![](bg7.png)
managed to solve instances to optimality with up to
n = 200 advertising media in less than 10 minutes on
a simple standard PC with 2.2 GHz and 2 GB Ram.
For ensuring a good user experience UPPER Net-
work however requested that the optimized marketing
campaign of MARMIND has to be computed in less
than 3 seconds. Moreover, we recall that all data of
our QKP instances is based on estimates and does not
represent assured values. Thus, we can easily settle
for a good approximate solution.
For our optimization tool we implemented a ge-
netic algorithm and imposed a time limit of 3 seconds.
It turned out that this gave solutions for all instances
of the required size (≥ 200 items) with an average de-
viation of less than 1% from optimality.
Our algorithm is a modified version of (Julstrom,
2005) which worked well for the random test in-
stances generated according to the same method used
in (Caprara et al., 1999). (Julstrom, 2005) reports test
data for ten instances of 100 items and ten instances
of 200 items. Every instance was solved 50 times and
the algorithm was able to find the optimal solution
value in about 90 percent of the runs, although the
running time sometimes exceeds 1 minute. Note that
our implementation was especially tuned for getting
high quality results in a very short time but often suc-
ceeded to yield results similar or better than (Julstrom,
2005).
Recently (Yang et al., 2013) published a well per-
forming metaheuristic that combined GRASP with
tabu search. On 100 randomly generated benchmark
instances that follow the same scheme as in (Caprara
et al., 1999) the metaheuristic was able to find the op-
timal solution 99 times in less than 0.8 seconds. In
the remaining case the gap to the optimal solution
was negligibly small. Moreover, they were able to get
good solutions for instances of up to 2000 variables
(the solution quality was justified by comparison to
known upper bounds) in less than 300 seconds.
Currently, we are working on a project to system-
atically test our genetic algorithm, compare it to the
other existing methods listed above and to introduce
harder benchmark instances for QKP. The results of
this comprehensive computational study will be pub-
lished as they become available.
7 CONCLUSIONS
We developed an optimization system to offer mar-
keting managers an evidence-based suggestion for the
media mix to be used for a given promotional cam-
paign. It relies on a comparison of the current cam-
paign to past campaigns based on their parameters
and goals.
Building an optimization model with the com-
puted direct and pairwise effect estimations gives
rise to a Quadratic Knapsack Problem which can be
solved almost to optimality in all real-world scenar-
ios within a time limit of 3 seconds. The optimization
tool is currently used within the industrial software
solution MARMIND.
Future developments include a revision of some of
the effect estimations by stochastic models as soon as
a suitable set of test data derived from real world ap-
plications is available. Furthermore, the estimations
will be adjusted to include a “memory” effect, i.e.,
giving a smaller weight to campaigns in the more dis-
tant past. It may also be interesting to take trends
into accounts. Based on classical tools of statistical
analysis it should be possible to detect certain trends
of advertising media increasing or decreasing in im-
portance, or in their effect for certain goals or target
groups.
ACKNOWLEDGEMENTS
This research was supported by the Austrian Research
Promotion Agency (FFG) under project “MARMIND
media mix optimization“ and by the Austrian Science
Fund (FWF): [P 23829-N13].
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