Surrogate-assisted sine Phasmatodea population evolution algorithm applied to 3D coverage of mobile nodes

Deploying static wireless sensor nodes is prone to network coverage gaps, resulting in poor network coverage. In this paper, an attempt is made to improve the network coverage by moving the locations of the nodes. A surrogate-assisted sine Phasmatodea population evolution algorithm (SASPPE) is used to evaluate the network coverage. A 50 x 50 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50 \times 50$$\end{document} hill simulation environment was tested for the number of nodes of 30 and 40 and radii of 3, 5 and 7, respectively. The results show that the SASPPE algorithm has the highest coverage, which can be up to 23.624% higher than the PPE algorithm, and up to 5.196% higher than the PPE algorithm, ceteris paribus. The SASPPE algorithm mixes the GSAM with LSAMs, which balances the computational cost of the algorithm and the algorithm's ability to find optimal results. The use of hierarchical clustering enhances the stable type of the LSAMs. In addition, LSAMs are easy to fall into local optimality when they are modeled with local data, and the use of sine Phasmatodea population evolution algorithm (Sine-PPE) for searching in LSAMs alleviates the time for the algorithm to fall into local optimality. On 30D, 50D, and 100D, the proposed algorithm was tested by 7 test functions. The results show that the algorithm has significant advantages on most functions.