Automation and Remote Control

, Volume 80, Issue 1, pp 43–52 | Cite as

Variable Neighborhood Search for a Two-Stage Stochastic Programming Problem with a Quantile Criterion

  • S. V. IvanovEmail author
  • A. I. Kibzun
  • N. Mladenović
Stochastic Systems


We consider a two-stage stochastic programming problem with a bilinear loss function and a quantile criterion. The problem is reduced to a single-stage stochastic programming problem with a quantile criterion. We use the method of sample approximations. The resulting approximating problem is considered as a stochastic programming problem with a discrete distribution of random parameters. We check convergence conditions for the sequence of solutions of approximating problems. Using the confidence method, the problem is reduced to a combinatorial optimization problem where the confidence set represents an optimization strategy. To search for the optimal confidence set, we adapt the variable neighborhood search method. To solve the problem, we develop a hybrid algorithm based on the method of sample approximations, the confidence method, variable neighborhood search.


quantile criterion two-stage problem sample approximation variable neighborhood search confidence method 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Moscow Aviation Institute (National State University)MoscowRussia
  2. 2.Emirates College of TechnologiesAbu DhabiUAE
  3. 3.Ural Federal UniversityYekaterinburgRussia

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