QUBO-based mine combination optimization method and system

Abstract

The invention relates to the technical field of intelligent mines, in particular to a mine combination optimization method based on QUBO. Comprising the following steps: obtaining the type, quantity, purchase cost, operation efficiency and matching relation data of mining equipment, and constructing an initial data set; based on the initial data set, establishing a mathematical model with maximized total profit as an objective function and budget constraint and equipment matching relation as constraint conditions; the objective function and the constraint condition are converted into a QUBO model, and the QUBO model is solved through a quantum computer or a simulated annealing algorithm; and a subQUBO method is adopted to perform decomposition and iterative solution on a large-scale quantum bit problem, and a dynamic optimization result under a complex combination scene is generated. According to the method, the equipment purchasing and matching scheme under the multi-constraint condition is efficiently solved through the quantum computing technology, the problems that a traditional optimization method is low in computing efficiency and high in error rate are solved, limitation of quantum hardware resources is broken through, and long-term mine profit maximization is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of smart mines, and more specifically, to a QUBO-based mine combination optimization method and system thereof. Background Art

[0002] With the development of smart mining technology, optimizing mining equipment combinations has become a core challenge in improving operational efficiency. Traditional optimization methods primarily rely on linear programming (LP) and heuristic algorithms (such as genetic algorithms and particle swarm optimization), but they have significant limitations when dealing with multivariable, multi-constrained combinatorial optimization problems. The following analyzes specific issues and deficiencies based on existing technologies and literature:

[0003] Limitations of Traditional Optimization Methods

[0004] Low computational efficiency: When dealing with high-dimensional combinatorial optimization problems, the computational complexity of linear programming algorithms (such as the simplex method) increases exponentially. For example, when the number of variables exceeds 100, the solution time of traditional LP algorithms exceeds the practical tolerance range.

[0005] They are prone to getting stuck in local optimal solutions: While heuristic algorithms (such as simulated annealing and genetic algorithms) can avoid the complexity of global search, their convergence speed is significantly affected by parameter settings. In the case of mining equipment matching, traditional simulated annealing has an error rate as high as 15%-20%, and it is difficult to guarantee the optimality of the solution.

[0006] Weak multi-constraint processing capabilities: Mining equipment must meet multiple constraints, including budget, equipment type, and operational efficiency. Traditional methods often simplify the problem by relaxing constraints, resulting in solutions that deviate from actual needs. Existing technologies struggle to balance the weights of the objective function and the constraints, easily leading to infeasible solutions.

[0007] Application bottlenecks of quantum computing technology

[0008] Hardware resource limitations: While quantum computing technologies (such as the Coherent Ising Machine (CIM)) offer potential for parallel computing, they are limited by the number of qubits and cannot directly solve large-scale QUBO models. Existing CIM equipment only supports problems with fewer than 100 qubits, while mining equipment optimization problems often require more than 200 qubits, making direct application difficult.

[0009] Insufficient error rate and stability: The quantum annealing algorithm is susceptible to interference in noisy environments, and the error rate for solving combinatorial optimization problems is generally higher than 10%, which makes it difficult to meet industrial-level precision requirements.

[0010] Lack of targeted modeling methods: Existing QUBO models mostly target theoretical problems (such as the traveling salesman problem) and lack adaptation to practical factors such as equipment matching and dynamic costs in mining scenarios. General QUBO modeling without domain knowledge will lead to poor coupling between the objective function and the constraints, affecting the solution efficiency.

[0011] In short, existing technologies lack customized QUBO modeling methods for mining equipment optimization, and their accuracy and efficiency remain insufficient under complex constraints (such as budget constraints and equipment matching). Furthermore, existing quantum solvers are often limited by the number of qubits when processing large-scale problems, making them difficult to directly apply in real-world scenarios.

[0012] Therefore, we proposed a QUBO-based mine combination optimization method and system to solve the above problems. Summary of the Invention

[0013] In order to overcome the above-mentioned defects of the prior art, the embodiments of the present invention provide a mine combination optimization method and system based on QUBO to solve the problems raised in the above-mentioned background technology.

