A method for geographical site selection based on quantum computing

Abstract

The present invention belongs to the field of spatial optimization technology in geographic information science, and specifically discloses a geographic site selection method based on quantum computing, including: defining a geographic maximum coverage site selection model, determining an optimization objective function, constraints and decision-making method; converting the geographic maximum coverage site selection model into a quadratic unconstrained binary optimization model solvable by quantum annealing calculation; introducing slack variables, converting high-dimensional inequality constraints into quadratic penalty term constraints, and adding slack variables to the quadratic unconstrained binary optimization model; based on quantum annealing calculation, setting coherence time and sampling frequency, solving the quadratic unconstrained binary optimization model, and obtaining the optimal solution for service facility configuration; carrying out a spatial coverage consistency test between service facilities and demand points for the optimal solution for service facility configuration, and verifying the solution accuracy and effectiveness of the quantum computing method. The present invention solves the spatial optimization problem in geographic information science.

Description

Technical Field

[0001] The present invention relates to the field of space optimization technology of geographic information science, and in particular to a geographic site selection method based on quantum computing. Background Art

[0002] The problem of service facility location selection in geographic information science usually relies on geographic spatial optimization models, but existing technologies have many shortcomings when dealing with spatial optimization models with high complexity. For example, the maximum coverage location selection problem model needs to consider multiple inequality constraints, but traditional solution methods are inefficient in dealing with combinatorial optimization problems in multidimensional space and are prone to fall into local optimality. Especially when the number of service facilities increases and time-varying factors intensify, the solution space presents a "high-dimensional multi-peak" problem, resulting in a significant decrease in solution efficiency and accuracy. In addition, existing methods are difficult to effectively deal with the complexity and variability of large-scale dynamic facility configuration scenarios, such as hospital relocation and emergency vehicle layout. The solution space is limited by factors such as resource capacity and service demand fluctuations, resulting in unstable solution quality. Current optimization models usually use slack variables when dealing with inequality constraints, but this technology has limited improvements in combinatorial optimization and is difficult to meet actual needs.

[0003] Therefore, the existing technology has bottlenecks in solving the dynamic configuration optimization of large-scale service facilities, which is also a difficulty in the theory of multivariate information adaptive computing. There is an urgent need to solve the combinatorial explosion problem of high-dimensional multi-peaks. Summary of the invention

[0004] The present invention aims to provide a geographic site selection method based on quantum computing to solve or improve the problem that the solution space of the above-mentioned service facility site selection problem presents a "high-dimensional multi-peak" combinatorial explosion, which causes the solution process to easily fall into local search and causes bottlenecks in spatial optimization in geographic information science.

[0005] In view of this, the present invention provides a geographical site selection method based on quantum computing. It includes:

[0006] S1. Define the geographical maximum coverage site selection model, determine the optimization objective function, constraints and decision-making method;

[0007] S2. An algorithm flow of a maximum coverage site selection model based on a quadratic unconstrained binary optimization model, converting the geographic maximum coverage site selection model into a quadratic unconstrained binary optimization model solvable by quantum annealing calculation;

[0008] S3. Introducing slack variables, converting high-dimensional inequality constraints into quadratic penalty constraints, and adding the slack variables to the quadratic unconstrained binary optimization model;

[0009] S4. Based on the quantum annealing calculation, the coherence time and the sampling frequency are set to solve the quadratic unconstrained binary optimization model to obtain the optimal solution for the service facility configuration;

[0010] S5. Carry out a spatial coverage consistency check between the service facilities and the demand points for the optimal solution of the service facility configuration to verify the solution accuracy and effectiveness of the quantum computing method.

[0011] Compared with the prior art, the present invention has the following beneficial effects:

[0012] 1. The present invention solves the geographical location optimization problem by using quantum annealing calculation, which improves the calculation efficiency and solution quality, and can obtain the optimal layout plan of service facilities in a shorter time;

[0013] 2. The present invention adopts a quadratic unconstrained binary optimization model to transform the geographical location model, and obtains an efficient solution structure suitable for quantum computing, which solves the defect that traditional algorithms are prone to fall into local optimality in large-scale location optimization problems;

[0014] 3. The present invention converts complex high-dimensional inequality constraints into quadratic penalty constraints by introducing slack variables, so that the quantum annealing machine can process high-dimensional constraints while maintaining accuracy, ensuring the consistency of coverage requirements of the site selection plan. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0016] Figure 1 A flowchart of a method for geographical site selection based on quantum computing provided in an embodiment of the present invention;

[0017] Figure 2 A schematic diagram of the fitting relationship between the annealing time and the sampling energy based on the D-wave quantum solver provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0018] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0019] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0020] Figure 1A flowchart of a geographic site selection method based on quantum computing provided in an embodiment of the present invention.

