RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskretn. Anal. Issled. Oper.: Year: Volume: Issue: Page: Find

 Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 3, Pages 5–22 (Mi da900)

Bilevel “defender–attacker” model with multiple attack scenarios

V. L. Beresnevab, I. A. Davydovab, P. A. Kononovaab, A. A. Melnikovab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 1 Pirogov St., 630090 Novosibirsk, Russia

Abstract: We consider a bilevel “defender–attacker” model built on the basis of the Stackelberg game. In this model, given is a set of the objects providing social services for a known set of customers and presenting potential targets for a possible attack. At the first step, the Leader (defender) makes a decision on the protection of some of the objects on the basis of his/her limited resources. Some Follower (attacker), who is also limited in resources, decides then to attack unprotected objects, knowing the decision of the Leader. It is assumed that the Follower can evaluate the importance of each object and makes a rational decision trying to maximize the total importance of the objects attacked. The Leader does not know the attack scenario (the Follower's priorities for selecting targets for the attack). But, the Leader can consider several possible scenarios that cover the Follower's plans. The Leader's problem is then to select the set of objects for protection so that, given the set of possible attack scenarios and assuming the rational behavior of the Follower, to minimize the total costs of protecting the objects and eliminating the consequences of the attack associated with the reassignment of the facilities for customer service. The proposed model may be presented as a bilevel mixed-integer programming problem that includes an upper-level problem (the Leader problem) and a lower-level problem (the Follower problem). The main efforts in this article are aimed at reformulation of the problem as some one-level mathematical programming problems. These formulations are constructed using the properties of the optimal solution of the Follower's problem, which makes it possible to formulate necessary and sufficient optimality conditions in the form of linear relations. Bibliogr. 16.

Keywords: bilevel programming, complementarity slackness, optimality criteria.

 Funding Agency Grant Number Russian Science Foundation 17-11-01021 The authors were supported by the Russian Science Foundation (project no. 17-11-01021).

DOI: https://doi.org/10.17377/daio.2018.25.612

Full text: PDF file (334 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2018, 12:3, 417–425

Document Type: Article
UDC: 519.8

Citation: V. L. Beresnev, I. A. Davydov, P. A. Kononova, A. A. Melnikov, “Bilevel “defender–attacker” model with multiple attack scenarios”, Diskretn. Anal. Issled. Oper., 25:3 (2018), 5–22; J. Appl. Industr. Math., 12:3 (2018), 417–425

Citation in format AMSBIB
\Bibitem{BerDavKon18} \by V.~L.~Beresnev, I.~A.~Davydov, P.~A.~Kononova, A.~A.~Melnikov \paper Bilevel defender--attacker'' model with multiple attack scenarios \jour Diskretn. Anal. Issled. Oper. \yr 2018 \vol 25 \issue 3 \pages 5--22 \mathnet{http://mi.mathnet.ru/da900} \crossref{https://doi.org/10.17377/daio.2018.25.612} \elib{http://elibrary.ru/item.asp?id=32729776} \transl \jour J. Appl. Industr. Math. \yr 2018 \vol 12 \issue 3 \pages 417--425 \crossref{https://doi.org/10.1134/S1990478918030031} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052105444}