CN102761881A - Method for solving optimal coverage control set of static node in wireless sensor network - Google Patents

Abstract

The invention discloses a method for solving the optimal coverage control set of static nodes in a wireless sensor network. Under the premise of maintaining a certain coverage rate, the invention makes some nodes enter a dormant state, thereby reducing the number of working nodes, reducing network energy consumption, and extending network coverage. survival time. Furthermore, instead of considering the energy consumption of inter-node communication and calculation, only the energy consumption of the node sensing module is considered, and the properties of nodes with adjustable sensing radius are used to find a group with a small number of working nodes and a suitable combination of sensing radii. A set of nodes with low consumption and meeting certain coverage requirements. Three sub-functions of network node sensing module energy consumption, network coverage rate and network node dormancy rate are established. These three sub-functions together constitute the fitness function of the genetic algorithm, and the genetic algorithm is used to solve the model. An optimal combination of working nodes and an optimal combination of sensing radius of working nodes with large coverage, few working nodes and low energy consumption are obtained.

Description

Solving Method of Optimal Covering Control Set for Static Nodes in Wireless Sensor Networks

technical field

The invention relates to a method for solving an optimal coverage control set based on static nodes in a wireless sensor network, and belongs to the fields of sensor technology and wireless communication technology.

Background technique

The wireless sensor network is a wireless network composed of a large number of micro sensor nodes with limited energy distributed in the monitoring area and with perception, computing and communication capabilities through self-organization. With the rapid development of technologies such as computer communication and integrated circuits, the wide application of wireless sensor networks has become possible. But before the specific application, the deployment scheme of the sensor nodes must be determined according to the specific application environment criteria. In one case, the sensor nodes are static, focusing on how to reasonably arrange the nodes or schedule the working status of the nodes according to the monitoring area. Another situation is that the nodes in the network are mobile, and the main research is how to optimize the node layout. Coverage control, as a basic problem in wireless sensor networks, mainly studies these two situations, that is, how to maximize the network coverage and provide reliable monitoring services under the premise of ensuring a certain quality of service.

Since mobile nodes are usually expensive, in order to ensure network coverage performance and control costs, a large number of static sensor nodes are often deployed in the monitoring area for areas where it is not easy to deploy nodes deterministically, and the distribution of nodes is usually random. There will be an overlap between the sensing ranges. In this case, a certain point or a certain area in the monitoring area is often monitored by multiple nodes at the same time, and the data collected by nodes with similar positions will be highly correlated and highly redundant, causing nodes to transmit data. It will contain a lot of redundant information, and redundant data will increase energy consumption; in addition, the more working nodes are located in the same area, the more intense the channel competition will be, and the greater the possibility of data packet collision.

Therefore, it is necessary to schedule the dormancy/working state of the nodes to make the nodes with strong correlations work alternately, so as to reduce the extra energy consumption as much as possible, reduce the density of working nodes, avoid communication conflicts, and prolong the life of the network. That is to optimize the control of randomly deployed wireless sensor networks, reduce the number of working nodes and find an optimal coverage combination under the premise of ensuring a certain coverage performance.

The wireless sensor node energy consumption module includes a sensor module, a processor module and a wireless communication module. With the development of integrated circuit technology, the power consumption of the processor and sensor module becomes very low, and most of the energy is consumed in the wireless communication module.

Contents of the invention

The object of the present invention is to provide a method for solving the optimal coverage control set of static nodes in a wireless sensor network aiming at the defects existing in the prior art.

The method for solving the optimal coverage control set of the wireless sensor network static node in the present invention is as follows:

The coordinates of the node S _i in the wireless sensor network are ( _xi , y _i ), and the coordinates of any point p in the two-dimensional plane monitoring area are (x _p , y _p ), then the detection probability of the node n _i to the target point p for:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; ifd</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>}& \mathrm{<span\; class="notranslate">\; if</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; otherwise</span>}\end{array}\right.$

Among them, d(n _i , p) is the Euclidean distance between the sensor node n _i and the target point p; _Re (0<R _e <R _s ) is the measurement reliability parameter of the sensor node; α ₁ =R _e -R _s +d(n _i , p), α ₂ =R _e +R _s -d(n _i ,p); λ ₁ , λ ₂ , β ₁ , β ₂ are measurement parameters related to the sensor node characteristics;

Therefore, the joint detection probability of n sensor nodes in the entire two-dimensional plane monitoring area for the target point p is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, n _all is the set of sensor nodes that measure the target point, and the joint detection probability is not lower than the threshold c _th set according to the network requirements, then the condition that the target point can be effectively detected is:

$\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Divide the area to be tested into m×n grids, and then simplify the cells into pixels. The network coverage is defined as the ratio of the number of cells that meet the requirements of formula (2) to the total number of cells, namely:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

According to formula (2) and formula (3), the network coverage function f ₁ can be obtained:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, the monitoring area is divided into m×n grid units, and the joint detection probability of point p in the monitoring area must be greater than the probability threshold c _th to be included in the network coverage.

