Robust Optimization

A Benders decomposition method for locating stations in a one-way electric car sharing system under demand uncertainty

  • Hatice Calik
  • Bernard Fortz
    • Categories Branch and Cut Algorithms, Robust Optimization, Transportation Tags , , , , ,

    We focus on a problem of locating recharging stations in one-way station based electric car sharing systems which operate under demand uncertainty. We model this problem as a mixed integer stochastic program and develop a Benders decomposition algorithm based on this formulation. We integrate a stabilization procedure to our algorithm and conduct a large-scale experimental … Read more

    The robust vehicle routing problem with time windows: compact formulation and branch-price-and-cut method

  • Douglas Alem
  • Jonathan De La Vega
  • Jacek Gondzio
  • Reinaldo Morabito
  • Pedro Munari
  • Alfredo Moreno
    • Categories Applications - OR and Management Sciences, Robust Optimization, Transportation

    We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods … Read more

    Tutorial on risk neutral, distributionally robust and risk averse multistage stochastic programming

  • Alexander Shapiro
    • Categories Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this tutorial we discuss several aspects of modeling and solving multistage stochastic programming problems. In particular we discuss distributionally robust and risk averse approaches to multistage stochastic programming, and the involved concept of time consistency. This tutorial is aimed at presenting a certain point of view of multistage stochastic programming, and can be viewed … Read more

    Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

  • Martin Robinius
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Detlef Stolten
  • Lara Welder
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more

    A deterministic algorithm for solving stochastic minimax dynamic programmes

  • Regan Baucke
  • Anthony Downward
  • Golbon Zakeri
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , , , , , , , ,

    In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more

    Multi-model Markov Decision Processes

  • Brian T. Denton
  • David L. Kaufman
  • Lauren Steimle
    • Categories Robust Optimization

    Markov decision processes (MDPs) have found success in many application areas that involve sequential decision making under uncertainty, including the evaluation and design of treatment and screening protocols for medical decision making. However, the usefulness of these models is only as good as the data used to parameterize them, and multiple competing data sources are … Read more

    Bicriteria Approximation of Chance Constrained Covering Problems

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Combinatorial Optimization, Robust Optimization, Stochastic Programming

    A chance constrained optimization problem involves constraints with random data which can be violated with probability bounded above by a prespecified small risk parameter. Such constraints are used to model reliability requirements in a variety of application areas such as finance, energy, service and manufacturing. Except under very special conditions, chance constrained problems are extremely … Read more

    Wasserstein Distributionally Robust Optimization and Variation Regularization

  • Xi Chen
  • Rui Gao
  • Anton J. Kleywegt
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming

    Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although the connection between Wasserstein DRO and regularization has been established in several settings, existing results often require restrictive assumptions, such as smoothness or convexity, that are not satisfied by … Read more

    Reducing conservatism in Robust Optimization

  • Dick den Hertog
  • Ernst Roos
    • Categories Robust Optimization Tags , ,

    Although Robust Optimization is a powerful technique in dealing with uncertainty in optimization, its solutions can be too conservative when it leads to an objective value much worse than the nominal solution or even to infeasibility of the robust problem. In practice, this can lead to robust solutions being disregarded in favor of the nominal … Read more

    Robust optimization for models with uncertain SOC and SDP constraints

  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Ernst Roos
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , , ,

    In this paper we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem … Read more