Wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm

Abstract

The invention discloses a wireless charging electric vehicle scheduling optimization method based on a quantum approximation optimization algorithm, and the method comprises the steps: carrying out the joint optimization of the driving path of an electric vehicle and the planning position of a charging road section according to the actual operation condition and charging demands of the electric vehicle, constructing a target function and a constraint condition by taking the maximum residual electric quantity of the electric vehicle as a target, and forming a scheduling model; and solving the scheduling model by using a quantum approximate optimization algorithm. According to the invention, quantum computing and dynamic wireless charging technologies are combined, and a dynamic traffic network optimization scheduling model covering multiple electric vehicles is constructed; complex dynamic traffic scenes and wireless charging road section distribution are simulated, charging road section deployment and electric vehicle paths and charging strategies are globally optimized by adopting a quantum algorithm, a better deployment scheme is obtained, the expenditure cost is saved, the remaining electric quantity of vehicles and the overall traffic system efficiency are remarkably improved, and the system performance is improved. And an innovative solution is provided for green and sustainable development of an intelligent traffic system.

Description

Technical Field

[0001] The present invention relates to the field of electric vehicle scheduling optimization in intelligent transportation systems, and particularly to a wireless charging electric vehicle scheduling optimization method based on a quantum approximate optimization algorithm. Background Art

[0002] An electric vehicle is a new type of transportation vehicle mainly driven by electric energy, which uses a rechargeable battery to replace the traditional fuel engine, promoting the green transformation of the transportation field. Its goal is to reduce carbon emissions, improve energy utilization efficiency, and provide a more environmentally friendly way of traveling. The characteristics of electric vehicles include zero emissions, quiet operation, and low energy costs, but they also face problems such as limited driving range, long charging time, and insufficient charging infrastructure.

[0003] A wireless charging section is an innovative facility that transmits energy to a moving electric vehicle in an electromagnetic induction manner by embedding wireless power transfer system technology, achieving dynamic charging. Its goal is to overcome the time and space limitations of fixed charging piles for vehicle charging, improving charging convenience and vehicle driving range. The characteristics of wireless charging sections include no physical contact, high energy transfer efficiency, little impact on traffic operation, and also high automation and real-time adaptation capabilities.

[0004] With the rapid development of intelligent transportation systems and the popularization of the electric vehicle industry, the scheduling optimization problem of wireless charging electric vehicles has attracted increasing attention. To meet the needs of green and low-carbon travel, the dynamic wireless charging technology aims at "efficient charging, high intelligence, and high energy utilization". By optimizing the technical route, reasonably planning the distribution of charging facilities, and improving the energy transfer efficiency, it significantly enhances the operation ability of the transportation system, ensuring the realization of intelligent and efficient traffic management.

[0005] Currently, the optimization research on wireless charging systems mostly focuses on hierarchical models. Researchers gradually decompose problems such as vehicle path planning, distribution of charging sections, and dynamic scheduling strategies through comprehensive analysis of charging demands and traffic networks, and formulate optimal solutions from the global to the local in combination with various constraint factors such as vehicle battery characteristics, traffic flow, and charging power. This hierarchical optimization method effectively improves energy utilization efficiency and reduces resource waste, and is an important tool for solving complex traffic scheduling problems. However, in the process of electric vehicle scheduling optimization, due to the dynamic changes of vehicle demands and traffic conditions over time, the optimal charging strategy and path planning for each task will also be different. Although significant achievements have been made in existing optimization algorithms, there is still room for further optimization in how to make real-time adjustments to charging sections and vehicle path planning under the dynamic influences of costs, the number of vehicles, and real-time road conditions. Exploring how to comprehensively consider the cost and demand change laws in a dynamic environment and determine the optimal charging configuration and scheduling strategy is an important research direction for the optimization of intelligent transportation systems. Summary of the Invention

[0006] Object of the Invention: Aiming at the above problems, the object of the present invention is to provide an optimization method for wireless charging electric vehicle scheduling based on the quantum approximate optimization algorithm, which realizes maximizing the remaining power of all vehicles when they reach the destination by reasonably planning the vehicle driving routes and setting the charging sections, so as to improve the endurance and overall operation efficiency of electric vehicles.

[0007] Technical Solution: An optimization method for wireless charging electric vehicle scheduling based on the quantum approximate optimization algorithm of the present invention includes:

[0008] According to the actual operation conditions and charging requirements of electric vehicles, by jointly optimizing the planned positions of the driving routes and charging sections of electric vehicles, a target function and constraint conditions are constructed with the maximum remaining power of electric vehicles as the goal, and a scheduling model is formed;

[0009] The quantum approximate optimization algorithm is used to solve the scheduling model.

[0010] Further, before constructing the target function, it includes:

[0011] A directed graph G(V, E) is constructed according to the actual traffic routes in the target area, where V is the set of nodes, E is the set of edges, and it is stipulated that electric vehicles drive at a constant speed on each edge, and each electric vehicle passes through each node at most once.

[0012] Further, the target function is:

[0013]

[0014] In the formula, Q total represents the remaining power of the electric vehicle, N represents the number of electric vehicles, s k represents the initial power of the kth electric vehicle, r k represents the power consumption rate of the kth electric vehicle, represents the length of the path i-j, represents whether the kth electric vehicle selects the i-j path, 1 means selected, 0 means not selected, p k represents the charging power of the kth electric vehicle, represents the driving time of the kth electric vehicle on the i-j edge, w ij ∈{0, 1} represents whether the i-j path is a charging section, 1 means it is a charging section, 0 means it is not a charging section.

[0015] Further, the constraint conditions include: path constraint conditions, time constraint conditions, energy constraint conditions and charging section constraint conditions;

[0016] The formula for the path constraint conditions is:

[0017]

[0018] Wherein, a and b represent the starting point and the ending point of the electric vehicle; u and v represent the intermediate nodes of the path;

[0019] The formula for the time constraint condition is:

[0020]

[0021] Wherein, T k represents the maximum allowable driving time of the k-th electric vehicle;

[0022] The formula for the energy constraint condition is:

[0023]

[0024] Wherein, represents the remaining power of the k-th electric vehicle at the n-th node, and c k represents the battery capacity of the k-th vehicle;

[0025] The formula for the charging section constraint condition is:

[0026]

[0027] Wherein, M represents the number of the maximum allowable charging sections.

