Luca Mossina

Andrea Lodi, Luca Mossina, Emmanuel Rachelson

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.

Luca Mossina, Emmanuel Rachelson, Daniel Delahaye

We study how Reinforcement Learning can be employed to optimally control parameters in evolutionary algorithms. We control the mutation probability of a (1+1) evolutionary algorithm on the OneMax function. This problem is modeled as a Markov Decision Process and solved with Value Iteration via the known transition probabilities. It is then solved via Q-Learning, a Reinforcement Learning algorithm, where the exact transition probabilities are not needed. This approach also allows previous expert or empirical knowledge to be included into learning. It opens new perspectives, both formally and computationally, for the problem of parameter control in optimization.

Luca Mossina, Emmanuel Rachelson

This article focuses on the question of learning how to automatically select a subset of items among a bigger set. We introduce a methodology for the inference of ensembles of discrete values, based on the Naive Bayes assumption. Our motivation stems from practical use cases where one wishes to predict an unordered set of (possibly interdependent) values from a set of observed features. This problem can be considered in the context of Multi-label Classification (MLC) where such values are seen as labels associated to continuous or discrete features. We introduce the \nbx algorithm, an extension of Naive Bayes classification into the multi-label domain, discuss its properties and evaluate our approach on real-world problems.