[0021] A method for geographic site selection based on quantum computing according to some embodiments of the present invention is described below.

[0022] like Figure 1 As shown, the method includes:

[0023] S1. Define the geographical maximum coverage site selection model, determine the optimization objective function, constraints and decision-making method;

[0024] The definition of the geographical maximum coverage site selection model includes:

[0025] Mapping the actual geospatial optimization problem into a maximum coverage site selection model;

[0026] Establish a set of supply points and a set of demand points, and set the maximization objective function of covering the demand;

[0027] The maximization objective function is transformed into a minimization objective function form through a dual optimization method.

[0028] In addition, constraints are defined to ensure consistency in the number of facility configurations and coverage of demand points to optimize the rationality of the geographic space layout.

[0029] Specifically, the geographic maximum coverage location model is often used for commercial service facility location selection and IoT service facility location selection. The model is described as: maximizing demand coverage by locating a fixed number of facilities within a maximum service distance or time standard. The variable definition and model representation in MCLP are given as follows:

[0030] Among them, MCLP (Maxmuim cover location model) is the geographical maximum coverage location selection model.

[0031] – Number of configuration facilities;

[0032] – Demand Points The scale of demand, such as the number of people in need;

[0033] – Node and The travel time or distance between them;

[0034] – Around the demand point The set of supply points that can provide services within the range is referred to as the reachable supply point set;

[0035] – A binary decision variable for whether to configure facilities at the supply point

[0036]

[0037] – Demand point coverage result binary variable:

[0038]

[0039] The MCLP model is expressed as:

[0040] Objective function:

[0041] (1)

[0042] Where M represents the total number of supply points.

[0043] Restricted to:

[0044] (2)

[0045] (3)

[0046] (4)

[0047] The objective function (1) aims to The coverage demand obtained under the configuration of service facilities is maximized; the constraint function (2) aims to control if the demand point The actual construction result of the reachable supply point set is greater than or equal to 1, then the demand point is also covered, and at this time Set to 1; if the demand point The actual construction result of the reachable supply point set is equal to 0, indicating that the demand point Not covered by the service, Set to 0; constraint function (3) aims to control the total amount of configured service facilities. indivual.

[0048] In order to adapt to the quantum annealing solution, it is necessary to convert the maximization problem into a dual optimization problem, turning it into a minimum optimization problem. First, the demand point coverage result binary variable Convert to binary inverse variable of demand point coverage result :

[0049] (5)

[0050] Substitute formula (5) into the objective function (1) and obtain the minimum objective function after simplification:

[0051] (6)

[0052] Similarly, by substituting formula (5) into constraint (2), we can obtain the constraint for finding the minimum objective function:

[0053] (7)

[0054] The subsequent QUBO-MCLP algorithm process will be carried out for the minimum objective function (6) and constraints (7), (3), and (4).

[0055] Among them, QUBO-MCLP (Maxmuim cover location model based on QuadraticUnconstrained Binary Optimization) is a maximum coverage location model based on quadratic unconstrained binary optimization.

[0056] S2. An algorithm flow of a maximum coverage site selection model based on a quadratic unconstrained binary optimization model, converting the geographic maximum coverage site selection model into a quadratic unconstrained binary optimization model solvable by quantum annealing calculation;

[0057] The algorithm flow of the maximum coverage site selection model based on the quadratic unconstrained binary optimization model includes:

[0058] Declare symbolic variables and define reachable sets between demand points and supply points;

[0059] Construct the symbolic expression string of the objective function, and form the symbolic expressions of the inequality constraints and the total amount constraints one by one;

[0060] The symbolic expressions of the inequality constraint terms and the total amount constraint terms are concatenated to form a symbolic expression of a quadratic unconstrained binary optimization model, and are converted into actual polynomials through an expansion function.

[0061] In one embodiment, the geographic maximum coverage site selection model is converted into a form suitable for quantum annealing solution. First, the symbolic expressions of the objective function and constraints are defined, and the quadratic unconstrained model is gradually constructed, and the corresponding penalty terms are added to the objective function to ensure that the site selection plan meets the geographic space coverage requirements. After the conversion is completed, the quadratic unconstrained binary optimization model can be effectively solved in the quantum annealing computer to achieve the optimal site configuration of the service facilities.

[0062] Specifically, S2.1, symbolic variable declaration. According to the supply point set and demand point set formed by mapping during model definition, symbolic variable declaration is completed based on symbolic operations to meet the subsequent symbolic calculations;

[0063] S2.2. Build each demand point The set of reachable supply points . For the constraints, traverse the demand points one by one , filter out the distance demand points Less than or equal to distance threshold All supply points , supply point join , forming demand points The set of reachable supply points;

[0064] S2.3. Construct the symbolic calculation expression string of the objective function Based on the objective function (6), a symbolic computation expression is formed by concatenating the corresponding variables.

