
The set Packing problem with two objectives is defined as
follow:
Max sum{i=1,…,n} c1(i) x(i)
Max sum{i=1,…,n} c2(i) x(i)
s/t sum{i=1,…,n} t(i,j) x(i) <= 1 for j=1,…,m
x(i)=0 or 1 for i=1,...,n
Description
There are currently 120 data files.
They correspond to 20 biobjective set packing problems.
For each problem, 6 variants are given: class A, B, C, D, E and F.
A: the costs are uniformly generated
B: created from A by replacing the second vector of costs by the first one in reverse order
C: vector of costs generated with plateaus of values
D: created from C by replacing the second vector of costs by the first one in reverse order
E: one unicost objective and one randomly generated objective
F: one unicost objective and one randomly generated objective with plateaus of values
These data files are the test problem sets from
Xavier Gandibleux, Fabien Degoutin and Xavier Delorme
A first feedback on set packing problems with two
objectives
Workshop "Multiple Objective Metaheuristics"
November 0405, 2002, Carré des Sciences, Paris,
France. (poster
here)
Format
The format is originally from the OR library extended for
handling multiple objectives.
The format of all of these data files is:
number of rows (m), number of columns (n)
the cost of each column for objective 1 c1(i),i=1,...,n
the cost of each column for objective 2 c2(i),i=1,...,n
for each row j (j=1,...,m): the number of columns which cover
row j followed by a list of the columns which cover row j
