3 Presentations

• 
  03:30 PM - 03:55 PM

  Explaining decisions in contextual stochastic optimization

  • Alexandre Forel, presenter, Polytechnique Montreal
  • Axel Parmentier, CERMICS, École des Ponts
  • Thibaut Vidal, CIRRELT & SCALE-AI Chair in Data-Driven Supply Chains, Polytechnique Montréal

  Contextual stochastic optimization combines auxiliary information and machine learning to solve problems subject to uncertainty. While this integrated approach can improve performance, it leads to complex decision pipelines that lack transparency. Yet, practitioners need to understand and trust new solutions in order to replace an existing policy. To explain the solutions of contextual stochastic problems, we revisit the concept of counterfactual explanations introduced in the classification setting. Thus, we identify minimum changes in the features of the context that lead to a change in the optimal decisions. We formalize the explanation problem and develop mixed-integer linear models to find optimal explanations of decisions obtained through random forests and nearest-neighbor predictors. We apply our approach to selected operations research problems, such as inventory management and routing, and show the value of the explanations obtained.
• 
  03:55 PM - 04:20 PM

  Conditional Robust Optimization: A Framework for Decision Making under Uncertainty

  • Abhilash Chenreddy, presenter, Department of Decision Sciences, HEC Montréal
  • Delage Erick, Professor, Department of Decision Sciences, HEC Montréal

  Conditional Robust Optimization (CRO) is a decision-making framework that blends the flexibility of robust optimization (RO) with the ability to incorporate additional information regarding the structure of uncertainty. This approach solves the RO problem where the uncertainty set accounts for the most recent side information provided by a set of covariates. In this presentation, we will introduce two data-driven approaches to CRO: a sequential predict-then-optimize method and an integrated end-to-end method. We will demonstrate the application of both approaches and we will examine how each approach can incorporate additional information about the distribution of uncertainty into the optimization model. Finally, we will compare CRO with other contextual and non-contextual decision-making frameworks to emphasize their advantages and limitations.
• 
  04:20 PM - 04:45 PM

  A learning approach for constraint customization in optimization models

  • Mahdis Bayani, presenter, Polytechnique Montreal
  • Yossiri Adulyasak, HEC Montreal
  • Louis-Martin Rousseau, Polytechnique Montreal

  Decision-makers in different industries make use of optimization software for planning and decision-making and often customize the solutions obtained by software based on some implicit internal operational rules and preferences. To ensure that such considerations and hidden constraints can be systematically taken into account without requiring explicit knowledge obtained from human experts, one can leverage data-driven methods to embed side constraints in known classical mixed integer linear programs (MILP). By building upon previous research, we propose a framework to indirectly learn such rules from the historical data of executed plans by customers. Rather than relying on a simple linear regression model, we extend the framework by incorporating regularized linear regression and decision trees in the optimization model. To motivate the method, we discuss different combinations of rules settings in the linear and binary knapsack problem as well as a nurse rostering problem. The optimal solutions obtained by the method suggest that the approaches could learn the adjustments from the data and perform effectively compared to the previous work in this area in more complex settings.

  Keywords: Constraint customization, Data-driven methods, Mixed integer linear programming, Decision tree