from scipy.optimize import linear_sum_assignment
import numpy as np#cost =np.array([[4,1,3],[2,0,5],[3,2,2]])
cost =np.array([
[2,10,9,7],
[15,4,14,8],
[13,14,16,11],
[4,15,13,9]])
row_ind,col_ind=linear_sum_assignment(cost)
print(row_ind)#开销矩阵对应的行索引
print(col_ind)#对应行索引的最优指派的列索引
print(cost[row_ind,col_ind])#提取每个行索引的最优指派列索引所在的元素，形成数组
print(cost[row_ind,col_ind].sum())#数组求和#输出指派矩阵
p = np.zeros((4,4))
p[row_ind,col_ind]=1
print(p)

# -*- coding: utf-8 -*-
import numpy as np
import copyc=[2,10,9,7,
15,4,14,8,
13,14,16,11,
4,15,13    ,9
]c = np.array(c)
c = c.reshape((4,4))all_p=[]class obj:def _init_(self):self.p=[]self.cost=0for i in range(4):for j in range(4):if j==i:continue   for u in range(4):if u==i or u==j :continuefor v in range(4):if v==i or v==j or v==u:continuep = np.zeros((4,4))p[0,i]=p[1,j]=p[2,u]=p[3,v]=1 ans = obj()ans.p = copy.deepcopy(p)ans.cost = sum(sum(c*ans.p))all_p.append(ans)all_p.sort(key=lambda ans: ans.cost, reverse=False)
print(all_p[0].p)
print(all_p[0].cost)        

clear
C=[2    10    9    7
15    4    14    8
13    14    16    11
4    15    13    9];A = perms(1:4);%perm显示1，2，3，4四个数的全排列
L = length(A)
best=999
best_mat=[]
for i=1:La = zeros(4,4);b = A(i,:);%遍历全排列中的每一种  c = 1:4;a(sub2ind(size(a), b, c))=1;%a矩阵指定的位置赋值为1s = sum(sum(a.*C));%求出费用和if best>s %挑出最大的best_mat=a;best=s;end
end
best_mat
best

clear
n=4;
A=perms(1:n);
G=size(A);  %24 4   size(A,1) 24   size(A,2) 24
n0=G(1);   %24
B=[2,10,9,7;15,4,14,8;13,14,16,11;4,15,13,9];
for n1=1:n0%C为第n1中排列情况下，费用的4个取值C(1)=B(1,A(n1,1));C(2)=B(2,A(n1,2));C(3)=B(3,A(n1,3));C(4)=B(4,A(n1,4));%D{n1}表示第n1种情况下的4个取值D{n1}=[C(1),C(2),C(3),C(4)];s(n1)=sum(D{n1});
end
%找到最小的，返回a为行左边，b为纵坐标，a=1,b=9
[a,b]=find(s==min(s));
K=A(b,:)

clear
C=[2   10  9   7
15  4   14  8
13  14  16  11
4   15  13  9];A = perms(1:4);%perm显示1，2，3，4四个数的全排列
L = length(A)
for i=1:La = zeros(4,4);b = A(i,:);%遍历全排列中的每一种  c = 1:4;a(sub2ind(size(a), b, c))=1;%a矩阵指定的位置赋值为1D{i}=a;S(i)=sum(sum(a.*C));%求出费用和
end
[a,b]=find(S==min(S))
D{b}
S(b)

clear
A=[2 15 13 4];B=[10 4 14 15];C=[9 14 16 13];D=[7 8 11 9];
Y=zeros(1,1000);s=64;x=zeros(1,4);
for i= 1:1000X=randperm(4);Y(i)=A(X(1))+B(X(2))+C(X(3))+D(X(4));if Y(i)<ss=Y(i);x=X;end
end
s,x

%适用于任意n阶系数矩阵
clear all；
C=[2   10  9   7,
15  4   14  8,
13  14  16  11,
4   15  13  9,
];%效率矩阵C
n=size(C,1);%计算C的行列数n
C=C(:);%计算目标函数系数，将矩阵C按列排成一个列向量即可。
A=[];B=[];%没有不等式约束
Ae=zeros(2*n,n^2);%计算等约束的系数矩阵a
for i=1:nfor j=(i-1)*n+1:n*iAe(i,j)=1;endfor k=i:n:n^2Ae(n+i,k)=1;end
end
Be=ones(2*n,1);%等式约束右端项b
Xm=zeros(n^2,1);%决策变量下界Xm
XM=ones(n^2,1);%决策变量上界XM
[x,z]=linprog(C,A,B,Ae,Be,Xm,XM);%使用linprog求解
x=reshape(x,n,n);%将列向量x按列排成一个n阶方阵
disp('最优解矩阵为:');%输出指派方案和最优值
Assignment=round(x)%使用round进行四舍五入取整
disp('最优解为:');
z

%线性规划
c=[2,10,9,7,15,4,14,8,13,14,16,11,4,15,13,9];
Aeq=[1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1;1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0;0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0;0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0;0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1];
beq=[1,1,1,1,1,1,1,1];
lb=zeros(16,1);
ub=ones(16,1);
[x,fval] = linprog(c,[],[],Aeq,beq,lb,ub)