Multi-objective optimization for balanced Q-coverage problem in under-provisioned directional sensor networks

Abstract

This study investigates the target $Q$-coverage problem in under-provisioned directional sensor network (DSN). The coverage imbalance is a serious issue in under-provisioned networks. In $Q$-coverage, some targets may get the required coverage while others may be partially covered or even not covered. We have proposed a new balancing index $Q_{b}I$ to measure the balanced coverage of the network. In this study, we have modified four existing multi-objective genetic algorithms (MOGAs), strength Pareto evolutionary algorithm 2 (SPEA2), nondominated sorting genetic algorithm II (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), and two-stage evolutionary strategy based MOEA/D (MOEA/D-TS), where the objectives are maximization of the balanced coverage based on the proposed $Q_{b}I$ and minimization of the number of active sensors in the DSN. Keeping their generic structures the same, we have modified the MOGAs to make them suitable for implementing the proposed $Q$-coverage problem. For this purpose, a new mutation operator is also designed. As per our limited knowledge, no work in the literature considered the target $Q$-coverage problem in multi-objective paradigm. We have analyzed the impact of five different network parameters on the two objectives mentioned above: the number of targets, the number of sensors, the number of orientations, the sensing radius, and the coverage requirement. To compare the performances among the MOGAs, we have considered three different performance metrics: Hypervolume (HV), Inverted generational distance (IGD), and spread. The sensitivity analysis is done on three different network parameters to show the robustness of the modified MOGAs. Additionally, the performances of four MOGAs are compared with a genetic algorithm, existing in the literature, for the $Q$-coverage problem. The modified MOGAs are also tested on large scale, very large scale, and real networks, and the results show the effectiveness of the proposed MOGAs on the $Q$-coverage problem. Finally, statistical tests are performed on the three performance metrics to validate the results. The modified MOGAs improve the overall coverage and $Q_{b}I$ value by at least 13% and 21%, respectively compared to the existing algorithm.