[0065] S2.4. Construct the symbolic calculation expression string of the inequality constraint term . For constraint (7), traverse each demand point one by one The set of reachable supply points , first determine The number of elements in the formula is analyzed in four cases:

[0066] (1) If the number of elements is equal to 0, this indicates that the demand point There are no supply points to serve. , no further solution is needed;

[0067] (2) If the number of elements is equal to 1, add the demand point coverage result binary inverse variable , then there are two variables in the quadratic penalty equality constraint, and the binary quadratic penalty constraint is constructed:

[0068] (8)

[0069] in, Represents the penalty coefficient.

[0070] (3) If the number of elements is equal to 2, add the demand point coverage result binary inverse variable , then there are 3 variables in the quadratic penalty equality constraint, constructing a ternary quadratic penalty constraint:

[0071] (9)

[0072] in, represents the decision variable, represents the decision variable, and Represents auxiliary variables.

[0073] (4) If the number of elements is greater than or equal to 3, it means that the inequality constraint is a high-dimensional inequality constraint, and the high-dimensional inequality constraint conversion operator based on slack variables designed by the present invention needs to be used to construct a quadratic penalty constraint.

[0074] S2.5. Construct the symbolic calculation expression string of P total constraint item . Assuming configuration , construct the formula of binary decision variables of supply point , and so on.

[0075] (10)

[0076] in, Represents the penalty coefficient.

[0077] S2.6, construct H symbolic calculation expression string and symbolic polynomial. , multiple inequality constraint symbol calculation expression string 、P total constraint term symbol calculation expression string Splice to form Symbolic evaluation expression string. Based on the exec() function The symbolic calculation expression string is converted into an actual symbolic polynomial and then expanded using the expand() function.

[0078] (11)

[0079] S2.7. Construct a QUBO key-value pair dictionary that can be sampled and calculated. For the expanded H symbolic polynomial, parse it term by term, parse out the mapping relationship between the coefficient and the binary variable, the coefficient value, and the independent constant term in each quadratic term, and construct a QUBO key-value pair dictionary.

[0080] S2.8. Execute the quantum annealing calculation sampling operator to generate a sampling result.

[0081] S3. Introducing slack variables, converting high-dimensional inequality constraints into quadratic penalty constraints, and adding the slack variables to the quadratic unconstrained binary optimization model;

[0082] In one embodiment, during the model construction process, by introducing slack variables, high-dimensional inequality constraints are converted into the form of quadratic penalty terms to adapt the quadratic unconstrained binary optimization model. Slack variables are used to process multi-dimensional and complex constraints, so that the geographical location problem with more inequality constraints can be effectively represented in the model. After the slack variables are introduced, the quadratic penalty term of the model is combined with the objective function to ensure the accuracy of each constraint when the quantum annealing calculation is solved. The introduction of slack variables of the present invention makes the model more applicable and conforms to the binary optimization model format.

[0083] The introducing of slack variables comprises:

[0084] For high-dimensional inequality constraints and binary variables greater than or equal to 4, inequality constraints are transformed into high-dimensional multivariate quadratic penalty constraints by introducing slack variables.

[0085] Specifically, S3.1, the first step is the less than sign form transformation:

[0086] (12)

[0087] S3.2, Step 2 The boundary conditions are , then the boundary conditions are all assumptions, assuming ,get .

[0088] S3.3, non-negative transformation, add both sides of the inequality , converted to:

[0089] (13)

[0090] Introduction and ,get:

[0091] (14)

[0092] S3.4. According to formula (13), the high-dimensional multivariate quadratic penalty constraint term is derived:

[0093] (15)

[0094] in, Demand point The quadratic penalty equality constraint of represents the penalty coefficient, The number of qubits required is , where the number of auxiliary variables is .

[0095] The present invention adopts the above method to ensure the constraint form that conforms to the quadratic unconstrained binary optimization model.

[0096] S4. Based on the quantum annealing calculation, the coherence time and the sampling frequency are set to solve the quadratic unconstrained binary optimization model to obtain the optimal solution for the service facility configuration;

[0097] In one embodiment, first, the coherence time and sampling frequency of the quantum annealer are set to ensure the stability of the calculation process and the accuracy of the results. During the annealing process, the quantum state gradually converges to the state with the lowest energy, which is close to the optimal solution of the model. Through multiple sampling, the reliability of the solution is further improved, so as to obtain the optimal solution for the service facility configuration that meets the geographical space coverage requirements. Finally, the optimal solution provides the optimal location suggestion for the facility layout, which can achieve the maximum coverage of the demand points.