[0028] Furthermore, solving the scheduling model by using the quantum approximate optimization algorithm includes:

[0029] Converting the scheduling model into a QUBO problem and then into a Hamiltonian;

[0030] Initializing the quantum state and constructing a QAOA quantum circuit corresponding to the Hamiltonian, and finding the optimal quantum state in the QAOA quantum circuit.

[0031] Furthermore, converting the scheduling model into a QUBO problem and then into a Hamiltonian includes:

[0032] When converting the goal of maximizing the remaining power at the end point into the QUBO form, it needs to be converted into the minimized form, that is, minH 1 =-Q total Then, there is:

[0033]

[0034] The QUBO adopts the method of penalty function to convert the constraint conditions into penalty terms, and the path constraint conditions are respectively converted into the following penalty terms:

[0035]

[0036] The time constraint is transformed into the following penalty term:

[0037]

[0038] The energy constraint is transformed into the following penalty term:

[0039]

[0040] When the penalty term H 8 increases;

[0041]

[0042] When the penalty term H 8 increases;

[0043] The charging section constraint is transformed into the following penalty term:

[0044]

[0045] Then the objective function of the QUBO problem is:

[0046] H = H 1 + p 1 H 2 + p 2 H 3 + p 3 H 4 + p 4 H 5 + p 5 H 6 + p 6 H 7 + p 7 H 8 + p 8 H 9 + p 9 H 10

[0047] where p i is the penalty coefficient used to adjust the constraint strength to ensure that all constraint conditions are satisfied during the optimization process;

[0048] The original QUBO problem is partitioned according to vehicles, and for each vehicle, a sub - problem is constructed;

[0049] Then the Hamiltonian is constructed.

[0050] Furthermore, constructing the QUBO problem into a Hamiltonian includes:

[0051] The state and interaction of qubits are represented using Pauli operators. For binary variables and w ij , the Pauli operator σ z is used for representation, where the eigenvalues of σ z are ±1, corresponding to the binary variables 0 and 1; let then when , corresponds to When , corresponds to Similarly, for w ij , let

[0052] The Hamiltonian corresponding to the objective function is:

[0053]

[0054] The path constraint condition is transformed into a Hamiltonian, expressed as:

[0055]

[0056]

[0057] The Hamiltonian for flow balance is:

[0058]

[0059] The path constraint condition restricting paths starting from intermediate nodes is transformed into a Hamiltonian as:

[0060]

[0061] The time constraint condition is transformed into a Hamiltonian as:

[0062]

[0063] The energy constraint condition is transformed into a Hamiltonian as:

[0064]

[0065] Among them, represents the set of edges that vehicle k passes through from the starting point a to node n;

[0066] The non - negativity of energy is transformed into a Hamiltonian as:

[0067]

[0068]

[0069] The energy not exceeding the maximum energy of the battery is converted into the Hamiltonian as follows:

[0070]

[0071] The constraint conditions of the charging section are converted into the Hamiltonian as follows:

[0072]

[0073] The final total Hamiltonian H is the sum of the Hamiltonian of the objective function term and the Hamiltonians of all constraint condition terms, that is:

[0074] H = H obj + H path1 + H path2 + H path3 + H path4 + H flow + H nodeout + H time +

[0075] H energy1 + H energy2 + H charge 。

[0076] Furthermore, finding the optimal quantum state in the QAOA quantum circuit includes the following steps:

[0077] S21, encoding the position, destination, charging demand of the electric vehicle and the road section information into the state of quantum bits, and converting the scheduling model into the input of the QAOA quantum circuit;

[0078] S22, measuring the bit string of the quantum state in the QAOA quantum circuit, calculating the value of the loss function using the bit string of the quantum state, and updating the parameters γ of the cost Hamiltonian and the parameter β of the mixing Hamiltonian;

[0079] S23, repeating step S22 until the solution of the sub-problem reaches stability or satisfies the termination condition and stops the iteration;

[0080] S24, fusing the optimal solutions of all sub-problems to construct an approximation of the global optimal solution;

[0081] S25, evaluating the quality of the solution vector using the objective function of the original problem to find the optimal solution.

[0082] Beneficial effects: Compared with the prior art, the significant advantages of the present invention are:

[0083] The present invention combines quantum computing and dynamic wireless charging technologies, proposes a wireless charging electric vehicle scheduling optimization method based on the quantum approximate optimization algorithm, and constructs a scheduling model for optimizing the dynamic traffic network covering multiple electric vehicles on this basis. By simulating complex dynamic traffic scenarios and the distribution of wireless charging sections, a quantum algorithm is used to globally optimize the deployment of charging sections, the paths of electric vehicles, and the charging strategies, obtaining a better deployment plan and saving costs, significantly improving the remaining battery power of vehicles and the efficiency of the overall traffic system, and providing an innovative solution for the green and sustainable development of intelligent transportation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 is a flowchart of a wireless charging electric vehicle scheduling optimization method based on the quantum approximate optimization algorithm;

[0085] Figure 2 is the measurement gate of qubits in QAOA;

[0086] Figure 3 is a partial quantum circuit diagram constructed;

[0087] Figure 4 is an iterative process diagram of the quantum approximate optimization algorithm;

[0088] Figure 5 is a traffic network diagram;

[0089] Figure 6 is a deployment diagram of charging sections planned by classical algorithm calculation;

[0090] Figure 7 is a deployment diagram of charging sections planned by quantum approximate optimization algorithm calculation;

[0091] Figure 8 is the vehicle path of the typical vehicle EV1 calculated by classical algorithm;

[0092] Figure 9 is the vehicle path of the typical vehicle EV1 calculated by quantum approximate optimization algorithm;

[0093] Figure 10 is a comparison diagram of the maximum remaining battery power between classical algorithm and quantum algorithm. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0094] In order to make the objectives, technical solutions, and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0095] The wireless charging electric vehicle scheduling optimization method based on the quantum approximate optimization algorithm described in this embodiment has a flowchart as Figure 1 shown, and this method includes the following steps:

[0096] S110. According to the actual operation conditions and charging requirements of electric vehicles, by jointly optimizing the planned positions of the driving routes and charging sections of electric vehicles, a target function and constraint conditions are constructed with the maximum remaining power of the electric vehicle as the goal, forming a scheduling model.

