sample average approximation

Sample Average Approximation for Stochastic Nonconvex Mixed Integer Nonlinear Programming via Outer Approximation

  • David E. Bernal Neira
  • Kevin C Furman
  • Ignacio E. Grossmann
  • Can Li
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , ,

    Stochastic mixed-integer nonlinear programming (MINLP) is a very challenging type of problem. Although there have been recent advances in developing decomposition algorithms to solve stochastic MINLPs, none of the existing algorithms can address stochastic MINLPs with continuous distributions. We propose a sample average approximation-based outer approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs … Read more

    Transmission Switching Under Wind Uncertainty Using Linear Decision Rules

  • Grani A. Hanasusanto
  • Yuqi Zhou
  • Hao Zhu
    • Categories Applications - Science and Engineering Tags , , ,

    Increasing penetration of wind and renewable generation poses significant challenges to the power system operations and reliability. This paper considers the real-time optimal transmission switching (OTS) problem for determining the generation dispatch and network topology that can account for uncertain energy resources. To efficiently solve the resultant two-stage stochastic program, we propose a tractable linear … Read more

    Improving sample average approximation using distributional robustness

  • Edward Anderson
  • Andrew B. Philpott
    • Categories Stochastic Programming Tags , ,

    We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sample performance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under … Read more

    Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation

  • James R. Luedtke
  • Alejandra Pena-Ordieres
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , , ,

    We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation, and illustrate empirically that the reformulation can … Read more

    A Scenario-Based Approach for the Vehicle Routing Problem with Roaming Delivery Locations under Stochastic Travel Times

  • Joris Kinable
  • Afonso Sampaio
  • Lucas Veelenturf
  • Tom Van Woensel
    • Categories Meta Heuristics, Stochastic Programming, Transportation Tags , ,

    We address a stochastic variant of the Vehicle Routing Problem with Roaming Delivery Locations. In this model, direct-to-consumer deliveries can be made in the trunk of the customer’s car, while the vehicle is parked at a location along the customer’s itinerary. The stochasticity arises from the uncertainty in travel times and the problem is formulated … Read more

    Identifying Effective Scenarios for Sample Average Approximation

  • Lijian Chen
    • Categories Stochastic Programming Tags

    We introduce a method to improve the tractability of the well-known Sample Average Approximation (SAA) without compromising important theoretical properties, such as convergence in probability and the consistency of an independent and identically distributed (iid) sample. We consider each scenario as a polyhedron of the mix of first-stage and second-stage decision variables. According to John’s … Read more

    An Efficient Linear Programming Based Method for the Influence Maximization Problem in Social Networks

  • Evren Güney
    • Categories 0-1 Programming, Approximation Algorithms, Network Optimization Tags , , ,

    The influence maximization problem (IMP) aims to determine the most influential individuals within a social network. In this study first we develop a binary integer program that approximates the original problem by Monte Carlo sampling. Next, to solve IMP efficiently, we propose a linear programming relaxation based method with a provable worst case bound that … Read more

    Stochastic Decomposition for Two-stage Stochastic Linear Programs with Random Cost Coefficients

  • Harsha Gangammanavar
  • Yifan Liu
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , , , ,

    Stochastic decomposition (SD) has been a computationally effective approach to solve large-scale stochastic programming (SP) problems arising in practical applications. By using incremental sampling, this approach is designed to discover an appropriate sample size for a given SP instance, thus precluding the need for either scenario reduction or arbitrary sample sizes to create sample average … Read more

    Shortfall Risk Models When Information of Loss Function Is Incomplete

  • Erick Delage
  • Shaoyan Guo
  • Huifu Xu
    • Categories Linear Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    Utility-based shortfall risk measure (SR) has received increasing attentions over the past few years for its potential to quantify more effectively the risk of large losses than conditional value at risk. In this paper we consider the case that the true loss function is unavailable either because it is difficult to be identified or the … Read more

    Convergence Analysis of Sample Average Approximation of Two-stage Stochastic Generalized Equations

  • Xiaojun Chen
  • Alexander Shapiro
  • Hailin Sun
    • Categories Stochastic Programming Tags , , , ,

    A solution of two-stage stochastic generalized equations is a pair: a first stage solution which is independent of realization of the random data and a second stage solution which is a function of random variables. This paper studies convergence of the sample average approximation of two-stage stochastic nonlinear generalized equations. In particular an exponential rate … Read more