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

by   Andrea Lodi, et al.

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.


page 1

page 2

page 3

page 4


Formulation of problems of combinatorial optimization for solving problems of management and planning of cloud production

The application of combinatorial optimization problems to solving the pr...

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

Combinatorial optimization has found applications in numerous fields, fr...

Computational Models based on Synchronized Oscillators for Solving Combinatorial Optimization Problems

The equivalence between the natural minimization of energy in a dynamica...

Generalization of Machine Learning for Problem Reduction: A Case Study on Travelling Salesman Problems

Combinatorial optimization plays an important role in real-world problem...

On a class of data-driven combinatorial optimization problems under uncertainty: a distributionally robust approach

In this study we analyze linear combinatorial optimization problems wher...

Combinatorial Optimization for Panoptic Segmentation: An End-to-End Trainable Approach

We propose an end-to-end trainable architecture for simultaneous semanti...

Learning Combined Set Covering and Traveling Salesman Problem

The Traveling Salesman Problem is one of the most intensively studied co...

Please sign up or login with your details

Forgot password? Click here to reset