Node sleep rate function f ₂ :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where |S'| represents the number of working nodes, and |S| is the total number of nodes deployed;

表示节点n_i的传感半径，且 表示节点n_i的覆盖面积，

表示节点n_i的能量消耗；Among the nodes deployed in the monitoring area, the set of working nodes is N={n ₁ , n ₂ ,...n _n }, and the node sensing radius is in

denotes the sensing radius of node n _i , and Indicates the coverage area of node n _i ,

Indicates the energy consumption of node n _i ;

The coverage area of a working node is the union of the coverage areas of all working nodes:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

The average energy consumption in the coverage area is:

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="E.\; no"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">E.</figure-callout></span><figure-callout\; id="1"\; label="E.\; no"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="S\; no"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">S</figure-callout></span><figure-callout\; id="1"\; label="S\; no"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{{\mathrm{<span\; class="notranslate">\; </span>}}_{}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\mathrm{<span\; class="notranslate">\; u</span>}$

The coverage area average energy consumption sub-function _f3 describing the coverage consumption of the entire wireless sensor network is:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; work</span>}$

表示工作节点n_i的传感半径，S_work表示工作节点集合所覆盖的区域面积；总体目标函数为：in,

Represents the sensing radius of the working node n _i , S_work represents the area covered by the working node set; the overall objective function is:

f=w ₁ f ₁ +w ₂ f ₂ -w ₃ f ₃ (7)

Among them, w ₁ +w ₂ +w ₃ =1, the overall objective function value f is between 0 and 1, and the larger the value, the better the coverage optimization effect.

For the high-density node distribution in the monitoring area, the so-called optimal coverage set refers to the minimum set of nodes that can maintain the coverage of the entire network without being affected. This set of nodes can cover the area to the greatest extent, and the nodes outside this subset can be in a low-power sleep state.

Based on the consideration of saving energy consumption and network coverage, the invention optimizes the coverage control of the wireless sensor network, and establishes an area coverage optimization model aimed at saving energy consumption and meeting certain coverage requirements. On the basis of ensuring a certain coverage rate, let some redundant nodes enter a low-power sleep state to form an optimal node set for coverage. The node search task is to select a group of optimal nodes from a large number of sensor nodes, and use genetic algorithm to solve the model.

Furthermore, instead of considering the energy consumption of inter-node communication and calculation, only the energy consumption of the node sensing module is considered, and the properties of nodes with adjustable sensing radius are used to find a group with a small number of working nodes and a suitable combination of sensing radii. A set of nodes with low consumption and meeting certain coverage requirements. Established three sub-functions of network node sensor module energy consumption, network coverage rate, and network node dormancy rate. These three sub-functions together constitute the fitness function of the genetic algorithm. The genetic algorithm is used to solve the model, and a large coverage area is obtained. , the optimal working node combination with few working nodes and low energy consumption and the optimal sensing radius combination of working nodes.

Description of drawings

Figure 1 Genetic Algorithm Flowchart;

Figure 2 Schematic diagram of encoding.

Detailed ways

Optimal Covering Set Based on Genetic Algorithm

According to the characteristics of wireless sensor networks, it is assumed that:

1) Nodes in the network have the ability to switch working/sleeping states, and the network contains a central node, which has strong data processing and computing capabilities, and is used to optimize the selection of wireless sensor network nodes;

2) The location information of each node in the network can be obtained in some way;

3) Each node in the network has the same initial energy, perception radius R _s and communication radius R _c , and R _c =2R _s .

Assuming that N nodes are randomly deployed in the monitoring area, and n _i represents the i-th node in the wireless sensor network, the node set is S={n ₁ , n ₂ , n ₃ ,...,n _N }. Divide the monitoring area into grid points, set the coordinates of any grid point p in the area as (x _p , y _p ), find a subset S′ of working nodes, so that the network coverage rate Cr(S′) is the largest, and the working The number of nodes |S'| is the least. Transformed into a function representation, that is, the value of the maintenance coverage function f ₁ is the largest, and the node sleep rate function f ₂ is also large.

