Predictive Machine Learning of Objective Boundaries for Solving COPs

TL;DR

This paper demonstrates that machine learning models can effectively estimate tight objective boundaries for constraint optimization problems, significantly reducing search space and aiding solvers in finding near-optimal solutions efficiently.

Contribution

It introduces a boundary estimation framework using machine learning for constraint programming, evaluating different models and demonstrating practical benefits on multiple COPs.

Findings

Boundaries reduced the objective domain size by 60-88%.

Estimated boundaries enable earlier discovery of near-optimal solutions.

The framework shows minimal overhead in boundary estimation.

Abstract

Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known boundaries and extracted features of COPs, it is possible to train the model to estimate boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP) which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver to find an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver to find near-optimal solutions early during search.