A Machine Learning-Based Warm Start Approach to Improve the Solvability of Optimization Problems

Abstract

In this research, we explore the use of machine learning (ML) techniques, notably logistic regression and decision tree algorithms, for improving the solvability of optimization problems. Recognizing that the computational time required to solve a linear programming problem can be heavily influenced by the choice of a starting basis (referred to as "warm start"), we apply classification techniques to apriori decide the decision variables that are most likely to be part of the optimal basis. Problem parameters and their combinations (including interactions) that yield the most effective warm start basis are identified. We also explore more advanced ML methods such as neural networks that can aid in improving the identification of advanced bases. Our detailed computations show that the use of such advanced ML techniques can significantly improve the solvability of optimization problems.