CN106875686B - Car OD extraction method based on signaling and floating car data - Google Patents

Car OD extraction method based on signaling and floating car data Download PDF

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CN106875686B
CN106875686B CN201710246602.9A CN201710246602A CN106875686B CN 106875686 B CN106875686 B CN 106875686B CN 201710246602 A CN201710246602 A CN 201710246602A CN 106875686 B CN106875686 B CN 106875686B
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CN106875686A (en
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陈艳艳
吴克寒
唐夕茹
陈兴斌
赖见辉
陈宁
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Beijing University of Technology
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0108—Measuring and analyzing of parameters relative to traffic conditions based on the source of data
    • G08G1/0112—Measuring and analyzing of parameters relative to traffic conditions based on the source of data from the vehicle, e.g. floating car data [FCD]
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0108—Measuring and analyzing of parameters relative to traffic conditions based on the source of data
    • G08G1/012—Measuring and analyzing of parameters relative to traffic conditions based on the source of data from other sources than vehicle or roadside beacons, e.g. mobile networks
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing

Abstract

The invention discloses a car OD extraction method based on signaling and floating car data, and belongs to the technical field of transportation. Aiming at the problem that the current dynamic OD estimation lacks a dynamic prior OD, the invention provides a dynamic prior OD acquisition method based on mobile phone signaling data and traffic survey data; aiming at the problems of limited coverage and insufficient constraint of observed traffic flow in the dynamic OD process, the invention provides a travel distribution characteristic constraint condition based on floating car data and provides a travel distribution characteristic calculation method under different sample amount conditions; in order to bring the road section flow constraint and the trip distribution characteristic constraint into the OD estimation process, the invention establishes a double-constraint-condition maximum entropy OD estimation model and provides a solving method, which can effectively solve the problem that the dynamic prior OD in the current dynamic OD estimation is difficult to obtain, and provides sufficient constraint conditions under the current data condition so as to realize the dynamic OD estimation of the car.

Description

Car OD extraction method based on signaling and floating car data
Technical Field
The invention belongs to the technical field of transportation, and provides a dynamic travel OD matrix for an urban car at different time periods based on mobile phone signaling data and floating car data.
Background
Obtaining car travel OD is a necessary condition for reasonably formulating traffic management strategies and traffic plans, and is mainly realized by large-scale manual investigation at present, which is time-consuming, labor-consuming and low in precision, about 3000 thousands of 5 th resident travel investigation developed in 2014 in beijing city costs time, nearly one year, the sampling rate is less than 1%, and the information which can be investigated is very limited. The OD estimation technology is an important way for obtaining the OD of the car, and the reliable prior OD and the sufficient constraint condition are necessary conditions for obtaining an accurate OD estimation result. However, at present, it is difficult to obtain a reliable dynamic prior OD, and the dynamic observed traffic in the urban road network, which is used as the constraint condition for OD estimation, is limited, so that it is difficult to obtain the dynamic OD of the car by the OD estimation technology.
Disclosure of Invention
The invention provides a car dynamic OD estimation method based on signaling data and floating car data, which mainly comprises the following steps:
the invention provides a dynamic prior OD acquisition method based on mobile phone signaling data and traffic survey data, aiming at the problem that the current dynamic OD estimation is lack of dynamic prior OD; the invention provides a travel distribution characteristic constraint condition based on floating car data and provides a travel distribution characteristic calculation method under different sample volume conditions, aiming at the problems of limited coverage and insufficient constraint of observed traffic flow in the dynamic OD process; thirdly, in order to bring the road section flow constraint and the travel distribution characteristic constraint into the OD estimation process, the invention establishes a double-constraint-condition maximum entropy OD estimation model and provides a solving method.
In order to achieve the purpose, the technical scheme adopted by the method is a car OD extraction method based on signaling and floating car data, and the method is implemented specifically as follows:
1) method for acquiring dynamic prior OD of car based on signaling data
At present, a technology for extracting a full-traffic mode travel OD based on signaling data is mature, although real-time signaling data is difficult to obtain, the dynamic prior OD of a car can be extracted by virtue of the advantages of large sample amount and time-sharing, and a basic condition is provided for dynamic OD estimation. However, the OD matrix obtained by the signaling data is usually an "all-around OD", which cannot be directly used as the car prior OD matrix.