[0014] To achieve the above objectives, the present invention provides the following technical solutions: a QUBO-based mine combination optimization method, comprising the following methods: obtaining data on the type, quantity, procurement cost, operating efficiency, and matching relationship of mining equipment to construct an initial data set; based on the initial data set, establishing a mathematical model with maximizing total profit as the objective function and with budget constraints and equipment matching relationships as constraints; converting the objective function and constraints into a QUBO model, solving the QUBO model using a quantum computer or a simulated annealing algorithm to obtain the optimal equipment procurement plan and equipment matching relationship; and using the subQUBO method to decompose and iteratively solve large-scale quantum bit problems to generate dynamic optimization results in complex combination scenarios.

[0015] In a preferred embodiment, the construction of the QUBO model includes: defining the equipment quantity decision variable as a binary variable and replacing the binary variable with an Ising variable; embedding the constraint condition into the objective function through a penalty factor to form an unconstrained quadratic optimization model; generating the QUBO Hamiltonian matrix, which is expressed as:

[0016] min W=X T QX+c

[0017] Where Q is the QUBO symmetric matrix, X T represents the transpose of X, and c represents a constant.

[0018] In a preferred embodiment, the modeling of the equipment matching relationship includes the following: constructing a multidimensional matching constraint matrix based on the bucket width compatibility of the excavator and the mining car; converting the matching relationship into linear or nonlinear constraints, and integrating it into the QUBO model through a penalty factor.

[0019] In a preferred embodiment, the subQUBO method includes the following steps: decomposing the original QUBO model into multiple sub-QUBO problems; solving each sub-problem separately using a simulated annealing algorithm, and obtaining a global optimal solution by iteratively integrating the sub-problem solutions; and dynamically adjusting the sub-problem scale to adapt to the limit on the number of quantum bits.

[0020] In a preferred embodiment, the solution process adopts a hybrid optimization strategy, including: using a simulated annealing algorithm for preliminary solution to generate a set of candidate solutions; performing secondary optimization on the candidate solution set through CIM to reduce the error rate; comparing the results of different solvers and selecting the optimal solution with an error rate lower than 5.5%.

[0021] In a preferred embodiment, the method further includes a sensitivity analysis step: performing multiple value tests on the penalty factor to verify the stability of the model under different constraint strengths; and determining the optimal penalty factor range to be 7700-50000 by balancing the error rate with profit maximization.

[0022] In a preferred embodiment, the method is further extended to the hyperparameter tuning of artificial intelligence models, including: converting the hyperparameter selection problem into a QUBO model; accelerating the hyperparameter search process through quantum computing to improve model training efficiency.

[0023] In a preferred embodiment, the QUBO-based mine combination optimization system includes the following: a data acquisition module: used to obtain equipment type, cost, efficiency and matching relationship data; a modeling module: used to construct the objective function and constraints and convert them into a QUBO model; a solution module: integrating the simulated annealing algorithm, CIM solver and subQUBO method to solve the QUBO model; an output module: generating an equipment procurement plan, a matching relationship table and a profit maximization report.

[0024] The technical effects and advantages of the present invention are as follows:

[0025] By accelerating the optimization process through quantum computing, computing efficiency can be improved by more than 30% compared to traditional algorithms.

[0026] Maximize long-term profits under budget constraints with an error rate of less than 6%.

[0027] Supports large-scale equipment combination optimization (such as 10 types of equipment) to meet the complex scenario requirements of smart mines. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the idea of the present invention;

[0029] Figure 2 The specific flow chart for solving the QUBO model of the present invention;

[0030] Figure 3 The flowchart of solving the QUBO problem by simulated annealing of the present invention is as follows;

[0031] Figure 4 This is the CIM core technology diagram of the present invention;

[0032] Figure 5 A three-dimensional view of the invention's profit versus excavator type and quantity;

[0033] Figure 6 A visualization diagram of the maximum gain and error rate of the simulated annealing solver of the present invention;

[0034] Figure 7 A visualization diagram of the maximum benefit and error rate of the CIM simulator of the present invention;

[0035] Figure 8 The simulated annealing solution result diagram of the present invention;

[0036] Figure 9 This is a diagram showing the matching relationship between ten excavators and mining vehicles of the present invention;

[0037] Figure 10 This is a profit result diagram of the subQUBO simulated annealing of the present invention;

[0038] Figure 11 The optimal matching solutions of ten excavators and mining vehicles of the present invention are as follows;

