CN106197455B - A kind of real-time dynamic multipath mouth path navigation quantum searching method of urban road network - Google Patents

Abstract

The invention discloses a real-time dynamic multi-intersection route navigation quantum search method for urban traffic road network, which combines the preference value generated by the influence of the road itself on the route and the cost value generated by the mutual influence of vehicles during operation to form a comprehensive evaluation index utility value. The size of the value evaluates the pros and cons of the path navigation scheme, and uses quantum computing to calculate the utility values of all path navigation schemes in parallel, and uses quantum search to efficiently search for a path navigation scheme that meets the requirements. The present invention fully considers various factors affecting smooth roads, quantifies the degree of influence of various factors on traffic and finally integrates them to obtain a utility value, and uses the utility value to accurately judge the pros and cons of a route navigation scheme. At the same time, quantum computing and quantum search are introduced, so that the calculation results of the utility value can be obtained in real time, and a suitable route navigation scheme can be obtained from this. On the premise of satisfying the personal interests of each driver, the traffic congestion of the entire urban road network can be significantly improved. .

Description

A quantum search method for real-time dynamic multi-intersection route navigation in urban traffic network

technical field

The invention belongs to the technical fields of computer science and intelligent traffic systems, and in particular relates to a quantum search method for real-time dynamic multi-intersection path navigation in urban traffic road networks.

Background technique

The traffic network of large and medium-sized cities is increasingly congested, and the time cost, management cost and economic cost caused by congestion are increasing. Traffic congestion increases the travel time of residents, affects people's work efficiency and quality of life, and restricts urban development. It reduces energy consumption and exhaust emissions, aggravates environmental pollution, and solves the congestion problem of urban traffic network, which is beneficial to the country and the people. However, the pattern of urban traffic road network has been hard to change, and road resources are limited. Efficient route navigation and reasonable road resource allocation have become the main ways to solve urban road network congestion.

Path navigation can be divided into static path navigation and dynamic path navigation. Static path navigation refers to seeking the shortest path based on conditions such as physical geographic information and traffic rules. Dynamic path navigation is based on static path navigation combined with real-time Traffic information adjusts the pre-planned optimal driving route in a timely manner until the destination is reached and finally the optimal route is obtained. At present, most of the mature route navigation systems put into the market are based on static route navigation, mainly including Dijkstra algorithm, Lee algorithm, Floyd algorithm, blind search, A* heuristic algorithm, etc. However, in the face of traffic reality with many unstable factors, Users are not satisfied with the existing system. Although static path navigation can quickly find the optimal path for a single vehicle, it is difficult to avoid local road congestion and other local resources are relatively idle due to the lack of coordination between vehicles, and when traffic accidents and traffic jams occur, static path navigation cannot be based on road conditions in real time. Information changes course in time. Therefore, it is very important to provide real-time dynamic path navigation for vehicles to alleviate road traffic congestion. Vehicle dynamic route navigation predicts future traffic flow based on historical and current traffic information data, and is used to adjust and update the optimal driving route in time, thereby effectively reducing road congestion and traffic accidents. The importance of traffic prediction in dynamic route navigation is gradually highlighted. More and more researchers have conducted in-depth research on traffic information prediction using Kalman filter method, time series method, neural network method, Markov prediction and gray prediction theory. Although with the vigorous development of the network, it is not difficult to provide real-time route navigation information for vehicles, but the simple dynamic real-time predictive flow model limits the accuracy of the real-time predictive model, resulting in a relatively low ability to deal with real-time traffic emergencies. However, the complex dynamic real-time forecasting model considers many factors, and the computational complexity increases exponentially with the increase of the road network scale. Therefore, the current dynamic route navigation is still immature, and most of them remain in the theoretical stage. The contradiction between the accuracy and complexity of dynamic real-time prediction models limits the development of dynamic route navigation.

Contents of the invention

In order to solve the above-mentioned technical problems, the present invention provides a real-time dynamic multi-intersection route navigation quantum search method of urban traffic road network, by comprehensively considering various factors affecting traffic and quantifying these factors to evaluate the route navigation scheme to obtain an effective traffic relief method. Congested navigation solutions, and maximize the utilization of road resources in the urban traffic network.

