CN113947889B - Pedestrian crossing control method for automatic driving intersection - Google Patents
Pedestrian crossing control method for automatic driving intersection Download PDFInfo
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Abstract
The invention discloses a control method for pedestrian crossing at an automatic driving intersection, which determines the weight of the flowing vehicles and pedestrians according to the traffic demand of each flowing vehicle and the pedestrian crossing demand, takes the sum of the product of each flowing weight and the flowing flow as a maximum objective function, takes the time proportion of allowing the vehicles to pass and the state of a pedestrian signal lamp as decision variables, sets constraint conditions according to traffic capacity limit, green light time and the like, and establishes an intersection control model. The method disclosed by the invention is mainly used for distributing time for passing vehicles and pedestrians according to different street crossing requirements of the vehicles and the pedestrians at the intersection in an automatic driving scene, optimizing the space-time utilization rate of the intersection, and improving the street crossing efficiency of the pedestrians while ensuring that the pedestrians can safely cross the street.
Description
Technical Field
The invention belongs to the field of intelligent traffic control, and relates to the technical field of traffic control of urban intersections for pedestrian crossing under an automatic driving scene.
Background
The automatic driving technology is a trend of future traffic development, and an intersection control method for automatic driving vehicles is a current research hotspot, but is also a difficult point, particularly considering the situations of automatic driving vehicle passing and pedestrian crossing. Many researches show that under the automatic driving environment, traffic control objects face vehicle individuals or fleets, collision among vehicles is avoided, vehicles can pass through intersections in a mutually-coordinated and interspersed mode without signal control, but most researches do not consider the problem of pedestrian crossing in the mode. If the pedestrians still pass according to the existing no-signal intersection passing rule, a large number of random conflict points exist in the passing track of the automatic driving vehicles and the passing track of the pedestrians, so that great potential safety hazards exist in traffic operation of the intersection. Therefore, how to make pedestrians safely and efficiently pass through the intersection by using a traffic control means in an automatic driving scene is a problem to be solved by the patent.
Therefore, the invention provides a pedestrian crossing control method in an automatic driving scene, which determines the weight of each flow to the pedestrians and the vehicles according to the crossing demand of the pedestrians and the traffic demand of the vehicles, provides relatively long traffic time for the flow with higher weight, namely the flow with higher demand at the intersection, and improves the utilization rate of the intersection. How to calculate the demand of pedestrian and vehicle dynamically, for vehicle and pedestrian distribution transit time, avoid between the vehicle, the conflict in the inside of crossing between vehicle and the pedestrian that crosses the street, and make full use of the space-time resource at crossing is the problem that this patent was mainly solved.
Disclosure of Invention
The technical problem is as follows: aiming at the defects of the existing street crossing research on the pedestrians at the automatic driving intersection, the invention aims to provide a street crossing method for the pedestrians at the automatic driving intersection, simultaneously considers the passing safety and efficiency of the pedestrians and the vehicles at the intersection, and coordinates the passing of the vehicles and the pedestrians by establishing a traffic control model.
