Authors: Ivanov, Sergey
Kibzun, Andrey
Mladenović, Nenad 
Title: Variable Neighborhood Search for a Two-Stage Stochastic Programming Problem with a Quantile Criterion
Journal: Automation and Remote Control
Volume: 80
Issue: 1
First page: 43
Last page: 52
Issue Date: 1-Jan-2019
Rank: M23
ISSN: 0005-1179
DOI: 10.1134/S0005117919010041
Abstract: 
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.
Keywords: confidence method | quantile criterion | sample approximation | two-stage problem | variable neighborhood search
Publisher: Springer Link
Project: Russian Ministry of Science and Education, Project no. 2.2461.2017/4.6
“Development of Information Technologies and Systems for Stimulation of Personality’s Sustainable Development as One of the Bases of Development of Digital Kazakhstan”, grant no. BR05236839

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