The technical scheme adopted in the present invention is: a real-time dynamic multi-intersection route navigation quantum search method for urban traffic road network, which maps the real road network into a model graph R (B, E), where B represents a collection of intersection nodes, B _i ( i=1,2,...,r) represents a single intersection node, r is the total number of intersections, and E represents a set of road sections with directions; assuming that there are n vehicles in the road network, any vehicle w has a current start starting point P _s and destination end point P _d , then a feasible path of the vehicle is expressed as {P _s ,...,P _i ,...,P _d } by continuous adjacent intersection nodes; each vehicle chooses A feasible path, the driving paths of all vehicles form a feasible path set FPS _n , that is, a path navigation scheme;

It is characterized in that the method comprises the following steps:

Step 1: Initialize the vehicle set {v ₁ ,v ₂ ,...,v _n } and the set of optional paths according to the number n of vehicles, the information of the starting and ending points, and the optional path of each vehicle where v _i represents the i-th vehicle, Indicates an optional path for the i-th vehicle;

Step 2: Carry out quantum encoding {|0>,|1>,...,|2 _n ^×h -1>} on the vehicle and its optional paths 0,1,...,bi, and determine that the quantum state can be Completely represent all route navigation schemes; where b _i represents the number of optional routes for the i-th vehicle, and h represents the minimum number of binary digits required for encoding the optional routes;

Step 3: Determine the independent multiplication factors α _i , β _j of each influencing factor according to the road condition information, and determine the utility value calculation function U(x); where each route navigation scheme corresponds to the value of the independent variable x;

Step 4: Prepare the equal-weight superposition state |x> of the route navigation scheme, calculate the utility value |U(x)| corresponding to each route navigation scheme x, and obtain the equal-weight superposition state |U(x)> of the utility value function;

Step 5: Determine the empirical value k of the utility value, conduct a quantum search on the equal-weighted superposition state |U(x)> of the utility value function, and search out the utility value |U _s > that meets the requirements;

Step 6: Output the utility value U _s that meets the requirements and the corresponding route navigation scheme, and perform route guidance for each vehicle.

Preferably, the utility value function U(x) described in step 3 is:

U(x)=Fr(x)×(α1×Rs(x)+α2×Sl(x)+α3×Ls(x)+α4×Os(x)+α5×Fd(x))-(β1× Ta(x)+β2×Tc(x)+β3×De(x)+β4×Oc(x)+β5×Tl(x))

Among them, Fr(x) indicates whether the road section is reachable, 1 means it is reachable, and 0 means it is not reachable; Rs(x) means the condition of the road section, and the value is [0, 1]; Sl(x) means the speed limit, and the value is [ 0, 1]; Ls(x) represents the lighting condition of the road section, and the value is [0, 1]; Os(x) represents the degree of compliance of the driver to the system recommendation, and the value is [0, 1]; Fd(x) represents the driver’s Familiarity of the road section, the value is [0, 1]; Ta(x) represents the road impact caused by sudden traffic accidents or temporary control, etc., the value is [0, 1]; Tc(x) represents the cost of the selected path The time cost of the selected path, the value is [0, ∞]; De(x) represents the distance cost of the selected path, the value is [0, ∞]; Oc(x) represents the fuel cost of the selected path, the value is [ 0, ∞]; Tl(x) represents the influence of traffic lights, and the value is [0, 1]; α _i (i=1,2,...,5), β _i (i=1,2,... .,5) respectively represent the independent multiplication factors corresponding to each influencing factor.

As preferably, the specific realization of step 4 includes the following sub-steps:

Step 4.1: Use the Hadamard gate to prepare the quantum equal-weight superposition state of the initial independent variable path navigation scheme where N represents the total number of quantum states;

Step 4.2: Design the unitary transformation circuit U _U(x) corresponding to the function and the auxiliary qubit |z> that can be used to realize the function calculation;

Step 4.3: Input the equal-weight superposition state of the path navigation scheme, and calculate the function U(x) in parallel:

Step 4.4: Obtain the equal weight superposition state |U(x)> of the utility value function.

As preferably, the specific realization of step 5 includes the following sub-steps:

Step 5.1: Give the oracle function f(y) used to determine the target state, and set the corresponding quantum circuit;

The equal-weighted superposition state of the utility value function|U(x)>after being discriminated by the oracle function, the state whose function value f(x) is 1 is the target state;

Step 5.2: Accumulate the target state to obtain the target state number m and calculate the comprehensive utility value target state |U _a >;

Among them, a _i represents the target state, and |a _i > represents the quantum form of the target state;

Step 5.3: Determine the oracle query O according to |U _a >, and determine the transformation of O;

O＝I-2| _Ua >< _Ua |;

where I denotes an equal-weighted superposition state with the same qubit number as | _Ua >, and < _Ua | denotes the conjugate vector of | _Ua >;

Step 5.4: According to the equal weight superposition state Determine the D transformation;

in, is an equal-weighted superposition of all elementary states, H represents the Hadamard transformation, which is used to prepare the equal weight superposition state, Indicates the preparation of an equal-weight superposition state of n×h bits; N indicates the total number of quantum states, and |i> indicates the i-th quantum state;

Step 5.5: Determine a G transform G=DO by O transform and D transform;

Step 5.6: Perform the equal-weight superposition state |U(x)> of the utility-value function times of G transformation, round represents the nearest integer;

Step 5.7: Observing the output utility value state |U _out > and the corresponding path navigation scheme |x _out >, searching for the utility value |U _s > that meets the requirements within the time limit;

Step 5.8: Output the utility value state | U _s > the navigation path selected for each vehicle in the corresponding path navigation scheme x _s .

