scenario reduction

Enhancing explainability of stochastic programming solutions via scenario and recourse reduction

  • Tushar Rathi
  • Rishabh Gupta
  • Jose M. Pinto
  • Qi Zhang
    • Categories Stochastic Programming Tags , , ,

    Stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse … Read more

    Optimization-based Scenario Reduction for Data-Driven Two-stage Stochastic Optimization

  • Dimitris Bertsimas
  • Nishanth Mundru
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , ,

    We propose a novel, optimization-based method that takes into account the objective and problem structure for reducing the number of scenarios, m, needed for solving two-stage stochastic optimization problems. We develop a corresponding convex optimization-based algorithm, and show that as the number of scenarios increase, the proposed method recovers the SAA solution. We report computational … Read more

    Optimal design of an electricity-intensive industrial facility subject to electricity price uncertainty: stochastic optimization and scenario reduction

  • Adam R. Brandt
  • Holger Teichgraeber
    • Categories Chemical Engineering, Production and Logistics, Stochastic Programming Tags , , , ,

    When considering the design of electricity-intensive industrial processes, a challenge is that future electricity prices are highly uncertain. Design decisions made before construction can affect operations decades into the future. We thus explore whether including electricity price uncertainty into the design process affects design decisions. We apply stochastic optimization to the design and operations of … Read more

    Optimal scenario generation and reduction in stochastic programming

  • RenĂ© Henrion
  • Werner Romisch
    • Categories Semi-infinite Programming, Stochastic Programming Tags , , ,

    Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based on distances containing minimal information, i.e., on data appearing … Read more

    Scenario Reduction Revisited: Fundamental Limits and Guarantees

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Kilian Schindler
  • Wolfram Wiesemann
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure … Read more

    Optimization Driven Scenario Grouping

  • Shabbir Ahmed
  • Santanu S. Dey
  • Deepak Rajan
  • Kevin Ryan
    • Categories 0-1 Programming, Stochastic Programming Tags ,

    Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves upon these bounds by re-enforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into ‘groups’. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve … Read more

    SDDP for multistage stochastic programs: Preprocessing via scenario reduction

  • Jitka Dupacova
  • Vaclav Kozmik
    • Categories Stochastic Programming Tags , , ,

    Even with recent enhancements, computation times for large-scale multistage problems with risk-averse objective functions can be very long. Therefore, preprocessing via scenario reduction could be considered as a way to significantly improve the overall performance. Stage-wise backward reduction of single scenarios applied to a fixed branching structure of the tree is a promising tool for … Read more

    Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

  • J.M. Damazio
  • Welington de Oliveira
  • Maria Elvira P. Maceira
  • Claudia Sagastizábal
  • D.D. Penna
    • Categories Stochastic Programming Tags , ,

    The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences … Read more