Boosting Combinatorial Problem Modeling with Machine Learning

TL;DR

This paper surveys how machine learning techniques can improve the modeling phase in combinatorial optimization, making it more accurate and efficient by learning constraints and objectives from data.

Contribution

It provides a comprehensive overview of recent ML-based approaches to enhance combinatorial problem modeling, highlighting common themes and connections to related research.

Findings

ML can automate and improve constraint modeling

Learning from data refines objective functions

Survey identifies key trends and future directions

Abstract

In the past few years, the area of Machine Learning (ML) has witnessed tremendous advancements, becoming a pervasive technology in a wide range of applications. One area that can significantly benefit from the use of ML is Combinatorial Optimization. The three pillars of constraint satisfaction and optimization problem solving, i.e., modeling, search, and optimization, can exploit ML techniques to boost their accuracy, efficiency and effectiveness. In this survey we focus on the modeling component, whose effectiveness is crucial for solving the problem. The modeling activity has been traditionally shaped by optimization and domain experts, interacting to provide realistic results. Machine Learning techniques can tremendously ease the process, and exploit the available data to either create models or refine expert-designed ones. In this survey we cover approaches that have been recently proposed to enhance the modeling process by learning either single constraints, objective functions, or the whole model. We highlight common themes to multiple approaches and draw connections with related fields of research.