[0039] Figure 12 Draw a technical roadmap for the QUBO model based on artificial intelligence hyperparameter tuning for this invention;

[0040] Figure 13 The QUBO model algorithm and expression of the present invention;

[0041] Figure 14 It is the QUBO accuracy distribution box plot of the present invention;

[0042] Figure 15 It is a diagram illustrating symbols of the present invention;

[0043] Figure 16 This is a table diagram of the results of solving the QUBO problem by simulated annealing in the present invention;

[0044] Figure 17 This is a table showing the results of solving the QUBO problem using CIM in the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] Problem 1: Assuming the excavator's service life is not considered, build a QUBO model based on the discounted long-term profit estimates for each excavator type given in the table. Use the simulated annealing solver and CIM simulator built into the Kaiwu SDK to find a solution that maximizes total profit within the budget. Problem 2: Assuming the excavator and mining cart have a service life of 5 years, build a QUBO model and solve for the required excavator models and quantity, as well as the matching relationship between excavators and mining carts, to maximize total profit over 5 years. Problem 3: Consider the scenario in Problem 2, where 10 types of mining carts have been purchased, the number of excavators available is 10, and the total number of excavator models included cannot be less than 5. Based on the excavator and mining cart matching table and the initial capital of 40 million yuan, build a QUBO model and use the Kaiwu SDK to find the optimal procurement plan and the matching relationship between excavators and mining carts. Problem 4: Based on a practical application, provide an example of a scenario that can potentially be optimized through the construction of an appropriate QUBO model, and model and predict the solution.

[0047] Analysis of Question 1

[0048] For Problem 1, we need to estimate the maximum long-term discounted profit value of a smart mine in a simplified scenario and develop a corresponding procurement plan. First, we calculate the expression for the discounted profit value by summing the profit multiplied by the quantity of each type of excavator. Considering the constraints of the problem—no fewer than three types of excavators and a budget of 24 million yuan—we introduce the relevant constraints and objective function. Based on the principles of the Qubo model, we define binary variables and a quadratic function to be minimized under these binary constraints. For each element, we define a binary variable and find a combination of binary variables that maximizes the final long-term profit. We then use the simulated annealing solver and the CIM simulator in the Kaiwu SDK to solve and compare the problem, finding a combination of binary variables that minimizes the Qubo matrix and corresponds to the maximum long-term discounted profit value. Finally, based on the maximized profit, we determine the types and quantities of excavators to be purchased.

[0049] Analysis of Question 2

[0050] For Problem 2, based on the conditions of Problem 1, we need to find the maximum profit for the excavator and mining cart combination and propose a corresponding procurement plan. In this problem, constraints are added, such as the matching relationship between the excavator and mining cart. First, calculate profit = revenue - cost, where revenue is the revenue from the ore mined by the excavator, and cost is the cost of the excavator and the cost of the mining cart. Next, express the objective function and constraints, and introduce a penalty factor to transform the objective function into a quadratic unconstrained binary optimization problem using the QUBO model. The QUBO model is then converted into a Hamiltonian for quantum bits. The minimum energy state of this Hamiltonian is solved using a simulated annealing solver and a CIM solver. The resulting quantum bit state is the optimal solution, which is then solved using a quantum computer. Finally, maximize profit and, subject to the constraints, determine the optimal solution and the matching relationship between the excavator and mining cart.

[0051] Analysis of Question 3

[0052] For Problem 3, with an increased budget and the increasing number and types of excavators and mining carts, we still need to find the optimal profit and procurement plan based on the matching relationship. Based on Problem 2, we first construct the objective function and constraints, then transform them into a quadratic, unconstrained equation using the QUBO model. However, due to the large number of qubits required for the solution using simulated annealing and CIM, we considered using a modified simulated annealing method called subQUBO. SubQUBO solves sub-QUBO problems multiple times, effectively tackling large-scale data or computationally complex situations. Therefore, we solve for the optimal profit, the types and numbers of excavators, and the matching relationship between excavators and mining carts.

[0053] Analysis of Question 4

[0054] Regarding question 4, we illustrate a potential application scenario for decision optimization using the QUBO model: hyperparameter tuning for AI models. By comparing quantum computing with traditional algorithms, we highlight the advantages of the QUBO model for hyperparameter tuning for AI models.