[0097] S120. Use the quantum approximate optimization algorithm to solve the scheduling model.

[0098] The present invention relates to the field of electric vehicle scheduling optimization in intelligent transportation systems, specifically focusing on the optimization problem of the scheduling strategy of wireless charging electric vehicles during driving. The aim is to solve the problem of how to maximize the remaining power of all vehicles when they reach the destination by reasonably planning the vehicle driving routes and setting the charging sections on the premise of ensuring that all electric vehicles reach the destination before the specified deadline, thereby improving the endurance and overall operation efficiency of electric vehicles. Combining quantum computing and dynamic wireless charging technology, the quantum approximate optimization algorithm (QAOA) is used to globally optimize the deployment of charging sections, the paths of electric vehicles, and the charging strategies, obtaining a better deployment plan and saving the expenditure cost, significantly improving the remaining power of the vehicles and the efficiency of the overall transportation system, and providing an innovative solution for the green and sustainable development of intelligent transportation systems.

[0099] The operation cycle of wireless charging electric vehicles consists of manufacturing, initial deployment, actual use, and subsequent maintenance. During the manufacturing and initial deployment stages, the vehicles and wireless charging sections have not been put into actual operation. Therefore, the scheduling optimization in this example mainly targets the use stage of electric vehicles. According to the actual operation conditions and charging requirements of electric vehicles, on the premise of meeting the constraints of paths, time, power, and charging sections, the deployment of section paving and the driving routes and charging strategies of vehicles are optimized to maximize their remaining power while minimizing the operation cost.

[0100] Further, before constructing the target function, it includes:

[0101] A directed graph G(V, E) is constructed according to the actual traffic routes in the target area, where V is the set of nodes, E is the set of edges, and it is stipulated that the electric vehicle travels at a constant speed on each edge, and each node can be passed by the electric vehicle at most once.

[0102] Since the scheduling optimization of wireless charging electric vehicles requires higher charging efficiency and lower operating costs of the system on the premise of ensuring that all vehicles arrive at their destinations on time, the costs here mainly refer to the setup costs of charging facilities and the energy consumption costs of vehicles. Since in this example, not only the driving routes of electric vehicles need to be optimized, but also the setup locations of the charging sections need to be optimized, which belongs to a multi-objective optimization problem. Therefore, in this example, the linear weighting method is used to transform the multi-objective problem into a single-objective problem for solution. So the optimization objective of this problem is: by planning the layout of the charging sections in the traffic network and determining the best driving route for each vehicle, while satisfying the constraints of routes, time, energy, and charging sections, a target function is constructed with the goal of maximizing the remaining battery power of electric vehicles. The target function is:

[0103]

[0104] In the formula, Q total represents the remaining battery power of the electric vehicle, N represents the number of electric vehicles, s k represents the initial battery power of the k-th electric vehicle, r k represents the power consumption rate of the k-th electric vehicle, represents the length of the path i-j, represents whether the k-th electric vehicle selects the i-j path. 1 means selection, 0 means non-selection, p k represents the charging power of the k-th electric vehicle, represents the driving time of the k-th electric vehicle on the i-j edge, w ij ∈{0,1} represents whether the i-j path is a charging section. 1 means it is a charging section, 0 means it is not a charging section. i and j are the starting and ending points of each edge.

[0105] To ensure meeting the actual operation requirements, the following constraint conditions are further introduced. The constraint conditions include: path constraint conditions, time constraint conditions, energy constraint conditions, and charging section constraint conditions.

[0106] Path constraint means ensuring that a unique path from the starting point to the ending point is generated for each vehicle. Since in many algorithms, such as path search and traversal algorithms, they are designed according to the logic of expanding outward from the established starting point, and the reverse does not conform to the strategy of this example. Therefore, the following constraints are set to prevent it from selecting a path from the remaining nodes to the starting point. It is expressed by the formula as:

[0107]

[0108] To facilitate the orderly progress and efficient allocation of resources, a logic of extending outward from the starting point is set up to ensure that only one path from the starting point to the remaining nodes can be selected. The following constraints are set and expressed by the formula as:

[0109]

[0110] Since the calculation logic can be simplified from the remaining nodes to the end point, and complex backtracking and confusion can be avoided, the constraint that only one path from the remaining nodes to the end point can be selected is set, which can be expressed as:

[0111]

[0112] Starting from the end point in reverse will destroy the logical order and result accuracy, so it is set that a path constraint cannot be selected from the end point to the remaining nodes, which can be expressed as:

[0113]

[0114] The above four path constraints ensure that the vehicle path starts from the starting point and ends at the destination.

[0115] In the directed graph algorithm of vehicle path planning, if the vehicle can pass through the same node multiple times, it will fall into a circular path, resulting in resource waste, chaotic travel, and inability to effectively approach the target. Limiting the path to only pass once can ensure the unidirectionality and efficiency of the path, follow the optimal path search strategy, and make the planning orderly and accurate. Therefore, the following three constraints are set to ensure that the vehicle can only pass through a node once, avoiding the situation of going around in circles in the directed graph.

[0116] Ensure that the inflow and outflow of vehicles at any intermediate node are balanced, avoid vehicles appearing or disappearing without reason, and prevent unreasonable circulation and flow imbalance, which can be expressed as:

[0117]

[0118] Each vehicle is restricted to depart from any intermediate node and can only choose one path to leave at most, preventing the vehicle from going in multiple directions from an intermediate node at the same time, ensuring the uniqueness and unidirectionality of the path, which can be expressed as:

[0119]

[0120] It is ensured that each vehicle can reach any intermediate node through at most one path. Together with the previous constraint, it limits the path selection of the vehicle at the intermediate node from both the departure and arrival aspects, ensuring that the vehicle does not pass through the node repeatedly. It can be expressed as:

[0121]

[0122] Where a and b represent the starting point and end point of the electric vehicle; u and v represent the intermediate nodes of the path.

