Robust Optimization

Distributionally Robust Optimization: A Review

  • Hamed Rahimian
  • Sanjay Mehrotra
    • Categories Robust Optimization, Stochastic Programming

    The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. … Read more

    Near-optimal Robust Bilevel Optimization

  • Miguel F. Anjos
  • Mathieu Besançon
  • Luce Brotcorne
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , , , ,

    Bilevel optimization studies problems where the optimal response to a second mathematical optimization problem is integrated in the constraints. Such structure arises in a variety of decision-making problems in areas such as market equilibria, policy design or product pricing. We introduce near-optimal robustness for bilevel problems, protecting the upper-level decision-maker from bounded rationality at the … Read more

    A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

  • Brian Dandurand
  • Kibaek Kim
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Robust Optimization Tags , , ,

    We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … Read more

    Adjustable Robust Optimization Reformulations of Two-Stage Worst-case Regret Minimization Problems

  • Erick Delage
  • Mehran Poursoltani
    • Categories Applications - OR and Management Sciences, Linear Programming, Robust Optimization Tags , , ,

    This paper explores the idea that two-stage worst-case regret minimization problems with either objective or right-hand side uncertainty can be reformulated as two-stage robust optimization problems and can therefore benefit from the solution schemes and theoretical knowledge that have been developed in the last decade for this class of problems. In particular, we identify conditions … Read more

    Decomposition-based approaches for a class of two-stage robust binary optimization problems

  • Ayse Nur Arslan
  • Boris Detienne
    • Categories 0-1 Programming, Robust Optimization Tags , , ,

    In this paper, we study a class of two-stage robust binary optimization problems with objective uncertainty where recourse decisions are restricted to be mixed-binary. For these problems, we present a deterministic equivalent formulation through the convexification of the recourse feasible region. We then explore this formulation under the lens of a relaxation, showing that the … Read more

    Distributionally robust chance constrained geometric optimization

  • Jia Liu
  • Abdel Lisser
  • Zhiping Chen
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more

    Tight tail probability bounds for distribution-free decision making

  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Wouter Van Eekelen
  • Ernst Roos
  • Johan Van Leeuwaarden
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more

    Data-Driven Distributionally Robust Appointment Scheduling over Wasserstein Balls

  • Ruiwei Jiang
  • Minseok Ryu
  • Guanglin Xu
    • Categories Robust Optimization, Scheduling, Stochastic Programming

    We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second … Read more

    Adjustable robust treatment-length optimization in radiation therapy

  • Ali Ajdari
  • Thomas Bortfeld
  • Dick den Hertog
  • Stefan ten Eikelder
    • Categories Biomedical Applications, Robust Optimization Tags , ,

    Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients’ response to therapy. However, recent technological advancements have enabled monitoring individual patient response during the RT course, in the form of biomarkers. Although biomarker data remains subject to substantial uncertainties, information extracted from … Read more

    An exact algorithm for robust influence maximization

  • Giacomo Nannicini
  • Roberto Wolfler Calvo
  • Giorgio Sartor
  • Emiliano Traversi
    • Categories Branch and Cut Algorithms, Robust Optimization Tags , ,

    We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with … Read more