The technical scheme is as follows: in order to solve the technical problem, the method of the invention comprises the following steps:
step 1: collecting basic physical parameters of the intersection, including the size of the intersection, the number of lanes and the width of lanes; dividing the study period into equidistant time windows, wherein the length of each time window is T; inputting current traffic related parameters, including: using i to represent the inlet direction of the intersection, using j to represent the outlet direction, wherein i belongs to { E, S, W, N }, j belongs to { E, S, W, N }, and E, S, W, N respectively represent east, south, west and north; the vehicle is driven from the inlet direction of the i to the outlet direction of the j by i → j; with q of i→j (t) represents the traffic demand of the vehicle flow direction i → j in the t time window, and the unit is vehicle; by d i→j (t) the arrival number of the vehicles driving to the exit direction j from the entrance direction of the intersection i in the t-th time window is represented by the unit of a vehicle; by c i→j The lane traffic capacity of the vehicle from the inlet i to the outlet j is shown, and the unit is vehicle/hour; the position of the pedestrian arriving at the intersection is represented by a, the target position of the pedestrian crossing the street is represented by B, a belongs to { A, B, C, D }, B belongs to { A, B, C, D }, A, B, C, D respectively represent the northwest corner, southwest corner, southeast corner and northeast corner of the intersectionAn angle; the crosswalk is denoted by k; by using
Representing the average arrival rate of the pedestrians walking from the intersection position point a to the intersection position point b; with C k Representing the traffic capacity of the pedestrian crossing k;
and 2, step: the method dynamically predicts the traffic demand of each entrance lane and the pedestrian demand in each direction at the intersection, determines the weight of each flow direction according to the vehicle demand and the pedestrian street crossing demand, and establishes the constraint conditions of traffic capacity and green light time, and comprises the following steps:
step 21: the t +1 time window is the traffic demand q of the intersection driving from the inlet direction i to the outlet direction j i→j The calculation of (t +1) is shown in formula (1); at the t-th time window, the actual traffic y of the vehicle from the i entrance to the j exit i→j (t) satisfies the constraint of equation (2):
q i→j (t+1)＝q i→j (t)+d i→j (t)-y i→j (t) (1)
y i→j (t)＝min{c i→j ·s i→j (t)，q i→j (t)} (2)
in the formula (1), y i→j (t) is the t-th time window, the actual traffic volume in the unit of vehicle, which travels from the entrance direction i to the exit direction j i→j (t) the traffic demand of the t-th time window, wherein the intersection drives from the inlet direction i to the outlet direction j; in the formula (2), s i→j (t) is the t-th time window, and the time proportion of the vehicle which is driven from the inlet i to the outlet j and allowed to pass is calculated;
in the t +1 th time window, for the pedestrians with the street crossing requirement from the position point a to the position point b, the time from the last green light release to the red light in the current time period uses tau a→b (t +1) in seconds, as shown in equation (3);
in the formula (3), the pedestrian signal from the position point a to the position point bLamp state S a→b (t) represents, S a→b (t) — 1 denotes that the pedestrian signal light of the position point a → b is green, S a→b (t) ═ 0 indicates that the pedestrian signal lamp of the position point a → b is a red lamp, and the pedestrian signal lamp in each time window can only be a green lamp or a red lamp; q a→b (t) represents the t-th time window, the pedestrian crossing street demand from the position point a to the position point b;
pedestrian demand D at t-th time window, position point a → b a→b (t) is equal to the pedestrian arrival rate
The time tau of crossing the street with the pedestrian a→b (t) as shown in equation (4):
the pedestrian crossing from the position point a to the position point b adopts a secondary crossing mode and is divided into two stages, wherein the pedestrian crossing number in the first stage meets the constraint of a formula (5):
Y a→b，1 (t)＝min{C k ·S a→b ， 1 (t)，Q a→b，1 (t)} (5)
in the formula (5), Y a→b，1 (t) the actual number of pedestrians crossing the first stage from the intersection position point a to the intersection position point b in the t-th time window; s a→b，1 (t) the pedestrian signal lamp state of the first stage from the position point a to the position point b in the t-th time window, S a→b，1 (t) < 1 indicates that the pedestrian signal lamp is green, S a→b，1 (t) ═ 0 indicates that the pedestrian signal lamp is red; qa →b，1 (t) the demanded quantity of the pedestrians crossing the street in the first stage from the position point a to the position point b in the t-th time window;
the demanded quantity Q of pedestrians crossing the street in the first stage from the position point a to the position point b in the t +1 th time window a→b，1 (t +1) is represented by formula (6):
Q a→b，1 (t+1)＝Q a→b，1 (t)+D a→b (t)-Y a→b，1 (t) (6)
