CN114253265A - On-time arrival probability maximum path planning algorithm and system based on fourth-order moment - Google Patents
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Abstract
The invention provides an on-time arrival probability maximum path planning algorithm and an on-time arrival probability maximum path planning system based on fourth-order moments, wherein the algorithm comprises the following steps: obtaining fourth-order moment of each path node in the strategy through a Bellman equation; converting the obtained fourth moment to meet the calculation requirement of the node on-time arrival probability upper bound; calculating the upper bound of the inequality obtained by conversion according to the fourth moment; and selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies. Along with the gradual increase of the size of the road network, the time consumption of the algorithm is increased linearly, and the time consumption of other algorithms is increased exponentially; this algorithm performs better than other algorithms, both in terms of effectiveness and time consumption, than it does.
Description
Technical Field
The invention relates to the technical field of intelligent traffic, in particular to an on-time arrival probability maximum path planning algorithm and an on-time arrival probability maximum path planning system based on fourth-order moments.
Background
In the related application of the current intelligent traffic system, uncertainties caused by various weather conditions, vehicle faults, even natural disasters and the like are very common, and finding the shortest path under the uncertainty has become a common research direction. However, finding the shortest path algorithm does not meet the requirements of all users, such as the users who catch up with airplanes want to take the most reliable path with the maximum probability of arriving on time.
The simplest goal to solve this problem is to find a shortest time path, which has been applied in large-scale road networks by many efficient algorithms, such as a dynamic planning algorithm that recursively updates the value of the time for each node to reach the end point according to the previously obtained estimated values until convergence, which requires raw road network data as input, which generally contains the travel time, variance, and assumptions satisfying various distributions for each road segment, but this dynamic planning method involves convolution calculation, is computationally intensive, requires a complete travel time distribution as input, and is poor in the actual performance of the road network.
Disclosure of Invention
The invention aims to provide an on-time arrival probability maximum path planning algorithm and an on-time arrival probability maximum path planning system based on fourth-order moments, and aims to solve the problems pointed out in the background art.
The embodiment of the invention is realized by the following technical scheme: the on-time arrival probability maximum path planning algorithm based on the fourth moment comprises the following steps:
s1, obtaining a fourth order moment of each path node in the strategy through a Bellman equation;
s2, converting the obtained fourth moment to meet the calculation requirement of the node on-time arrival probability upper bound;
s3, calculating the upper bound of the inequality obtained by conversion according to the fourth moment;
and S4, selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies.
Further, step S1 includes:
deducing a recursion relation between a node i and a node j in the extended Bellman equation, wherein the node j is the next node of the node i in the strategy, and obtaining the following expression:
in the above formula, cijRepresents the travel time, G, of the route ijπ(j) Represents the travel time from the node j to the end point in the strategy pi according to
To
And recursively updating the time of each node reaching the end point until the fourth moment converges.
Further, step S2 includes:
according to the inequality
And converting the obtained fourth moment to obtain the following expression:
in the above formula, o represents a starting point, and x is an upper bound. .
Further, step S4 includes:
modifying the path of the initial strategy pi to obtain a strategy pi ', comparing the initial strategy pi with the upper bound of the non-timely arrival probability of the strategy pi', selecting a strategy with small upper bound of the non-timely arrival probability to modify the path to obtain a new strategy pi*And selecting the strategy with the minimum non-timely arrival probability upper bound as the optimal strategy until all paths are traversed.
The invention also provides an on-time arrival probability maximum path planning system based on fourth moment, which is applied to the algorithm and comprises the following steps:
the extended Bellman equation module is used for obtaining the fourth-order moment of each path node in the strategy through a Bellman equation;
the conversion module is used for converting the obtained fourth moment so as to meet the calculation requirement of the node on-time arrival probability upper bound;
the fourth moment calculation module is used for calculating the upper bound of the inequality obtained by the conversion;
and the strategy updating module is used for selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies.
The invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements an algorithm as described above.
The technical scheme of the embodiment of the invention at least has the following advantages and beneficial effects: along with the gradual increase of the size of the road network, the time consumption of the algorithm is increased linearly, and the time consumption of other algorithms is increased exponentially; this algorithm performs better than other algorithms, both in terms of effectiveness and time consumption, than it does.
Drawings
Fig. 1 is a schematic flow chart of a path planning algorithm provided in embodiment 1 of the present invention;
fig. 2 is a logic block diagram of a path planning system provided in embodiment 1 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Example 1
The applicant researches and finds that, at present, a dynamic planning algorithm applied to a large-scale road network by many efficient algorithms needs to take original road network data as input, wherein the original road network data generally comprises travel time, variance and assumptions meeting various distributions of each road segment, and the dynamic planning algorithm is poor in actual performance of the road network due to the fact that the original road network data generally comprises the travel time, the variance and the assumptions meeting various distributions of each road segment according to a previously obtained estimated value in a recursive updating mode. Based on the above, the embodiment of the invention provides the fourth-order-moment-based on-time arrival probability maximum path planning algorithm which is superior to other algorithms in performance and time consumption. The method specifically comprises the following steps:
step S1, obtaining a fourth order moment of each path node in the strategy through a Bellman equation; in the step, a recursion relation between a node i and a node j in the extended bellman equation is deduced, wherein the node j is the next node of the node i in the strategy, and the following expression is obtained:
in the above formula, cijRepresents the travel time, G, of the route ijπ(j) Represents the travel time from the node j to the end point in the strategy pi according to
To
And recursively updating the time of each node reaching the end point until the fourth moment converges.
