New perspectives on the optimal placement of detectors for suicide bombers using metaheuristics

TL;DR

This work formulates a defender’s problem of optimally placing detectors to minimize the expected casualties $W$ from suicide-bomber attacks on a discretized threat area. It models attacker behavior under two strategies (proportional target value and worst-case equilibrium) and evaluates four metaheuristics—Greedy, Hill Climbing, Tabu Search, and Evolutionary Algorithm—on coastal, urban, and historic town layouts with rigorous preprocessing. The results show that adversarial settings are harder for all methods, with the Evolutionary Algorithm delivering superior performance in worst-case scenarios and Hill Climbing performing well under proportional attack models. The study highlights the value of population-based, diversified search in complex, adversarial defense problems and points to promising future work in hybrid memes and dynamic or multi-type detector deployments.

Abstract

We consider an operational model of suicide bombing attacks -- an increasingly prevalent form of terrorism -- against specific targets, and the use of protective countermeasures based on the deployment of detectors over the area under threat. These detectors have to be carefully located in order to minimize the expected number of casualties or the economic damage suffered, resulting in a hard optimization problem for which different metaheuristics have been proposed. Rather than assuming random decisions by the attacker, the problem is approached by considering different models of the latter, whereby he takes informed decisions on which objective must be targeted and through which path it has to be reached based on knowledge on the importance or value of the objectives or on the defensive strategy of the defender (a scenario that can be regarded as an adversarial game). We consider four different algorithms, namely a greedy heuristic, a hill climber, tabu search and an evolutionary algorithm, and study their performance on a broad collection of problem instances trying to resemble different realistic settings such as a coastal area, a modern urban area, and the historic core of an old town. It is shown that the adversarial scenario is harder for all techniques, and that the evolutionary algorithm seems to adapt better to the complexity of the resulting search landscape.

Figures (6)

• Figure 1: A shortest path going from entrance $e_i$ to objective $o_j$. Areas monitored by detectors $d_k$ and $d_k'$ are those enclosed by circumferences. The segments of this path detected by each detector are shown with a dotted line and denoted by $l_{ijk}$ and $l_{ijk'}$ respectively.
• Figure 2: Examples of each of the three scenarios considered. (a) harbour (b) newtown (c) oldtown.
• Figure 3: Deviation (%) from the best known solution for each algorithm and data set as a function of the number of detectors used in the proportional selection scenario. Notice the different scale on the Y axis in each subfigure.
• Figure 4: Deviation (%) from the best known solution for each algorithm and data set as a function of the number of detectors used in the worst-case equilibrium scenario. Notice the different scale on the Y axis in each subfigure.
• Figure 5: Cumulative boxplot of deviations (%) from the best know solution for each algorithm. The main plot focus on the iterative heuristics, and the inset includes the greedy algorithm as well. (a) Proportional selection (b) Worst-case equilibrium. Notice the different scale on the Y axis in each subfigure.