CN111277951B - Greedy submodule-based wireless chargeable sensor network charger deployment method - Google Patents

Greedy submodule-based wireless chargeable sensor network charger deployment method Download PDF

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CN111277951B
CN111277951B CN202010090862.3A CN202010090862A CN111277951B CN 111277951 B CN111277951 B CN 111277951B CN 202010090862 A CN202010090862 A CN 202010090862A CN 111277951 B CN111277951 B CN 111277951B
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monitoring point
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trolley
route
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CN111277951A (en
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徐佳
蔡威
徐力杰
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L53/00—Methods of charging batteries, specially adapted for electric vehicles; Charging stations or on-board charging equipment therefor; Exchange of energy storage elements in electric vehicles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L53/00—Methods of charging batteries, specially adapted for electric vehicles; Charging stations or on-board charging equipment therefor; Exchange of energy storage elements in electric vehicles
    • B60L53/10—Methods of charging batteries, specially adapted for electric vehicles; Charging stations or on-board charging equipment therefor; Exchange of energy storage elements in electric vehicles characterised by the energy transfer between the charging station and the vehicle
    • B60L53/12—Inductive energy transfer
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J50/00—Circuit arrangements or systems for wireless supply or distribution of electric power
    • H02J50/20—Circuit arrangements or systems for wireless supply or distribution of electric power using microwaves or radio frequency waves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/18—Network planning tools
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/70—Energy storage systems for electromobility, e.g. batteries
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
    • Y02T10/7072—Electromobility specific charging systems or methods for batteries, ultracapacitors, supercapacitors or double-layer capacitors
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02T90/10—Technologies relating to charging of electric vehicles
    • Y02T90/14—Plug-in electric vehicles

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  • Transportation (AREA)
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Abstract

The invention discloses a deployment method of a wireless chargeable sensor network charger based on a greedy sub-model, which comprises the steps of firstly, constructing a 0-1 integer programming model for solving an optimal deployment scheme of a wireless charger by taking minimum charging power as a target according to information such as a periodic moving route of each moving trolley, electric quantity consumption rate in the moving process, residence time of each monitoring point on the route, distance between each monitoring point and the like; secondly, a monotonically increasing sub-model function is constructed according to the model, and finally, a greedy strategy based on the sub-model function is adopted to iteratively select the position of a monitoring point for deploying the wireless charger, so that a deployment scheme is finally obtained. The invention has better average charging power consumption performance and can be widely applied to application scenes in which a plurality of mobile trolleys are adopted to execute periodic monitoring tasks in a wireless chargeable sensor network.

Description

Greedy submodule-based wireless chargeable sensor network charger deployment method
Technical Field
The invention belongs to the field of wireless chargeable sensor networks, and particularly relates to a greedy submodule-based wireless chargeable sensor network charger deployment method.
Background
The wireless sensor network is a multi-hop wireless ad hoc network formed by a plurality of cheap micro sensor nodes randomly distributed in a monitored area through a wireless communication mode. The system can cooperatively sense, collect and process information of an object to be sensed in a covered geographic area, and distribute the information to users needing the information finally through a user interface, and the system has wide application in the fields of environmental monitoring, intelligent transportation, medical monitoring, scientific exploration, national defense and military and the like. Unlike a traditional ad hoc network, an application scenario of a wireless sensor network generally requires a system to continuously run for a long time, meanwhile, battery energy of sensor nodes is limited, and a complex deployment environment generally causes frequent replacement of the node batteries to be difficult, so energy efficiency optimization becomes a primary design target of the wireless sensor network. With the rapid development of wireless power transmission technology, researchers consider applying the technology to a wireless sensor network, and supply battery energy to sensor nodes by way of wireless electromagnetic wave charging to ensure the continuous operation of the system, and such a sensor network supporting wireless electromagnetic wave charging is generally called as a wirelessly chargeable sensor network.
In a wireless rechargeable sensor network, a plurality of mobile carts equipped with rechargeable sensors are generally used to perform various data monitoring tasks through respective specific periodic travel routes, and in order to ensure that the mobile carts can have sufficient electric energy to continuously perform the data monitoring tasks, it is considered to provide continuous charging services for the mobile carts by using a wireless electric energy transmission technology. In particular, it is possible to optimize the deployment of a plurality of static chargers in the network so that each mobile vehicle travelling on a respective specific periodic route is able to continuously perform monitoring tasks.