[0123] Time constraint means ensuring that each vehicle arrives at the destination before the specified time. In the scenarios of logistics distribution and transportation, time is of crucial importance. Ensuring that vehicles arrive at the destination before the specified time can meet the timeliness requirements of customers, avoid default fines, and enhance service credibility. At the same time, it is conducive to reasonably arranging subsequent trips, optimizing the overall allocation of traffic resources, maintaining the efficient and stable operation of the transportation system, and safeguarding the interests and benefits of all parties.

[0124] The formula for the time constraint condition is:

[0125]

[0126] In the formula, T k represents the maximum allowable driving time of the kth electric vehicle.

[0127] Energy constraint means ensuring that the energy of each vehicle during driving is non - negative and does not exceed the maximum battery capacity. Vehicle driving requires stable energy support. Non - negative energy can ensure normal operation and avoid breaking down midway. Not exceeding the maximum battery capacity can prevent safety hazards caused by overcharging or overloading and extend the battery life. Through energy constraint, it helps to maintain the safety and stability of the vehicle system, ensure the smooth progress of the journey, and improve driving reliability and vehicle use efficiency.

[0128] The formula for the energy constraint condition is:

[0129]

[0130] In the formula, represents the remaining power of the kth electric vehicle at the nth node, and c k represents the battery capacity of the kth vehicle.

[0131] The charging section constraint means that the number of charging sections is not greater than a given upper bound. In vehicle operation planning, limiting the number of charging sections not to be greater than a given upper bound can, on the one hand, control the charging cost and time consumption and avoid affecting the transportation efficiency due to over - reliance on charging facilities; on the other hand, it can prompt reasonable route planning, accurately arrange the journey according to the vehicle's endurance and charging layout, and ensure the high efficiency and economy of the overall operation.

[0132] The formula for the charging section constraint condition is:

[0133]

[0134] In the formula, M represents the number of the maximum allowable charging sections.

[0135] Using the above - constructed constraint conditions and objective function, a scheduling model for the dynamic wireless charging section layout and vehicle path planning of electric vehicles based on 0 - 1 programming and multi - objective optimization is constructed. This scheduling model is a mixed - integer linear programming with progressive - relationship constraints.

[0136] Furthermore, using the Quantum Approximate Optimization Algorithm (QAOA) to solve the scheduling model includes:

[0137] Converting the scheduling model into a QUBO problem and then into a Hamiltonian;

[0138] Initializing the quantum state and constructing a QAOA quantum circuit corresponding to the Hamiltonian to find the optimal quantum state in the QAOA quantum circuit.

[0139] Furthermore, converting the scheduling model into a QUBO problem and then into a Hamiltonian includes:

[0140] When converting the remaining circuit with the goal of maximizing the end point into QUBO form, it needs to be converted into a minimized form, i.e., minH 1 =-Q total .

[0141]

[0142] Constraint conversion:

[0143] QUBO uses the method of penalty function to convert the constraint conditions into penalty terms.

[0144] (1) Path constraint conversion into penalty terms

[0145] It is not possible to select a path from the end point to the start point:

[0146]

[0147] Ensure that each vehicle has a unique starting path:

[0148]

[0149] Ensure that each vehicle has a unique end path:

[0150]

[0151] It is not possible to select a path from the end point to the remaining nodes:

[0152]

[0153] Vehicle path flow conservation to prevent loops:

[0154]

[0155] (2) Time constraint conversion into penalty terms to ensure that each vehicle arrives at the destination within the specified time:

[0156]

[0157] (3) The energy constraint is transformed into a penalty term to ensure that the energy of each vehicle is non - negative during driving:

[0158]

[0159] When the penalty term H 7 increases;

[0160] To ensure that the battery charge of each vehicle does not exceed the maximum battery capacity, the penalty term is:

[0161]

[0162] When the penalty term H 8 increases;

[0163] (4) The charging section constraint is transformed into a penalty term as:

[0164]

[0165] The objective function of the final QUBO problem is:

[0166] H = H 1 + p 1 H 2 + p 2 H 3 + p 3 H 4 + p 4 H 5 + p 5 H 6 + p 6 H 7 + p 7 H 8 + p 8 H 9 + p 9 H 10

[0167] where p i is a penalty coefficient used to adjust the constraint strength to ensure that all constraint conditions are satisfied during the optimization process.

[0168] The original QUBO problem is converted into sub - problems. The original QUBO problem is partitioned according to vehicles, and for each vehicle, a sub - problem is constructed. The objective function and constraint conditions of the sub - problem contain terms related to that vehicle, and the validity and global optimality of the solution are guaranteed when fusing the solutions of the sub - problems.

[0169] Then the Hamiltonian is constructed, including:

[0170] The Pauli operators are used to represent the states and interactions of qubits. For binary variables and w ij , using the Pauli operator σ z to represent, where the eigenvalues of σ z are ±1, corresponding to the binary variables 0 and 1. Let then when , corresponds to When , corresponds to Similarly, for w ij , let

[0171] The Hamiltonian corresponding to the objective function is:

[0172]

[0173] (1) The path constraint is transformed into a Hamiltonian as:

[0174] For the path constraint that a path from the remaining nodes to the starting point cannot be selected, it is transformed into:

[0175]

[0176] For the path constraint that only one path from the starting point to the remaining nodes can be selected, it is transformed into:

[0177]

[0178] The path constraint from the remaining nodes to the end point is transformed into:

[0179]

[0180] The path constraint that a path from the end point to the remaining nodes cannot be selected is transformed into:

[0181]

[0182] Flow balance:

[0183]

[0184] The path constraint restricting the departure from the intermediate nodes is transformed into:

[0185]

[0186] (2) The time constraint is transformed into a Hamiltonian as:

[0187]

[0188] (3) The energy constraint is transformed into a Hamiltonian as:

[0189]

[0190] Among them, represents the set of edges that vehicle k passes from the starting point a to node n; the energy is non - negative:

[0191]

[0192] The energy does not exceed the maximum energy of the battery:

[0193]

[0194]

[0195] (4) The charging section constraint is transformed into a Hamiltonian as:

[0196]

[0197] The final total Hamiltonian H is the sum of the Hamiltonian of the objective function term and the Hamiltonians of all constraint condition terms, that is:

[0198] H = H obj + H path1 + H path2 + H path3 + H path4 + H flow + H nodeout + H time

[0199] + H energy1 + H energy2 + H charge

[0200] Each decision is transformed into a binary variable, such as whether to set a wireless charging section on a certain section, whether the vehicle is traveling on a certain section, and whether the vehicle is charging on a certain section. Then, a target function is constructed by maximizing the remaining battery power, and the combinations of all decision variables are associated with the target to form a quadratic unconstrained binary optimization (QUBO) problem. However, when there are more electric vehicles to be optimized, the road conditions are more complex or there are more constraint conditions, the original QUBO problem will contain a large number of variables, which undoubtedly increases the complexity of quantum computing and poses higher requirements for the number of qubits. At this time, by transforming it into the sub - problem subQUBO method, some key variables can be screened out from the original QUBO problem to form a series of smaller sub - problems. These sub - problems can be solved independently, and then the solution results are integrated through iterative updating to continuously approach the global optimal solution of the problem.

