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Risk averse stochastic programming: time consistency and optimal stopping

  • Alois Pichler
  • Alexander Shapiro
    • Categories Dynamic Programming, Stochastic Programming Tags , , , , ,

    Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more

    Improved Decision Rule Approximations for Multi-Stage Robust Optimization via Copositive Programming

  • Grani A. Hanasusanto
  • Guanglin Xu
    • Categories Dynamic Programming, Linear, Cone and Semidefinite Programming, Robust Optimization

    We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and consider quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP-hard but … Read more

    Numerical Results for the Multi-objective Trust Region Algorithm MHT

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization Tags , , , ,

    A set of 78 test examples is presented for the trust region method MHT described in J. Thomann, G. Eichfelder, A trust region algorithm for heterogeneous multi-objective optimization, 2018 (available as preprint: http://optimization-online.org/DB_HTML/2018/03/6495.html) . It is designed for multi-objective heterogeneous optimization problems where one of the objective functions is an expensive black-box function, for example … Read more

    Multi-objective Ranking and Selection: Optimal Sampling Laws and Tractable Approximations via SCORE

  • Eric A. Applegate
  • Guy Feldman
  • Susan R. Hunter
  • Raghu Pasupathy
    • Categories Multi-Criteria Optimization, Optimization of Simulated Systems

    Consider the multi-objective ranking and selection (MORS) problem in which we select the Pareto-optimal set from a finite set of systems evaluated on three or more stochastic objectives. Solving this problem is difficult because we must determine how to allocate a simulation budget among the systems to minimize the probability that any systems are misclassified. … Read more

    A Wolfe line search algorithm for vector optimization

  • L. R. Lucambio Pérez
  • Leandro Fonseca Prudente
    • Categories Multi-Criteria Optimization

    In a recent paper, Lucambio Pérez and Prudente extended the Wolfe conditions for the vector-valued optimization. Here, we propose a line search algorithm for finding a step-size satisfying the strong Wolfe conditions in the vector optimization setting. Well definiteness and finite termination results are provided. We discuss practical aspects related to the algorithm and present … Read more

    Branching with Hyperplanes in the Criterion Space: the Frontier Partitioner Algorithm for Biobjective Integer Programming

  • Marianna De Santis
  • Giorgio Grani
  • Laura Palagi
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Multi-Criteria Optimization

    We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an … Read more

    A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization

    In this paper, scalarizing functions defined with the help of the Hiriart-Urruty signed distance are used to characterize set order relations and weak optimal solutions in set optimization studied with Kuroiwa’s set approach and to introduce a new concept of slope for a set-valued map. It turns out that this slope possesses most properties of … Read more

    Resilience assessment for interdependent urban infrastructure systems using dynamic network flow models

  • Panagiotis Angeloudis
  • Nils Goldbeck
  • Washington Ochieng
    • Categories Civil and Environmental Engineering, Optimization of Simulated Systems, Transportation

    Critical infrastructure systems in cities are becoming increasingly interdependent, therefore exacerbating the impacts of disruptive events through cascading failures, hindered asset repairs and network congestion. Current resilience assessment methods fall short of fully capturing such interdependency effects as they tend to model asset reliability and network flows separately and often rely on static flow assignment … Read more

    Assessment of systemic vulnerabilities in container shipping networks with consideration of transhipment

  • Pablo E. Achurra-Gonzalez
  • Panagiotis Angeloudis
  • Nils Goldbeck
  • Daniel J. Graham
  • Marc Stettler
  • Konstantinos Zavitsas
    • Categories Game Theory, Supply Chain Management, Transportation

    The global container shipping network is vital to international trade. Current techniques for its vulnerability assessment are constrained due to the lack of historical disruption data and computational limitations due to typical network sizes. We address these modelling challenges by developing a new framework, composed by game-theoretic attacker-defender model and a cost-based container assignment model … Read more

    Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

  • Anja Kramer
  • Vanessa Krebs
  • Martin Schmidt
    • Categories Finance and Economics, Game Theory, Robust Optimization Tags , , , ,

    This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable … Read more