The mobile trolley responsible for the data monitoring task has the following properties: firstly, the movable trolleys have fixed and periodic traveling paths, each traveling period starts from an initial monitoring point, a series of fixed monitoring points pass through the middle of each traveling period, and after one traveling period is finished, the traveling periods can return to the initial monitoring point and continue to perform a monitoring task of the next period; secondly, the mobile trolley stays for a period of time at each monitoring point where the mobile trolley passes through to execute a monitoring task, and if a charger is deployed at a certain monitoring point, the mobile trolley passes through the monitoring point to execute the monitoring task and simultaneously supplements battery energy through the charger deployed at the monitoring point; finally, the monitoring points through which the travel routes of the multiple mobile vehicles pass may overlap, i.e., each monitoring point may be passed by multiple mobile vehicles.
The wireless charger deployment algorithm is a popular problem in the research of the field of wireless chargeable sensor networks, and a plurality of scholars propose related solutions, but most methods consider how to optimize the deployment of the wireless charger under the condition that the sensor equipment is statically fixed, and do not consider how to optimize the deployment of the wireless charger under the condition that the sensor equipment moves so as to provide continuous electric energy for the sensor equipment. In fact, many application scenarios utilize the mobile sensor to perform the monitoring task, and therefore, how to optimize and deploy the wireless charger to continuously provide the electric energy for the mobile sensor device is a very important and practical problem.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a greedy submodule-based wireless chargeable sensor network charger deployment method with better average charging power consumption performance.
The invention content is as follows: the invention discloses a deployment method of a wireless chargeable sensor network charger based on a greedy submodule, which specifically comprises the following steps:
(1) according to information such as periodic moving routes of the mobile trolleys, electric quantity consumption rate in the moving process, residence time of monitoring points on the routes, distances between the monitoring points and the like, a 0-1 integer programming model for solving the optimal deployment scheme of the wireless charger is constructed by taking the minimum charging power as a target;
(2) constructing a monotonically increasing sub-model function according to the 0-1 integer programming model established in the step (1);
(3) and selecting the position of the monitoring point for deploying the wireless charger by adopting a greedy algorithm, thereby finally obtaining a deployment scheme.
Further, the step (1) specifically includes the steps of:
(11) set of mobile carts in a network V ═ V1，v2，...vmS ═ S, set of monitoring points1，s2，..snIs provided with any trolley viMonitoring point sequence set passed by the movement route belonging to the V
Figure GDA0002449374820000021
Figure GDA0002449374820000022
Wherein
Figure GDA0002449374820000023
And n isiShowing the car viThe number of monitoring points passed by the moving route, for any monitoring point
Figure GDA0002449374820000024
Order to
Figure GDA0002449374820000025
And
Figure GDA0002449374820000026
respectively show the carriages viIn that
Figure GDA0002449374820000027
Thus, the car v can be modelediAt the monitoring point
Figure GDA0002449374820000028
The amount of charge power that can be obtained during the dwell time of
Figure GDA0002449374820000029
Wherein
Figure GDA00024493748200000210
Is a monitoring point
Figure GDA00024493748200000211
The charger charging power that is allowed to be deployed,
Figure GDA00024493748200000212
is a binary variable, and is characterized in that,
Figure GDA00024493748200000213
if and only if at the monitoring point
Figure GDA00024493748200000214
Deploying a charger;
(12) by passing
Figure GDA00024493748200000215
Calculating any trolley viFrom the monitoring point
Figure GDA00024493748200000216
Energy consumed moving to the next monitoring point of its route, wherein
Figure GDA0002449374820000031
Showing the car viMonitoring point on moving route
Figure GDA0002449374820000032
Distance to its next monitoring point, piShowing the car viRate of power consumption during mobility; here, if j ∈ [1, n ]i-1]Monitoring point
Figure GDA0002449374820000033
