CN113379159B - Taxi driver passenger searching route recommendation method based on gray model and Markov decision process - Google Patents

Taxi driver passenger searching route recommendation method based on gray model and Markov decision process Download PDF

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CN113379159B
CN113379159B CN202110758914.4A CN202110758914A CN113379159B CN 113379159 B CN113379159 B CN 113379159B CN 202110758914 A CN202110758914 A CN 202110758914A CN 113379159 B CN113379159 B CN 113379159B
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passenger
road
driver
taxi
road section
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CN113379159A (en
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田源
贺孟曦
周天宇
陈零壹
薛泽楷
曹逸波
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Nanjing Institute of Technology
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Nanjing Institute of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
    • G06Q30/06—Buying, selling or leasing transactions
    • G06Q30/0601—Electronic shopping [e-shopping]
    • G06Q30/0605—Supply or demand aggregation
    • G06Q50/40—

Abstract

The invention discloses a taxi driver passenger searching route recommendation method based on a gray model and a Markov decision process. The method considers the carpooling service which is continuously popularized when taxis are dropped, and further provides a carpooling route recommendation method for drivers under the condition of considering the route recommendation of unloaded taxis. The invention aims to improve the passenger searching efficiency and the taxi sharing success rate of taxi drivers, and adds the tolerance degree of passengers on detours as a limiting condition, so that the passenger riding experience is improved to a certain extent while the passenger searching efficiency is improved. Aiming at order competition among taxi drivers, predicting the real-time supply and demand relation between the drivers and passengers by using a gray model, combining the supply and demand relation with a general rule of historical data mining to obtain the real-time taxi taking success rate, and substituting the real-time taxi taking success rate into a Markov decision process to obtain a recommended route of the driver through strategy iteration.

Description

Taxi driver passenger searching route recommendation method based on gray model and Markov decision process
Technical Field
The invention relates to the field of intelligent transportation, in particular to a taxi driver passenger searching route recommendation method based on a gray model and a Markov decision process.
Background
Under the large background of the high-speed development of mobile communication technology, the method for improving the utilization rate of taxi traffic resources, optimizing the income of drivers and guaranteeing the travel smoothness of citizens as much as possible is significant in improving taxi service.
Existing taxi track studies fall into three categories: recommending a taxi to find a route of a next passenger; guiding city planning and social functions; the passenger is recommended to select a location to wait for a taxi to be left empty. For example: as for searching the optimal route of the next passenger, recent researches focus on recommending the route with the greatest profit to help a taxi driver to search the next passenger, so as to provide a taxi dispatching out-of-view control method based on real-time sensing data of a metropolitan area.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide a taxi driver passenger searching route recommending method based on a gray model and a Markov decision process, comprehensively considers the condition of no-load and carpooling searching of a driver, combines real-time information and historical data of passengers and taxis, establishes a Markov decision process model, recommends an optimal passenger searching route for the driver, and simultaneously considers the tolerance of the passengers on detours so as to improve the taxi taking experience of both the driver and the passengers.
The invention is realized by the following technical scheme:
a taxi driver passenger searching route recommending method based on a Markov decision process comprises the following steps:
step one: modeling a road network, splitting a road into road sections based on intersections, and describing a state set and an action set of a taxi driver and basic information description under a passenger road section model by using a road section model;
step two: based on taxi history data, a probability model is established, and probability distribution conditions of successful passenger searching of drivers in all time periods on a road section are described;
step three: under the condition of considering carpooling, based on the limitation of the detour degree, establishing a feasible action set in the state that a driver seeks carpooling and solving the probability distribution situation that the driver is successful in carpooling in each time period on a road section;
step four: considering competition among drivers, adding a gray prediction model, and combining probability distribution conditions of historical data mining to obtain real-time probability distribution conditions of passenger searching and car sharing success;
step five: substituting the parameters and the like obtained in the steps into a Markov decision process model to carry out strategy iteration, and obtaining the route recommendation of a taxi driver.
Further, the road model comprises basic attributes of the road section, wherein the attributes comprise a length and a starting point and an ending point; the attributes of the passenger road section model comprise boarding points, alighting points of passengers and the degree of detour which can be tolerated by the passengers; the taxi model comprises a state set model and an action set model.
