Bilevel “Defender–Attacker” Model with Multiple Attack Scenarios Full article
Journal |
Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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Output data | Year: 2018, Volume: 12, Number: 3, Pages: 417-425 Pages count : 9 DOI: 10.1134/s1990478918030031 | ||||
Tags | bilevel programming; complementarity slackness; optimality criteria | ||||
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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.
Cite:
Beresnev V.L.
, Davydov I.A.
, Kononova P.A.
, Melnikov A.A.
Bilevel “Defender–Attacker” Model with Multiple Attack Scenarios
Journal of Applied and Industrial Mathematics. 2018. V.12. N3. P.417-425. DOI: 10.1134/s1990478918030031 Scopus OpenAlex
Bilevel “Defender–Attacker” Model with Multiple Attack Scenarios
Journal of Applied and Industrial Mathematics. 2018. V.12. N3. P.417-425. DOI: 10.1134/s1990478918030031 Scopus OpenAlex
Original:
Береснев В.Л.
, Давыдов И.А.
, Кононова П.А.
, Мельников А.А.
Двухуровневая модель «защитник—атакующий» при альтернативных сценариях атаки
Дискретный анализ и исследование операций. 2018. Т.25. №3. С.5-22. DOI: 10.17377/daio.2018.25.612
Двухуровневая модель «защитник—атакующий» при альтернативных сценариях атаки
Дискретный анализ и исследование операций. 2018. Т.25. №3. С.5-22. DOI: 10.17377/daio.2018.25.612
Identifiers:
Scopus: | 2-s2.0-85052105444 |
OpenAlex: | W2888334040 |