The aim of this article is to study the two-objective coverage problem of wireless sensor networks (WSNs) by means of differential evolution algorithm. Firstly, in order to reduce the computing redundancy of multi-objective optimization, namely to reduce the number of individuals which participate in non-dominated solution sorting, we introduced a fast two-objective differential evolution algorithm (FTODE). The FTODE contains a fast non-dominated solution sorted and a uniform crowding distance calculation method. The fast sorting method just handles the highest rank individuals but not all individuals in the current population. Meanwhile, during the individuals sorted, it can choose some of individuals into next generation and reduce the time complexity. The uniform crowding distance calculation can enhance the diversity of population due to it will retain the outline of optimal solution set by choosing the individual uniformly. Secondly, we use the FTODE framework to research the two-objective coverage problem of WSNs. The two objectives are formulated as: the minimum number of sensor used and the maximum coverage rate. For this specific problem, decimal integer encoding are used and a recombination operation is introduced into FTODE, which performs after initialization and guarantees at least one critical target’s sensor is divided into different disjoint sets. Finally, the simulation experiment shows that the FTODE provides competitive results in terms of time complexity and performance, and it also obtains better solutions than comparison algorithms on the two-objective coverage problem of WSNs.

中文翻译：

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WSNs两目标覆盖问题的快速两目标差分演化

本文旨在通过差分进化算法研究无线传感器网络（WSN）的两目标覆盖问题。首先，为了减少多目标优化的计算冗余，即减少参与非支配解排序的个体数量，我们引入了一种快速的两目标差分进化算法（FTODE）。FTODE包含快速分类的非主导解和统一的拥挤距离计算方法。快速排序方法仅处理最高级别的个人，但不适用于当前人口中的所有个人。同时，在对个体进行分类的过程中，可以选择一些个体进入下一代并降低时间复杂度。统一的拥挤距离计算可以增强种群的多样性，因为它可以通过均匀地选择个体来保留最优解集的轮廓。其次，我们使用FTODE框架来研究WSN的两目标覆盖问题。制定了两个目标：最少使用传感器数量和最大覆盖率。对于此特定问题，使用十进制整数编码，并将重组操作引入FTODE，FTODE在初始化后执行，并确保至少一个关键目标的传感器被分为不同的不交集。最后，仿真实验表明FTODE在时间复杂度和性能方面提供了有竞争力的结果，