Further, the attributes of the taxi state set model comprise the position of the taxi, the carrying state set and the current time period of the driver; taxi action set model: taking the current road section of the driver as a starting axis, taking the ending point of the current road section as an axis point, and marking clockwise to obtain the road section road of the driver i All optional action sets
Further, in the second step, the calculation method of the probability of successful seeking is as follows:
the historical probability distribution of successful seeking is obtained through analyzing the historical data of each road section in time intervals:
wherein X is i Is a random variable representing the number of successful driving on the current road segment, current period, i=1, 2,..n, n being the total number of roads; y is Y j Is a random variable representing the number of empty taxis through the current road segment for the current time period, j=1, 2..m, m being the … total;representing the probability of the successful number of the system getting in the current road section and the current period in the state i,/for the system>Indicating that the system is idling through the current road section during the current periodProbability that the number of taxis is in state j.
Further, the specific steps of the third step are as follows:
3.1 estimating the probability of passengers arriving at different destinations per time period, per zone, from the processing and analysis of historical data, i.e. calculating the passenger's probability of getting from the road during time period t i Go to road j Probability P of (2) destination ：
Where n (i, j, t) is the period t from head in the historical order i To head j Is a total order quantity of (1); n (i, t) is the period t from head in the historical order i Total order quantity for departure;
3.2, considering the situation that after a driver carries one passenger, the second passenger is about to be carried to carry out carpooling so as to realize the maximum benefit, leading in the passenger objects of the carpooling to be represented by the passenger 1 and the passenger 2, and leading in the parameter alpha to control the detour degree of the driver; typically, the passengers 1 and 2 are received first and then the passengers 1 and 2 are delivered first and then the next passenger is delivered next near the destination, that is:
record D min (i) To receive the shortest path from passenger i to destination D act (i) To receive the actual distance travelled by passenger i, up to the departure of passenger i, the following is satisfied: d (D) act (i)≤αD min (i) After receiving passenger 1, if passenger 1 is sent to the destination first, no matter whether the car is successfully assembled, then there are:
wherein,respectively the start and end of passenger 1, L 1 The definition domain of e isPassenger 1 origin->The feasible solution obtained is action set A of road sections after receiving passengers allowed The method comprises the steps of carrying out a first treatment on the surface of the For each feasible solution, satisfy D act (i)≤αD min (i) A collection L 'of possible destinations for potential passengers 2 in the road section' 1 Then the successful probability of the car sharing in the road section is: p (P) coride (k)＝P find (k)×∑ j∈L′ P destination (k，j，t)，
I.e. in road section road i The probability of the taxi driver finding the passenger is corrected to p=p coride The method comprises the steps of carrying out a first treatment on the surface of the Wherein, road k ∈L 1 ，L i Is a collection of destinations for passenger i;
if the car is successfully assembled at the road section i+1, the passengers are sent to the terminal according to the mode, and if the car is not successfully assembled, the car is assembled at the road section road k The method comprises the following steps:
solving a feasible solution set L 2 For the driver on road section road k Action set A of (2) allowed ，
Solving the successful rate of the carpooling corresponding to all feasible solutions by the same process;
3.3 for L' 1 Solving: it is assumed that it is received at the passenger 2,noting the start point (x 1, y 1) end point (x 2, y 2) of passenger 1, the start point (x 3, y 3) end point (x 4, y 4) of passenger 2, wherein x1, x2, x3, y1, y2, y3 are all constants, if k=1, i.e. passenger 1 is sent first, then there are:
|x3-x2|+|y3-y2|+|x4-x2|+|y4-y2|≤α(|x4-x3|+|y4-y3|)
in this state, a feasible solution set of x4, y4 is obtained
If k=2, i.e. passenger 2 is sent first, then there are:
D act (l p1 .s，l p2 .s)+|x4-x3|+|y4-y3|+|x2-x4|+|y2-y4|≤α(|x2-x3|+|y2-y3|)；
solving a feasible solution setThen there is
Wherein Road is a Road segment set.
Further, the specific process of the fourth step is as follows:
4.1, performing data processing on the obtained geographic position data to enable the obtained geographic position number to be expressed as: l (L) (0) ＝(l 0 (1)，l 0 (2)，...l 0 (n))
Wherein l (0) For a given observation column, l 0 (n) is a data sequence obtained by n times of accumulation;
4.2, assuming that the gray scale model meets the basic fitting condition.