the second stage is the pedestrian crossing number Y a→b，2 (t) satisfies the constraint of equation (7):
Y a→b，2 (t)＝min{C k ·S a→b，2 (t)，Q a→b，2 (t)} (7)
in the formula (7), Y a→b，2 (t) the actual number of pedestrians crossing the second stage from the intersection position point a to the intersection position point b in the t-th time window; s a→b，2 (t) the second stage pedestrian signal lamp state from position a to position b in the tth time window, S a→b，2 (t) '1' indicates that the pedestrian signal lamp is green, S a→b，2 (t) ═ 0 indicates that the pedestrian signal light is red; q a→b，2 (t) the demanded quantity of pedestrians crossing the street in the second stage from the position point a to the position point b in the t-th time window;
the demanded quantity Q of pedestrians crossing the street in the second stage from the t +1 th time window to the position point a a→ b ，2 (t +1) is represented by formula (8):
Q a→b，2 (t+1)＝Q a→b，1 (t)+Y a→b，1 (t)-Y a→b，2 (t) (8)
step 22: setting the vehicle weight w for the tth time window i→j (t) is equal to the traffic demand multiplied by a weighting factor, and the flow direction with a larger traffic demand will get more right of way, as shown in equation (9):
w i→j (t)＝λq i→j (t) (9)
in formula (9), λ is a weight coefficient;
the pedestrian crossing weight setting needs to consider the pedestrians at two ends of the pedestrian crossing, and the pedestrian crossing weight of the kth pedestrian crossing in the tth time window is W k (t) as shown in equation (10);
W k (t)＝(1-λ)(Q a→b，1 (t)+Q b→a，2 (t)) (10)
step 23: in order to ensure that the space-time resources at the intersection can be utilized to the maximum extent, the number y of vehicles allowed to pass through the t-th time period flowing to i → j is limited i→j (t) so that it does not exceed the current vehicle demands on the approach laneQuantity q i→j (t), satisfying the constraint of formula (11); when the pedestrian signal lamp is green and the vehicle running track is crossed with the pedestrian crossing, the flow direction does not allow the vehicle to pass; when the pedestrian signal lamp is green and the vehicle running track does not conflict with the pedestrian crosswalk, the actual traffic flow of the flow direction is limited to the traffic capacity of the pedestrian crosswalk, and the constraint of a formula (12) is met;
0≤y i→j (t)≤q i→j (t) (11)
in the formula (11), the reaction mixture,
indicating that the vehicle travel locus i → j intersects with the crosswalk k,
it means that there is no conflict point between the vehicle travel path i → j and the crosswalk k.
In order to avoid conflict among motor vehicles arriving at an intersection at the same time, when the vehicles are controlled to release, the sum of the allowed time proportion of the conflict phases in unit time cannot exceed 1, and the conflict-free phases can be released together at the moment; grouping the conflicting phases into a set, r 1 ，r 2 ，r 3 ，r 4 Representing four sets containing conflicting phases; E. w, S, N, the east, west, south and north directions are shown in formulas (13) - (16);
r 1 ＝{N→E,S→N,E→S,W→E} (13)
r 2 ＝{N→E,S→N,W→N,E→W} (14)
r 3 ＝{E→S,W→E,S→W,N→S} (15)
r 4 ＝{S→W,N→S,W→N,E→W} (16)
the sum of the time proportions of flows within the same conflict set allowed to run per unit time should not exceed 100%, while flows not within the same conflict set can be allowed to pass together, satisfying the constraints of equations (17) - (20).
And 3, step 3: according to the weight of pedestrian crossing and vehicle passing, optimizing and obtaining a timing scheme of each vehicle and pedestrian crossing by taking the sum of the product of each flow direction weight and the flow rate of the flow direction at the intersection as a target, wherein the target function is shown as a formula (21);
max∑ i→j w i→j (t)·y i→j (t)+∑ k W k (t)·S k (t)·C k (21)
has the advantages that: compared with the prior art, the invention has the following advantages:
the pedestrian crossing demand can be obtained by multiplying the red light time of the pedestrian signal lamp by the pedestrian arrival rate in the automatic driving scene, the weight of the vehicles and the pedestrians in each flow direction is determined according to the vehicle demand and the pedestrian crossing demand, the maximum sum of the product of the weight of the vehicles and the pedestrians in each flow direction at the intersection and the flow of the vehicles and the pedestrians in each flow direction at the intersection is the target, space-time resources can be distributed according to the real-time traffic demand of the intersection, and the intersection traffic benefit can be improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of a crossroad crossing for pedestrians to cross the street;
FIG. 3 is a schematic diagram of a phase structure;
FIG. 4 is a cross-walk numbering diagram.
Detailed Description
The invention will be further explained below with reference to fig. 1 to 4 and examples, without the embodiments of the invention being restricted thereto. The embodiments of the present invention are not limited to the embodiments described above, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and they are included in the scope of the present invention.