The method realizes the prior OD extraction method of the car by improving the signaling OD. Let the full-form OD matrix of t time period extracted by the signaling data be
Figure BDA0001270844250000021
The number of trips from cell i to cell j is
Figure BDA0001270844250000022
Under ideal conditions, if the car traveling proportion from cell i to cell j in the corresponding time interval can be obtained
Figure BDA0001270844250000023
The number of cars traveling from cell i to cell j in the period
Figure BDA0001270844250000024
Comprises the following steps:
Figure BDA0001270844250000025
the car travel OD matrix in the time period is as follows:
Figure BDA0001270844250000026
wherein C is(t)For car travel proportion matrices between traffic cells, i.e.
Figure BDA0001270844250000027
However, when the proportion of travel modes is actually investigated, only the starting cell of a trip is considered, the destination of the trip is not considered, and investigation is performed in few time intervals, so that the travel proportions of cars in all trips from the i cell to other cells are all ciAt this time, only can be right
Figure BDA0001270844250000031
Performing rough estimation:
Figure BDA0001270844250000032
then, the estimation result of the car travel OD matrix in the time period is:
Figure BDA0001270844250000033
wherein C is a car travel proportion matrix between any two cells which do not distinguish time intervals. Obviously, the accuracy of the obtained car OD at each time interval is limited, if historical flow data of a part of road sections can be obtained, the accuracy of the car OD at each time interval can be further improved by an OD estimation method, and finally, a reliable dynamic prior OD of the car is obtained based on signaling data, traffic mode survey data and historical flow data.
2) Travel distribution characteristic constraint condition extraction based on floating car data
At present, the constraint conditions which can be used when urban road network dynamic OD estimation is carried out are dynamic flow observation data, however, the constraint conditions are less when OD estimation is carried out by taking road section flow as the constraint conditions due to the fact that the existing road flow observation equipment is limited, and therefore the accuracy of the whole road network dynamic OD estimation is low. The method provides a car travel distribution characteristic concept, and brings the concept into an OD estimation process as a concurrent constraint condition outside flow constraint so as to improve OD estimation precision.
For any cell, the proportion distribution of cars departing from the cell to different cells is called as the car travel distribution characteristic of the cell. Floating cars in a road network, namely passenger taxis, are regarded as partial samples of the cars in the road network, and the trip distribution characteristics of the cars can be effectively reflected, so that the trip distribution characteristics of the cars are extracted by using the data of the floating cars:
Figure BDA0001270844250000041
wherein, PijThe traffic of the cars from the i cell to the j cell accounts for all the small cars from the i cellThe proportion of the traffic volume of the vehicle,
Figure BDA0001270844250000044
is the proportion of the floating car traffic volume from cell i to cell j to all the floating car traffic volume from cell i, TijCar traffic volume from cell i to cell j, FijIs the floating car traffic from cell i to cell j. { Pi*And the j is a travel distribution characteristic matrix of the i cell.
Due to the limited data sample size of the floating cars, the floating car flow F between the individual cells appearsijIn the case of 0, the car travel distribution ratio between the cells obtained from the floating car data is 0, which may not be in accordance with the objective case. To avoid this, equation 1 is modified to describe for a certain cell i only i cells to F with floating car dataijTravel distribution of multiple destination cells > 0:
Figure BDA0001270844250000042
wherein, JijFor all cell sets that satisfy the following condition: i float traffic flow F from cell to these cellsij>0；P′ijIs i cell to the JijThe car traveling distribution proportion of j cells in the cell set;
Figure BDA0001270844250000043
is i cell to the JijAnd the distribution proportion of the floating vehicle traveling of the j cells in the cell set. { P'i*And the improved traveling distribution characteristic matrix of the i cell is obtained. Under the condition that the sample size of the floating car is sufficient, the travel distribution characteristic extraction based on the floating car data can be completed by the formula.