As preferably, the specific realization of step 5.7 includes the following sub-steps:

Step 5.7.1: Observing the output after the G transformation is completed, and obtaining the utility value U _out and the current search elapsed time t _s ;

Step 5.7.2: If t _s <t _max , then perform the following step 5.7.3, where t _max represents the maximum navigation time interval that can ensure the real-time performance of route navigation; otherwise, perform the following step 5.7.5;

Step 5.7.3: If U _out <k, then t _s =t _s +t _c , and perform the step 5.7.2 in turn, where t _c represents the time required to execute the RGQS method once; otherwise, perform the following steps 5.7.4;

Step 5.7.4: If U _out <k _m , then k=U _out , t _s =t _s +t _c , and turn back to step 5.7.2, where k _m represents the ideal utility value set according to experience ; Otherwise, perform the following step 5.7.5;

Step 5.7.5: U _s =U _out , output U _s .

The present invention constructs a real-time dynamic multi-intersection traffic model of urban traffic road network, integrates various influencing factors of urban traffic into utility values to evaluate the pros and cons of route navigation schemes; introduces quantum computing and quantum search to solve the real-time For calculation and search problems, after the initial road conditions are determined, the algorithm provided by the invention can be used to calculate and search in real time to obtain suitable utility values and corresponding suitable route navigation schemes, providing route guidance for all vehicles, so that the entire city Traffic is effectively alleviated and the utilization rate of urban road traffic resources is maximized.

Description of drawings

FIG. 1 is a mapping diagram of a real road network and a model according to an embodiment of the present invention.

Fig. 2 is a flow chart of the RGQS method of the embodiment of the present invention.

Fig. 3 is a flowchart of the UVCQC algorithm of the embodiment of the present invention.

Fig. 4 is a schematic diagram of the quantum parallel computing process of the UVCQC algorithm according to the embodiment of the present invention.

Fig. 5 is a schematic diagram of the RNUQS algorithm of the embodiment of the present invention.

Fig. 6 is a G transformation in the RNUQS algorithm of the embodiment of the present invention and Schematic diagram of the geometry of the secondary G-transform.

Detailed ways

In order to facilitate those of ordinary skill in the art to understand and implement the present invention, the present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the implementation examples described here are only used to illustrate and explain the present invention, and are not intended to limit this invention.

In order to effectively alleviate traffic congestion and provide real-time route navigation for driving vehicles, the present invention proposes a real-time dynamic multi-intersection route navigation quantum search method for urban traffic road networks. This method calculates the route utility value for a large number of vehicles at multiple intersections in the urban road network. There are many factors that need to be considered, including not only the driver’s objective attributes and subjective preferences for the road, but also the cost corresponding to the route selection, and Uncertain factors such as possible emergencies on the road. Use quantum computing and quantum search to calculate and search the influencing factors and route navigation schemes in real time, and obtain appropriate utility values and corresponding route navigation schemes. While satisfying the individual interests of driving vehicles, the utilization rate of road resources in the entire urban road network can be realized. maximize.

The present invention maps the real road network (as shown in Figure 1 (a)) into a model graph R (B, E) (as shown in Figure 1 (b)), B is a node, E is a vector arrow with direction between nodes, and R is formed by Diagram composed of B and E. The intersections in Figure 1(a) are sequentially mapped to nodes B ₁ , B ₂ ,...,B ₁₂ in Figure 1(b), and the road sections in Figure 1(a) are mapped to the directional nodes in Figure 1(b). Vector arrows, the real road network in Figure 1(a) is mapped to graph R in Figure 1(b). Each node B represents an intersection in Figure 1(a), node B _i (i=1,2,...,r) represents the i-th intersection, where r is the total number of intersections, and each vector arrow E represents a section. Assuming that there are n vehicles in the road network, and any vehicle w has a current starting point P _s and a destination end point P _d , then a feasible path of this vehicle can be expressed as {P _s ,. ...,P _i ,...,P _d }. Each vehicle chooses a feasible path, and the driving paths of all vehicles form a feasible path set FPS _n , that is, a path navigation scheme. Since the number of vehicles and the number of feasible paths for each vehicle are large, the number of route navigation schemes is huge, and the problem to be solved in the present invention can be transformed into searching for the best route, that is, finding the best FPS _n . In the real road network, because the road conditions are constantly changing, the search process of the path navigation scheme must be updated in real time within a certain period of time to ensure the effectiveness of the path navigation scheme, so it is necessary to ensure that the best path is searched within a limited time and updated in real time.