A pedestrian crossing control method for an automatic driving intersection comprises the following steps:
step 1: acquiring basic physical parameters of the intersection, including the size, the number and the lane width of the intersection, and inputting current traffic related parameters, including current traffic demand of each entrance lane of the intersection, pedestrian arrival rates of four corners of the intersection and the like;
step 2: dynamically predicting traffic demand of each entrance road and pedestrian demand in each direction of the intersection, determining the weight of each flow direction vehicle and pedestrian according to the vehicle demand and the pedestrian street crossing demand, and establishing constraint conditions of traffic capacity and green light time;
and step 3: and (4) considering the secondary street crossing of the pedestrian at the intersection, and optimizing to obtain a pedestrian street crossing traffic control scheme by taking the maximum sum of the product of the weight of each flow-direction vehicle and pedestrian at the intersection and the flow rate of the flow-direction vehicle and pedestrian as an objective.
The information collected in the step 1 is used as the input of a control model, and basic information of an intersection is collected, in the embodiment, the intersection is an orthogonal crossroad, six bidirectional lanes are arranged, three lanes are respectively arranged at an inlet and an outlet in each direction, the lanes are respectively left-turning, straight-going and right-turning, and the lane width is 3.0 meters; the pedestrian crosswalk is 18.0 meters in length and 5.0 meters in width; dividing eight time windows by taking 30 seconds as a time window; the current traffic related parameters are input, and the current vehicle traffic demand of each entrance lane at the intersection is shown in table 1:
table 1 present vehicle traffic demand in the embodiment
| Inlet direction → outlet direction | East → south | East → west | East → North | West → north | West → east | West → |
| Vehicle demand | ||||||
| 5 | 3 | 4 | 2 | 4 | 3 | |
| Inlet direction → outlet direction | South → west | South → north | South → east | North → east | North → south | North → |
| Vehicle demand | ||||||
| 4 | 4 | 3 | 6 | 2 | 4 |
Step 21, dynamically predicting traffic demand of vehicles at each entrance road of the intersection according to the formulas (1) to (2), and dynamically predicting pedestrian crossing demand of each position point and the safety island according to the formulas (3) to (8); in the example, pedestrian arrival rates at each location point are shown in table 2 in units of people/minute:
table 2 pedestrian arrival rate table in the embodiment
| Start point → end point | A→B | A→D | A→C | B→A | B→D | B→C |
| |
6 | 4 | 4 | 2 | 2 | 2 |
| Start point → end point | D→A | D→B | D→C | C→A | C→B | C→D |
| |
6 | 2 | 6 | 2 | 6 | 2 |
Step 22, calculating the weight of each vehicle and pedestrian flow direction according to the demand quantity obtained in step 21; step 23 is to set constraints including traffic capacity constraints, and collision avoidance constraints. According to the constraint equations (10) - (20) in step 23 and the objective function equation (21) in step 3, the number of vehicles and pedestrians allowed to pass through the intersection in each time window can be calculated according to the crosswalk number diagram in fig. 4, as shown in tables 3 and 4.
Table 3 actual traffic volume of each flow in the example
Table 4 shows the number of pedestrians crossing the street in each time window
The embodiments of the present invention are not limited to the embodiments described above, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and they are included in the scope of the present invention.