3) Travel distribution characteristic estimation method under condition of insufficient sample volume
The method provides a sample quantity demand calculation method when the car travel distribution characteristics are extracted based on floating car data. For a certain OD pair ij, any passenger floating car departing from the cell i is regarded as a bernoulli test, and the test results include two types: the floating car departs from the cell i to the cell j, and the floating car departs from the cell i to the cell j. Because the absolute quantity of the floating car sample is large, the sample size analysis is carried out by combining the normal distribution property, and the finally obtained sample size requirement is as follows:
Figure BDA0001270844250000051
wherein the content of the first and second substances,
Figure BDA0001270844250000052
in order to calculate the total sample size of the floating cars needed by the i cell when the cars travel distribution characteristics among ij are characterized,
Figure BDA0001270844250000053
for the distribution proportion, delta, of the travel between ij calculated by using the data of the existing floating carijFor the error tolerance range, (1- α) is the confidence level, it can be seen that the higher the confidence level required, the smaller the error range, and the smaller the travel distribution ratio, the larger the sample size required for the starting cell i.
Under the condition that the sample size meets the requirement, calculating the trip distribution characteristics of the car by directly adopting a formula 2; when the sample size is insufficient, a travel distribution characteristic estimation method based on a clustering algorithm is provided. The basic principle is to gather to a specific d cell by a cell clustering method
Figure BDA0001270844250000059
And (4) forming an abstract fusion cell k by the clustered cells with high approximation possibility and insufficient sample size, and taking the sample set of the cells as the sample of the fusion cell k. Obviously, the samples of the merging cell k will be significantly enlarged compared to the individual constituent cells, which is more likely to meet the sample size requirement. If the sample size of the cell meets the requirement, completing the cell fusion by the sample set
Figure BDA0001270844250000054
And assigning the calculation results to the respective constituent cells, the respective constituentsThe cell will eventually get the same
Figure BDA0001270844250000055
And (6) estimating the value. When clustering is performed, it is difficult to perform clustering based on the existing sample because the existing sample amount is insufficient
Figure BDA0001270844250000056
Similarity determination based on a large amount of historical data
Figure BDA0001270844250000057
Implementing the current time period
Figure BDA0001270844250000058
The judgment of the potential similarity is that the similarity judgment standard among the cells in clustering is
Figure BDA0001270844250000061
Clustering is performed using a variety of clustering algorithms.
After clustering is completed, for the fused cells meeting the sample requirements, travel distribution characteristic estimation of all the constituent cells can be completed by using the fused cells, and for the cells which still cannot meet the sample requirements, travel distribution characteristic estimation is performed by using historical synchronization data.
4) Flow and travel distribution characteristic dual-constraint OD estimation model
After the travel distribution characteristics of the car are obtained based on the floating car data, the travel distribution characteristics and the road section flow are used as coexistence constraints, and the estimation of the dynamic OD of the car can be realized by combining the dynamic prior OD. An OD estimation method under double constraints is constructed based on a maximum entropy thought model.
Figure BDA0001270844250000062
Figure BDA0001270844250000063
Figure BDA0001270844250000064
Figure BDA0001270844250000065
Figure BDA0001270844250000066
Figure BDA0001270844250000067
Wherein, VaRepresenting observed traffic flow on road segment a;
Figure BDA0001270844250000068
is the traffic volume T between OD pair ijijThe proportion of the route sections a that are routed through,
Figure BDA0001270844250000069
usually obtained by traffic distribution models, as a known condition in OD estimation; and n is the total number of the traffic cells. J. the design is a squareiFor all cell sets that satisfy the following condition: current time period, i cell to these floating traffic flow Fij>0。P′ijIs the cell to the JijThe car traffic volume of the cell J in the cell set occupies the cell to JijThe proportion of the traffic volume of all the cells in the community. { tijThe is the prior OD matrix of the current epoch.
The OD estimation model can be expanded by a Lagrange multiplier method to obtain nonlinear equations with the same number as the unknown quantity, and then the solution is realized.
The solving method of the nonlinear equation is realized by adopting a genetic algorithm or an ant colony algorithm and the like.