1. Fitness function

The fitness value is the value obtained by calculating the fitness function, and its size is the basis for updating the individual extremum in the genetic algorithm. In the process of wireless sensor network coverage optimization, the fitness function is the judgment of optimization search, and it is the link with the largest amount of calculation.

The node probability detection model probability is used as the measurement model to calculate the network coverage. Let the coordinates of node _si in the wireless sensor network be ( _xi , _yi ). Assuming that the coordinates of any point p in a two-dimensional plane monitoring area are (x _p , y _p ), the detection probability of node n _i to target point p is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; ifd</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>}& \mathrm{<span\; class="notranslate">\; if</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="0"\; label="R\; e"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; otherwise</span>}\end{array}\right.$

Among them, d(n _i , p) is the Euclidean distance between the sensor node n _i and the target point p; _Re (0<R _e <R _s ) is the measurement reliability parameter of the sensor node; α ₁ =R _e -R _s +d(n _i , p), α ₂ =R _e +R _s -d(n _i ,p); λ ₁ , λ ₂ , β ₁ , β ₂ are measurement parameters related to the sensor node characteristics.

Therefore, the joint detection probability of n sensor nodes in the entire two-dimensional plane monitoring area to the target point p is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, n _all is the set of sensor nodes that measure the target point. In order to meet the coverage requirements, it is usually required that the joint detection probability is not lower than the threshold c _th set according to the network requirements, then the conditions for the target point to be effectively detected are:

$\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The monitoring area of randomly arranged wireless sensor nodes is usually irregular, and the coverage area of the network cannot be directly calculated by analytical methods. In order to effectively evaluate the network coverage performance, the grid method is used to divide the area to be monitored into grids, and then the cells are simplified into points, and the coverage rate of each wireless sensor node to the point is analyzed, and the distance between adjacent grids Determined by coverage accuracy.

Assume that the area to be tested is divided into m×n grids, and then the cells are simplified into pixels. In the present invention, network coverage is defined as the ratio of the number of cells meeting the requirements of formula (2) to the total number of cells, that is:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

According to formula (2) and formula (3), the network coverage function f ₁ can be obtained:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="HDA00001783791900012.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, the monitoring area is divided into m×n grid units, and the joint detection probability of point p in the monitoring area must be greater than the probability threshold c _th to be included in the network coverage.

Node sleep rate function f ₂ :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where |S′| represents the number of working nodes, and |S| is the total number of nodes deployed. In order to convert these two sub-functions into the maximum value function, the overall objective function is defined as:

f=w ₁ f ₁ +w ₂ f ₂ (6)

Among them, w ₁ and w ₂ are the weights corresponding to the sub-objective functions, and the sum of the two is 1. The overall objective function value f is between 0 and 1, and the larger the value, the better the effect of coverage optimization. The objective function f in formula (6) is directly used as the fitness function of GA, and the larger the better criterion is adopted.

2. Coding

Aiming at the characteristics of random distribution of nodes in the wireless sensor network, the binary coding method is adopted, because the binary coding is relatively simple to encode and decode, and the crossover and mutation are also easy to realize. A string of binary codes a _i ={a ₁ , a ₂ ,..., a _N } represents whether the node in the network is selected or not, the selection of the node corresponds to the chromosome individual, and 1 represents the node at this position Selected as a working node, 0 means not selected.

Suppose the population is composed of M individuals, there are N nodes in the monitoring area, and the initial population is coded as 0/1:

$\mathrm{<span\; class="notranslate">\; p</span>}\begin{array}{}\end{array}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}\end{array}\right\}$

3. Algorithm operation

In the optimization algorithm proposed by the present invention, the selection operation adopts the commonly used roulette method to select individuals; adopts single-point crossover; in order to ensure that the genes of the parents are retained in the offspring as much as possible, the method of cyclic recombination is adopted; in addition, if The replacement operation occurs when the fitness function value of the offspring exceeds that of the replaced individual. The specific flow chart is shown in Figure 1.

Optimal Coverage Set with Adjustable Node Sensing Radius

Considering a large number of sensor nodes, they are randomly deployed in the target monitoring area. Establish a scheduling method so that only a few nodes are in the working state, while the other nodes are in the dormant state. On this basis, the node has the attribute of adjustable sensing radius, and the goal is to establish a set of nodes with a small number of working nodes, a suitable combination of sensing radius, low energy consumption, and certain coverage requirements.

