I have the following data set of a human population. The data set captures households and relationships of the persons living in those households. My problem is how to group the individuals into households to get the optimal set of household configurations (permutations)
Following is an excerpt from my contingency table.
RnC RU15c RO15c RUO15c SA SU15c SO15c SUO15c Chld Total
HH1 22 17 38 7 11 1 0 0 0 96
HH2 45 35 76 15 22 1 1 0 40 235
HH3 41 31 69 13 19 1 1 0 36 211
Total 108 83 183 35 52 3 2 0 76 542
HH1 = household with only one member
HH2 = household with only two members
Rnc = An adult person in a marital relationship and has no children
RU15c = An adult person in a marital relationship and has age under 15 children
RO15c= An adult person in a marital relationship and has age over 15 children
RUO15c = An adult person in a marital relationship and has over 15 children and under 15 children
SA = single adult person (age over 15 persons)
SU15c = Single adult person who has under 15 children
Chld = Child (Under 15)
HH1,RnC = 22 This means that there are 22 persons who are 'in a martial relationship and has no children' living alone
HH3,RnC = 19 This means that there are 19 persons who are in a relationship that are part of a 3 member households (Following is a possible permutation An adult (RnC) living with her father (RO15c) and mother (RO15c) ).
Persons who are in relationships may not live with their partner. Under 15 children must always live with at least one adult (parent)
This is bit similar to knapsack problem, but I am dealing with multiple knapsacks that are of different sizes.
I understand that there are multiple correct household configurations. My objective is finding one of these correct ones.
My question is, are there any known mathematical approaches for solving this type of problems?