
    taoshu(:,i+1) = sol.x;

end

final = [jieguo;taoshu]
目标函数文件

function f = qiujie(x)
%房型面积；
b=[77 98 117 145 156 167 178 126 103 129 133];
%房型开发成本；
    c=[4263 4323 4532 5288 5268 5533 5685 4323 2663 2791 2982];
%房型单元售价；
p=[12000 10800 11200 12800 12800 13600 14000 10400 6400 6800 7200];

%容积率R；
sum1=0;
for i=1:8;
sum1=sum1+x(i)*b(i);
end
R=sum1/102077.6
%建筑总面积B；
B=0;
for i=1:11;
B=B+x(i)*b(i);
end
B
%普通宅的建筑总面积b1；
b1=0;
for i=1:3;
b1=b1+x(i)*b(i);
end
b1
%非普通宅的建筑总面积b2；
b2=0;
for i=4:8;
b2=b2+x(i)*b(i);
end
b2=b2+x(11)*b(11)
%非普通宅的售房总收入sum2；
sum2=0;
for i=4:8;
sum2=sum2+x(i)*b(i)*p(i);
end
sum2=sum2+x(11)*b(11)*p(11);
for i=9:10;
sum2=sum2+x(i)*b(i)*p(i)*b2/(b1+b2);
end
sum2
%非普通宅的扣除项目总金额sum3
17
s1=0;
for i=4:8
s1=s1+x(i)*b(i);
end
s1=s1+x(11)*b(11);
for i=9:10
s1=s1+x(i)*b(i)*b2/(b1+b2);
end
s1=777179627*s1/B;
s2=0;
for i=4:7;
s2=s2+x(i)*b(i)*c(i);
end
for i=9:10
s2=s2+x(i)*b(i)*c(i)*b2/(b1+b2);
end
s2
s3=(s1+s2)*0.3;
s4=0;
for i=4:8;
s4=s4+x(i)*b(i)*p(i);
end
s4=s4+x(11)*b(11)*p(11);
for i=9:10;
s4=s4+x(i)*b(i)*p(i)*b2/(b1+b2);
end
s4=s4*0.0565;
sum3=s1+s2+s3+s4
%非普通住宅增值额与扣除金额比例：
R2=(sum2-sum3)/sum3

%非普通住宅增值税计算
T2 = (sum2-sum3)*0.3
% if R2 <= 0.5
%     T2 = (sum2-sum3)*0.3;
% elseif R2 <= 1
%     T2 = (sum2-sum3)*0.4;
% elseif R2 <= 2
%     T2 = (sum2-sum3)*0.5;
% else
%     T2 = (sum2-sum3)*0.6;
% end


%普通宅的售房总收入sum4；
sum4=0;
for i=1:3;
sum4=sum4+x(i)*b(i)*p(i);
end
for i=9:10;
sum4=sum4+x(i)*b(i)*p(i)*b1/(b1+b2);
end
sum4
%普通宅的扣除项目总金额sum5；
ss1=0;
for i=1:3
ss1=ss1+x(i)*b(i);
end

for i=9:10
ss1=ss1+x(i)*b(i)*b1/(b1+b2);
end
ss1=777179627*ss1/B;
ss2=0;
for i=1:2;
ss2=ss2+x(i)*b(i)*c(i);
end
for i=9:10
ss2=ss2+x(i)*b(i)*c(i)*b1/(b1+b2);
end
ss3=(ss1+ss2)*0.3;
ss4=0;
for i=1:3;
ss4=ss4+x(i)*b(i)*p(i);
end
for i=9:10
ss4=ss4+x(i)*b(i)*p(i)*b1/(b1+b2);
end
ss4=ss4*0.0565;
sum5=ss1+ss2+ss3+ss4
%普通住宅增值额与扣除金额比例；
R1=(sum4-sum5)/sum5

%普通住宅增值税计算
T1 = (sum4-sum5)*0.3
% if R1 <= 0.5
%     T1 = (sum4-sum5)*0.3;
% elseif R2 <= 1
%     T1 = (sum4-sum5)*0.4;
% elseif R2 <= 2
%     T1 = (sum4-sum5)*0.5;
% else
%     T1 = (sum4-sum5)*0.6;
% end

%总增值税
T = T1 + T2

%房地产开发成本S1；
S1=0;
for i=1:11;
S1=S1+x(i)*b(i)*c(i);
end
S1
%房地产开发费用S2；
S2=(777179627+S1)*0.1
%与转让房地产有关的税金S3；
S3=0;
for i=1:11;
S3=S3+x(i)*b(i)*p(i);
end
S3=S3*0.0565
%其他扣除项目S4；
%S4=(777179627+S1)*0.2
%总的成本投入chengben；
%chengben=777179627+S1+S2+S3+S4
chengben=777179627+S1+S2+S3
%总的收入zong；
zong=S3/0.0565
f = (zong-chengben - T)/(chengben + T)

参考

1. https://ww2.mathworks.cn/help/optim/ug/optimproblem.html
2. https://zhuanlan.zhihu.com/p/359408474