[0201] Initializing the quantum state means setting all qubits to the zero state |0>, and then converting them into a uniform superposition state by applying the Hadamard gate

[0202] First, set all qubits to the zero state |0>, which means that the state of each qubit is in the 0 state at the lowest energy level. This can be achieved by applying specific quantum gate operations to each qubit separately. After that, apply the Hadamard gate to transform the qubits. The Hadamard gate is a common quantum gate that can transform a qubit from the 0 state to a uniform superposition state of the 0 state and the 1 state. This makes each qubit enter a superposition state that is neither 0 nor 1, but an equal-probability mixture of the two possibilities of 0 and 1. This uniform superposition state contains rich quantum information and lays the foundation for subsequent quantum computing and quantum information processing.

[0203] The process of constructing a QAOA quantum circuit corresponding to the Hamiltonian is as follows:

[0204] (1) Construct the QAOA quantum circuit

[0205] The QAOA circuit consists of alternating cost Hamiltonian H C and mixing Hamiltonian H M to form a p-layer cycle. The cost Hamiltonian H C corresponds to the objective function of the problem, while the mixing Hamiltonian H M is used to make a smooth transition between different qubit configurations.

[0206] When designing a quantum circuit, first perform quantum state encoding to encode the parameters of the problem, such as the position of the vehicle, the destination, the charging demand, the section information, etc., into the state of the qubits. At the same time, problem instance encoding is also required to transform the entire problem instance into the input of the quantum circuit. Then, select quantum gates to implement the iterative optimization process of the algorithm. In this example, QAOA is used, so the selected quantum gates can be the identity gate (U3), the CNOT gate, the identity gate (U3), the CNOT gate, etc. Finally, design the quantum gate sequence. By considering the connectivity between qubits and how to simulate the constraints of the problem in the quantum circuit, design the sequence of gate operations to implement the operations specified in QAOA.

[0207] Figure 2It is the measurement gate for qubits in QAOA. The red bar part represents the QAOA circuit. By adding a measurement gate to each qubit after the circuit, the result after quantum computing can be obtained. Subsequently, this circuit will be input into the PassManager for compilation and optimization. The role of the qubit measurement gate: In the QAOA circuit, after each qubit undergoes a series of quantum gate operations, the QAOA circuit represented by the red bar part here, adding a measurement gate, aims to obtain the state information of the qubit after quantum computing. Since qubits are in quantum states such as superposition states during the computing process, and the measurement operation will collapse the quantum state to a definite classical state, usually 0 or 1, thus obtaining a result that can be used for subsequent analysis and processing. 1 represents choosing this path or this path being a charged circuit section. A partial circuit diagram is as shown in Figure 3 shown. In the figure, q represents a qubit, which is the basic information unit in quantum computing, similar to a bit in classical computing, but has quantum mechanical properties such as superposition states and entanglement states. For example, q 20 , q 64 , q 16 etc. are different qubits. R Z is a quantum gate operation. Specifically, it is a rotation gate around the Z-axis. The parameters following the R Z gate, such as n / 2, -n, etc., represent the rotation angle or related parameters, and these parameters will affect the state transformation of the qubit. is also a quantum gate operation, called the square root X gate. It performs a specific transformation operation on the qubit and is one of the basic elements for constructing quantum circuits and implementing quantum algorithms. Ancilla refers to an auxiliary qubit. In quantum computing, auxiliary qubits are often used to assist the main qubits in completing some complex computing tasks or quantum error correction operations. For example, the ancilla 36 and ancilla 37 in the figure are auxiliary qubits. Meas represents measurement. In quantum computing, measurement is an operation to obtain the state information of a qubit, but measurement will cause the state of the qubit to collapse, from a quantum state such as a superposition state to a definite classical state such as 0 or 1. Meas 65 in the figure represents measurement at a certain step or position, and 65 is a certain parameter or identifier related to the measurement. Ecr usually refers to the echo cross resonance gate, which is a quantum gate that acts on two qubits and is used in quantum circuits to achieve specific qubit state manipulation and quantum logic operations. It is one of the basic elements for constructing quantum algorithms and quantum circuits. By adding a measurement gate to each qubit after the circuit, the result after quantum computing can be obtained. Subsequently, this circuit will be input into the Pass Manager for compilation and optimization.

[0208] (2) Parameterized quantum gate

[0209] In each layer, the cost Hamiltonian and the mixer Hamiltonian are applied, and these Hamiltonians are implemented through parameterized quantum gates. Denote these parameters as γ for the cost Hamiltonian and β for the mixer Hamiltonian. The optimization of the parameters γ and β is a key step in the QAOA algorithm and can be performed on a classical computer. The optimization objective is to minimize the expected value of the cost Hamiltonian, that is, to find a set of parameters that minimize the energy value of the quantum state. This process uses the gradient descent method, and by iteratively adjusting the values of γ and β, it gradually approaches the optimal solution. In each layer, the application order of the parameterized quantum gates is to first perform the evolution operation of the cost Hamiltonian and then perform the evolution of the mixer Hamiltonian. This order is repeated in the loop of p layers, forming the structure of the entire QAOA quantum circuit. Through carefully selected parameters and quantum gate operations, the QAOA quantum circuit can effectively explore the solution space of the problem and finally approach the approximate optimal solution of the problem.

