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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 bi-objective 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 04-05, 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
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