The white differential equation corresponding to the gray differential equation of GM (1, 1) is:
solving the equation to obtain
Wherein b is the ash action amount, and c is the development coefficient;
from this the following predictions are derived:
the final predicted values are as follows:
4.3, proving to conform to the gray model and meeting fitting conditions;
and (3) verification:
wherein, the E (k) is a relative residual error, when the E (k) is less than 0.1, the method is suitable for the gray model, the error is smaller, and if the E (k) is less than 0.2, the method basically reaches the standard;
and (3) verification:
wherein ρ (k) is a step ratio deviation value, λ (k) is a level ratio of the sequence; when |ρ (k) | <0.1, the method is suitable for the model, the error is small, and when |ρ (k) | <0.2, the method basically reaches the standard.
Further, in the fifth step, specifically:
5.1, under the condition of no load of the driver, the probability of the driver reporting the successful carrying of passengers on the road section is that after the driver receives a group of passengers, the probability of the driver reporting the successful carpooling is that the road section is road i The driver's state-value function is:
optimal state-value function:
V π (L taxi )＝max{V(R i )}
where like is a set of loading states, denoted like= {0,1,2}, where 0 is empty, 1 is a set of passengers loaded,2 is successful in carpooling, L taxi Is the position of the taxi driver, road i Is L taxi Adjacent road segments; pi is the recommended route for seeking the guest; STOP is a forced termination condition for iterative computation;
and 5.2, solving a Markov decision process by adopting a value iterative algorithm to obtain the route recommendation of the passengers for the driver.
The invention has the beneficial effects that:
the invention provides a Markov decision model based on a cross network, and when the traffic busy state is considered, the real supply and demand problem of 'less passengers and more passengers' is not negligible, and the carpool state is added when the Markov decision is used for recommendation, so that win-win situations of maximizing the benefit of a driver as much as possible and meeting the requirement of more passengers for getting on the vehicle can be achieved. On the other hand, the problem of competition among multiple drivers is solved by using the game theory besides considering the problem of route recommendation of a single driver, and the method has the practical significance of the current city.
Drawings
FIG. 1 is a method flow diagram of a taxi driver passenger-seeking route recommendation method based on a gray model and a Markov decision process of the present invention;
FIG. 2 is a road segment modeling of the present invention;
FIG. 3 is a flow chart of the present invention considering only no load;
FIG. 4 is a flow chart of the present invention considering carpooling.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention provides a taxi driver passenger searching route recommending method based on a gray model and a Markov decision process, as shown in FIG. 1, which is a basic flow chart of the method, and specifically comprises the following steps of
Step one: modeling a road network, specifically splitting a road into road sections based on an intersection, and describing a state set and an action set of a taxi driver and basic information description under a passenger road section model by using a road section model;
TABLE 1 model base symbol description of passenger driver on road section
1.1 Based on the intersection, splitting the road into segments, i.e., the road model is represented as follows:
road segment set Road, i-th Road segment Road i ，road i E Road, road section Road i Having an attribute start point r i S, termination point r i E, road segment length r i L; position l, for any position l, there is a head i So that l is epsilon road i . As shown in fig. 2.
1.2 Passenger section model is represented as follows:
start point for passenger iAnd endpoint->
1.3 A taxi model for describing a taxi driver's status set and action set, expressed as follows:
the taxi model is constructed in two aspects: a taxi status set model and a taxi action set model.
The taxi state set model comprises: taxi is locatedThe loading state set take= {0,1,2}, wherein 0 is no-load, 1 is loading a group of passengers, 2 is successful in carpooling, and the current time period (time stamp) t of the driver is located.
Taxi action set model: taking the current road section of the driver as a starting axis, taking the ending point of the current road section as an axis point, and marking clockwise to obtain the road section road of the driver i All optional action sets
Step two: based on taxi history data, establishing a probability model for describing probability distribution conditions of successful passenger searching of drivers in each time period on a road section;
the probability model is to analyze the historical data of each road section in time intervals to obtain the probability distribution of the success of historical passenger searching:
wherein P is find X is the probability of successful seeking i Is a random variable representing the current road segment (i=1, 2,..n, n is the total number of roads), the number of successful hits for the current time period; y is Y j Is a random variable representing the number of empty taxis passing through the current road segment for the current time period, j=1, 2.Representing the probability of the successful number of the system getting in the current road section and the current period in the state i,/for the system>The probability that the system is in state j through the number of empty taxis of the current road section in the current period is represented.