The invention has the following beneficial effects:
the basic data of the invention is derived from signaling data, floating car data and road detector data which are widely used at present, the problem that the dynamic prior OD is difficult to obtain in the current dynamic OD estimation can be effectively solved, and sufficient constraint conditions are provided under the current data condition so as to realize the dynamic OD estimation of the car.
Drawings
FIG. 1 shows the process of the present invention.
Fig. 2 shows an omni-directional OD extraction result based on signaling data.
FIG. 3 shows cells heading for 50108 cell
Figure BDA0001270844250000071
And (5) obtaining a final result.
Detailed Description
The present invention will be described in detail with reference to fig. 1.
The whole process is as shown in figure 1: the calculation flow of the method is shown. The method comprises the following three contents: obtaining a car dynamic prior OD based on signaling data, obtaining travel distribution characteristics based on floating car data, and estimating the OD under double constraints.
The OD estimation of a car from one hour to another within 6:00 to 22:00 of a working day in 2015 of Beijing is taken as an example for explanation.
1. Acquisition of dynamic prior OD of car
(1) Dynamic omni-directional OD acquisition
Firstly, the original omnidirectional travel OD extraction in the analysis period is completed by the signaling data, and the processes such as cleaning and sample expansion are performed, and then the OD splitting is performed at intervals of 1 hour to obtain the omnidirectional travel OD of each hour, as shown in fig. 2.
(2) Acquisition of dynamic prior OD of car
On the basis of the full formula OD, travel mode survey data and flow survey data are further combined to extract the dynamic prior OD of the car. In the embodiment, the fourth time traffic survey data in Beijing is taken as an example for dividing, manual survey data of large-scale traffic flow in Beijing in 2015 is taken as flow survey data, calibration of prior OD is completed by adopting a static maximum entropy OD estimation method, and the prior OD of the car in each hour between 6:00 and 22:00 is obtained.
2. Car trip distribution feature extraction based on floating car
(1) OD pick-up of passenger taxi
The original data of the floating car records information such as the position, the passenger carrying state, the longitude and latitude, the time and the like of the car, as shown in table 1.
TABLE 1 original floating car data content example Table
Figure BDA0001270844250000081
Travel event information of the passenger-carrying taxi can be processed by the original data of the floating taxi, wherein the travel event information mainly comprises information such as travel starting and stopping positions, time and the like, and is shown in table 2.
Table 2 example of extraction result of information of passenger trip event on floating car
Figure BDA0001270844250000082
Figure BDA0001270844250000091
After the passenger taxi trip starting and ending point is matched with the traffic district, the passenger taxi trip OD matrix of each hour can be obtained, and further the passenger taxi trip OD matrix can be used for proposing the car trip distribution characteristics.
(2) Car trip distribution feature extraction
When the travel distribution characteristic extraction is carried out on the basis of the floating car data, the sample size satisfaction test is carried out, and in the example, the sample satisfaction test is carried out by taking an 80% confidence level and a 25% error allowable range as examples. Through inspection, the satisfaction rate of the floating car samples in all the cells in 16 time periods in the whole day is only 8.4%, so that a clustering algorithm is adopted to carry out travel distribution characteristic estimation.
In the embodiment, a neighbor propagation clustering algorithm (AP algorithm) is adopted for cell clustering. And (2) adding 17: taking a certain cell (No. 50108) as a destination cell in a time period of 00-18: 00 as an example, 298 cells are shared in the time period before clustering (shown in figure 3) until the sample size of the cell is insufficient, 75% of the clustered cells meet the sample size requirement, and the rest 25% of the clustered cells are estimated by using historical synchronization values. Finally, the characteristics of the travel distribution from each cell to the 50108 cell are shown in fig. 3.
After the method is adopted to calculate the car travel distribution characteristics among the ODs in 16 time periods all day, the sample satisfaction rate reaches 76.1%, the improvement effect is obvious compared with that of 8.4% before clustering, and for the part of the ODs with the sample amount still insufficient in the current time period, the historical synchronization value is adopted to estimate, so that the car travel distribution characteristic extraction based on floating car data is completed.