[0098] The quantum annealing calculation sampling includes:

[0099] Use a quantum-classical hybrid solver and configure the number of reads and coherence time parameters;

[0100] Based on the quantum annealing machine, the quadratic unconstrained binary optimization model is sampled and the optimal solution for the service facility configuration is output.

[0101] The expression of the optimal solution of the facility configuration is as follows:

[0102]

[0103] Among them, Q(x) represents the optimal solution of facility configuration, q ij represents the coefficient, x i represents the i-th supply point, x j represents the jth supply point, q i Represents a binary coefficient, where i and j both represent positive integers greater than 1, and c represents a constant term.

[0104] The quantum annealing calculation adopts a variety of solvers including a classical heuristic solver, a quantum solver, and a quantum-classical hybrid solver.

[0105] In one embodiment, in order to improve the solution efficiency and adapt to geographical site selection problems of different scales, multiple types of solvers are used, including classical heuristic solvers, pure quantum solvers, and quantum-classical hybrid solvers. Classical heuristic solvers provide approximate solutions through methods such as simulated annealing, which are suitable for smaller-scale problems; quantum solvers directly use the superposition and entanglement characteristics of quantum states to run solutions on quantum annealing machines, which are suitable for handling larger-scale optimization problems; quantum-classical hybrid solvers combine the advantages of classical computing and quantum computing, and by decomposing the problem into sub-problems suitable for the quantum part and the classical part, complex geographical site selection problems can be efficiently solved in existing quantum annealing equipment. The combination of the above multiple solvers ensures the accuracy and efficiency of model solving.

[0106] S5. Carry out a spatial coverage consistency check between the service facilities and the demand points for the optimal solution of the service facility configuration to verify the solution accuracy and effectiveness of the quantum computing method.

[0107] In one embodiment, a spatial coverage consistency check operator for MCLP results is executed to check the consistency of the spatial coverage relationship between the supply points and the demand points. After obtaining the optimal solution for the service facility configuration, in order to ensure the accuracy of the solution, the consistency check of the spatial coverage relationship between the facility and the demand points is performed.

[0108] The spatial coverage consistency check includes:

[0109] Traversing the demand points, and determining the coverage relationship between the supply points and the demand points;

[0110] Builds a facility collection of configured services and verifies coverage consistency.

[0111] The above method realizes the efficient solution of service facility configuration problems of different scales.

[0112] In one embodiment, by traversing all demand points, the coverage relationship between supply points and demand points is checked to ensure that each demand point is properly covered. First, the demand points are judged one by one whether they are within the coverage of the configured facilities, that is, the service accessibility between the demand points and the corresponding supply points is verified. Then, a set of facilities with configured services is constructed to record and check the coverage consistency of each demand point and the facilities, ensuring that the site selection plan generated when solving the model can meet the spatial coverage requirements of the demand points. Through consistency verification, the actual reliability and coverage effectiveness of the facility layout plan are ensured.

[0113] Specifically, the spatial coverage consistency check operator for MCLP results is , The binary variable results are implicitly mapped to the MCLP problem to conduct the consistency of the spatial coverage relationship between the demand points and the configured service facility supply points, including:

[0114] S5.1. Traversal reading Carry out inspection on the covered demand points and find the demand points ;

[0115] S5.2. Build a set of facility supply points for configured services. The set of supply points is defined as ;

[0116] S5.3, ,like , it means that the spatial coverage relationship between the demand point and the configured service facility supply point is inconsistent; if , it means that the spatial coverage relationship between the demand points and the configured service facility supply points is consistent.

[0117] The spatial coverage consistency check also includes: if the coverage is inconsistent, adjusting the penalty coefficient to correct the quadratic unconstrained binary optimization model to ensure that the supply and demand relationship meets the constraint conditions.

[0118] In one embodiment, it is not only used to verify the coverage effect of the facility configuration, but also includes a mechanism for handling inconsistencies. If the test results show that the demand point is not covered by the corresponding supply point, it means that the supply and demand relationship does not meet the original constraints. In this case, by adjusting the penalty coefficient in the quadratic unconstrained binary optimization model, the uncovered demand points are brought back into the coverage range. Specifically, the weights of the relevant penalty items are increased to guide the model to give priority to meeting the coverage requirements during the solution process, and then the objective function of the quadratic unconstrained binary optimization model is corrected, so that the subsequent solution results are more in line with the actual spatial coverage requirements, ensuring the effectiveness and reliability of the overall site selection plan.

[0119] The method includes: tuning parameters of a quadratic unconstrained binary optimization model, wherein the adjustment content includes setting different sampling frequencies, reading times and coherence times.

