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Avtomat. i Telemekh., 2019, Issue 1, Pages 54–66 (Mi at15005)  

Stochastic Systems

Variable neighborhood search for a two-stage stochastic programming problem with a quantile criterion

S. V. Ivanova, A. I. Kibzuna, N. Mladenovićbc

a Moscow Aviation Institute (National State University), Moscow, Russia
b Ural Federal University, Yekaterinburg, Russia
c Emirates College of Technologies, Abu Dhabi, UAE

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2.2461.2017/4.6
Ministry of Education and Science of the Republic of Kazakhstan BR05236839
The work of A.I. Kibzun was done as part of the state assignment of the Russian Ministry of Science and Education, project no. 2.2461.2017/4.6. The work of N. Mladenovi'c is partially covered by the framework of the grant no. BR05236839 “Development of Information Technologies and Systems for Stimulation of Personality's Sustainable Development as One of the Bases of Development of Digital Kazakhstan”.

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DOI: https://doi.org/10.1134/S0005231019010045

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English version:
Automation and Remote Control, 2019, 80:1, 43–52

Bibliographic databases:

Presented by the member of Editorial Board: Á. Ì. Ìèëëåð

Received: 15.03.2018
Revised: 15.08.2018
Accepted: 08.11.2018

Citation: S. V. Ivanov, A. I. Kibzun, N. Mladenović, “Variable neighborhood search for a two-stage stochastic programming problem with a quantile criterion”, Avtomat. i Telemekh., 2019, no. 1, 54–66; Autom. Remote Control, 80:1 (2019), 43–52

Citation in format AMSBIB
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\paper Variable neighborhood search for a two-stage stochastic programming problem with a quantile criterion
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\crossref{https://doi.org/10.1134/S0005231019010045}
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\jour Autom. Remote Control
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