3. Dynamic OD estimation for cars
By adopting the dynamic prior OD in each hour and the car travel distribution proportion obtained by the above contents, OD estimation can be completed by using a formula 4 by further combining the data of the flow detector, and a genetic algorithm is adopted in a solving algorithm. In this example, hourly flow data obtained by observation with a microwave detector of the fast path in Beijing on the day of analysis is used as a flow constraint condition.
Obtaining the following results after OD estimation and traffic distribution: the total quantity of cars traveling in Beijing on the analysis day is 489 thousands of times, and the average distance of cars traveling is 36.6 kilometers. Verifying an OD estimation result according to the fitting degree of a model calculation result and an observation result of the road section flow, and displaying a verification result: the average error of the flow of the expressway sections in each hour is 8.6 percent, the average error of the flow of the secondary main road and the main road is 14.3 percent, the verification result is ideal, the OD estimation result is accurate, and the dynamic OD estimation of the car under the existing data condition is realized.
Finally, it should be noted that: the above examples are only intended to illustrate the invention and do not limit the technical solutions described in the present invention; thus, while the present invention has been described in detail with reference to the foregoing examples, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted; all such modifications and variations are intended to be included herein within the scope of this disclosure and the appended claims.

Claims (2)

1. A car OD extraction method based on signaling and floating car data is characterized in that: the specific implementation content of the method is as follows:
1) method for acquiring dynamic prior OD of car based on signaling data
The prior OD extraction method of the car is realized by improving the signaling OD; let the full-form OD matrix of t time period extracted by the signaling data be
Figure FDA0002401416300000011
The number of trips from cell i to cell j is
Figure FDA0002401416300000012
Under ideal conditions, if the car traveling proportion from cell i to cell j in the corresponding time interval can be obtained
Figure FDA0002401416300000013
The number of cars traveling from cell i to cell j in the period
Figure FDA0002401416300000014
Comprises the following steps:
Figure FDA0002401416300000015
the car travel OD matrix in the time period is as follows:
Figure FDA0002401416300000016
wherein C is(t)For car travel proportion matrices between traffic cells, i.e.
Figure FDA0002401416300000017
All trips from the i cell to other cells have the trip proportion of ciAt this time, only can be right
Figure FDA0002401416300000018
Performing rough estimation:
Figure FDA0002401416300000019
then, the estimation result of the car travel OD matrix in the time period is:
Figure FDA00024014163000000110
wherein C is a car travel proportion matrix between any two cells which do not distinguish time periods;
2) travel distribution characteristic constraint condition extraction based on floating car data
The travel distribution characteristics of the cars are taken as coexistence constraint conditions outside flow constraint and are brought into the OD estimation process to improve the OD estimation precision;
for any cell, the proportion distribution forming condition of cars from the cell to different cells is called as the car traveling distribution characteristic of the cell; floating cars in a road network, namely passenger taxis, are regarded as partial samples of cars in the road network, and the trip distribution characteristics can effectively reflect the trip distribution characteristics of the cars, so that the trip distribution characteristics of the cars are extracted by using the data of the floating cars:
Figure FDA0002401416300000021
wherein, PijIs the proportion of the traffic volume of the cars from cell i to cell j to the traffic volume of all the cars from cell i,
Figure FDA0002401416300000022
is the proportion of the floating car traffic volume from cell i to cell j to all the floating car traffic volume from cell i, TijCar traffic volume from cell i to cell j, FijIs the floating car traffic volume from cell i to cell j; { Pi*The method comprises the steps of (1) taking a travel distribution characteristic matrix of an i cell as a reference;
due to the limited data sample size of the floating car, floating between individual cells occursBullet train flow FijIf the data is 0, the car travel distribution proportion among the cells obtained by the floating car data is 0, which may not be in accordance with the objective situation; to avoid this, equation 1 is modified to describe for a certain cell i only i cells to F with floating car dataijTravel distribution of multiple destination cells > 0:
Figure FDA0002401416300000023
wherein, JijFor all cell sets that satisfy the following condition: i float traffic flow F from cell to these cellsij>0；P′ijIs i cell to the JijThe car traveling distribution proportion of j cells in the cell set;
Figure FDA0002401416300000024