[0120] Among them, the parameter tuning of the quadratic unconstrained binary optimization model can adapt to geospatial optimization problems of different scales. The whole content includes setting different sampling frequencies, reading times and coherence times, thereby improving the solution efficiency and accuracy of the model in the quantum annealing calculation process. The method of the present invention is suitable for the quantum bit scale and coherence time constraints in a noisy mesoscale quantum environment, and solves geospatial optimization problems of different scales through parameter tuning.

[0121] The present invention solves the geographic site selection optimization problem by using quantum annealing calculation, thereby improving the calculation efficiency and the quality of the solution, and can obtain the optimal layout plan of service facilities in a shorter time; a quadratic unconstrained binary optimization model is used to transform the geographic site selection model, and an efficient solution structure suitable for quantum computing is obtained, which solves the defect that traditional algorithms are prone to fall into local optimality in large-scale site selection optimization problems; by introducing slack variables, complex high-dimensional inequality constraints are converted into quadratic penalty constraints, so that the quantum annealer can process high-dimensional constraints while maintaining accuracy, ensuring the consistency of coverage requirements of the site selection plan.

[0122] Embodiment 1: The experiment is divided into two scenarios: theoretical geospatial experiment and real geospatial experiment. The corresponding data are theoretical geospatial dataset TGD, referred to as TGD dataset and real geospatial dataset. The TGD dataset is divided into 5 instances, represented by 3×3, 4×4, 5×5, and 6×5 scale demand points, respectively. 2 service facilities are configured in 3 candidate points, 2 service facilities are configured in 5 candidate points, 3 service facilities are configured in 6 candidate points, and 4 service facilities are configured in 8 candidate points, forming 5 specific instances, namely: 3×3_3_2, 4×4_3_2, 5×5_5_2, 5×5_6_2, 6×5_8_4, and the specific instances are named: TGD3332, TGD4432, TGD5552, TGD5562, and TGD6584; the real geospatial dataset selects the city of São José dos Campos, São Paulo, Brazil (So José dos Campos Campos, referred to as SJC) city dataset, source public dataset: http: / / www.lac.inpe.br / ∼lorena / instancias.html, specific dataset instances are SJC302, SJC402, SJC500, SJC708, 4 service facilities are configured in 9 candidate points, forming 4 specific instances, namely: 302_9_4, 402_9_4, 500_9_4, 708_9_4, specific instances are named: SJC30294, SJC40294, SJC50094, SJC70894, collectively referred to as SJC dataset. Among them, SJC (So José dos Campos, referred to as SJC) is the city of São José dos Campos, São Paulo State, Brazil.

[0123] Among them, TGD (Theoretical geospatial datasets) is a theoretical geospatial dataset.

[0124] The hardware environment of the experimental system is as follows: (1) The client computer configuration: CPU Intel(R)Core(TM)i9-7590; memory 32GB; GPU NVIDIA GeForce GT2080TI; system software environment: operating system: Windows10 64Bit; programming language Python, GDAL; GIS platform: ESRI ArcGIS 10.6; (2) The server computer configuration: CPU Intel(R)Core(TM)i9-7590; memory 32GB; GPU NVIDIA GeForce GT2080TI; system software environment: operating system: Ubuntu 18; commercial solvers: Gorubi 10.2; (3) The quantum computing platform configuration: including classical heuristic solvers, quantum-classical hybrid solvers, and pure quantum solvers (QPU solvers). The classical heuristic solver uses the D-Wave qbsolv quantum computing simulation package, and the quantum-classical hybrid solver uses the D-Wave hybrid_binary_quadratic_model_version2 cloud service, and the quantum solver uses D-Wave Advantage_system4.1 cloud service. Classical heuristic solvers mainly include: simulated annealing (dwave-neal), taboo search (dwave-tabu) and steepest descent (dwave-greedy). The quantum-classical hybrid solver is designed to simplify the integration of quantum computing in problem-solving applications. The hybrid workflow uses classical resources to find the core part of the problem and send it to the QPU, or decomposes a large problem into small pieces that can be solved on the QPU and then reassembled. D-WaveAdvantage_system 4.1 uses the quantum mechanical tunneling effect to seek low-energy states for optimization problems, with more than 5,000 qubits; it uses the Pegasus connection architecture to support highly connected topologies, which improves the system's flexibility and problem mapping capabilities.

[0125] Specific experimental process: First, the effectiveness of the geographic maximum coverage site selection model is verified for the TGD and SJC data sets. Step 1: Define the geographic maximum coverage site selection model, determine the optimization objective function, constraints and decision-making method, and map the real geographic space optimization and site selection problem into the MCLP model, forming a set of supply points and a set of demand points, and transform the objective function into the minimum objective function.