On a trolley viIs the next monitoring point on the moving route
Figure GDA0002449374820000034
If j is equal to niMonitoring point
Figure GDA0002449374820000035
On a trolley viIs the next monitoring point on the moving route
Figure GDA0002449374820000036
(13) Order to
Figure GDA0002449374820000037
Showing the car viAt the monitoring point
Figure GDA0002449374820000038
Energy consumed by executing monitoring tasks, and sequentially modeling any trolley viAt each monitoring point
Figure GDA0002449374820000039
Residual energy after the end of the dwell time
Figure GDA00024493748200000310
Initially, the start-up of the plant is carried out,
Figure GDA00024493748200000311
Figure GDA00024493748200000312
wherein I represents a cart viAt the initial monitoring point
Figure GDA00024493748200000313
Initial energy of, setting the initial energy
Figure GDA00024493748200000314
To ensure viAt the monitoring point
Figure GDA00024493748200000315
Can initially complete the first monitoring task to obtain the residual energy of the initial position
Figure GDA00024493748200000316
When j is equal to [2, n ]i]When the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000317
when the trolley viReturning to the monitoring point after the end of a moving period
Figure GDA00024493748200000327
In preparation for entering the next movement period,
Figure GDA00024493748200000318
Figure GDA00024493748200000319
(14) for any car viAnd any monitoring point on its route
Figure GDA00024493748200000320
Must satisfy
Figure GDA00024493748200000321
Wherein, when j is equal to [1, n ]i-1]When the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000322
when j is equal to niWhen the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000323
Figure GDA00024493748200000324
in order to ensure that the charging power is minimized under the constraint, a 0-1 integer programming model is constructed as follows:
Figure GDA00024493748200000325
further, the step (2) comprises the steps of:
(21) by analysis, the 0-1 integer programming model (1) actually has
Figure GDA00024493748200000326
Each comprises x(s)1)，x(s2)，...，x(sn) The inequality of these n variables constrains the conditions, so the model (1) can be transformed equivalently to the form:
Figure GDA0002449374820000041
wherein,
Figure GDA0002449374820000042
and a isijAnd biIs a non-negative parameter that can be calculated by the model (1), i.e.
Figure GDA0002449374820000043
Figure GDA0002449374820000044
(22) The function f is constructed from the model (2) as follows: for any one set
Figure GDA0002449374820000046
Definition of
Figure GDA0002449374820000047
(x) is a monotonically increasing submodular function; the optimization problem of the model (2) is converted into a minimum weight submodel coverage problem, namely how to find a set
Figure GDA0002449374820000048
So as to make sigmaj∈Xp(sj) Minimization, where the set X must satisfy the following constraints: for all X ∈ X, there is f (X utou { X }) ═ f (X).
Further, the step (3) comprises the steps of:
(31) initialization settings set
Figure GDA0002449374820000049
(32) Let I (X) be { (i | ∑ E)l∈Xail＜biAnd adding an index j, j belonging to { 1.,. n } into the set X in each iteration process through a greedy strategy, so that the index j, j belongs to { 1.,. n }, and the set X is obtained
Figure GDA00024493748200000410
Reaches a maximum until sigma is not present for all j e {1i∈I(X)min{aij，bi-∑l∈XailWhen the rate is larger than 0;
(33) obtaining a final set X after iteration of the step (32), and obtaining a monitoring point set S of the optimal deployment charger*＝{sjI j ∈ X }, and the approximation ratio of the deployment method is 1+ ln γ, where
Figure GDA00024493748200000411
Figure GDA00024493748200000412
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: 1. by effectively deploying the wireless charger at a monitoring point with minimum charging power cost, a plurality of mobile trolleys which are provided with a plurality of monitoring tasks and are provided with the chargeable sensors can continuously run, wherein each mobile trolley periodically runs on a specific route to execute the monitoring tasks; 2. the method can be widely applied to the application scene that a plurality of mobile trolleys are adopted to execute periodic monitoring tasks in a wireless chargeable sensor network, and has better average charging power consumption performance.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a wireless rechargeable sensor network according to the present embodiment;
fig. 3 is a schematic diagram of the finally determined wireless charger arrangement in the embodiment.
