Dick den Hertog

Robust optimization of dose-volume metrics for prostate HDR-brachytherapy incorporating target- and OAR volume delineation uncertainties

  • Marleen Balvert
  • Dick den Hertog
  • Aswin Hoffmann
    • Categories Biomedical Applications, Robust Optimization Tags , , , ,

    In radiation therapy planning, uncertainties in target volume definition yield a risk of underdosing the tumor. The classical way to prevent this in the context of external beam radiotherapy (EBRT) has been to expand the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept … Read more

    The impact of the existence of multiple adjustable robust solutions

  • Ruud C.M. Brekelmans
  • Frans J.C.T. de Ruiter
  • Dick den Hertog
    • Categories Applications - OR and Management Sciences, Robust Optimization

    In this note we show that multiple solutions exist for the production-inventory example in the seminal paper on adjustable robust optimization in [2]. All these optimal robust solutions have the same worst-case objective value, but the mean objective values differ up to 21.9% and for individual realizations this difference can be up to 59.4%. We … Read more

    Robust Dual Response Optimization

  • Dick den Hertog
  • Jack P.C. Kleijnen
  • Ihsan Yanıkoğlu
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization, Robust Optimization

    This article presents a robust optimization reformulation of the dual response problem developed in response surface methodology. The dual response approach fits separate models for the mean and the variance, and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may … Read more

    When are static and adjustable robust optimization with constraint-wise uncertainty equivalent?

  • Dick den Hertog
  • Ahmadreza Marandi
    • Categories Robust Optimization Tags , , ,

    Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraint-wise and the adjustable variables lie … Read more

    Centered Solutions for Uncertain Linear Equations

  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization

    Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of … Read more

    Robust optimization with ambiguous stochastic constraints under mean and dispersion information

  • Aharon Ben-Tal
  • Dick den Hertog
  • Krzysztof Postek
  • Bertrand Melenberg
    • Categories Robust Optimization Tags , , ,

    In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal … Read more

    Robust nonlinear optimization via the dual

  • Dick den Hertog
  • Bram L. Gorissen
    • Categories Robust Optimization Tags

    Robust nonlinear optimization is not as well developed as the linear case, and limited in the constraints and uncertainty sets it can handle. In this work we extend the scope of robust optimization by showing how to solve a large class of robust nonlinear optimization problems. The fascinating and appealing property of our approach is … Read more

    Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization

    We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, … Read more

    Safe Approximations of Chance Constraints Using Historical Data

  • Dick den Hertog
  • Ihsan Yanıkoğlu
    • Categories Robust Optimization, Stochastic Programming

    This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, … Read more

    Multi-stage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set

  • Dick den Hertog
  • Krzysztof Postek
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , , ,

    In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period … Read more