  Combinatorial optimization plays an important role in real-world problem
solving. In the big data era, the dimensionality of a combinatorial
optimization problem is usually very large, which poses a significant challenge
to existing solution methods. In this paper, we examine the generalization
capability of a machine learning model for problem reduction on the classic
travelling salesman problems (TSP). We demonstrate that our method can greedily
remove decision variables from an optimization problem that are predicted not
to be part of an optimal solution. More specifically, we investigate our
model's capability to generalize on test instances that have not been seen
during the training phase. We consider three scenarios where training and test
instances are different in terms of: 1) problem characteristics; 2) problem
sizes; and 3) problem types. Our experiments show that this machine learning
based technique can generalize reasonably well over a wide range of TSP test
instances with different characteristics or sizes. While the accuracy of
predicting unused variables naturally deteriorates as a test instance is
further away from the training set, we observe that even when tested on a
different TSP problem variant, the machine learning model still makes useful
predictions about which variables can be eliminated without significantly
impacting solution quality.
