# Learning to Handle Parameter Perturbations in Combinatorial Optimization: an Application to Facility Location

## TL;DR

This paper introduces a machine learning approach to adapt solutions of facility location problems to new instances by predicting solution applicability and magnitude of change, enhancing optimization with historical data.

## Contribution

It develops a novel method combining classifiers and regressors to incorporate past experience into combinatorial optimization, applicable beyond facility location problems.

## Key findings

- Classifier predicts if reference solution applies to new instance
- Regressor estimates the extent of solution change needed
- Empirical results show improved adaptation to new problem instances

## Abstract

We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning, applied to the single source, capacitated, facility location problem. Our study is framed in the context where a reference facility location optimization problem is given. Assuming there exist data for many variations of the reference problem (historical or simulated) along with their optimal solution, we study how one can exploit these to make predictions about an unseen new instance. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a new instance. In case the reference solution is partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the new instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation. We present an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach. Although presented through the application to the facility location problem, the approach developed here is general and explores a new perspective on the exploitation of past experience in combinatorial optimization.