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

2.3 Computational Study 13
separators. Thus, evaluating the performance of each separator for all possible combinations
of these choices is practically impossible. Inspired by the work of Gu,
Nemhauser and Savelsbergh [30], we use for each separator the following approach
in our computational study. We give a default algorithm, which represents a set of
choices which are basic, i.e., the set does not contain choices which are modifications
of algorithmic aspects that may lead to an improved performance. Then, we present
computational results which compare the performance of the default algorithm to
the performance of an algorithm in which a single choice has been altered. We only
modify this approach if not using a basic choice for an algorithmic aspect leads to
such a small number of cuts found by the default algorithm that the results for
altering other single choices would not be very meaningful.
The results will be presented in the following way. In the tables containing the results
for the default algorithms (Table B.3, B.22, B.28, B.36, and B.48), we state the
performance measures Gap closed %, Cuts, Sepa Time and Sepa Time Average (there
will be three default algorithms for the cutting plane separator for the 0-1 knapsack
problem, because we consider three classes of valid inequalities). At the bottom of
the tables, in the row labelled Total, we give the sum of the values of each performance
measure over all instances, and in the row labelled Geom. Mean, we give the
geometric mean of the values of each performance measure over all instances where
individual values smaller than one were replaced by one. In the tables containing
the results for altering a single choice for each cutting plane separator (see e.g. Table
B.4), we report in addition for each performance measure the difference to the
corresponding default algorithm. Here numbers in blue color indicate that the value
of the performance measure obtained by the altered algorithm is better than the
one obtained by the default algorithm, and numbers in red color indicate that the
value of the performance measure obtained by the altered algorithm is worse than
the one obtained by the default algorithm. Note that for Gap closed % the △ value
for each instance, for Total and for Geom. Mean is given in percentage points, not
in percentage.