4 Presentations

• 
  10:45 AM - 11:10 AM

  Machine learning for combinatorial optimization

  • Yoshua Bengio, Mila, UdeM
  • Andrea Lodi, Polytechnique Montreal
  • Antoine Prouvost, presenter, Polytechnique Montréal

  Studying the optimal decisions of real-world (combinatorial) optimization problems (a field known as Operations Research) can lead to dramatic improvements and savings (with respect to non-optimal or informal ones). Given the hard nature of these problems, state-of-the-art methodologies involve algorithmic decisions that either require too much computing time or are not mathematically well understood. Thus, machine learning looks like a promising candidate to effectively deal with those decisions.
  We draw inspiration from previous literature to derive a methodology that integrates machine learning in the framework of combinatorial optimization algorithms. We interpret optimization problems as data points for a specific distribution of instances and see how we can learn parts of the algorithm used to solve them. Under the machine learning methodology, we discuss what can and cannot be expected from learned algorithms.
• 
  11:10 AM - 11:35 AM

  Improving optimization bounds using machine learning: Decision diagrams meet deep reinforcement learning

  • Quentin Cappart, presenter, Cirrelt
  • Emmanuel Goutierre, Ecole Polytechnique
  • David Bergman, University of Connecticut
  • Louis-Martin Rousseau, Polytechnique Montréal

  Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bounds achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.
• 
  11:35 AM - 12:00 PM

  A deep reinforcement learning model for the single container loading problem

  • Hajlaoui Yakin, presenter, Polytechnique Montréal, ENIT
  • Bhar Layeb Safa, UR-OASIS, National Engineering School of Tunis, University of Tunis El Manar, Tunis, Tunisia
  • Amel Jaoua, Université de Montréal
  • Michel Gamache, Polytechnique Montréal

  In this work, we investigate the capability of the Deep Reinforcement Learning in solving the Single Container Loading Problem. The objective is to measure the effectiveness of this algorithmic approach in solving such NP-hard combinatorial optimization problem. Preliminary computational results on benchmark instances reveal the good performance of the proposed model.

  Keywords :Single Container Loading Problem, Deep Reinforcement Learning.
• 
  12:00 PM - 12:25 PM

  A language processing algorithm for predicting tactical solutions to operational planning problems under uncertainty

  • Eric Larsen, DIRO, Université de Montréal
  • Emma Frejinger, presenter, DIRO and CIRRELT

  We address the fast prediction of tactical solutions (output) to operational problems (input), focusing on train load planning. We extend Larsen et al. 2018 (arXiv:1807.11876) by predicting more detailed, variable-length solutions. The machine learning model originates from language processing and we construct vocabularies and syntaxes describing the problem instances and solutions. Extensive numerical results demonstrate excellent predictive accuracy.

  Keywords: stochastic programming, integer linear programming, supervised learning, deep learning