[0126] Secondly, the effectiveness of the QUBO-MCLP algorithm process is verified for the TGD and SJC data sets. Step 2: The algorithm process of the maximum coverage site selection model based on the quadratic unconstrained binary optimization model, converting the geographic maximum coverage site selection model into a quadratic unconstrained binary optimization model that can be solved by quantum annealing calculation; Step 2.1: Symbolic variable declaration; Step 2.2: Construct each demand point The set of reachable supply points ; Step 2.3, construct the symbolic calculation expression string of the objective function ; Step 2.4, construct the symbolic calculation expression string of the inequality constraint term ; Step 2.5, construct the symbolic calculation expression string of the P total constraint item ; Step 2.6, construct the H symbolic calculation expression string and symbolic polynomial, select the exec() function in Python to convert the H symbolic calculation expression string into an actual symbolic polynomial, and expand the symbolic polynomial through the expand() function in the symbolic operation package; Step 2.7, construct a QUBO key-value pair dictionary that can be sampled and calculated; Step 2.8, execute the quantum annealing calculation sampling operator.

[0127] Step 3: introducing slack variables, converting the high-dimensional inequality constraints into quadratic penalty constraints, and adding the slack variables into the quadratic unconstrained binary optimization model;

[0128] For the TGD and SJC data sets, the effectiveness of the high-dimensional inequality constraint conversion operator based on slack variables is verified. For high-dimensional inequality constraints, especially those with more than or equal to 4 binary variables, slack variables are specially introduced to realize the conversion of high-dimensional inequality constraints into high-dimensional multivariate quadratic penalty constraints, see formula (15) for details.

[0129] Here is a high-dimensional inequality constraint transformation and verification case of a demand point y167 in the SJC30294 example experiment. The storage JSON format of the demand point y167 is: ,in Indicates demand point The set of reachable supply points , we get the quadratic penalty constraint term of formula (2):

[0130]

[0131] Four QUBO solvers, including classical heuristic solvers, quantum solvers, quantum-classical hybrid solvers, and commercial solvers, were used for sampling and solving, and the results were all: . Substituting this result into Formula, verifying that it meets the constraint relationship and satisfies the inequality relationship of constraint condition (7), indicating that the high-dimensional inequality constraint term designed by the present invention is effectively and feasible to transform into a high-dimensional multivariate quadratic penalty constraint term. The design of this transformation mechanism breaks through the polynomial inequality constraints in the current QUBO transformation process.

[0132] Step 4: Based on the quantum annealing calculation, the coherence time and the sampling frequency are set to solve the quadratic unconstrained binary optimization model to obtain the optimal solution for the service facility configuration;

[0133] The experimental set verifies the effectiveness of the quantum annealing computing sampling operator. Solve the QUBO problem, set key parameters such as coherence time and number of reads, use the quantum annealing machine to solve the sampling, achieve fast and high-quality quantum computing, and calculate the approximate optimal solution.

[0134] Experiment 1: Verify the QUBO-MCLP algorithm flow experiment based on quantum-classical hybrid solver, classical heuristic solver, and commercial solver. The specific solver situation is as follows: The classical heuristic solver selects the dimod.ExactSolver() general sampler in the QBSolv package. The quantum solver and quantum-classical hybrid solver set the parameter sampling read number (num_reads) to increase, which will increase the computing time and resource consumption, response = sampler.sample(model,num_reads=50,anneal_time=80). Output the single optimal solution and the corresponding objective function value, response.first.sample gives an approximate optimal solution. The commercial solver defines binary decision variables and uses the optimize() method of the GRBP.Model() object to directly solve the MCLP problem as a standard control result. The experimental results of the three solvers are shown in Tables 1, 2, and 3. The results of Tables 1-3 are analyzed and the following analysis conclusions are obtained:

[0135] Table 1. Results of solving MCLP problems using the quantum Qbsolv solver

[0136]

[0137] Table 2. Results of quantum hybrid solver for MCLP problem

[0138]

[0139] Table 3. Results of solving MCLP problems with the classic Gurobi solver

[0140]

[0141] Note: - Inequality constraint penalty coefficient; – P is the total constraint penalty coefficient; QTime – QUBO conversion time (S); – Solving time; Gap - Value Gap (%) Gap = (Gurobi target value - quantum solver target value) / Gurobi target value.

[0142] (1) The quantum-classical hybrid solver and the classical heuristic solver can solve the MCLP problem on the TGD and SJC datasets, and can also solve the configuration problem with P>2. For example, TGD5563 and TGD6584 can solve the problem with P=3 and P=4 respectively, which shows that the inequality constraint conversion operator based on slack variables proposed in this paper is effective.