Step three: with reference to fig. 3 and 4, under the condition of considering carpooling, based on the limitation of the detour degree, establishing a feasible action set in the state that a driver seeks carpooling and solving the probability distribution situation that the driver is successful in carpooling in each time period on a road section; the process is as follows:
step 3.1, estimating each period, each time period, based on the processing and analysis of the historical dataThe probability of a passenger in an area reaching a different destination, i.e. calculating the passenger's probability of going from road during time period t i Go to road j Probability P of (2) destionation ：
Where n (i, j, t) is the period t from head in the historical order i To head j Is a total order quantity of (1); n (i, t) is the period t from head in the historical order i Total order quantity for departure.
And 3.2, considering the situation that after a driver has carried one passenger, the second passenger is about to be carried to carry out carpooling so as to realize the maximum benefit, introducing the passenger objects of the carpooling into the passenger 1 and the passenger 2, and controlling the detour degree of the driver by introducing the parameter alpha. Typically, passenger 1 is received first, passenger 2 is received during the journey, and then passenger 1 and passenger 2 are delivered first and then next near the end point, that is:
record D min (i) For receiving the shortest path from passenger i to the destination; d (D) act (i) To receive the actual distance travelled by passenger i until passenger i gets off, the following is satisfied:
D act (i)≤αD min (i) (3)
after receiving the passenger 1, if it is assumed that whether the car is successfully assembled or not, the passenger 1 is sent to the destination first, then there are:
L 1 is defined asThe feasible solution obtained is action set A of road sections after receiving passengers allowed The method comprises the steps of carrying out a first treatment on the surface of the For each feasible solution, find the one that satisfies equation (3)The set of possible destinations L'1 for the potential passenger 2 in the road segment, the probability of successful taxi sharing on that road segment is
P coride (k)＝P find (k)×∑ j∈L′ P destination (k，j，t) (5)
I.e. in road section road i The probability of the taxi driver finding the passenger is corrected to p=p coride Wherein head is a head k ∈L 1 ，
If the car is successfully assembled at the road section i+1, the passengers are sent to the terminal according to the mode, and if the car is not successfully assembled, the car is assembled at the road section road k The method comprises the following steps:
solving a feasible solution set L 2 For the driver on road section road k Action set A of (2) allowed ，
And the same principle can be used for solving the car sharing success probability corresponding to all feasible solutions.
3.3 for L' 1 Solving: it is assumed that it is received at the passenger 2,noting the start point (x 1, y 1) end point (x 2, y 2) of passenger 1, the start point (x 3, y 3) end point (x 4, y 4) of passenger 2, wherein x1, x2, x3, y1, y2, y3 are all constants, if k=1, i.e. passenger 1 is sent first, then there are:
|x3-x2|+|y3-y2|+|x4-x2|+|y4-y2|≤α(|x4-x3|+|y4-y3|) (7)
in this state, a feasible solution set of x4, y4 can be easily obtained
If k=2, i.e. passenger 2 is sent first, then there are:
solving a feasible solution setThen there is
Step four: considering competition among drivers, adding a gray prediction model, and combining probability distribution conditions of historical data mining to obtain real-time probability distribution conditions of passenger searching and car sharing success;
4.1 S-constructing the obtained geographical position data as l (0) ＝(l 0 (1)，l 0 (2)，...l 0 (n)) and l (0) For a given observation column, l 0 (n) is a data column obtained by n times of accumulation, n=1, 2.
4.2 Assuming that the gray model satisfies the basic fitting condition, a fitting state judgment is given in formulas (15) (16);
the white differential equation corresponding to the gray differential equation of GM (1, 1) is:
wherein b, c is a parameter value, so that the value deducing process of the unknown quantity of l is limited by equation (11), the parameter values of b and c are firstly obtained by using regression analysis before the (12) th equation, and then the following operation is continued;
solving the following predicted values:
the final predicted values are as follows:
it is demonstrated below that it conforms to the gray scale model.