The present invention adopts the energy consumption model, and only considers the energy consumption of the node sensing module, without considering the communication and calculation energy expenditure. When the perception radius of a node is zero, the energy consumption of the node is also zero. According to different energy consumption models, the energy consumption of a sensing module of a working node is proportional to R _s ² or R _i ⁴ , and R _s is the sensing radius of the working node. In the present invention, taking the energy consumption of the sensing module as u*R _s ² as an example, u is a constant.

其中

表示节点n_i的传感半径，且

表示节点n_i的覆盖面积，

表示节点n_i的能量消耗。Assume that among the nodes deployed in the monitoring area, the set of working nodes is N={n ₁ , n ₂ ,...n _n }, and the node sensing radius is

in

denotes the sensing radius of node n _i , and

Indicates the coverage area of node n _i ,

Indicates the energy consumption of node n _i .

The coverage area of a working node is the union of the coverage areas of all working nodes:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$

The average energy consumption in the coverage area is:

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\mathrm{<span\; class="notranslate">\; u</span>}$

Therefore, on the basis of formula (6), an average energy consumption sub-function f ₃ in the coverage area can be added to describe the coverage consumption of the entire wireless sensor network, which is recorded as:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; work</span>}$

表示工作节点n_i的传感半径，S_work表示工作节点集合所覆盖的区域面积。为了将这3个子函数转换成最大值函数，故定义总体目标函数为：in,

Indicates the sensing radius of the working node n _i , and S_work indicates the area covered by the working node set. In order to transform these three sub-functions into the maximum function, the overall objective function is defined as:

f=w ₁ f ₁ +w ₂ f ₂ -w ₃ f ₃ (7)

In this wireless sensor network, formula (7) is used as the fitness function of the genetic algorithm, which involves the optimal combination of working nodes and the combination of optimal sensing radius of working nodes; w ₁ +w ₂ +w ₃ =1,w _1. Specific values of w ₂ and w ₃ may be determined according to network coverage performance requirements.

coding design

编码长度与节点可调半径的范围，以及节点数有关，其中节点半径转换成二进制编码的长度为：Also use the genetic algorithm to solve the model, using the binary code form, such as

The code length is related to the range of node adjustable radius and the number of nodes, where the length of node radius converted into binary code is:

Among them, R _max and R _min represent the upper and lower limits of the node adjustable radius. Assuming that the network has N nodes, the length of each individual in the group is N*R_Bit+N, and the first N bits of each individual code indicate whether the 1st to Nth nodes in the network are selected. 1 means The node is selected, 0 means not selected; the following N*R_Bit corresponds to the radius code of the network node, the radius code of node i is b _i ={b _i0 b _i1 … _{bi(R_bit-1)} }, the length is R_Bit bit. Specifically shown in Figure 2.

The radius of each node can be calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; si</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; bit</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\underset{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; bit</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; ib</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; b</span>}}$

Algorithm operation

The purpose of genetic manipulation is to select superior individuals from the initial population for evolution, which includes three ways: copying excellent individuals, crossing two parent individuals at a single point, and mutating a single individual. For the evolved offspring group, re-determine the optimization criterion, and so on, until the termination judgment condition is reached. The following mainly introduces the three basic operations of the genetic algorithm when combined with the coverage optimization problem:

1. Choose

The present invention uses a "roulette method" to select individuals. After obtaining the fitness value of each individual, the individual fitness value in the whole group is normalized; then the selection probability value is accumulated, and in each round, a random number in [0, 1] is generated as Pointer to determine the selected individual.

2. cross

In order to ensure that the genes of the parents are retained in the offspring as much as possible, the method of cyclic recombination is adopted, such as selecting m parent individuals {1, 2, i, ..., m}, the first selection (1, 2), Select (2, 3) as the parents for the second time, and select parent individual i and parent individual i+1 for the i-th time to perform single-point crossover.

Randomly generate an integer within [1, 8] as the intersection position. For example, if the intersection position is 3, the parent individual codes will be exchanged from 4 to obtain i and child i+1.

3. Variation

In the mutation operation, different mutation rates are used for the selected node and the radius combination of the node, and the mutation operation is performed. The former has a higher mutation rate in order to increase the number of new individuals as much as possible, while the latter is only a radius combination, and the mutation rate is smaller. Reduce algorithm overhead, because it is possible that the corresponding node is not selected, and the change of its radius does not have much meaning. For example, two operation positions 3 and 8 are randomly selected, and the corresponding codes are reversed, such as 0 becomes 1, and 1 becomes 0.

