Benchmarks for the Set Packing Problem
The Set Packing problem can be mathematically defined as follows:
Max sum{i=1,…,n} c(i) x(i)
st sum{i=1,…,n} t(i,j) x(i) <= 1, for j=1,…,m
x(i)=0 or 1
The format of these 64 data files available below is:
-
Number of constraints m
- Number of variables n
- The coefficients (values) of each variables c(i), i=1,…, n
- For each constraints j (j=1,…, m) in matrix t: the number of non-null coefficients in this constraints, and then the index list of variables i with a coefficient t(i,j) equal to 1
Max-One represents the maximum number of non-null coefficients per line of the matrix t.
When the value of the best known solution is optimal, it is followed by an asterisk. You can alternatively download the whole set (instances.tar.gz).
The Bi-Objective Set Packing problem can be mathematically defined as follows:
Max sum{i=1,…,n} c1(i) x(i)
Max sum{i=1,…,n} c2(i) x(i)
st sum{i=1,…,n} t(i,j) x(i) <= 1, for j=1,…,m
x(i)=0 or 1
The format of these 120 data files available below is:
-
Number of constraints m
- Number of variables n
- The coefficients (values) of each variables c1(i), i=1,…, n
- The coefficients (values) of each variables c2(i), i=1,…, n
- For each constraints j (j=1,…, m) in matrix t: the number of non-null coefficients in this constraints, and then the index list of variables i with a coefficient t(i,j) equal to 1
Instance files have been regrouped into 20 families. All instances from one family have the same number of constraints and variables as well as the same matrix t, but they have different vectors of coefficients c1 and c2.
