Two novel combined approaches based on TLBO and PSO for a partial interdiction/fortification problem using capacitated facilities and budget constraint

Abstract

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.