The present invention uses the utility value U to evaluate the quality of the route navigation scheme. There are many factors that affect the utility value, including constant factors, such as the number of lanes, the speed limit of the road section, the duration of traffic lights, the degree of compliance of the driver to the recommended navigation scheme, etc. It also includes factors that change over time, such as the distance of the optional path, time-consuming, road conditions, etc. In the present invention, the constant factors are integrated into the preference value P, and the changing factors are integrated into the cost value C. The calculation formula of the utility value is as follows: (1) shown.

U=P-C (1)

The utility value U is an important index to evaluate the quality of the route navigation scheme, that is, when the route guidance scheme is determined, the U value is also determined, and the larger the U value, the better the route guidance scheme. According to the formula (1), the U value depends on the preference value P and the cost value C. The influencing factors of the preference value are shown in Table 1, and the influencing factors of the cost value are shown in Table 2. When the route navigation scheme is determined, the U value Determined by the factors in Table 1 and Table 2.

Table 1 Influencing factors and parameter definitions of preference value P

Table 2 Influencing factors and parameter definitions of cost value C

The various factors in Table 1 and Table 2 have different influences on the utility value U. Therefore, in the process of calculating the U value, each factor will be assigned a corresponding weight according to the city size and route navigation goals. The preference value P is a deterministic factor. Table 1 defines the factors that affect the preference value. After any vehicle determines the origin and destination, the preference value is determined. Therefore, the formula for calculating the preference value P of a road section is shown in formula (2).

P=Fr×(α1×Rs+α2×Sl+α3×Ls+α4×Os+α5×Fd) (2)

Among them, α _i (i=1,2,...,5) are independent multiplication factors corresponding to each influencing factor, and their values are related to the city size and the setting of decision-making goals. The larger the value of the multiplication factor, the more important the factor , the greater the impact on the utility value U, in the same traffic network, all factor values are determined. In any optional path, the accumulation of the preference values of each road section is the preference value of the path, and the larger the preference value, the better the path.

For each road, the size of the preference value P is determined, and the size of the cost value C is not only related to the selected path itself, but also considers the mutual influence between vehicles. Table 2 defines the influencing factors of the cost value. After a vehicle determines the route, the values of Ta, De and Tl can be calculated accordingly, but the fuel cost Oc is determined comprehensively by time cost Tc, distance cost De and driving speed, while the value of time cost Tc is not easy to obtain and Calculation, because the time spent is not only affected by the length of the path, but also the congestion degree of each road section in the path, the number of vehicles on the road section has a direct relationship with the congestion coefficient of the road, and the congestion coefficient of the road is inversely related to the average driving speed of the road. relevant. For a specific road section, the average running speed of the road section can be estimated by the number of vehicles in operation, the present invention uses the traffic congestion coefficient γ to represent the congestion situation of the road, and the average speed of vehicles on the road is closely related to the traffic congestion coefficient , the actual number of vehicles on the road section is n, the threshold capacity is H, and the congestion capacity is L, then the calculation of the congestion coefficient γ is shown in formula (3).

After the time cost Tc is determined, the oil volume cost Oc and cost value C can also be calculated. When the feasible paths of all vehicles are determined, the cost value C of any path can be calculated according to formula (4).

C＝β ₁ ×Ta+β ₂ ×Tc+β ₃ ×De+β ₄ ×Oc+β ₅ ×Tl (4)

Among them, β _i (i=1,2,...,5) is an independent multiplication factor of each influencing factor affecting the cost value C, and its value is related to the city scale and decision-making goal setting, and their sizes represent the The degree of influence of the influencing factors on the cost value C also represents its importance. When the cost value C of a route is smaller, the route is better, and the cost value of all vehicles is accumulated to be the final cost value of the route navigation solution.

The utility value U can measure the pros and cons of a route navigation scheme, and high utility value is also an important feature of a traffic system running well. When the driving path of all vehicles (that is, a route navigation scheme) is determined, its utility value can be calculated. The average utility value of the vehicle represents the pros and cons of the vehicle route navigation scheme. The higher the utility value, the better the navigation scheme. The better it is. When the utility value U of all possible navigation schemes is obtained, the path navigation scheme with the best utility value U _max is selected for vehicle guidance, and the best traffic navigation is realized. However, for a large urban road network, the number of all possible route navigation schemes is huge. When using ordinary computers to calculate and search, due to the limitation of calculation speed and search speed, it is impossible to realize real-time vehicle scheduling of the entire road network. Searching for the best navigation solution within a limited time has practical application value. Therefore, the present invention proposes a real-time dynamic multi-intersection route navigation quantum search method RGQS in the urban traffic road network, as shown in Figure 2, the process of the RGQS method is shown in Table 3; the RGQS method is composed of the UVCQC algorithm and the RUNQS algorithm. The parallel capability of the quantum computer and the search capability of the quantum search algorithm break through the limitations of calculation speed and search speed, and realize the real-time navigation of the entire road network path.