Detailed Description
The technical scheme of the invention is described in detail in the following with reference to the accompanying drawings, and the greedy sub-model-based wireless chargeable sensor network charger deployment method enables a plurality of movable trolleys equipped with chargeable sensors to continuously run by effectively deploying the wireless chargers at monitoring points with minimum charging power cost, wherein each movable trolley periodically runs on a specific route to perform monitoring tasks. As shown in fig. 1, the method specifically comprises the following steps:
1. and constructing a 0-1 integer planning model for solving the optimal deployment scheme of the wireless charger by taking the minimum charging power as a target according to information such as the periodic moving route of each moving trolley, the electric quantity consumption rate in the moving process, the residence time of each monitoring point on the route, the distance between each monitoring point and the like.
(1) Suppose the set of mobile vehicles in the network, V ═ V1，v2，...vmS ═ S, set of monitoring points1，s2，..snIs provided with any trolley viMonitoring point sequence set passed by the movement route belonging to the V
Figure GDA0002449374820000051
Wherein
Figure GDA0002449374820000052
And n isiShowing the car viThe number of monitoring points passed by the moving route, for any monitoring point
Figure GDA0002449374820000053
Order to
Figure GDA0002449374820000054
And
Figure GDA0002449374820000055
respectively show the carriages viIn that
Figure GDA0002449374820000056
Thus, the car v can be modelediAt the monitoring point
Figure GDA0002449374820000057
The amount of charge power that can be obtained during the dwell time of
Figure GDA0002449374820000058
Wherein
Figure GDA0002449374820000059
Is a monitoring point
Figure GDA00024493748200000510
The charger charging power that is allowed to be deployed,
Figure GDA00024493748200000511
is a binary variable, and is characterized in that,
Figure GDA00024493748200000512
if and only if at the monitoring point
Figure GDA00024493748200000513
A charger is deployed.
(2) By passing
Figure GDA00024493748200000514
Calculating any trolley viFrom the monitoring point
Figure GDA00024493748200000515
Energy consumed moving to the next monitoring point of its route, wherein
Figure GDA00024493748200000516
Showing the car viMonitoring point on moving route
Figure GDA00024493748200000517
Distance to its next monitoring point, piShowing the car viRate of power consumption during mobility; here, if j ∈ [1, n ]i-1]Monitoring point
Figure GDA00024493748200000518
On a trolley viIs the next monitoring point on the moving route
Figure GDA00024493748200000519
If j is equal to niMonitoring point
Figure GDA00024493748200000520
On a trolley viIs the next monitoring point on the moving route
Figure GDA00024493748200000521
(3) Order to
Figure GDA0002449374820000061
Showing the car viAt the monitoring point
Figure GDA0002449374820000062
Energy consumed by executing monitoring tasks, and sequentially modeling any trolley viAt each monitoring point
Figure GDA0002449374820000063
Residual energy after the end of the dwell time
Figure GDA0002449374820000064
Initially, the start-up of the plant is carried out,
Figure GDA0002449374820000065
Figure GDA0002449374820000066
wherein I represents a cart viAt the initial monitoring point
Figure GDA0002449374820000067
Can set the initial energy
Figure GDA0002449374820000068
To ensure viAt the monitoring point
Figure GDA0002449374820000069
The first monitoring task can be completed initially, so that the residual energy of the initial position can be obtained
Figure GDA00024493748200000610
When j is equal to [2, n ]i]When the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000611
Figure GDA00024493748200000612
when the trolley viReturning to the monitoring point after the end of a moving period
Figure GDA00024493748200000613
In preparation for entering the next movement period,
Figure GDA00024493748200000614
here, it can be considered that the capacity of the rechargeable battery is generally large and the charging power is not generally large, so that the battery full charge overflow does not generally occur in the entire charging schedule process.
(4) In order to ensure that each mobile vehicle can periodically and continuously run in the network, the requirement that the residual energy of each monitoring point of each vehicle on the route of each vehicle can be enough to move to the next monitoring point and perform the monitoring task at the next monitoring point is met. That is, for any vehicle viAnd any monitoring point on its route
Figure GDA00024493748200000615
Must satisfy
Figure GDA00024493748200000616
Wherein, when j is equal to [1, n ]i-1]When the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000617
when j is equal to niWhen the temperature of the water is higher than the set temperature,
Figure GDA00024493748200000618
in order to minimize the charging power under the constraint condition, the following 0-1 integer programming model can be constructed:
Figure GDA00024493748200000619
2. and (3) constructing a monotonically increasing sub-model function according to the 0-1 integer programming model established in the step (1).
