A Novel Integer-Coded Memetic Algorithm for the Set $k$ -Cover Problem in Wireless Sensor Networks

The Set k-Cover problem aims to partition a set of nodes for the maximal number of covers. This problem is crucial for extending the lifetime of wireless sensor networks (WSNs) under the constraint of covering all targets. More specifically, the Set k-Cover problem enables partitioning the set of sensors into several covers over all targets and activating the covers by turns to effectively extend the WSN lifetime. To resolve this problem, we propose a novel memetic algorithm (MA) based on integer-coded genetic algorithm and local search. This paper adapts the crossover and mutation operators to integer representation and, furthermore, designs a new fitness function that considers both the number of covers and the contribution of each sensor to covers. A local improvement method, called the recycling operator, is developed to enhance the performance on the Set k-Cover problem. Experimental results show that the proposed MA significantly outperforms five evolutionary algorithms in terms of the number of covers obtained, hit rate (HR), and running time. In particular, the new MA increases 38.1% HR and saves 78.7% running time of state-of-the-art MA on average. The preferable results validate the effectiveness and efficiency of the proposed MA for the Set k-Cover problem.