[0143] (2) For the large-scale SJC dataset, the QUBO polynomial matrix converted in this paper has an overall better effect on the quantum-classical hybrid solver than the classical heuristic solver, and is closer to the optimal target value of the Gurobi commercial solver. For example, TGD6584, SJC32494, SJC50094, and SJC81894 have a smaller gap. This shows that the overall QUBO-MCLP algorithm process in this paper can be run in a quantum annealing real machine environment, breaking through the original small-scale theoretical geospatial optimization quantum computing route and forming a quantum solution route for large-scale geospatial optimization problems.

[0144] (3) As the problem size increases, the quantum-classical hybrid solver has a higher degree of randomness than the classical heuristic solver and is more susceptible to the influence of coherence time and number of reads, which is consistent with the characteristics of the quantum annealing real machine under the NISQ environment. It is mainly limited by the interaction distance of the quantum bit Chiramei topological network connection diagram, the continuous coherence time of the quantum bit, the scale of the logical quantum bit, etc. The further promotion of the subsequent quantum technology route for large-scale geospatial optimization problems is largely limited by the high-fidelity logical quantum bit scale of the quantum computing real machine under the NISQ environment.

[0145] Step 5: Perform a spatial coverage consistency check between the service facilities and the demand points for the optimal solution of the service facility configuration to verify the solution accuracy and effectiveness of the quantum computing method.

[0146] Figure 2 A schematic diagram of the fitting relationship between the annealing time and the sampling energy based on the D-wave quantum solver provided in an embodiment of the present invention.

[0147] Experiment 2: Pure quantum solver verification of QUBO-MCLP algorithm flow experiment. By running the TGD and SJC data sets on a quantum processing unit (QPU) real machine, we get the results in Table 4. Figure 2 . Analyzing Table 4, we get:

[0148] Table 4. Spatial consistency test results of the quantum D-wave Advantage_system real machine solver on the MCLP problem

[0149]

[0150] (1) The QUBO-MCLP problem designed in this paper can be solved in a quantum solver and can be solved in the case of P>2, such as TGD5563 and SJC70894. The experimental results show that the existing QUBO transformation mechanism introduces multiple auxiliary variables due to a large number of candidate variables, and the number of quantum logic bits of the pure quantum solver is limited, resulting in unstable solutions. At the same time, this result also verifies the necessity of the spatial coverage consistency check algorithm proposed in this paper in the study of quantum solutions to MCLP problems.

[0151] (2) When the scale of the MCLP problem exceeds TGD5552, the spatial coverage consistency check will fail, which is mainly limited by the objective QPU physical conditions (the impact of integrated control errors and other errors) and key parameter settings of the quantum bit Chirame topological network connection diagram, the quantum bit continuous coherence time, the logical quantum bit scale, etc.

[0152] (3) For the TGD5563 data, the correlation between the coherence time parameter and the energy value is analyzed, such as Figure 2 As shown, it is not difficult to find that the coherence time setting will directly affect the evolution process of the quantum Hamiltonian. A longer annealing time can give the system more time to find the global optimal solution, but it will also increase the accumulation of noise.

[0153] At present, we are in the NISQ (Noisy Intermediate-Scale Quantum) stage, focusing on the development of medium-scale quantum computers that break through noise. Quantum annealing computers are finely controlled quantum bit interactions and external magnetic fields, realizing the quantum annealing process to solve complex optimization problems. Currently, many indicators directly affect the effect and accuracy of quantum annealing. The further promotion of the subsequent quantum technology route for large-scale geographic spatial optimization problems is largely limited by the high-fidelity logical quantum bit scale of the quantum computing real machine in the NISQ environment. At the same time, Table 4 also proves the effectiveness of the spatial coverage consistency check operator.

[0154] The spatial optimization problem based on the inequality constraints of slack variables is converted into a QUBO model. As the scale of configured service facilities increases, the density of slack variables increases significantly, which restricts the research on the spatial optimization model problem with inequality constraints. In the future, a new improvement method will be proposed to take into account the quadratic penalty function correlation coefficient method of the scale of service facilities to re-optimize the inequality constraints of the spatial optimization model to reduce the number of linear variables and quadratic variables, thereby satisfying the logical bits and topological structure constraints of the quantum solver under NISQ conditions.

[0155] The above experiments verify that the effectiveness of the spatial coverage consistency check operator on the MCLP results of the TGD and SJC datasets has been fully verified in Experiments 1 and 2.