(1) By analysis, the 0-1 integer programming model (1) actually has
Figure GDA00024493748200000620
Each comprises x(s)1)，x(s2)，...，x(sn) The inequality of these n variables constrains the conditions, so the model (1) can be transformed equivalently to the form:
Figure GDA0002449374820000071
wherein,
Figure GDA0002449374820000072
and a isijAnd biIs a non-negative parameter that can be calculated by the model (1), i.e.
Figure GDA0002449374820000073
Figure GDA0002449374820000074
(2) The function f is constructed from the model (2) as follows: for any one set
Figure GDA0002449374820000076
Definition of
Figure GDA0002449374820000077
It can be shown that f (x) is a monotonically increasing sub-modulus function. Thus, the optimization problem of model (2) can be transformed into a minimum weight submodel coverage problem, i.e. how to find a set
Figure GDA0002449374820000078
So as to make sigmaj∈Xp(sj) Minimization, where the set X must satisfy the following constraints: for all X ∈ X, there is f (X utou { X }) ═ f (X).
3. And selecting the position of the monitoring point for deploying the wireless charger by adopting a greedy algorithm, thereby finally obtaining a deployment scheme.
(1) Initialization settings set
Figure GDA0002449374820000079
(2) Let I (X) be { (i | ∑ E)l∈Xail＜biAnd adding an index j, j belonging to { 1.,. n } into the set X in each iteration process through a greedy strategy, so that the index j, j belongs to { 1.,. n }, and the set X is obtained
Figure GDA00024493748200000710
Reaches a maximum until sigma is not present for all j e {1i∈I(X)min{aij，bi-∑l∈XailUntil it is > 0.
(3) Obtaining a final set X after the iteration of the step (2), thereby obtaining a monitoring point set S for optimally deploying the charger*＝{sjI j ∈ X }, it can be proved that the approximation ratio of the deployment method is 1+ ln γ, where
Figure GDA00024493748200000711
The invention is described in further detail below with reference to an embodiment, which is applied to a wireless chargeable sensor network consisting of a plurality of monitoring points and a plurality of moving trolleys. As shown in fig. 2, each trolley has its own periodic movement path, and a charger is deployed at a monitoring point so that all trolleys can continuously run.
Set of mobile carts in a network V ═ V1，v2S ═ S, set of monitoring points1，s2，s3，s4}, route S of the carriage1＝{s1，s2，s4}，S2＝{s1，s2，s3，s4}. Let each trolleyThe charging time and charging efficiency are the same at the same monitoring point, so t(s)1)＝1，t(s2)＝3，t(s3)＝1，t(s4) 1, charging power p(s)i) And charging efficiency η(s)i) The number of the charging points is 1, so that the charging capacity obtained by the trolley in the stay time of the monitoring points can be obtained. Such as a trolley v1At monitoring point s2Obtaining the charging electric quantity as Q1(s2)＝η(s2)·t(s2)·p(s2)·x(s2)＝3·x(s2)。
Trolley v1，v2The distance from the monitoring point to its next monitoring point is 0.5 and the rate of power consumption is set to 1, then the energy consumed by each car between the two monitoring points passed by it is 0.5.
Trolley v1，v2The energy consumed for executing the monitoring task at each monitoring point is 0.5, so that the vehicle v can be calculated1At monitoring point s2The residual capacity for completing the monitoring task is
Figure GDA0002449374820000081
Figure GDA0002449374820000082
The residual electric quantity of the trolley at other monitoring points can also be directly solved.
