A machine learning based algorithm selection method to solve the minimum cost flow problem

TL;DR

This paper presents a machine learning approach to select the fastest solver for the minimum cost flow problem based on instance features, achieving over 90% accuracy in prediction.

Contribution

It introduces a data-driven method using classifiers trained on 81,000 instances to predict the optimal solver, improving solver selection efficiency.

Findings

Tree-based models outperform other classifiers.

Achieved over 90% accuracy in solver prediction.

Effective hyperparameter optimization enhances performance.

Abstract

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%.