  The minimum cost flow problem is one of the most studied network optimization
problems and appears in numerous applications. Some efficient algorithms exist
for this problem, which are freely available in the form of libraries or
software packages. It is noticeable that none of these solvers is better than
the other solution methods on all instances. Thus, the question arises whether
the fastest algorithm can be selected for a given instance based on the
characteristics of the instance. To this end, we train several machine learning
classifiers to predict the fastest among a given set of solvers. We accomplish
this by creating a representative data set of 81,000 instances and
characterizing each of these instances by a vector of relevant features. To
achieve better performance, we conduct a grid search to optimize the
hyperparameters of the classifiers. Finally, we evaluate the different
classifiers by means of accuracy. It is shown that tree-based models appear to
adapt and exploit the relevant structures of the minimum-cost flow problem
particularly well on a large number of instances, predicting the fastest solver
with an accuracy of more than 90%.