For the automation of the trolley, the residual electricity quantity of each monitoring point needs to be satisfied
Figure GDA0002449374820000083
The following 0-1 integer programming model can be constructed:
Figure GDA0002449374820000084
and constructing a monotonically increasing sub-model function according to the established 0-1 integer programming model. Through analysis, one of the 0-1 integer programming models (3) actually contains x(s)1)，x(s2)，...，x(s4) The 4 piecesThe inequality constraints of the variables, from the model (3), construct the function f as follows: for any one set
Figure GDA0002449374820000085
Definition of
Figure GDA0002449374820000086
It can be shown that f (X) is a monotonically increasing sub-modulus function, where biAnd ailIs a non-negative parameter in a constraint in the model (3), e.g. when
Figure GDA0002449374820000087
f(X)＝0。
And selecting the monitoring point position for deploying the wireless charger by adopting a greedy algorithm according to the constructed sub-model function, thereby finally obtaining a deployment scheme. Initialization settings set
Figure GDA0002449374820000088
Let I (X) be { (i | ∑ E)l∈Xail＜biSubstituting j (j is equal to {1, 2, 3, 4}) into j (j is equal to {1, 2, 3, 4}) in the first iteration through a greedy strategy
Figure GDA0002449374820000091
Figure GDA0002449374820000092
And calculating the weight of each monitoring point, and when j is 1,
Figure GDA0002449374820000093
the same can be obtained:
w2＝5，w3＝3，w4＝4
selecting the maximum weight to add into X, wherein X is {1 };
for the second iteration, selecting j e {2, 3, 4}
When j is 2, all constraints may be satisfied, i.e., w is set2＝+∞；
When j is 3, the number of the adjacent groups is 3,
the constraint conditions at this time are:
x(s1)+3x(s2)≥2
x(s1)+3x(s2)≥2
x(s1)+3x(s2)+x(s3)≥3
2x(s1)+3x(s2)+x(s4)≥4
2x(s1)+3x(s2)+x(s3)+x(s4)≥4
2x(s1)+3x(s2)+x(s3)+x(s4)≥5
then there are:
Figure GDA0002449374820000094
the same can be obtained: w is a4＝4；
Obtaining X ═ {1, 2 };
at this time, sigma does not existi∈I(X)min{aij，bi-∑l∈Xail0 is multiplied; thus we get the final result X ═ {1, 2 }. Obtaining a final set X after iteration, thereby obtaining a monitoring point set S of the optimal deployment charger*＝{s1，s2}. Fig. 3 is a schematic diagram of the wireless charger layout finally determined in the present embodiment.
The above description is only an example of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention and the inventive concept thereof within the scope of the present invention.

Claims (1)

1. A deployment method of a wireless chargeable sensor network charger based on a greedy submodule is characterized by comprising the following steps:
(1) according to information such as periodic moving routes of the mobile trolleys, electric quantity consumption rate in the moving process, residence time of monitoring points on the routes, distances between the monitoring points and the like, a 0-1 integer programming model for solving the optimal deployment scheme of the wireless charger is constructed by taking the minimum charging power as a target;
(2) constructing a monotonically increasing sub-model function according to the 0-1 integer programming model established in the step (1);
(3) selecting the monitoring point position for deploying the wireless charger by adopting a greedy algorithm, thereby finally obtaining a deployment scheme;
the step (1) specifically comprises the following steps:
(11) set of mobile carts in a network V ═ V1，v2，...vmS ═ S, set of monitoring points1，s2，..snIs provided with any trolley viMonitoring point sequence set passed by the movement route belonging to the V
Figure FDA0002843840610000011
Wherein
Figure FDA0002843840610000012
Figure FDA00028438406100000132
And n isiShowing the car viThe number of monitoring points passed by the moving route, for any monitoring point
Figure FDA0002843840610000013
Order to
Figure FDA00028438406100000131
And
Figure FDA0002843840610000015
respectively show the carriages viIn that
Figure FDA00028438406100000133
Thus, the car v can be modelediAt the monitoring point
Figure FDA0002843840610000016
The amount of charge power that can be obtained during the dwell time of
Figure FDA0002843840610000017
Figure FDA0002843840610000018
Wherein
Figure FDA0002843840610000019
Is a monitoring point
Figure FDA00028438406100000110
The charger charging power that is allowed to be deployed,
Figure FDA00028438406100000111
is a binary variable, and is characterized in that,