In addition, if the saved optimal solution is not updated during the iterative process, the individual with the highest fitness value in the nth generation is directly replaced with the individual with the lowest fitness value in the n+1 generation. Individuals with high fitness are passed directly to the next generation to avoid the situation of inability to reproduce genetically.

When the algorithm runs to the preset maximum iterative algebra, the algorithm stops. At this time, the chromosome with the largest fitness is the approximate optimal solution, and then the selected wireless sensor network nodes can be obtained by decoding it, and their The corresponding induction radius.

Claims (5)

1. A wireless sensor network static node optimal coverage control set solution method, characterized in that the method is as follows: The coordinates of the node n _i in the wireless sensor network are ( _xi , y _i ), and the coordinates of any point p in the two-dimensional plane monitoring area are (x _p , y _p ), then the detection probability of the node n _i to the target point p for: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; ifd</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>}& \mathrm{<span\; class="notranslate">\; if</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; otherwise</span>}\end{array}\right.$ Among them, d(n _i , p) is the Euclidean distance between the sensor node n _i and the target point p; _Re (0<R _e <R _s ) is the measurement reliability parameter of the sensor node; α ₁ =R _e -R _s +d(n _i , p), α ₂ =R _e +R _s -d(n _i ,p); λ ₁ , λ ₂ , β ₁ , β ₂ are measurement parameters related to the sensor node characteristics; Therefore, the joint detection probability of n sensor nodes in the entire two-dimensional plane monitoring area for the target point p is: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ Among them, n _all is the set of sensor nodes that measure the target point, and the joint detection probability is not lower than the threshold c _th set according to the network requirements, then the condition that the target point can be effectively detected is: $\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Divide the area to be tested into m×n grids, and then simplify the cells into pixels. The network coverage is defined as the ratio of the number of cells that meet the requirements of formula (2) to the total number of cells, namely: ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; all</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ According to formula (2) and formula (3), the network coverage function f ₁ can be obtained: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ Among them, the monitoring area is divided into m×n grid units, and the joint detection probability of point p in the monitoring area must be greater than the probability threshold c _th to be included in the network coverage. Node sleep rate function f ₂ : ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Where |S'| represents the number of working nodes, and |S| is the total number of nodes deployed; Among the nodes deployed in the monitoring area, the set of working nodes is N={n ₁ , n ₂ ,...n _n }, and the node sensing radius is

in

denotes the sensing radius of node n _i , and

Indicates the coverage area of node n _i , Indicates the energy consumption of node n _i ; The coverage area of a working node is the union of the coverage areas of all working nodes: ${\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$ The average energy consumption in the coverage area is: $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}{{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&cup;</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&cup;</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}\mathrm{<span\; class="notranslate">\; u</span>}$ The coverage area average energy consumption sub-function _f3 describing the coverage consumption of the entire wireless sensor network is: ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{{\mathrm{<span\; class="notranslate">\; sn</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; \_</span>\mathrm{<span\; class="notranslate">\; work</span>}$ in,

Represents the sensing radius of the working node n _i , S_work represents the area covered by the working node set; the overall objective function is: f=w ₁ f ₁ +w ₂ f ₂ -w ₃ f ₃ (7) Among them, w ₁ +w ₂ +w ₃ =1, the overall objective function value f is between 0 and 1, and the larger the value, the better the coverage optimization effect. 2. the wireless sensor network static node optimal coverage control set solution method according to claim 1, is characterized in that described overall objective function is used as the fitness function of genetic algorithm, and genetic algorithm comprises copying excellent individual, two parent individuals There are three ways to perform one-point crossover and mutation of a single individual. 3. The wireless sensor network static node optimal coverage control set solution method according to claim 2, characterized in that the copy excellent individual adopts "roulette method" to select individual: after obtaining the fitness value of each individual Finally, the individual fitness value in the whole group is normalized; then the selection probability value is accumulated, and in each round, the selected individual is determined by generating a random number in [0, 1] as a pointer. 4. The wireless sensor network static node optimal coverage control set solution method according to claim 2, characterized in that the single-point crossover method of the two parent individuals adopts the method of cyclic recombination. 5. The wireless sensor network static node optimal coverage control set solution method according to claim 2, characterized in that the variation of the single body: the combination of the radius of the selected node and the node adopts different mutation rates respectively to carry out the variation Operation, the mutation rate of the former is greater than that of the latter.

Images