Table 3 RGQS method flow

If there are n vehicles in the road network, the numbers are V ₁ , V ₂ ,...,V _n , each vehicle V _i has its own start point and end point, and the optional path between the start point and end point has one or Several paths, these paths are selected by the system for the driver to meet the requirements of the driver, assuming that the number of optional paths for the n vehicles is respectively b ₁ , b ₂ ,...,b _n , the paths are represented by intersection sets, V _{i, j} represent the j-th path of the i-th vehicle, a path navigation scheme is to extract a set of paths for each vehicle, such as the set (wherein, a _i (i=1,2,...,n) represents any optional route in the i-th vehicle) is a route navigation scheme.

There is a one-to-one correspondence between the path navigation scheme and its utility value. The path navigation scheme is an independent variable x, and the utility value U is a function. The functional relationship is shown in formula (5).

U(x)=P(x)-C(x) (5);

Among them, the value range of the independent variable x is The form of x in the computer is represented by bits 0 and 1, and the value of each x uniquely represents a route navigation scheme. For a clearer representation, the binary bit of the route navigation scheme x needs to indicate the route selected by each vehicle , then the optional path of each vehicle needs to be represented by a certain number of binary bits, and the minimum h value satisfying the formula max{b ₁ ,b ₂ ,...,b _n }≤2 ^h is used to encode x, The number of paths for each vehicle needs to be expressed in h-bit binary, and a total of n×h-bit binary is required to represent the number of route navigation schemes. For example, if the number of vehicles is 1000, and the path of each vehicle is coded with 3 bits, 3000 bits are required to represent one Path navigation schemes, the space required to store these schemes is ²³⁰⁰⁰ bits. Classical computers cannot store, let alone calculate. Quantum computers have excellent performance in data storage and parallel computing. Due to the existence of superposition states, ³⁰⁰⁰ qubits can theoretically store 23000 bits of data. Compared with classical computers, quantum computers have almost no storage capacity. Therefore, the storage problem of the path navigation scheme can be solved, and the most superior performance of the quantum computer lies in the parallel calculation of the continuous variable in the true sense (operating on all independent variables at the same time, and running once to get all the function values). Therefore, the parallel computing problem of utility value can be solved.

The basic unit stored in a quantum computer is a state. There are only two states of 0 and 1 in a classical computer, but there is a superposition state in a quantum computer, that is, there is a superposition state that can be neither 0 nor 1. Therefore, a 3000 state in a classical computer The binary bit can only represent one path navigation scheme _xi , but in a quantum computer, ³⁰⁰⁰ qubits can represent 23000 kinds of path navigation schemes, as long as the quantum state is not observed, it can be considered that these ²³⁰⁰⁰ path navigation schemes are simultaneously storage, quantum computers are very suitable for the storage of these continuous variables, and each path navigation scheme exists with the same probability, this probability is represented by the probability amplitude σ in quantum mechanics, the square σ ² of the probability amplitude of a certain path navigation scheme is equal to The probability that this route navigation solution can be output (probability of being observed at the output).

The present invention uses the independent variable x to represent the path navigation scheme, and the function U(x) represents the utility value of the navigation scheme. In the quantum computer, both of them are represented by quantum states, stored in two registers respectively, and the independent variable x is initialized as in the formula (6) shown.

As shown in Figure 3, the path navigation scheme is determined by the number of vehicles n and the information of the start and end points of the vehicle. All path navigation schemes can be expressed in binary code. The total number of navigation schemes is less than or equal to 2 ^n×h , and S=2 ^n×h , so all path navigation schemes can be fully represented by S quantum states. The equal-weighted superposition state of the independent variable x (that is, all path navigation schemes) is the input of the quantum calculation, in formula (6) Indicates the probability amplitude σ of the path navigation scheme (its square σ ² represents the probability of the corresponding path navigation scheme), and the S states respectively represent the values of N path navigation schemes x, where S=N, and all the path navigation schemes are in the superposition state The probability of existence of The quantum state in formula (6) is shorthand, for example, the state |0> is actually The total number of bits in all states is n×h bits, n represents the number of vehicles, and the path that each vehicle can choose is represented by h-bit binary. It is the first one (numbered as 0), these S quantum states comprehensively represent all the path navigation schemes, and the storage and input of the path navigation schemes can be effectively solved. The calculation of the function U(x) in the UVCQC algorithm is shown in formula (7).

Performing different quantum calculations requires different quantum circuits, and the quantum circuits need to be determined according to functions. When computing functions in a quantum computer, the unitary transformation U _f must be used. The subscript f refers to a certain function. Different unitary transformations use different For quantum circuits, an auxiliary qubit |z> is also needed in the quantum computer to realize the unitary transformation and obtain the function. The specific calculation process is shown in formula (8).

In this transformation, the input is unique for a particular output.