Figure FDA00028438406100000112
if and only if at the monitoring point
Figure FDA00028438406100000113
Deploying a charger;
(12) by passing
Figure FDA00028438406100000114
Calculating any trolley viFrom the monitoring point
Figure FDA00028438406100000115
Energy consumed moving to the next monitoring point of its route, wherein
Figure FDA00028438406100000116
Showing the car viMonitoring point on moving route
Figure FDA00028438406100000117
Distance to its next monitoring point, piShowing the car viRate of power consumption during mobility; here, if j ∈ [1, n ]i-1]Monitoring point
Figure FDA00028438406100000118
On a trolley viIs the next monitoring point on the moving route
Figure FDA00028438406100000119
If j is equal to niMonitoring point
Figure FDA00028438406100000120
On a trolley viIs the next monitoring point on the moving route
Figure FDA00028438406100000121
(13) Order to
Figure FDA00028438406100000122
Showing the car viAt the monitoring point
Figure FDA00028438406100000123
Energy consumed by executing monitoring tasks, and sequentially modeling any trolley viAt each monitoring point
Figure FDA00028438406100000124
Residual energy after the end of the dwell time
Figure FDA00028438406100000125
Initially, the start-up of the plant is carried out,
Figure FDA00028438406100000126
Figure FDA00028438406100000127
wherein I represents a cart viAt the initial monitoring point
Figure FDA00028438406100000128
Initial energy of, setting the initial energy
Figure FDA00028438406100000129
To ensure viAt the monitoring point
Figure FDA00028438406100000130
Can initially complete the first monitoring task to obtain the residual energy of the initial position
Figure FDA0002843840610000021
When j is equal to [2, n ]i]When the temperature of the water is higher than the set temperature,
Figure FDA0002843840610000022
when the trolley viReturning to the monitoring point after the end of a moving period
Figure FDA0002843840610000023
In preparation for entering the next movement period,
Figure FDA0002843840610000024
Figure FDA0002843840610000025
(14) for any car viAnd any monitoring point on its route
Figure FDA0002843840610000026
Must satisfy
Figure FDA0002843840610000027
Wherein, when j is equal to [1, n ]i-1]When the temperature of the water is higher than the set temperature,
Figure FDA0002843840610000028
when j is equal to niWhen the temperature of the water is higher than the set temperature,
Figure FDA0002843840610000029
Figure FDA00028438406100000210
in order to ensure that the charging power is minimized under the constraint, a 0-1 integer programming model is constructed as follows:
Figure FDA00028438406100000211
the step (2) comprises the following steps:
(21) by analysis, the 0-1 integer programming model (1) actually has
Figure FDA00028438406100000212
Each comprises x(s)1)，x(s2)，...，x(sn) The inequality of these n variables constrains the conditions, so the model (1) can be transformed equivalently to the form:
Figure FDA00028438406100000213
wherein,
Figure FDA00028438406100000214
and a isijAnd biIs a non-negative parameter that can be calculated by the model (1), i.e.
Figure FDA00028438406100000215
Figure FDA00028438406100000216
(22) The function f is constructed from the model (2) as follows: for any one set
Figure FDA00028438406100000217
Definition of
Figure FDA00028438406100000218
(x) is a monotonically increasing submodular function; the optimization problem of the model (2) is converted into a minimum weight submodel coverage problem, namely how to find a set
Figure FDA0002843840610000031
So as to make sigmaj∈Xp(sj) Minimization, where the set X must satisfy the following constraints: for all X ∈ X, there is f (X ∈ { X }) ═ f (X);
the step (3) comprises the following steps:
(31) initialization settings set
Figure FDA0002843840610000032
(32) Let I (X) be { (i | ∑ E)l∈Xail＜biAnd adding an index j, j belonging to { 1.,. n } into the set X in each iteration process through a greedy strategy, so that the index j, j belongs to { 1.,. n }, and the set X is obtained
Figure FDA0002843840610000033
Reaches a maximum until sigma is not present for all j e {1i∈I(X)min{aij，bi-∑l∈XailWhen the rate is larger than 0;
(33) obtaining a final set X after the iteration of the step (32) to obtain the optimal deployment chargerSet of monitoring points S*＝{sjI j ∈ X }, and the approximation ratio of the deployment method is 1+ ln γ, where
Figure FDA0002843840610000034
Figure FDA0002843840610000035
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