[0210] (3) Perform the evolution gate operation

[0211] Alternately apply the cost Hamiltonian H C and the mixer Hamiltonian H M to achieve a specific evolution on the quantum state, and this operation acts on the initial quantum state. First, prepare an initial quantum state, usually this state is a uniform distribution where each qubit is in a superposition state. Then, construct the evolution operation. The evolution operation of QAOA consists of the alternate application of the cost Hamiltonian and the mixer Hamiltonian, and the evolution operation of each layer includes: the evolution of the cost Hamiltonian and the evolution of the mixer Hamiltonian. Secondly, parameterize the quantum gates. The evolution operations of the cost Hamiltonian and the mixer Hamiltonian are implemented through parameterized quantum gates, and the parameters γ and β of these quantum gates will be optimized during the execution of the algorithm to achieve the goal of minimizing the expected value of the cost Hamiltonian. Finally, perform multi-layer evolution. The evolution operation is repeated in p layers, and each layer is the alternate application of the cost Hamiltonian and the mixer Hamiltonian, forming the entire QAOA quantum circuit.

[0212] Furthermore, finding the optimal quantum state in the QAOA quantum circuit includes the following steps:

[0213] S21, Encode the position, destination, charging demand, and road segment information of the electric vehicle into the state of qubits, and transform the scheduling model into the input of the QAOA quantum circuit;

[0214] S22, Measure the bit string of the quantum state in the QAOA quantum circuit, calculate the loss function value using the bit string of the quantum state, and update the parameters γ of the cost Hamiltonian and β of the mixer Hamiltonian;

[0215] S23, Repeat step 22 until the solution of the sub-problem reaches stability or satisfies the termination condition and stop the iteration;

[0216] S24. Integrate the optimized solutions of all sub-problems to construct an approximation of the global optimized solution.

[0217] S25. Use the objective function of the original problem to evaluate the quality of the solution vector and find the optimal solution.

[0218] After each QAOA evolution operation, to obtain a sample solution, i.e., a possible state of the quantum system under that specific parameter setting, the quantum state is measured. This process involves collapsing the quantum state from a superposition state to a classical state, which is achieved by measuring the states of all qubits. The measurement result represents a potential solution and can be used to evaluate the energy level under the current parameter setting. To optimize the parameters γ and β to make the quantum state closer to the optimal solution of the problem, an iterative process is required. In each iteration, the classical computer optimizes the parameters γ and β based on the energy of the sample solution obtained from the previous round of measurement results to reduce the expected energy value. This process is achieved by adjusting the parameters of the cost Hamiltonian and the mixing Hamiltonian, with the goal of making the quantum state closer to the low-energy state of the problem, thus making it more likely to find the optimal solution. In the sub-problem strategy, this iterative optimization process is carried out independently for each sub-problem. For each sub-problem, the classical computer optimizes the γ and β parameters to find the parameter set that can produce a low expected energy value. This process is repeated multiple times until the solution of the sub-problem reaches stability or meets the termination conditions, such as reaching a preset number of iterations or the energy improvement is no longer significant. Finally, the optimized solutions of all sub-problems are integrated to construct an approximation of the global optimized solution. This step obtains a solution that is closer to the optimal solution of the original problem by integrating the solutions of the sub-problems and considering their interactions in the global problem.

[0219] The solutions of the sub-problems are integrated into the global solution vector. Through the weighted average method, according to the quality and improvement degree of the sub-problem solutions, the global solution vector is gradually adjusted to make it closer to the optimal solution. Then, global optimization is carried out, focusing on the continuous evaluation of the quality of the solution vector and the adjustment of the strategy. The objective function of the original problem is used to evaluate the quality of the solution vector and monitor its closeness to the optimal solution. When the optimization process stalls or the quality improvement is not significant, strategies such as adjusting the sub-problem division method, the parameter optimization algorithm, or the number of iterations can be adopted to stimulate the vitality of the algorithm, as well as the setting of termination conditions, such as the upper limit of the number of iterations, the improvement threshold of the solution vector, or the preset standard of the energy level, to ensure that the algorithm stops at the appropriate time and avoid ineffective calculations.

[0220] After a series of iterative optimizations, the parameter set with the best performance can be locked, and these parameters are used to carefully prepare the target quantum state on a quantum computer. Immediately afterwards, this quantum state is measured independently multiple times, aiming to collect sufficient sample data from which an approximate optimal solution to the problem can be parsed. The in-depth analysis of the measurement results involves calculating the energy expectation value and carefully comparing it with the known optimal solution or the objective function of the problem. This process aims to evaluate the quality of the approximate solution. By carefully comparing the measurement results at different iterative stages, the progress of the optimization process and the convergence of the algorithm can be effectively examined, ensuring that the entire algorithm is on the right track and steadily approaching the optimal solution. When constructing an approximation of the global optimal solution, integrating the solutions of all sub-problems becomes a crucial step, which requires skillfully integrating the optimal solutions of each sub-problem into a coordinated overall solution. To ensure the high quality and feasibility of the global solution, additional optimization strategies may be needed, such as re-optimizing the global solution vector or applying more complex integration algorithms to properly handle potential conflicts between the solutions of sub-problems.

[0221] The effects of the wireless charging electric vehicle scheduling optimization method based on the quantum approximate optimization algorithm described in the present invention are further illustrated by the following examples.

[0222] Suppose the number of electric vehicles participating in the planning is m = 88, there are 119 nodes and 256 edges in the traffic network, and each electric vehicle has random starting and ending points [40, 100], initial battery energy E init = [30, 50] kWh and a fixed battery capacity [80, 100] kWh. It is stipulated that its energy consumption is linearly related to the driving mileage, and the power consumption rate is [10, 15] kWh / 100 km. The wireless charging section provides dynamic charging with a constant charging power of 100 kw, and the charging efficiency fluctuation is not considered for the time being. Each section in the traffic network has a distance, and the driving time of the vehicle on the section is related to the distance and the vehicle speed. It is assumed that the vehicle travels at a constant speed on each edge, and the driving speeds on different edges are different, with the speed range being [50, 120] km / h, and each node can be passed by the vehicle at most once. During the driving process of the electric vehicle on the wireless charging section, its charging process is closely coupled with the driving process, and the driving of the electric vehicle on a section with continuous wireless charging function can be regarded as a complete and inseparable process. According to the principles of traffic and energy engineering, each time the electric vehicle passes through a set wireless charging effective section is regarded as an effective unit time.