As shown in Figure 3, after the utility value function U(x) is determined, appropriate quantum circuits and auxiliary qubits need to be set according to U(x) to realize unitary transformation. Each state, that is, the independent variable x corresponds to a utility function value U(x), all independent variables perform the same operation at the same time, and the calculation of the utility value is completed in parallel. According to the nature of quantum mechanics, the calculation process can be obtained as shown in formula (9).

The result of running once in a quantum computing-specific circuit is shown in equation (10). Figure 4 shows the process of one quantum parallel calculation of the UVCQC algorithm.

All U values are stored in another register. Assuming that |i> is observed at one end of the argument, then the register storing the U value is also collapsed into |U(i)>. After i is observed, the register storing the U value is observed The value of is U(i) with probability 1, and vice versa. Through the above analysis, the UVCQC algorithm flow can be obtained as shown in Table 4.

Table 4 UVCQC algorithm

The foregoing solves the acquisition and calculation of various influencing factors of the utility value U. However, although the quantum computer can perform parallel calculations, the extraction of the results is not easy, and it must be a single output, that is, the quantum computer can calculate the utility of all navigation solutions. value, but it will definitely collapse when observed at the output end, and there is only one utility value that can finally obtain the output. For the route navigation problem of urban road network, it is only necessary to obtain an optimal route navigation scheme, so it is only necessary to obtain a corresponding utility value (best utility value). The aforementioned massive disordered utility values have been obtained, and at present, quantum computers already have an efficient algorithm for searching massive disordered data, that is, the quantum search algorithm. However, the quantum search algorithm can only solve the situation where the target state has been determined (the target state refers to the state that needs to be searched, here refers to the state corresponding to the best utility value), and it cannot be searched 100% successfully. In order to adapt to the solution of practical problems, this paper The invention proposes a road network utility value quantum search algorithm RNUQS, the purpose of which is to search the utility value that meets the requirements from the quantum superposition state |U(x)> of the utility value function obtained above, and obtain the corresponding path navigation scheme.

Obtaining the equal-weighted superposition state of the utility value above, the path navigation problem is transformed into an optimal result search problem, and the search set is {|U>}={|U(0)>,|U(1)>,... ,|U(N-1)>}, the number of utility value states is S, the target state (that is, the state to be output) is U _max (the maximum utility value), and the target state is unknown, so it cannot be directly passed through the quantum The search algorithm obtains the maximum utility value and the corresponding path navigation scheme, and the present invention proposes a RNUQS algorithm. In a real road network, the minimum utility value that will not cause congestion can be considered as a fixed experience value k, then any utility value greater than the experience value k can be output as a result, assuming that the number of utility values greater than the experience value k is m , then any one of these m satisfies the output condition.

The number of target states is m, and the function used to determine the target state in the RNUQS algorithm is called an oracle function, let y=U(x), and the oracle function used by RNUQS is shown in formula (11).

Utility value function state|U(x)>After being judged by the oracle function, the state whose function value f(x) is 1 is the target state, and m target states are locked accordingly. Is the function value corresponding to the passing state of the RNUQS algorithm 1 To judge whether the state is the target state, the RNUQS algorithm can obtain the correct output by increasing the probability amplitude of the target state.

In the search process, the oracle function is used to check whether each utility value is the target state, and then the probability range of the target state is expanded through the Grover transformation to increase the probability of the output of the target utility value state, as shown in Figure 5. G in the figure represents the Grover transformation, In the following description, it is referred to as G-transform for short. To perform a G-transform is to perform a specific quantum iteration. After a certain algebraic G-transform, the probability of the target utility value state increases to a certain extent, and finally outputs with a probability close to 1, thus obtaining Appropriate target utility value state.

Among them, G=DO, O means oracle query, assuming that |U _a > is the target state, after the oracle query, the unitary transformation I-2|U _a ><U _a | will be executed, if it is a non-target state, it will not This operation is performed, so the calculation of O is shown in equation (12).

O＝I-2|U _a ><U _a | (12)

The calculation of D is shown in formula (13).

in is an equal-weighted superposition of all elementary states, H represents Hadamard transformation (implemented by Hadamard gate), which is used to prepare equal weight superposition state, Indicates the preparation of an equal-weighted superposition state of n × h positions. After the initial equal-weight superposition state undergoes G transformation each time, the probability range of the target utility value state increases a little, and the non-target utility value state decreases a little. After a certain number of iterations of G transformation, the output probability of the target utility value state is close to 1. At this point, it can be observed at the output end to obtain a suitable utility value.

In order to better understand the role played by a G-transform, a G-transform can be regarded as a quantum transformation of a quantum state in two-dimensional space, which is divided into two steps, O-transform and D-transform. Figure 6(a) is a geometric diagram of a G transformation, and Figure 6(b) is the The geometric diagram of the second G transformation, |U _a > is the target state, and the projection of the current superposition state on the target state represents the output probability amplitude of the target state in the superposition state. After each G transformation, the original state turns to the target state at an angle of 2θ , as shown in Figure 6(a), The process of secondary G transformation is shown in Figure 6(b). The angle α in Figure 6(a) is any acute angle, and the angle θ in Figure 6(a) and 6(b) is equal ( ).

