In this paper, we introduce a novel continuous bi-level programming model of an interdiction/fortification problem, referred to as partial interdiction/fortification problem with capacitated facilities and Budget constraint (PIFCB). PIFCB is modeled as a Stackelberg game between a defender (leader) and an attacker (follower). The decisions of the defender are related to find optimal allocations of defensive resources as well as customer-facility assignments. So, the total system losses and demand-weighted distance are minimized. Following this action, the attacker seeks facilities to interdict for the capacity or service reduction and maximal losses resulting from a limited offensive budget. After modeling this problem, two combined methods, entitled particle swarm optimization with CPLEX (PSO-CPLEX) and teaching learning-based optimization with CPLEX (TLBO-CPLEX), are devised as solution procedures. For this bi-level programming problem, we executed two approaches which search the solution space of the defender’s subproblem, according to PSO and TLBO principles, and corresponding attacker’s subproblem is solved using CPLEX. To investigate the suggested methods, a comprehensive computational study is conducted and the effectiveness of the methods is compared together. The experimental results show the superiority of TLBO-CPLEX against PSO-CPLEX.
Continuous bi-level model Stackelberg game Capacitated facility Partial offense and defense Particle swarm optimization Teaching learning-based optimization
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The first author would like to thank Gonbad Kavous University for supporting this research work. The second and third authors would like to appreciate the research council of Shiraz University of Technology for supporting this research. Last but not least, the authors are very grateful to the editor and the reviewers for their valuable comments.
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Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
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