Dick den Hertog

Robustness Analysis for Adaptive Optimization With Application to Industrial Decarbonization in the Netherlands

  • Justin Starreveld
  • Dick den Hertog
  • Jaron Davelaar
    • Categories Applications - OR and Management Sciences, Energy, Robust Optimization Tags , , ,

    Robustness analysis assesses the performance of a particular solution under variation in the input data. This is distinct from sensitivity analysis, which assesses how variation in the input data changes a model’s optimal solution. For risk assessment purposes, robustness analysis has more practical value than sensitivity analysis. This is because sensitivity analysis, when applied to … Read more

    Counterfactual Explanations for Linear Optimization

  • Jannis Kurtz
  • Ş. İlker Birbil
  • Dick den Hertog
    • Categories Applications - OR and Management Sciences, Linear Programming Tags , , ,

    The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate, and analyze three different types of CEs: strong, weak, and relative. While deriving strong and weak CEs … Read more

    ROBIST: Robust Optimization by Iterative Scenario Sampling and Statistical Testing

  • Justin Starreveld
  • Dick den Hertog
  • Roger Laeven
  • Guanyu Jin
    • Categories Robust Optimization Tags , , ,

    In this paper, we propose ROBIST, a simple, yet effective, data-driven algorithm for optimization under parametric uncertainty. The algorithm first generates solutions in an iterative manner by sampling and optimizing over a relatively small set of scenarios. Then, using statistical testing, the robustness of the solutions is evaluated, which can be done with a much … Read more

    Optimizing the Path Towards Plastic-Free Oceans

  • Dick den Hertog
  • Jean Pauphilet
  • Yannick Pham
  • Bruno Sainte-Rose
  • Baizhi Song
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Transportation Tags , , ,

    Increasing ocean plastic pollution is irreversibly harming ecosystems and human economic activities. We partner with a non-profit organization and use optimization to help clean up oceans from plastic faster. Specifically, we optimize the route of their plastic collection system in the ocean to maximize the quantity of plastic collected over time. We formulate the problem … Read more

    Cone product reformulation for global optimization

  • Danique de Moor
  • Dick den Hertog
  • Dimitris Bertsimas
  • Jianzhe Zhen
  • Thodoris Koukouvinos
    • Categories Cone Programming, Global Optimization, Nonlinear Optimization

    In this paper, we study nonconvex optimization problems involving sum of linear times convex (SLC) functions as well as conic constraints belonging to one of the five basic cones, that is, linear cone, second order cone, power cone, exponential cone, and semidefinite cone. By using the Reformulation Perspectification Technique, we can obtain a convex relaxation … Read more

    A robust approach to food aid supply chains

  • Danique de Moor
  • Dick den Hertog
  • H Fleuren
  • Robert Poos
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    One of the great challenges in reaching zero hunger is to secure the availability of sufficient nourishment in the worst of times such as humanitarian emergencies. Food aid operations during a humanitarian emergency are typically subject to a high level of uncertainty. In this paper, we develop a novel robust optimization model for food aid … Read more

    A novel algorithm for a broad class of nonconvex optimization problems

  • Dimitris Bertsimas
  • Danique de Moor
  • Dick den Hertog
  • Thodoris Koukouvinos
  • Jianzhe Zhen
    • Categories Global Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we propose a new global optimization approach for solving nonconvex optimization problems in which the nonconvex components are sums of products of convex functions. A broad class of nonconvex problems can be written in this way, such as concave minimization problems, difference of convex problems, and fractional optimization problems. Our approach exploits … Read more

    Hidden convexity in a class of optimization problems with bilinear terms

  • Bram L. Gorissen
  • Meike Reusken
  • Dick den Hertog
    • Categories Nonlinear Optimization, Robust Optimization Tags , , ,

    In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more

    Minkowski Centers via Robust Optimization: Computation and Applications

  • Dick den Hertog
  • Jean Pauphilet
  • Mohamed Yahya Soali
    • Categories Robust Optimization Tags , , ,

    Centers of convex sets are geometric objects that have received extensive attention in the mathematical and optimization literature, both from a theoretical and practical standpoint. For instance, they serve as initialization points for many algorithms such as interior-point, hit-and-run, or cutting-planes methods. First, we observe that computing a Minkowski center of a convex set can be formulated as … Read more

    Mixed-Integer Optimization with Constraint Learning

  • Donato Maragno
  • Holly Wiberg
  • Dimitris Bertsimas
  • Ş. İlker Birbil
  • Dick den Hertog
  • Adejuyigbe Fajemisin
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Data-Mining Tags , , ,

    We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data using machine learning, and the trained models are embedded in an optimization formulation. We exploit the mixed-integer optimization-representability of many machine learning methods, including … Read more