Calculating relative residual errorWhen the E (k) is less than 0.1, the method is very suitable for the model, the error is small, and if the E (k) is less than 0.2, the method basically reaches the standard.
Calculating a level ratio offsetWhen |ρ (k) | <0.1, the method is very suitable for the model, the error is small, and when |ρ (k) | <0.2, the method basically reaches the standard. Where λ (k) is defined as the horizontal ratio of the sequences.
Step five: substituting the parameters and the like obtained in the steps into a Markov decision process model to carry out strategy iteration, and obtaining the route recommendation of a taxi driver. In the case of empty driver, the driver returns the probability P of successful passenger pick-up on the road section find After the driver receives a group of passengers, the probability P of successful carpooling is reported back by the driver coride Then in road section i The driver's state-value function is:
optimal state-value function:
V π (L taxi )＝max{V(Road i )} (15)
wherein L is taxi Is the position of the taxi driver, road i Is L taxi Adjacent road segments. Pi is the recommended route for seeking guests.
And solving a Markov decision process by adopting a value iterative algorithm to obtain the route recommendation of the passengers to the driver.
The above embodiments are merely for illustrating the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, the scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present invention are within the scope of the present invention.

Claims (5)

1. A taxi driver passenger searching route recommending method based on a Markov decision process is characterized by comprising the following steps:
step one: modeling a road network, splitting a road into road sections based on intersections, and describing a state set and an action set of a taxi driver and basic information description under a passenger road section model by using a road section model;
step two: based on taxi history data, a probability model is established, and probability distribution conditions of successful passenger searching of drivers in all time periods on a road section are described; the calculation method of the probability of successful seeking in the second step is as follows:
the historical probability distribution of successful seeking is obtained through analyzing the historical data of each road section in time intervals:
wherein X is i Is a random variable representing the successful number of driving in the current road section and the current period, i=1, 2, … n, n is the total number of roads; y is Y j Is a random variable representing the number of empty taxis passing through the current road section in the current period, j=1, 2, … m, m being … total;representing the probability of the successful number of the system getting in the current road section and the current period in the state i,/for the system>The probability that the system is in a state j through the number of empty taxis of the current road section in the current period is represented;
step three: under the condition of considering carpooling, based on the limitation of the detour degree, establishing a feasible action set in the state that a driver seeks carpooling and solving the probability distribution situation that the driver is successful in carpooling in each time period on a road section; the specific steps of the third step are as follows:
3.1 estimating the probability of passengers arriving at different destinations per time period, per zone, from the processing and analysis of historical data, i.e. calculating the passenger's probability of getting from the road during time period t i Go to road j Probability P of (2) destination ：
Where n (i, j, t) is the period t from head in the historical order i To head j Is a total order quantity of (1); n (i, t) is the period t from head in the historical order i Total order quantity for departure;
3.2, considering the situation that after a driver carries one passenger, the second passenger is about to be carried to carry out carpooling so as to realize the maximum benefit, leading in the passenger objects of the carpooling to be represented by the passenger 1 and the passenger 2, and leading in the parameter alpha to control the detour degree of the driver; typically, the passengers 1 and 2 are received first and then the passengers 1 and 2 are delivered first and then the next passenger is delivered next near the destination, that is:record D min (i) To receive the shortest path from passenger i to destination D act (i) To receive the actual distance travelled by passenger i, up to the departure of passenger i, the following is satisfied:
D act (i)≤αD min (i)
after receiving passenger 1, assuming passenger 1 is sent first to the destination whether or not the car is successfully assembled, then there are:
wherein,respectively the start and end of passenger 1, L 1 The definition field of e is passenger 1 origin +.>The feasible solution obtained is action set A of road sections after receiving passengers allowed The method comprises the steps of carrying out a first treatment on the surface of the For each feasible solution, satisfy D act (i)≤αD min (i) A collection L 'of possible destinations for potential passengers 2 in the road section' 1 Then the successful probability of the car sharing in the road section is:
P coride (k)＝P find (k)×∑ j∈L′ P destination (k,j,t)