Claims (2)
1. A pedestrian crossing control method at an automatic driving intersection is characterized by comprising the following steps:
step 1: acquiring basic physical parameters of the intersection, including the size of the intersection, the number of lanes and the lane width, and inputting current traffic related parameters, including current traffic demand, pedestrian arrival rates at four corners of the intersection and the like;
step 2: dynamically predicting traffic demand of each entrance road and pedestrian demand in each direction of the intersection, determining the weight of each flow direction vehicle and pedestrian according to the traffic demand and the pedestrian street crossing demand, and establishing constraint conditions of traffic capacity and green light time;
and step 3: considering the secondary street crossing of the pedestrian at the intersection, optimizing to obtain a pedestrian street crossing traffic control scheme by taking the maximum target of the sum of the product of the weight of each flow-direction vehicle and pedestrian at the intersection and the flow rate of the flow-direction vehicle and pedestrian;
the step 1 of collecting basic physical parameters of the intersection, including the size of the intersection, the number of lanes and the lane width, inputting current traffic related parameters, including current traffic demand and pedestrian arrival rates at four corners of the intersection, comprises the following steps:
step 11: collecting basic physical parameters of the intersection, including the size of the intersection, the number of lanes and the width of lanes; dividing the study period into equidistant time windows, wherein the length of each time window is T; inputting current traffic related parameters, including: using i to represent the inlet direction of the intersection, using j to represent the outlet direction, wherein i belongs to { E, S, W, N }, j belongs to { E, S, W, N }, and E, S, W, N respectively represent east, south, west and north; the vehicle is driven from the inlet direction of the i to the outlet direction of the j by i → j; with q i→j (t) representsthe traffic demand of the vehicle flow direction i → j of t time windows is in units of vehicles; by d i→j (t) the arrival number of the vehicles driving to the exit direction j from the entrance direction of the intersection i in the t-th time window is represented by the unit of a vehicle; by c i→j The lane traffic capacity of the vehicle from the inlet i to the outlet j is shown, and the unit is vehicle/hour; the method comprises the following steps of using a to represent the position of a pedestrian arriving at an intersection, using B to represent the target position of the pedestrian crossing the street, wherein a belongs to { A, B, C, D }, B belongs to { A, B, C, D }, and A, B, C, D respectively represent the northwest corner, the southwest corner, the southeast corner and the northeast corner of the intersection; the crosswalk is denoted by k; by using
Representing the average arrival rate of the pedestrians walking from the intersection position point a to the intersection position point b; with C k Representing the traffic capacity of the pedestrian crossing k;
step 2, dynamically predicting traffic demand and pedestrian demand in each direction of each entrance way of the intersection, determining the weight of each flow direction vehicle and pedestrian according to the traffic demand and the pedestrian crossing demand, and establishing constraint conditions of traffic capacity and green light time, comprising the following steps:
step 21: the t +1 time window is the traffic demand q of the intersection driving from the inlet direction i to the outlet direction j i→j The calculation of (t +1) is shown in formula (1); at the t-th time window, the actual traffic y of the vehicle from the i entrance to the j exit i→j (t) satisfies the constraint of equation (2):
q i→j (t+1)＝q i→j (t)+d i→j (t)-y i→j (t) (1)
y i→j (t)＝min{c i→j ·s i→j (t),q i→j (t)} (2)
in the formula (1), y i→j (t) is the t-th time window, the actual traffic volume in the unit of vehicle, which travels from the entrance direction i to the exit direction j i→j (t) the traffic demand of the t-th time window, wherein the intersection drives from the inlet direction i to the outlet direction j; in the formula (2), s i→j (t) is the t-th time window, allowing passage of vehicles from entrance i to exit jThe time proportion;
in the t +1 th time window, for pedestrians with street crossing requirements from the position point a to the position point b, the time from the last green light release to the red light in the current time period is tau a→b (t +1) in seconds, as shown in equation (3);
in formula (3), T represents the length of the unit time window; s for pedestrian signal lamp state from position point a to position point b a→b (t) represents, S a→b (t) — 1 denotes that the pedestrian signal light of the position point a → b is green, S a→b (t) ═ 0 indicates that the pedestrian signal lamp of the position point a → b is a red lamp, and the pedestrian signal lamp in each time window can only be a green lamp or a red lamp; q a→b (t) represents the t-th time window, the pedestrian crossing street demand from the position point a to the position point b;
