Stochastic Programming

Reactive Power Management using Firefly and Spiral Optimization under Static and Dynamic Loading Conditions

  • Ripunjoy Phukan
    • Categories Applications - Science and Engineering, Global Optimization Applications, Stochastic Programming Tags , , , ,

    Power System planning encompasses the concept of minimization of transmission losses keeping in mind the voltage stability and system reliability. Voltage profile decides the state of a system and its control is dependent on Generator source voltage, shunt/series injection, transformer taps etc. Optimal parameter setting in system level is needed for managing the available resources … Read more

    Decision Making Based on a Nonparametric Shape-Preserving Perturbation of a Reference Utility Function

  • Jian Hu
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper develops a robust optimization based decision-making framework using a nonparametric perturbation of a reference utility function. The perturbation preserves the risk-aversion property but solves the problem of ambiguity and inconsistency in eliciting the reference utility function. We study the topology of the perturbation, and show that in the decision-making framework the price of … Read more

    Computation of Stochastic Nash Equilibrium via Variable Sample Distributed Methods

  • Ming Dong
  • Lizhi Wang
  • Dali Zhang
    • Categories Game Theory, Stochastic Programming Tags

    In this paper, we propose a variable sample distributed algorithm for the computation of stochastic Nash equilibrium in which the objective functions are replaced, at each iteration, by sample average approximations. We investigate the contraction mapping properties of the variable sample distributed algorithm and show that the accuracy of estimators yielded in the algorithms to … Read more

    Robust Data-Driven Dynamic Programming

  • Grani A. Hanasusanto
  • Daniel Kuhn
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , ,

    In stochastic optimal control the distribution of the exogenous noise is typically unknown and must be inferred from limited data before dynamic programming (DP)-based solution schemes can be applied. If the conditional expectations in the DP recursions are estimated via kernel regression, however, the historical sample paths enter the solution procedure directly as they determine … Read more

    Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service System Staffing and Scheduling with Arrival Rate Uncertainty

  • Merve Bodur
  • James R. Luedtke
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    We study server scheduling in multiclass service systems under stochastic uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels, and then determine schedules for the servers that cover these targets. We propose a new stochastic integer programming model that integrates these two decisions, which can yield lower … Read more

    Optimal scenario set partitioning for multistage stochastic programming with the progressive hedging algorithm

  • Fabian Bastin
  • Pierre-Luc Carpentier
  • Michel Gendreau
    • Categories Stochastic Programming Tags , , ,

    In this paper, we propose a new approach to reduce the total running time (RT) of the progressive hedging algorithm (PHA) for solving multistage stochastic programs (MSPs) defined on a scenario tree. Instead of using the conventional scenario decomposition scheme, we apply a multi-scenario decomposition scheme and partition the scenario set in order to minimize … Read more

    Dynamic Linear Programming Games with Risk-Averse Players

  • Alejandro Toriello
  • Nelson A. Uhan
    • Categories Applications - OR and Management Sciences, Game Theory, Stochastic Programming Tags , ,

    Motivated by situations in which independent agents, or players, wish to cooperate in some uncertain endeavor over time, we study dynamic linear programming games, which generalize classical linear production games to multi-period settings under uncertainty. We specifically consider that players may have risk-averse attitudes towards uncertainty, and model this risk aversion using coherent conditional risk … Read more

    Time Consistency Versus Law Invariance in Multistage Stochastic Optimization with Coherent Risk Measures: Multilevel Optimization Modeling and Computational Complexity

  • Jonathan Eckstein
    • Categories Stochastic Programming Tags , ,

    Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which un-certainly is resolved at more than one stage, however, use of coherent risk measures within a standard single-level optimization framework presents the modeler with an uncomfortable choice between two desirable model properties, time consistency … Read more

    Optimization Models for Differentiating Quality of Service Levels in Probabilistic Network Capacity Design Problems

  • Zhihao Chen
  • Siqian Shen
    • Categories Network Optimization, Stochastic Programming, Transportation

    This paper develops various chance-constrained models for optimizing the probabilistic network design problem (PNDP), where we differentiate the quality of service (QoS) and measure the related network performance under uncertain demand. The upper level problem of PNDP designs continuous/discrete link capacities shared by multi-commodity flows, and the lower level problem differentiates the corresponding QoS for … Read more

    Data-Driven Chance Constrained Stochastic Program

  • Yongpei Guan
  • Ruiwei Jiang
    • Categories Stochastic Programming

    Chance constrained programming is an effective and convenient approach to control risk in decision making under uncertainty. However, due to unknown probability distributions of random parameters, the solution obtained from a chance constrained optimization problem can be biased. In addition, instead of knowing the true distributions of random parameters, in practice, only a series of … Read more