[0156] In summary, the present invention discloses a quantum computing method for the problem of geographical maximum coverage site selection. The geographical site selection and spatial optimization model problems of the present invention need to be converted into a quadratic unconstrained binary optimization model, and slack variables are introduced to realize the conversion of inequality constraints into quadratic penalty term equality constraints, and the quadratic penalty term constraint terms are added to the QUBO model. In view of the difficult problem of converting high-dimensional inequality constraints into quadratic penalty term constraints, a high-dimensional inequality constraint conversion operator based on slack variables is designed, and experimental verification is effective and feasible. Then 4 annealers can be used to solve and realize fast and high-quality quantum computing. The geographical maximum coverage site selection model can be widely used in special planning of urban service facilities, spatial layout of the Internet of Things and communication facilities, smart city governance and resource allocation. The method in this paper can adapt to the controllable quantum bit scale and effective coherence constraints under the current NISQ conditions, so as to adapt to the solution research of large-scale service facility site selection and other geographical space optimization problems.

[0157] The above embodiments are only used to illustrate the technical solutions of the present disclosure, rather than to limit them. Although the present disclosure has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should all be included in the protection scope of the present disclosure.

Claims

1. A geographical site selection method based on quantum computing, characterized in that: include: S1. Define the geographical maximum coverage site selection model, determine the optimization objective function, constraints and decision-making method; S2. An algorithm flow of a maximum coverage site selection model based on a quadratic unconstrained binary optimization model, converting the geographic maximum coverage site selection model into a quadratic unconstrained binary optimization model solvable by quantum annealing calculation; S3. Introducing slack variables, converting high-dimensional inequality constraints into quadratic penalty constraints, and adding the slack variables to the quadratic unconstrained binary optimization model; S4. Based on the quantum annealing calculation, the coherence time and the sampling frequency are set to solve the quadratic unconstrained binary optimization model to obtain the optimal solution for the service facility configuration. The quantum annealing calculation samples include: Use a quantum-classical hybrid solver and configure the number of reads and coherence time parameters; Based on the quantum annealing machine, the quadratic unconstrained binary optimization model is sampled and the optimal solution for the service facility configuration is output; S5. Conduct a spatial coverage consistency test between the service facilities and the demand points for the optimal solution of the service facility configuration to verify the accuracy and effectiveness of the solution of the quantum computing method. The expression of the optimal solution of the facility configuration is as follows: ； Among them, Q(x) represents the optimal solution of facility configuration, q ij represents the coefficient, x i represents the i-th supply point, x j represents the jth supply point, q i Represents a binary coefficient, where i and j both represent positive integers greater than 1, and c represents a constant term.

2. The method for geographical site selection based on quantum computing according to claim 1, characterized in that: The definition of the geographical maximum coverage site selection model includes: Mapping the actual geospatial optimization problem into a maximum coverage site selection model; Establish a set of supply points and a set of demand points, and set the maximization objective function of covering the demand; The maximization objective function is transformed into a minimization objective function form through a dual optimization method.

3. The method for geographical site selection based on quantum computing according to claim 1, characterized in that: The algorithm flow of the maximum coverage site selection model based on the quadratic unconstrained binary optimization model includes: Declare symbolic variables and define reachable sets between demand points and supply points; Construct the symbolic expression string of the objective function, and form the symbolic expressions of the inequality constraints and the total amount constraints one by one; The symbolic expressions of the inequality constraint terms and the total quantity constraint terms are concatenated to form a symbolic expression of a quadratic unconstrained binary optimization model, and are converted into actual polynomials through an expansion function.

4. The method for geographical site selection based on quantum computing according to claim 1, characterized in that: The introducing of slack variables comprises: For high-dimensional inequality constraints and binary variables greater than or equal to 4, inequality constraints are transformed into high-dimensional multivariate quadratic penalty constraints by introducing slack variables.

5. The method for geographical site selection based on quantum computing according to claim 1, characterized in that: The quantum annealing calculation adopts a variety of solvers including a classical heuristic solver, a quantum solver, and a quantum-classical hybrid solver.

6. The method for geographical site selection based on quantum computing according to claim 2, characterized in that: The spatial coverage consistency check includes: Traversing the demand points, and determining the coverage relationship between the supply points and the demand points; Builds a collection of facilities for configured services and verifies coverage consistency.

7. The method for geographical site selection based on quantum computing according to claim 6, characterized in that: The spatial coverage consistency check also includes: if the coverage is inconsistent, adjusting the penalty coefficient to correct the quadratic unconstrained binary optimization model to ensure that the supply and demand relationship meets the constraint conditions.

8. The method for geographical site selection based on quantum computing according to claim 1, characterized in that: The method also includes: tuning parameters of the quadratic unconstrained binary optimization model to adapt to geospatial optimization problems of different scales, and the adjustment content includes setting different sampling frequencies, reading times and coherence times.

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