Solving continuous single-objective defensive location problem based on hybrid directed tabu search algorithm

Abstract

In this paper, we introduce a novel optimal location problem on a network, called as continuous defensive location problem (CDLP). In this problem, a decision maker locates different kinds of defensive facilities (with different capacities) on the vertices of the network in order to prevent her/his aggressors from reaching a strategic site, called core, which is a vertex in the network. This problem is a generalization of the defensive location problem, introduced by Uno and Katagiri (European J Oper Res 188:76–84, 2008). The CDLP is formulated as a bi-level programming problem in which the defender and the aggressor are the upper and lower level of decision makers, respectively. This problem is a non-deterministic polynomial-time (NP) hard problem which is derived from the equilibrium conditions. Therefore, finding a solution for this problem in the large-scale setting is very severe. In order to solve this problem, a hybrid tabu search algorithm is proposed based on continuous tabu search (TS), the so-called directed tabu search (DTS), and the Levenberg-Marquardt (LM) method. This combination helps us to escape from local minima by using a global algorithm, i.e., DTS algorithm, and makes a high-speed convergence rate by employing a local minimizer algorithm, i.e., LM algorithm. We finally apply our hybrid scheme for solving several randomly generated CDLPs. Our numerical experiences show that the proposed algorithm has admirable performance in terms of both CPU time and solution accuracy and is one of the effective and robust approaches for solving these problems.