# American Institute of Mathematical Sciences

## Coverage control optimization algorithm for wireless sensor networks based on combinatorial mathematics

 Department of Electronics Information Engineering, Yuncheng Polytechnic College, Yuncheng 044000 China

* Corresponding author: Yongjie Wang

Received  April 2019 Revised  May 2019 Published  February 2020

The traditional wireless sensor network coverage control optimization algorithm has the problems of long completion time, high energy consumption and low coverage. A new algorithm based on combinational mathematics for wireless sensor network coverage control is proposed. The basic particle swarm optimization (PSO) algorithm is used to optimize the coverage control process of wireless sensor networks. Then, the combined mathematics method is used to detect the local convergence problem. Finally, the quasi-physical forces of quasi-gravity and Coulomb force are used to integrate the quasi-physical force into the particle. In the process of velocity evolution, the speed correction process of basic particle swarm optimization is optimized, which can effectively avoid the local convergence problem of particle swarm optimization algorithm, reduce the repeated coverage and expand the coverage. The experimental results show that compared with the traditional algorithm, the algorithm has short completion time, low energy consumption and high coverage.

Citation: Yongjie Wang. Coverage control optimization algorithm for wireless sensor networks based on combinatorial mathematics. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020264
##### References:

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##### References:
Rectangular graph of coverage varying with nodal induction radius
Rectangular graph with iteration number depending on node sensitive radius
Comparison of completion time of network coverage control with different methods
Test data of coverage performance by using the proposed algorithm and time synchronization-based coverage control optimization algorithm for wireless sensor networks
 Radius /m Algorithm based time synchronization The proposed algorithm Iteration times Coverage ($\%$) Iteration times Coverage ($\%$) 1.5 1621 32.65 1576 34.55 2 836 55.79 797 56.97 2.5 473 75.97 394 83.77 3 343 86.74 256 94.98 4 295 95.24 227 99.95 5 234 100 213 100
 Radius /m Algorithm based time synchronization The proposed algorithm Iteration times Coverage ($\%$) Iteration times Coverage ($\%$) 1.5 1621 32.65 1576 34.55 2 836 55.79 797 56.97 2.5 473 75.97 394 83.77 3 343 86.74 256 94.98 4 295 95.24 227 99.95 5 234 100 213 100
Comparison of energy consumption of network coverage control with different methods
 Number of scheduled tasks/(Number) Energy consumption/(J) Method 1 Method 2 Method 3 10 1102 1354 1654 20 1354 1645 1987 30 1411 1985 2132 40 1547 2001 2415 50 1699 2123 2879 60 1800 2536 3321
 Number of scheduled tasks/(Number) Energy consumption/(J) Method 1 Method 2 Method 3 10 1102 1354 1654 20 1354 1645 1987 30 1411 1985 2132 40 1547 2001 2415 50 1699 2123 2879 60 1800 2536 3321
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