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Stochastic Constraints and Variance Reduction Techniques

In: Handbook of Simulation Optimization

Author

Listed:
  • Tito Homem-de-Mello

    (Universidad Adolfo Ibañez)

  • Güzin Bayraksan

    (The Ohio State University)

Abstract

We provide an overview of two select topics in Monte Carlo simulation-based methods for stochastic optimization: problems with stochastic constraints and variance reduction techniques. While Monte Carlo simulation-based methods have been successfully used for stochastic optimization problems with deterministic constraints, there is a growing body of work on its use for problems with stochastic constraints. The presence of stochastic constraints brings new challenges in ensuring and testing optimality, allocating sample sizes, etc., especially due to difficulties in determining feasibility. We review results for general stochastic constraints and also discuss special cases such as probabilistic and stochastic dominance constraints. Next, we review the use of variance reduction techniques (VRT) in a stochastic optimization setting. While this is a well-studied topic in statistics and simulation, the use of VRT in stochastic optimization requires a more thorough analysis. We discuss asymptotic properties of the resulting approximations and their use within Monte Carlo simulation-based solution methods.

Suggested Citation

  • Tito Homem-de-Mello & Güzin Bayraksan, 2015. "Stochastic Constraints and Variance Reduction Techniques," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 245-276, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-1384-8_9
    DOI: 10.1007/978-1-4939-1384-8_9
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    Cited by:

    1. Krishna, Attoti Bharath & Abhyankar, Abhijit R., 2023. "Time-coupled day-ahead wind power scenario generation: A combined regular vine copula and variance reduction method," Energy, Elsevier, vol. 265(C).

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