Generalization of Machine Learning for Problem Reduction: A Case Study on Travelling Salesman Problems
This work addresses scalability issues in combinatorial optimization for real-world applications, but it is incremental as it applies an existing machine learning approach to a specific case study on TSP.
The paper tackles the challenge of high dimensionality in combinatorial optimization by using a machine learning model to greedily remove decision variables predicted not to be part of optimal solutions in traveling salesman problems (TSP), showing it generalizes reasonably well across different TSP characteristics, sizes, and variants, though accuracy deteriorates as test instances diverge from the training set.
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.