i.e. in road section road i The probability of the taxi driver finding the passenger is corrected to p=p coride The method comprises the steps of carrying out a first treatment on the surface of the Wherein, road k ∈L 1 ，L i Is a collection of destinations for passenger i;
the car is successfully assembled at the road section i+1, passengers are sent to reach the terminal, and if the car is not successfully assembled, the car is assembled at the road section road k The method comprises the following steps:
solving a feasible solution set L 2 For the driver on road section road k Action set A of (2) allowed ，
Solving the successful rate of the carpooling corresponding to all feasible solutions by the same process;
3.3 for L' 1 Solving: it is assumed that it is received at the passenger 2,noting the start point (x 1, y 1) end point (x 2, y 2) of passenger 1, the start point (x 3, y 3) end point (x 4, y 4) of passenger 2, wherein x1, x2, x3, y1, y2, y3 are all constants, if k=1, i.e. passenger 1 is sent first, then there are:
|x3-x2|+|y3-y2|+|x4-x2|+|y4-y2|≤α(|x4-x3|+|y4-y3|)
in this state, a feasible solution of x4, y4 is determinedCollection set
If k=2, i.e. passenger 2 is sent first, then there are:
solving a feasible solution setThen there is
Wherein Road is a Road segment set; step four: considering competition among drivers, adding a gray prediction model, and combining probability distribution conditions of historical data mining to obtain real-time probability distribution conditions of passenger searching and car sharing success;
step five: substituting the parameters and the like obtained in the steps into a Markov decision process model to carry out strategy iteration, and obtaining the route recommendation of a taxi driver.
2. The method for recommending a taxi driver's route for seeking passenger based on a markov decision process according to claim 1, wherein the road model comprises basic attributes of a road segment, the attributes comprising length, starting point and ending point; the attributes of the passenger road section model comprise boarding points, alighting points of passengers and the degree of detour which can be tolerated by the passengers; the taxi model comprises a state set model and an action set model.
3. The method for recommending a taxi driver's passenger searching route based on a markov decision process according to claim 2, wherein the attributes of the taxi state set model include the location of the taxi, the loading state set and the current time period of the driver; taxi action set model: taking the current road section of the driver asThe starting shaft, the end point of the current road section is the axis point, and the clockwise mark is given to obtain the road section road of the driver i All optional action sets
4. The method for recommending a taxi driver's route for seeking passengers based on a markov decision process according to claim 1, wherein the specific process of the fourth step is as follows:
4.1, performing data processing on the obtained geographic position data to enable the obtained geographic position number to be expressed as:
l (0) ＝(l 0 (1),l 0 (2),...l 0 (n))
wherein l (0) For a given observation column, l 0 (n) is a data sequence obtained by n times of accumulation;
4.2, supposing that the gray prediction model meets basic fitting conditions;
the white differential equation corresponding to the gray differential equation of GM (1, 1) is:
the solution to the equation is found:
wherein c is the coefficient of development, b is called the ash action amount;
from this the following predictions are derived:
the final predicted values are as follows:
4.3, proving to conform to the gray model and meeting fitting conditions;
and (3) verification:
when the epsilon (k) is the relative residual error and is shown as epsilon (k) is <0.1, the method is suitable for the gray model, the error is small, and if the epsilon (k) is <0.2, the method basically reaches the standard;
and (3) verification:
wherein ρ (k) is a step ratio deviation value, λ (k) is a level ratio of the sequence, and c is a development coefficient; when |ρ (k) | <0.1, the method is suitable for the model, the error is small, and when |ρ (k) | <0.2, the method basically reaches the standard.
5. The method for recommending a taxi driver's route for seeking passengers based on a markov decision process according to claim 1, wherein in step five, the method is specifically as follows:
5.1, under the condition of no load of the driver, the probability of the driver reporting the successful carrying of passengers on the road section is that after the driver receives a group of passengers, the probability of the driver reporting the successful carpooling is that the road section is road i The driver's state-value function is:
optimal state-value function:
V π (L taxi )＝max{V(R i )}
wherein like is a loading state set, expressed as like= {0,1,2}, wherein 0 is no-load, 1 is loading a group of passengers, 2 is successful in carpooling, L taxi Is the position of the taxi driver, road i Is L taxi Adjacent road segments; pi is the recommended route for seeking the guest; STOP is a forced termination condition for iterative computation;
and 5.2, solving a Markov decision process by adopting a value iterative algorithm to obtain the route recommendation of the passengers for the driver.
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