After the fourth moment is obtained, further executing step S2, converting the obtained fourth moment; in this embodiment, the inequality needed in step S3 is in the form of
Wherein x is an upper bound, and in order to meet the requirement of inequality requirements, the obtained fourth moment is converted to obtain the following expression:
in the above formula, o represents a starting point,
respectively representing the first, second, third and fourth moments of the origin o.
After the fourth moment is converted into the inequality required for calculation, step S3 is further executed to calculate the upper bound of the converted inequality from the fourth moment; in this embodiment, five upper bound calculation methods of the non-on-time arrival probability under different conditions are illustrated, which are specifically as follows:
case 1: when M is1(Z) is 0 and
when the temperature of the water is higher than the set temperature,
case 2: when M is1(Z) is 0 and
when the temperature of the water is higher than the set temperature,
case 3: in that
On the premise of (1), when M is1(Z)<At the time of 0, the number of the first,
when M is1(Z)>At the time of 0, the number of the first,
case 4: when in use
And is
When the temperature of the water is higher than the set temperature,
in the above formula, the first and second carbon atoms are,
v satisfies: -M1(Z)V3+3M2(Z)V2-2M4(Z)＝0
Case 5: when in use
And is
When the temperature of the water is higher than the set temperature,
after the upper bound of the non-on-time arrival probability is calculated, step S4 is further performed to compare the non-on-time arrival probabilities of different path planning strategiesAnd (4) selecting a strategy with the minimum non-timely arrival probability upper bound as an optimal strategy. In this embodiment, step S4 specifically includes: the path of the initial strategy pi is changed to obtain a strategy pi ', and the non-on-time arrival probability upper bound g of the initial strategy pi and the strategy pi' is usedπ,gπ′Comparing, selecting the strategy with small upper bound of non-on-time arrival probability to change the path to obtain a new strategy pi*And selecting the strategy with the minimum non-timely arrival probability upper bound as the optimal strategy until all paths are traversed.
Referring to fig. 2, an embodiment of the present invention further provides an on-time probability of arrival maximum path planning system based on fourth-order moments, which is applied to the algorithm described above, and includes:
the extended Bellman equation module is used for obtaining the fourth-order moment of each path node in the strategy through a Bellman equation;
the conversion module is used for converting the obtained fourth moment so as to meet the calculation requirement of the node on-time arrival probability upper bound;
the fourth moment calculation module is used for calculating the upper bound of the inequality obtained by the conversion;
and the strategy updating module is used for selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies.
An embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program implements the algorithm as described above.
In summary, the technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects: along with the gradual increase of the size of the road network, the time consumption of the algorithm is increased linearly, and the time consumption of other algorithms is increased exponentially; this algorithm performs better than other algorithms, both in terms of effectiveness and time consumption, than it does.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The on-time arrival probability maximum path planning algorithm based on the fourth moment is characterized by comprising the following steps of:
s1, obtaining a fourth order moment of each path node in the strategy through a Bellman equation;
s2, converting the obtained fourth moment to meet the calculation requirement of the node on-time arrival probability upper bound;
s3, calculating the upper bound of the inequality obtained by conversion according to the fourth moment;
and S4, selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies.
2. The fourth-moment-based on-time probability of arrival maximum path planning algorithm of claim 1, wherein step S1 comprises:
deducing a recursion relation between a node i and a node j in the extended Bellman equation, wherein the node j is the next node of the node i in the strategy, and obtaining the following expression:
in the above formula, cijRepresents the travel time, G, of the route ijπ(j) Represents the travel time from the node j to the end point in the strategy pi according to
To
And recursively updating the time of each node reaching the end point until the fourth moment converges.
3. The fourth-moment-based on-time probability of arrival maximum path planning algorithm of claim 2, wherein step S2 comprises:
according to the inequality
And converting the obtained fourth moment to obtain the following expression:
in the above formula, o represents a starting point, and x is an upper bound.
4. The fourth-moment-based on-time probability of arrival maximum path planning algorithm of claim 3, wherein the step S4 comprises:
modifying the path of the initial strategy pi to obtain a strategy pi ', comparing the initial strategy pi with the upper bound of the non-timely arrival probability of the strategy pi', selecting a strategy with small upper bound of the non-timely arrival probability to modify the path to obtain a new strategy pi*And selecting the strategy with the minimum non-timely arrival probability upper bound as the optimal strategy until all paths are traversed.
5. An on-time probability of arrival maximum path planning system based on fourth-order moments, applied to the algorithm of any one of claims 1 to 4, comprising:
the extended Bellman equation module is used for obtaining the fourth-order moment of each path node in the strategy through a Bellman equation;
the conversion module is used for converting the obtained fourth moment so as to meet the calculation requirement of the node on-time arrival probability upper bound;
the fourth moment calculation module is used for calculating the upper bound of the inequality obtained by the conversion;
and the strategy updating module is used for selecting the strategy with the minimum non-on-time arrival probability upper bound as the optimal strategy by comparing the non-on-time arrival probability upper bounds of different path planning strategies.
6. A computer-readable storage medium, having a computer program stored thereon, which, when executed by a processor, implements the algorithm of any one of claims 1 to 4.
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