[0223] When an electric vehicle is in a wireless charging state, the efficiency of power replenishment is restricted by various factors. The time taken to replenish the power to an effective unit is tentatively set at 6 minutes, which can be understood as the amount of power replenishment required to support the vehicle to continue driving a critical distance. Main factors considered include wireless charging power, the receiving efficiency of the vehicle battery, and the impact of the road environment on charging. According to experience and relevant tests, it takes an average of 36 minutes for the vehicle to charge from a lower power level to a higher power level. Therefore, the complete charging process from low power to high power should be regarded as 6 effective unit times.

[0224] The ultimate task of this part is to ensure that all electric vehicles can reach their respective destinations smoothly before the specified deadline. By strategically deciding which traffic network sections should be set as charging sections and planning the optimal driving routes for each vehicle, the remaining power of all vehicles when they reach their destinations can be maximized, aiming to improve the endurance performance and overall efficiency of electric vehicles. Moreover, through the calculation and comparison of the classical algorithm and the QAOA in the present invention, it is concluded that the QAOA solution is better.

[0225] To sum up, in the case of 88 wireless charging electric vehicles, the scheduling model for the dynamic wireless charging section layout and vehicle path planning of electric vehicles based on 0-1 programming and multi-objective optimization is as follows:

[0226]

[0227] The above-mentioned mixed integer linear programming with a progressive relationship can be solved using Python, Matlab, and an IBM quantum computer. The total remaining power of all vehicles calculated is:

[0228] Q toyal = 5659.39 kWh

[0229] Then, the above scheduling model is solved using the branch and bound method in the classical algorithm and the quantum approximate optimization algorithm described in this example respectively. After having the basic objective function and constraint conditions, the quantum approximate optimization algorithm is used to solve the scheduling model. Figure 4It is a diagram showing the iterative process of the Quantum Approximate Optimization Algorithm (QAOA). The optimizer is COBYLA and the number of iterations is 55. The abscissa of the diagram represents the number of iterations, which represents different iterative stages experienced by the algorithm or model during training; the ordinate represents the value of the loss function, which is an indicator measuring the difference between the model's prediction result and the actual result. There is a black broken line in the diagram, which connects the loss function values corresponding to each iteration number. This broken line shows the changing trend of the loss function value as the number of iterations increases. Initial stage (number of iterations close to 0): The loss function value is relatively high, around 11000 approximately. This indicates that in the initial stage of training, the difference between the model's prediction result and the actual result is relatively large, and the performance of the model is poor. Downward trend: As the number of iterations increases, the loss function value generally shows a downward trend. For example, when the number of iterations reaches around 10, the loss function value drops to approximately 9000; by the 20th iteration, it further drops to around 7000. This shows that the model continuously learns and optimizes during training, gradually improving the prediction accuracy and causing the loss function value to gradually decrease. Fluctuation situation: Although the overall trend is downward, the broken line does not decrease smoothly but shows some fluctuations. For example, when the number of iterations is close to 20, the loss function value has a small increase and then continues to decrease. Such fluctuations are quite common in the process of machine learning training and may be caused by factors such as the model encountering local optimal solutions or data randomness during the learning process. When using QAOA in quantum computing, the main reasons for the fluctuations in the loss function value include: the quantum state is vulnerable to environmental noise interference and the quantum gate operations are inaccurate, as well as the probabilistic nature of the quantum measurement results and the uncertainty caused by the limited number of samplings. These factors interact with each other, causing the loss function value to show a non-smooth fluctuation situation during the iterative process.

[0230] Figure 5 It is a traffic network diagram generated based on real data. This network diagram is a directed graph with a total of 119 nodes and 256 edges, and all nodes in the directed graph are connected.

[0231] The charging paths of the traffic network are calculated respectively through classical algorithms and the quantum algorithm described in this example, and a comparison diagram is obtained as Figures 6 to 7As shown in the figure, in a transportation network with a total of 256 edges, there are 67 charging sections optimized by the classical algorithm, and 63 charging sections optimized by the QAOA of the present invention. Although the difference in their numbers is not significant, in practical applications, considering the high construction cost of wireless charging sections, this difference will have an important impact on the overall cost. Under the branch and bound method corresponding to the classical algorithm, there are 67 charging sections, the deployment mileage is 484.45 km, and the construction cost is about 224 billion yuan; while under the QAOA algorithm, the number of charging sections is 63, the deployment mileage is 427.88 km, and the construction cost is about 198 billion yuan. By comparison, it can be seen that the quantum approximate optimization algorithm reduces the number of charging sections by about 5.97% on average, and the total construction cost is reduced by 11.6% on average. This shows that the quantum algorithm not only optimizes the layout of charging sections, but also shows significant advantages in cost control. Especially when the construction cost of wireless charging sections is high, this cost advantage is more prominent, and it can bring greater economic benefits to the charging facility planning of the transportation network.

[0232] Figure 8 and Figure 9 Taking the path planning of new energy vehicle EV1 as an example, in the figure, the triangle pointing upward is the starting point of the vehicle, and the downward one is the end point. The gray part is the transportation network diagram, and the black one is the driving route of EV1. After the branch and bound algorithm is calculated, after using the quantum approximate optimization algorithm, the remaining power of the vehicle increases by 48.12%, and the driving time is reduced by 12.5% on average, that is, the vehicle realizes the optimization of charging energy in a shorter time. The comparison data is shown in Table 1 below.

