A novel hybrid algorithm for solving continuous single-objective defensive location problem

The continuous defensive location problem (CDLP) is an NP-hard problem well investigated in the fields of competitive facility location. CDLP is a bi-level programming problem, where a decision maker locates defensive facilities with different capacities in the vertices of the network in order to avoid her/his aggressors from reaching core which is an important vertex in the network. In the present research, a hybrid method combining the imperialist competitive algorithm (ICA) and BFGS algorithm is presented to solve the CDLP. The proposed hybrid method integrates the ICA and the BFGS algorithm, providing a highly near-optimal solution. The upper-level problem solves the optimal location of defense facilities, and hybrid algorithm is applied. The lower-level problem is the shortest path problem which is solved by the Dijkstra method. The feasibility of the proposed hybrid method is demonstrated for a number of small, medium and large instances of the problem. The test results are compared with those obtained by genetic algorithm, particle swarm optimization and ICA in terms of solution accuracy and required CPU time. Simulation results reveal that the proposed hybrid method is feasible, robust and more effective in solving the CDLP than conventional metaheuristic methods.