In Figure 6(a), is the initial equal-weighted superposition state, |U _t > represents any current state, all G transformations are to transform |U _t >, |U _a > represents the sum of all target states, and its calculation process is as in formula (14 ) shown.

a _i represents the target state, Indicates the orthogonal state of |U _a >, perpendicular to |U _a >, |U _t > and The included angle is set to α, and The included angle is θ, the equal weight superposition state The projection (probability amplitude) on the target state |U _a > is The meaning is that the probability of observing the target state in the equal-weight superposition state is sin ² θ=m/N, the current state is |U _t >, after a G transformation, the current state is transformed into O|U _t >, |U _t > with O|U _t > on Symmetrical, O|U _t > undergoes a D transformation again, transforming into G|U _t >, O|U _t > and G|U _t > about Symmetrical, it is not difficult to calculate according to the angle relationship. The angle between G|U _t > and |U _t > is 2θ, which has nothing to do with α. After each G transformation, the current state rotates counterclockwise by 2θ.

Since the utility value state |U> is initially in an equal-weighted superposition state, after i-times of G transformations, and The included angle becomes (2i+1)θ. In order to make the target state output with a probability close to 1, (2i+1)θ≈1 should be made, where calculated round represents the nearest integer, so it only needs to perform i transformations to search for a suitable target utility value, and the required time complexity is only

It can be seen from the calculation of the value of i that since i can only take an integer, the probability of finally getting the target state is only very close to 1, so there is a possibility of output errors. In actual path navigation, errors are not allowed. To solve this problem, the present invention proposes a Quantum Error Detection Strategy (Quantum Error Detection Strategy, QEDS), and the QEDS strategy flow is shown in Table 5. The empirical value k can only guarantee a more suitable output, but the output cannot be guaranteed to be sufficiently optimized. In actual situations, an ideal empirical value k _m can be set, and multiple _searches can be performed. On the premise, search as many times as possible, set the time spent for one search as t _c , and the current time spent is t _s (initially 0).

Table 5 QEDS strategy

Therefore, the flow of the RNUQS algorithm proposed by the present invention is shown in Table 6.

Table 6 RNUQS algorithm

It should be understood that the parts not described in detail in this specification belong to the prior art.

It should be understood that the above-mentioned descriptions for the preferred embodiments are relatively detailed, and should not therefore be considered as limiting the scope of the patent protection of the present invention. Within the scope of protection, replacements or modifications can also be made, all of which fall within the protection scope of the present invention, and the scope of protection of the present invention should be based on the appended claims.

Claims (5)

