###### Abstract  
The wireless sensor network (WSN) has the advantages of low cost, high monitoring accuracy, good fault tolerance, remote monitoring and convenient maintenance. It has been widely used in various fields. In the WSN, the placement of node sensors has a great impact on its coverage, energy consumption and some other factors. In order to improve the convergence speed of a node placement optimization algorithm, the encoding method is improved in this paper. The degressiveary number encoding is further extended to a multi-objective optimization problem. Furthermore, the adaptive changing rule of any number is proposed by analyzing the experimental results of the \(N\)-ary number encoded algorithm. Then a multi-objective optimization algorithm adopting the adaptive degressive any number encoding method has been used in optimizing the node placement in WSN. The experiments show that the proposed adaptive degressive any number encoded algorithm can improve both the optimization effect and search efficiency when solving the node placement problem. wireless sensor networks; node placement; a fast non-dominated sorted genetic algorithm (NSGA2); degressive any number; adaptive +
Footnote †: journal:  
0000-0001-4899-22000/00000-0000-0000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-000000-000000-00  
can be adjusted whenever needed. In some harsh environments, sensor nodes can only be randomly placed. Then a node placement that meets the application requirements should be obtained by the node placement optimization algorithm, and the nodes will move to the appropriate positions. When node placement optimization is used, the sink node (or the base station) will run the optimization algorithm to get the moving information (direction and distance) of each node. Then the moving information will be sent to all the sensor nodes, which will move to the corresponding location according to the information. The key to the node placement optimization problem is to optimize the placement of sensor nodes and adjust the network topology so that the network can meet all the application requirements while meeting the coverage requirements of the target area. Furthermore, except for the rechargeable WSN, the energy limitation of sensor nodes brings a big challenge to WSNs, which means these WSNs may have insufficient energy to collect and send information [9]. Therefore, in addition to coverage, the energy consumption and balance of the network are also important measurement indexes. In general, an excellent node placement solution ensures that the WSN has higher coverage and longer lifetime. However, most of the proposed optimization algorithms have not considered the energy consumption caused by the node movement. This made those optimization algorithms be only used for the deterministic deployment of initial nodes. In previous studies [10], we have considered the movement of the nodes besides the coverage and lifetime. A directed evolved crossover operator and an adaptive range limit parameter are proposed to improve the optimization effect of A Fast Non-dominated Sorted Genetic Algorithm (NSGA2) on node placement problem. The improved algorithm, which called ADENSGA, can solve not only node placement problems, but also node redistribution problems. In the ordinary multi-objective optimization algorithm, the importance of several optimization objectives is the same. However, in practice, coverage is more important than other objectives. The proposed directed evolved crossover operator can made the algorithm focus more on coverage among multiple optimization objectives. Although ADENSGA has many advantages, it still has the defect of slow convergence speed. Since most WSNs have a large number of sensor nodes, the node placement optimization problem is generally high-dimensional. ADENSGA is encoded by the common binary encoding, which has the defects of local early convergence and slow convergence speed in a high-dimensional optimization problem.