chance constraints

Lagrangian relaxation based heuristics for a chance-constrained optimization model of a hybrid solar-battery storage system

  • Bismark Singh
  • Bernard Knueven
    • Categories Energy, Stochastic Programming Tags , , , , , , , ,

    Published in Journal of Global Optimization. https://doi.org/10.1007/s10898-021-01041-y We develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance … Read more

    On the Stochastic Vehicle Routing Problem with time windows, correlated travel times, and time dependency

  • Federica Bomboi
  • Christoph Buchheim
  • Jonas Prünte
    • Categories Stochastic Programming, Transportation Tags , , , ,

    Most state-of-the-art algorithms for the Vehicle Routing Problem, such as Branch-and- Price algorithms or meta heuristics, rely on a fast feasibility test for a given route. We devise the fi rst approach to approximately check feasibility in the Stochastic Vehicle Routing Problem with time windows, where travel times are correlated and depend on the time of … 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 Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

  • Jianqiang Cheng
  • Miguel A. Lejeune
  • Roya Karimi
    • Categories Stochastic Programming Tags , , , ,

    We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix, and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions ensuring convexity. … Read more

    Risk Aversion to Parameter Uncertainty in Markov Decision Processes with an Application to Slow-Onset Disaster Relief

  • Simge Küçükyavuz
  • Merve Merakli
    • Categories Integer Programming, Stochastic Programming, Supply Chain Management Tags , , , , ,

    In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost and transition probability uncertainty and aims to provide a mathematical framework to obtain policies minimizing the risk of high long-term … Read more

    A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

  • Rohit Kannan
  • James R. Luedtke
    • Categories Stochastic Programming Tags , , ,

    We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. To this end, we construct a reformulated problem whose objective is to minimize … Read more

    Machine learning approach to chance-constrained problems: An algorithm based on the stochastic gradient descent

  • Lukáš Adam
  • Martin Branda
    • Categories Stochastic Programming Tags , , , , ,

    We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more

    Bounds for Probabilistic Programming with Application to a Blend Planning Problem

  • Abdel Lisser
  • Francesca Maggioni
  • Shen Peng
    • Categories Stochastic Programming Tags , , , , ,

    In this paper, we derive deterministic inner approximations for single and joint probabilistic constraints based on classical inequalities from probability theory such as the one-sided Chebyshev inequality, Bernstein inequality, Chernoff inequality and Hoeffding inequality (see Pinter 1989). New assumptions under which the bounds based approximations are convex allowing to solve the problem efficiently are derived. … Read more

    Chance Constrained Programs with Gaussian Mixture Models

  • Zhaolin Hu
  • Wenjie Sun
  • Shushang Zhu
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper, we discuss input modeling and solution techniques for several classes of chance constrained programs (CCPs). We propose to use Gaussian mixture models (GMM), a semi-parametric approach, to fit the data available and to model the randomness. We demonstrate the merits of using GMM. We consider several scenarios that arise from practical applications … Read more

    The Distributionally Robust Chance Constrained Vehicle Routing Problem

  • Shubhechyya Ghosal
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming, Transportation Tags , ,

    We study a variant of the capacitated vehicle routing problem (CVRP), which asks for the cost-optimal delivery of a single product to geographically dispersed customers through a fleet of capacity-constrained vehicles. Contrary to the classical CVRP, which assumes that the customer demands are deterministic, we model the demands as a random vector whose distribution is … Read more