1. A real-time dynamic multi-intersection route navigation quantum search method for urban traffic road network, which maps the real road network into a model graph R (B, E), where B represents a collection of intersection nodes, B _i represents a single intersection node, and i=1 ,2,...,r; r is the total number of intersections, E represents the set of road sections with directions; suppose there are n vehicles in the road network, any vehicle w has the current starting point P _s and the destination end point P _d , then a certain feasible path of the vehicle is represented by continuous adjacent intersection nodes as {P _s ,...,P _i ,...,P _d }; The paths form a feasible path set FPS _n , that is, a path navigation scheme; It is characterized in that the method comprises the following steps: Step 1: Initialize the vehicle set {v ₁ ,v ₂ ,...,v _n } and the set of optional paths according to the number n of vehicles, the information of the starting and ending points, and the optional path of each vehicle where v _i represents the i-th vehicle, Indicates one of all optional paths for the i-th vehicle; Step 2: Carry out quantum encoding {|0>,|1>,...,|2 _n ^×h -1>} on the vehicle and its optional paths 0,1,...,bi, and determine that the quantum state can be Completely represent all route navigation schemes; where b _i represents the number of optional routes for the i-th vehicle, and h represents the minimum number of binary digits required for encoding the optional routes; Step 3: Determine the independent multiplication factors α _i , β _j of each influencing factor according to the road condition information, and determine the utility value calculation function U(x); where each route navigation scheme corresponds to the value of the independent variable x; Step 4: Prepare the equal-weight superposition state |x> of the route navigation scheme, calculate the utility value |U(x)| corresponding to each route navigation scheme x, and obtain the equal-weight superposition state |U(x)> of the utility value function; Step 5: Determine the empirical value k of the utility value, conduct a quantum search on the equal-weighted superposition state |U(x)> of the utility value function, and search out the utility value |U _s > that meets the requirements; Step 6: Output the utility value U _s that meets the requirements and the corresponding route navigation scheme, and perform route guidance for each vehicle. 2. the real-time dynamic multi-intersection path navigation quantum search method of urban traffic road network according to claim 1, is characterized in that, utility value function U (x) described in step 3 is: U(x)=Fr(x)×(α1×Rs(x)+α2×Sl(x)+α3×Ls(x)+α4×Os(x)+α5×Fd(x))-(β1× Ta(x)+β2×Tc(x)+β3×De(x)+β4×Oc(x)+β5×Tl(x)) Among them, Fr(x) indicates whether the road section is reachable, 1 means it is reachable, and 0 means it is not reachable; Rs(x) means the condition of the road section, and the value is [0, 1]; Sl(x) means the speed limit, and the value is [ 0, 1]; Ls(x) represents the lighting condition of the road section, and the value is [0, 1]; Os(x) represents the degree of compliance of the driver to the system recommendation, and the value is [0, 1]; Fd(x) represents the driver’s Familiarity of the road section, the value is [0, 1]; Ta(x) represents the road impact caused by sudden traffic accidents or temporary control, the value is [0, 1]; Tc(x) represents the cost of the selected route Time cost, the value is [0, ∞]; De(x) represents the distance cost of the selected path, and the value is [0, ∞]; Oc(x) represents the fuel cost of the selected path, and the value is [0 , ∞]; Tl(x) represents the influence of traffic lights, and the value is [0, 1]; α _i , β _i represent the independent multiplication factors corresponding to each influencing factor, i=1,2,...,5. 3. the real-time dynamic multi-intersection path navigation quantum search method of urban traffic road network according to claim 1, is characterized in that, the concrete realization of step 4 comprises the following sub-steps: Step 4.1: Use the Hadamard gate to prepare the quantum equal-weight superposition state of the initial independent variable path navigation scheme where N represents the total number of quantum states; Step 4.2: Design the unitary transformation circuit U _U(x) corresponding to the function and the auxiliary qubit |z> that can be used to realize the function calculation; Step 4.3: Input the equal-weight superposition state of the path navigation scheme, and calculate the function U(x) in parallel: Step 4.4: Obtain the equal weight superposition state |U(x)> of the utility value function. 4. the real-time dynamic multi-intersection path navigation quantum search method of urban traffic road network according to claim 1, is characterized in that, the concrete realization of step 5 comprises the following sub-steps: Step 5.1: Give the oracle function f(y) used to determine the target state, and set the corresponding quantum circuit; The equal-weighted superposition state of the utility value function|U(x)>after being discriminated by the oracle function, the state whose function value f(x) is 1 is the target state; Step 5.2: Accumulate the target state to obtain the target state number m and calculate the comprehensive utility value target state |U _a >; Among them, a _i represents the target state, |a _i > represents the quantum form of the i-th target state, and m represents the total number of target states; Step 5.3: Determine the oracle query O according to |U _a >, and determine the transformation of O; O＝I-2| _Ua >< _Ua |; where I denotes an equal-weighted superposition state with the same qubit number as | _Ua >, and < _Ua | denotes the conjugate vector of | _Ua >; Step 5.4: According to the equal weight superposition state Determine the D transformation; in, is an equal-weighted superposition of all elementary states, H represents the Hadamard transformation, which is used to prepare the equal weight superposition state, Indicates the preparation of an equal-weight superposition state of n×h bits; N indicates the total number of quantum states, and |i> indicates the i-th quantum state; Step 5.5: Determine a G transform G=DO by O transform and D transform; Step 5.6: Perform the equal-weight superposition state |U(x)> of the utility-value function times of G transformation, round represents the nearest integer; Step 5.7: Observing the output utility value state |U _out > and the corresponding path navigation scheme |x _out >, searching for the utility value |U _s > that meets the requirements within the time limit; Step 5.8: Output the utility value state | U _s > the navigation path selected for each vehicle in the corresponding path navigation scheme x _s . 5. the real-time dynamic multi-intersection path navigation quantum search method of urban traffic road network according to claim 4, is characterized in that, the concrete realization of step 5.7 comprises the following sub-steps: Step 5.7.1: Observing the output after the G transformation is completed, and obtaining the utility value U _out and the current search elapsed time t _s ; Step 5.7.2: If t _s <t _max , execute the following step 5.7.3, where t _max represents the maximum navigation time interval that can ensure the real-time performance of route navigation; otherwise, execute the following step 5.7.5; Step 5.7.3: If U _out <k, then t _s =t _s +t _c , and perform the step 5.7.2 in turn, where t _c means executing the real-time dynamic multi-intersection route navigation quantum of the urban traffic network once The time required for the search method; otherwise, perform step 5.7.4 below; Step 5.7.4: If U _out <k _m , then k=U _out , t _s =t _s +t _c , and perform step 5.7.2 in turn, where _km represents the ideal utility value set according to experience ; Otherwise, perform the following step 5.7.5; Step 5.7.5: U _s =U _out , output U _s .