pedestrian demand D at t-th time window, position point a → b a→b (t) is equal to the pedestrian arrival rate
Time tau of crossing street with pedestrian a→b (t) as shown in equation (4):
the pedestrians at the position points a and b cross the street in a secondary street crossing mode and are divided into two stages, wherein the pedestrian crossing quantity Y at the first stage a→b,1 (t) satisfies the constraint of equation (5):
Y a→b,1 (t)＝min{C k ·S a→b,1 (t),Q a→b,1 (t)} (5)
in the formula (5), Y a→b,1 (t) the actual number of pedestrians crossing the first stage from the intersection position point a to the intersection position point b in the t-th time window; s a→b,1 (t) the pedestrian signal lamp state of the first stage from the position point a to the position point b in the t-th time window, S a→b,1 (t) ═ 1 denotes that the pedestrian signal lamp is green, S a→b,1 (t) ═ 0 indicates that the pedestrian signal lamp is red; q a→b,1 (t) represents the first stage pedestrian crossing demand from position a to position b in the tth time window;
(t +1) th time window, position point a to position point b first stage pedestrian crossing demand Q a→b,1 (t +1) is represented by formula (6):
Q a→b,1 (t+1)＝Q a→b,1 (t)+D a→b (t)-Y a→b,1 (t) (6)
the second stage is the pedestrian crossing number Y a→b,2 (t) satisfies the constraint of equation (7):
Y a→b,2 (t)＝min{C k ·S a→b,2 (t),Q a→b,2 (t)} (7)
in the formula (7), Y a→b,2 (t) the actual number of pedestrians crossing the second stage from the intersection position point a to the intersection position point b in the t-th time window; s a→b,2 (t) the second stage pedestrian signal lamp state from position a to position b in the tth time window, S a→b,2 (t) '1' indicates that the pedestrian signal lamp is green, S a→b,2 (t) ═ 0 indicates that the pedestrian signal light is red; q a→b,2 (t) the demanded quantity of the pedestrians crossing the street in the second stage from the position point a to the position point b in the t-th time window;
the demanded quantity Q of pedestrians crossing the street in the second stage from the t +1 th time window to the position point a a→b,2 (t +1) is represented by formula (8):
Q a→b,2 (t+1)＝Q a→b,1 (t)+Y a→b,1 (t)-Y a→b,2 (t) (8)
step 22: setting the vehicle weight w of the t-th time window i→j (t) is equal to the traffic demand multiplied by a weighting factor, and the flow direction with a larger traffic demand will get more right of way, as shown in equation (9):
w i→j (t)＝λq i→j (t) (9)
in formula (9), λ is a weight coefficient;
the pedestrian crossing weight setting needs to consider the pedestrians at two ends of the pedestrian crossing, and the pedestrian crossing weight of the kth pedestrian crossing in the tth time window is W k (t) is expressed as shown in equation (10):
W k (t)＝(1-λ)(Q a→b,1 (t)+Q b→a,2 (t)) (10)
step 23: in order to ensure that the space-time resources at the intersection can be utilized to the maximum extent, the number y of vehicles allowed to pass through the t-th time period flowing to i → j is limited i→j (t) so that it does not exceed the current traffic demand q on the approach lane i→j (t) satisfying the constraint of formula (11); when the pedestrian signal lamp is green and the vehicle running track is crossed with the pedestrian crossing, the flow direction does not allow the vehicle to pass; when the pedestrian signal lamp is green and the vehicle running track does not conflict with the pedestrian crosswalk, the actual traffic flow of the flow direction is limited to the traffic capacity of the pedestrian crosswalk, and the constraint of a formula (12) is met;
0≤y i→j (t)≤q i→j (t) (11)
in the formula (12), the first and second groups,
indicating that the vehicle travel track i → j conflicts with the crosswalk k,
showing that the vehicle running track i → j and the crosswalk k have no conflict point;
in order to avoid conflict among motor vehicles arriving at an intersection at the same time, when the vehicles are controlled to be released, the sum of the time proportion of the phases with conflict allowed to pass in unit time cannot exceed 1, and the phases without conflict can be released together at the moment;the phases with conflict are in the same set, using r 1 ，r 2 ，r 3 ，r 4 Representing four sets containing conflicting phases; E. w, S, N, the east, west, south and north directions are shown in formulas (13) - (16);
r 1 ＝{N→E,S→N,E→S,W→E} (13)
r 2 ＝{N→E,S→N,W→N,E→W} (14)
r 3 ＝{E→S,W→E,S→W,N→S} (15)
r 4 ＝{S→W,N→S,W→N,E→W} (16)
the sum of the time proportions of the flows in the same conflict set allowed to run in unit time should not exceed 100%, while the flows not in the same conflict set can be released together, satisfying the constraints of equations (17) - (20);
2. the pedestrian crossing control method for the automatic driven intersection according to claim 1, wherein the step 3 comprises the following steps:
and step 3: according to the weight of the pedestrian crossing the street and the vehicle passing, optimizing a timing scheme for each vehicle and the pedestrian crossing the street by taking the maximum sum of the product of each flow direction weight and the flow direction at the intersection as an objective, wherein an objective function is shown as a formula (21);
max∑ i→j w i→j (t)·y i→j (t)+∑ k W k (t)·S k (t)·C k (21)。
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