Implementation of Cutting Plane Separators for Mixed Integer ... - ZIB

18
16
14
12
10
8
6
(4.68)
4
(2.1)
2
Gap closed in geometric mean in %
Sepa Time in geometric mean in CPU seconds
(13.48)
(2.7)
(14.51)
(3.0)
(15.41)
(3.5)
0 1 2 3 4 5 6 7 8 9 10
MAXAGGR
3.4 Computational Study 35
(16.13) (16.22) (16.29) (16.36) (16.45) (16.49) (16.52)
(3.9)
(4.2)
Figure 3.2: Computational results for the cutting plane separator for the class of c-MIR inequalities.
Parameter MAXAGGR. Use MAXAGGR = 0, . . . , 10.
improved performance of the separation algorithm. The initial gap closed in geometric
mean increases by 8.80 percentage points from 4.68 percent to 13.48 percent
when allowing one constraint to be added to a starting constraint. The results also
confirm Marchand’s and Wolsey’s observation that there is no significant increase
in the efficacy with MAXAGGR greater than 5. Thus, in our resulting algorithm (slow
version) we use MAXAGGR = 5.
Aggregation Heuristic
In Section 3.3.1, we stated an algorithm which adds a single mixed integer constraint
from the formulation of X to the current aggregated constraint in order to eliminate
a real variable appearing in the current aggregated constraint. This algorithm is the
first part of the construction of a mixed knapsack relaxation of X. The crucial aspect
of the aggregation heuristic is the selection of the real variable to be eliminated and
the constraint added. In Section 3.3.1, we stated four types of scores which can
be used to select the constraint used to eliminate a selected real variable. In the
default algorithm we use Score Type 1, i.e., we select the constraint found first. This
criterium is very simple, since it does not take into account any information about
the constraints which are candidates to be added.
In our computational study, we tested Score Type 3 and Score Type 4, but not
Score Type 2, since we want to obtain a deterministic separation algorithm. The
results for using Score Type 3 obtained on our main test set are given in Table B.4
and a summary of the results is contained in Table 3.1. The initial gap closed in
geometric mean increases by 5.17 percentage points. Thus, by taking into account
the LP solution of the dual variable corresponding to the original MIP row, the
density of the original MIP row, the slack value of the constraint and the number
(4.5)
(4.8)
(5.0)
(5.3)
(5.6)