robust optimization

Robust Optimization with Decision-Dependent Information Discovery

  • Phebe Vayanos
  • Angelos Georghiou
  • Han Yu
    • Categories Robust Optimization Tags , , ,

    Robust optimization (RO) is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, such as R&D project selection, production planning, or preference elicitation for product or policy recommendations, the time of information discovery is decision-dependent and the uncertain parameters only become observable after an often costly … Read more

    Robust Optimal Aiming Strategies in Concentrated Solar Tower Power Plants

  • Christina Büsing
  • Pascal Richter
  • Jeff Cumpston
  • Fynn Kepp
  • Sascha Kuhnke
    • Categories Robust Optimization Tags , , , ,

    A concentrated solar tower power plant consists of a receiver mounted atop of a central tower and a field of movable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle. Aiming strategies are used to assign each heliostat to an … 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

    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

    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

    Radius of Robust Feasibility for Mixed-Integer Problems

  • Frauke Liers
  • Lars Schewe
  • Johannes Thürauf
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines a value for the maximal “size” of the uncertainty set such that robust feasibility of the MIP can be guaranteed. To the best of our knowledge, the approaches for the RRF presented in the literature are restricted to continuous … Read more

    Γ-Robust Linear Complementarity Problems

  • Vanessa Krebs
  • Martin Schmidt
    • Categories Complementarity and Variational Inequalities, Game Theory, Robust Optimization Tags , , , ,

    Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems. Specific examples are game-theoretic settings like the bimatrix game or energy market models like for electricity or natural gas. While optimization under uncertainties is rather well-developed, the field of equilibrium models represented by complementarity problems under uncertainty … Read more

    The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objective

  • Christoph Buchheim
  • Dorothee Henke
    • Categories Robust Optimization Tags , ,

    We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower chooses an optimal packing according to his own profits, which may differ from those of the leader. To this bilevel problem, we add uncertainty in a natural way, assuming that the leader does not have full … Read more

    Optimal Residential Battery Storage Operations Using Robust Data-driven Dynamic Programming

  • Grani A. Hanasusanto
  • Benjamin Leibowicz
  • Nan Zhang
    • Categories Applications - Science and Engineering Tags , , , , ,

    In this paper, we consider the problem of operating a battery storage unit in a home with a rooftop solar photovoltaic (PV) system so as to minimize expected long-run electricity costs under uncertain electricity usage, PV generation, and electricity prices. Solving this dynamic program using standard techniques is computationally burdensome, and is often complicated by … Read more

    Submodularity in conic quadratic mixed 0-1 optimization

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , , , , , ,

    We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and … Read more