[0233] Table 1

[0234] Remaining battery power Driving time Branch and bound method 54.57 kWh 324s Quantum approximate optimization algorithm 80.83 kWh 288s

[0235] Figure 10This is a comparison chart of the maximum remaining battery capacity between classical algorithms and quantum algorithms, with data from a total of 88 vehicles. The breakpoints among them indicate that the solutions for some vehicles are invalid and will not be discussed. The dashed line represents the result obtained by the branch and bound method, and the solid line represents the result obtained by the quantum approximate optimization algorithm. It can be seen from the figure that for almost all EV vehicles, the remaining battery capacity calculated by quantum computing is greater than or equal to that calculated by classical algorithms, excluding the infeasible cases, indicating that the quantum algorithm generally has high accuracy. Due to its own characteristics, it can find a better solution than classical algorithms in the search space, making the overall approximation closer to the global optimum. The more obvious EV numbers are: EV1, EV12, EV46, EV63, EV71, etc., and the difference in remaining battery capacity can be more than 10 kWh. Summing up the remaining battery capacity of each vehicle, the total remaining battery capacity of EVs calculated by the classical algorithm is 5065.46 kWh, and the total remaining battery capacity of the quantum algorithm is 5659.39 kWh. The total remaining battery capacity is 11.7% better than that of the classical algorithm after using the quantum approximate optimization algorithm, further verifying the advantages of the quantum approximate optimization algorithm used in this example for the optimal scheduling of wireless charging electric vehicles. Moreover, the solution time of the branch and bound method is 721.5 s, while the quantum approximate optimization algorithm only takes 41.8 s. The total running time of the code is about 95% faster than that of the classical algorithm, indicating that the computing speed has been significantly improved.

Claims

1. A wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm, characterized in that: include: According to the actual operation and charging demand of electric vehicles, the driving path of electric vehicles and the planned location of charging sections are jointly optimized, and the objective function and constraint conditions are constructed with the goal of maximizing the remaining power of electric vehicles to form a scheduling model; The scheduling model is solved using quantum approximate optimization algorithms.

2. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 1 is characterized in that: Before constructing the objective function, include: A directed graph G(V,E) is constructed in the target area according to the actual traffic routes, where V is a set of nodes and E is a set of edges. It is stipulated that the electric vehicles on each edge travel at a constant speed and each node can be passed by an electric vehicle at most once.

3. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 2 is characterized in that: The objective function is: In the formula, Q total represents the total remaining power of all electric vehicles, N represents the number of electric vehicles, and s k represents the initial charge of the kth electric car, r k represents the power consumption rate of the kth electric car, represents the length of path ij, Indicates whether the kth electric car chooses the ij path, 1 means it chooses, 0 means it does not choose, p k represents the charging power of the kth electric vehicle, represents the travel time of the kth electric car on the ij side, w ij ∈{0,1+ indicates whether the ij path is a charging section, 1 indicates it is a charging section, and 0 indicates it is not a charging section.

4. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 3 is characterized in that: Constraints include: path constraints, time constraints, energy constraints, and charging section constraints; The formula for the path constraint is: In the formula, a and b represent the starting point and end point of the electric vehicle; u and v represent the intermediate nodes of the path; The formula for the time constraint is: Where, T k represents the maximum allowed driving time of the kth electric vehicle; The formula for the energy constraint is: In the formula, represents the remaining power of the kth electric car at the nth node, c k represents the battery capacity of the kth vehicle; The formula for the charging section constraint is: Where M represents the maximum number of allowed charging sections.

5. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 4 is characterized in that: Using quantum approximate optimization algorithms to solve scheduling models includes: Convert the scheduling model into a QUBO problem and then into a Hamiltonian; The quantum state is initialized using the Hadamard gate, and a QAOA quantum circuit corresponding to the Hamiltonian is constructed, and the optimal quantum state is found in the QAOA quantum circuit.

6. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 5 is characterized in that: Converting the scheduling model into a QUBO problem and then into a Hamiltonian includes: When the remaining power with the goal of maximizing the end point is converted into QUBO form, it is converted into a minimized form, that is, minH1 = -Q total , then: QUBO uses the penalty function method to convert constraints into penalty items, where the path constraints are converted into the following penalty items: The time constraint is transformed into the following penalty term: The energy constraint is transformed into the following penalty term: when When , the penalty term H8 increases; when When , the penalty term H8 increases; The charging section constraints are converted into the following penalty terms: Then the objective function of the QUBO problem is: H=H1+p1H2+p2H3+p3H4+p4H5+p5H6+p6H7+p7H8+p8H9+p9H 10 Among them, p i It is the penalty coefficient used to adjust the constraint strength to ensure that all constraints are met during the optimization process; The original QUBO problem is divided into vehicles. For each vehicle, a sub-problem is constructed and then constructed into a Hamiltonian.

7. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 6 is characterized in that: Formulating the QUBO problem as a Hamiltonian involves: The Pauli operator is used to represent the state and interaction of quantum bits. For binary variables and w ij , using the Pauli operator σ z To express, where σ z The eigenvalues ​​of are ±1, corresponding to binary variables 0 and 1; Then when hour, correspond when hour, correspond Similarly, for w ij ,make The Hamiltonian corresponding to the objective function is: The path constraints are converted into Hamiltonian and expressed as: The Hamiltonian for flow balance is: The path constraints starting from the intermediate nodes are transformed into the Hamiltonian: The time constraint is transformed into the Hamiltonian: The energy constraint condition is transformed into the Hamiltonian: in, represents the set of edges that vehicle k passes through from starting point a to node n; the non-negative energy is converted into the Hamiltonian: The energy that does not exceed the maximum energy of the battery is converted into the Hamiltonian: The charging section constraints are transformed into Hamiltonian: The final total Hamiltonian H is the sum of the Hamiltonian of the objective function term and the Hamiltonian of all constraint terms, that is: H=H obj +H path1 +H path2 +H path3 +H path4 +H flow +H nodeout +H time +H energy1 +H energy2 +H charge 。 8. The wireless charging electric vehicle scheduling optimization method based on quantum approximate optimization algorithm according to claim 7 is characterized in that: Finding the optimal quantum state in a QAOA quantum circuit includes the following steps: S21, encodes the location, destination, charging requirements and road section information of the electric vehicle into the state of quantum bits, and converts the scheduling model into the input of the QAOA quantum circuit; S22, measuring the bit string of the quantum state in the QAOA quantum circuit, calculating the loss function value using the bit string of the quantum state, and updating the parameter γ of the cost Hamiltonian and the parameter β of the mixed Hamiltonian; S23, repeat step S22 until the solution of the sub-problem reaches stability or satisfies the termination condition, and then stop the iteration; S24, merging the optimized solutions of all sub-problems to construct an approximation of the global optimized solution; S25, use the objective function of the original problem to evaluate the quality of the solution vector and find the optimal solution.

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