is i cell to the JijThe distribution proportion of the floating car trips of j cells in the cell set; { P'i*The improved trip distribution characteristic matrix of the i cell is obtained; under the condition that the sample amount of the floating car is sufficient, the travel distribution characteristic extraction based on the floating car data can be completed by a formula 2;
3) travel distribution characteristic estimation method under condition of insufficient sample volume
The method provides a sample quantity demand calculation method when the car travel distribution characteristics are extracted based on floating car data; for a certain OD pair ij, any passenger floating car departing from the cell i is regarded as a bernoulli test, and the test results include two types: the floating car departs from the cell i to the cell j, and the floating car departs from the cell i to the cell j; because the absolute quantity of the floating car sample is large, the sample size analysis is carried out by combining the normal distribution property, and the finally obtained sample size requirement is as follows:
Figure FDA0002401416300000031
wherein the content of the first and second substances,
Figure FDA0002401416300000032
in order to calculate the total sample size of the floating cars needed by the i cell when the cars travel distribution characteristics among ij are characterized,
Figure FDA0002401416300000033
is i cell to the JijDistribution proportion, delta, of floating car trips of j cells in cell setijThe higher the required confidence level, the smaller the error range and the smaller the travel distribution proportion, the larger the sample size required by the starting point cell i;
under the condition that the sample size meets the requirement, calculating the trip distribution characteristics of the car by directly adopting a formula 2; when the sample size is insufficient, a travel distribution characteristic estimation method based on a clustering algorithm is adopted; the basic principle is to gather to a specific d cell by a cell clustering method
Figure FDA0002401416300000034
The method comprises the following steps that (1) cells with high approximation possibility and insufficient sample size form an abstract fusion cell k after clustering, and a sample set of the cells is used as a sample of the fusion cell k; obviously, compared with each component cell, the samples of the fusion cell k will be obviously expanded, and the probability of meeting the sample size requirement is higher; if the sample size of the cell meets the requirement, completing the cell fusion by the sample set
Figure FDA0002401416300000041
And assigning the calculation results to the respective constituent cells, which will eventually obtain the same
Figure FDA0002401416300000042
An estimated value; when clustering is performed, it is difficult to perform clustering based on the existing sample because the existing sample amount is insufficient
Figure FDA0002401416300000043
Determination of similarity based on a large numberHistorical data
Figure FDA0002401416300000044
Implementing the current time period
Figure FDA0002401416300000045
The judgment of the potential similarity is that the similarity judgment standard among the cells in clustering is
Figure FDA0002401416300000046
Clustering is implemented by adopting a clustering algorithm;
after clustering is completed, for a fusion cell meeting the sample requirement, travel distribution characteristic estimation of each component cell is completed by using the fusion cell, and for a cell which still cannot meet the sample requirement, travel distribution characteristic estimation is performed by using historical synchronization data;
4) flow and travel distribution characteristic dual-constraint OD estimation model
After the travel distribution characteristics of the car are obtained based on the floating car data, the travel distribution characteristics and the road section flow are used as coexistence constraints, and the estimation of the dynamic OD of the car can be realized by combining the dynamic prior OD; an OD estimation method under double constraints is constructed based on a maximum entropy thought model;
Figure FDA0002401416300000047
wherein, VaRepresenting observed traffic flow on road segment a;
Figure FDA0002401416300000048
is the traffic volume T between OD pair ijijThe proportion of the route sections a that are routed through,
Figure FDA0002401416300000049
obtained by the traffic distribution model as a known condition in the OD estimation; n is the total number of the traffic cells; j. the design is a squareiFor all cell sets that satisfy the following condition: current time period, i cell to these floating traffic flowsFij>0；P′ijIs the cell to the JijThe car traffic volume of the cell J in the cell set occupies the cell to JijThe proportion of the traffic volume of all the cells in the community; { tijThe prior OD matrix of the current time interval is used as the matrix;
and the OD estimation model is expanded by a Lagrange multiplier method to obtain nonlinear equations with the same number as the unknown quantity, so as to realize solution.
2. The car OD extraction method based on signaling and floating car data as claimed in claim 1, wherein: the solving method of the nonlinear equation is realized by adopting a genetic algorithm or an ant colony algorithm.
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