Timaos123 / OptMatch

1.基于线性规划解决两两配对问题

大致原理见知乎：【模型工程】线性规划解决两两配对问题

1.1.读取数据

import  pandas as pd

teacherDf=pd.read_csv("data/teacher_info.csv")
teacherDf.head()

	teacher_id	major	grade	class
0	t1	电包	3	1班
1	t2	电包	3	2班
2	t3	电包	3	3班
3	t4	电商	3	4班
4	t5	电商	4	5班

studentDf=pd.read_csv("data/student_info.csv")
studentDf.head()

	student_id	major	grade	class
0	s1	电包	1	1班
1	s2	电包	1	2班
2	s3	电包	3	3班
3	s4	电商	3	4班
4	s5	电商	2	5班

1.2.构建带权邻接矩阵

import numpy as np
from OptMatch import matchLinearAdj

studentInfoList=studentDf.values.tolist()
teacherInfoList=teacherDf.values.tolist()
adjMat=np.matrix([[abs(teacherInfoList[teacherI][2]-studentInfoList[studentI][2]) for teacherI in range(len(teacherInfoList))] for studentI in range(len(studentInfoList))])
rx,result,status=matchLinearAdj(adjMat)

1.3.输出结果

pairList=[]
for xItem in rx:
    rowI=int(xItem.split("_")[1])
    colI=int(xItem.split("_")[2])
    pairList.append([teacherInfoList[colI][0],studentInfoList[rowI][0]])
pairList=[eval(pairItem) for pairItem in list(set([str(pairItem) for pairItem in pairList]))]
print("决策变量（前5条）：\n",pairList[:5])
print("最终结果：",result)
print("解答状态：",status)

决策变量（前5条）：
 [['t3', 's15'], ['t8', 's20'], ['t9', 's10'], ['t6', 's19'], ['t19', 's7']]
最终结果： 44.0
解答状态： 1

2.多人组匹配问题

2.1.构建带权邻接矩阵

2.1.1.人员名单构建

studentNameList=[row[0] for row in studentInfoList]
teacherNameList=[row[0] for row in teacherInfoList]
peopleNameList=studentNameList+teacherNameList
peopleInfoList=[row for row in studentInfoList]+[row for row in teacherInfoList]

2.1.2.关联权值构建（需要依据自己的业务逻辑进行构建），并过滤掉无效关联（权值为0的关联）

def matchOK(peopleItem1,peopleItem2):
    # 条件过滤

    # 两人不同约束
    if peopleItem1[0]==peopleItem2[0]:
        return 0

    # 二者都是学生
    if peopleItem1[0] in studentNameList and peopleItem2[0] in studentNameList:
        if peopleItem1[1]==peopleItem2[1]:# 学生同专业约束
            return 1
    
    # 二者都是教师
    if peopleItem1[0] in teacherNameList and peopleItem2[0] in teacherNameList:
        return 1
    
    # peopleItem1是学生，peopleItem2是教师
    if peopleItem1[0] in studentNameList and peopleItem2[0] in teacherNameList:# 教师与考生尽可能同年级
        return 4-abs(peopleItem2[2]-peopleItem1[2])

    # 筛除peopleItem1是教师，peopleItem2是学生的情况
    if peopleItem1[0] in teacherNameList and peopleItem2[0] in studentNameList:
        return 0

    return 0

pairList=[[peopleItem1[0],peopleItem2[0],matchOK(peopleItem1,peopleItem2)] for peopleItem1 in peopleInfoList for peopleItem2 in peopleInfoList]    
pairList=[row for row in pairList if row[2]>0]
myAdjMat=np.zeros([len(peopleNameList),len(peopleNameList)])
for pairItem in pairList:
    myAdjMat[peopleNameList.index(pairItem[0]),peopleNameList.index(pairItem[1])]=pairItem[2]

2.2.基于极大团进行组匹配

from OptMatch import matchCliqueAdj

studentMaxNum=10
teaMinNum=3
meetingList,remainStuList,remainTeaList=matchCliqueAdj(myAdjMat,studentNameList,studentMaxNum,teacherNameList,teaMinNum,teaMaxTime=1)

2.3.输出结果

for meetingItem in meetingList:
    print(meetingItem)

[['t3', 't17', 't2'], ['s11', 's16', 's12', 's23', 's18', 's22', 's10', 's4', 's6', 's5']]
[['t1', 't4', 't18'], ['s3', 's9', 's21', 's15', 's1', 's20', 's13', 's7', 's14', 's19']]
[['t20', 't16', 't23'], ['s17', 's24']]
[['t6', 't7', 't5'], ['s2', 's8']]

其中，每一行list中，左侧为该组中的教师名单，右侧为该组中的学生名单