[0055] Model assumptions:

[0056] In order to simplify the complexity of management and scheduling and reduce the risk of safety accidents caused by changing the matching, it is assumed that the matching relationship between excavators and mine carts is fixed; it is assumed that the data given in the question is true and reliable and remains unchanged for a long time; it is assumed that only the solution of the combined optimal solution is considered, and the impact of the small amount of data on accuracy is not considered; it is assumed that the excavator and mine cart are not damaged during the working hours, which does not affect the expenditure of income and cost; only the purchase cost of the excavator is required in the first year.

[0057] For detailed explanation of symbols, please refer to the appendix of the manual. Figure 15 .

[0058] Model establishment and solution

[0059] Based on the analysis of the above problems, we get the flow chart of ideas as follows Figure 1 As shown:

[0060] Here we regard the QUBO model as a gray box, put the data in the table in the box and solve the specific problem. The specific flow chart of QUBO model solution is as follows: Figure 2 As shown;

[0061] Establishment of profit maximization model

[0062] In Problem 1, we need to use the estimated long-term profits of different types of excavators given in the question to establish a profit-maximizing QUBO model to solve the optimal procurement plan (including the excavator model and corresponding quantity). The long-term profit discount table for excavators is shown in Table 1:

[0063] Table 1 Long-term profit discount table (unit: 10,000 yuan)

[0064]

[0065] In this problem, our goal is to maximize the long-term total profit while satisfying the budget and purchase quantity constraints. Therefore, we construct the profit maximization objective function W based on the long-term profit discount table of the excavator:

[0066] W=Maximize(h1w1+h2w2+h3w3+h4w4)(1)

[0067] Assume that h k The long-term discounted profit value of the k-th excavator, the decision variable w k represents the number of excavators of type k purchased, where k = 1, 2, 3, 4 correspond to excavator 1, excavator 2, excavator 3, and excavator 4 respectively.

[0068] However, solving the objective function requires considering the constraints. According to the question, we know that the constraints include the restriction that the number of excavators purchased cannot be less than 3, and the restriction that the budget is 24 million yuan.

[0069] In the QUBO model, we introduce binary 0-1 variables to better represent constraints. The QUBO model is a mathematical formalism for solving combinatorial optimization problems. In the model, variables are typically constrained to binary values (0 or 1). This is because the QUBO model is often used to describe decision-making problems, where each variable represents a decision variable and takes the value 0 or 1, indicating whether to make a decision or not, respectively.

[0070] Constraints on excavator purchase types

[0071] Using binary variables, we construct a 0-1 matrix for excavator types and their corresponding quantities. In this matrix, column vectors represent the excavator type, and row vectors represent the corresponding number of excavators. Therefore, based on the condition stated in the question that the purchase quantity cannot be less than three categories, we can derive the constraint function expression for the excavator purchase types:

[0072]

[0073] Here, we assume that w ki is the binary value of the k-th excavator when the number is i.

[0074] When w ki =1, it means that there are i excavators k purchased; when w ki =0, it means that there is no situation where k excavators i are purchased.

[0075] However, to simplify the solution, we need to make a rough estimate of the range of i. Considering that the project's initial capital is 24 million yuan, assuming that all excavators 1, which have the lowest procurement cost, are purchased, a total of 24 units can be purchased.

[0076] Therefore, i<24. Thus, we can get a more reasonable constraint expression for the type of excavator purchased:

[0077]

[0078] Budget constraint

[0079] From the title, we know that the project’s start-up capital is 24 million yuan.

[0080] Among them, the purchase price parameters of the four excavators are shown in Table 2:

[0081] Table 2 Purchase price list of excavators (unit: 10,000 yuan)

[0082]

[0083] Assume that w ki is the binary value of the k-th excavator when the number is i, t ki Represents the number of k-th excavators, that is: t ki =i.

[0084] Therefore, the constraint function expression when the budget limit is 24 million yuan is obtained:

[0085]

[0086] The QUBO model solution for smart mines can be solved through the Kaiwu SDK, a software development suite based on the coherent Ising machine. According to the problem, we use the simulated annealing solver and CIM solver built into the Kaiwu SDK to solve it. The basic principle of quantum annealing involves converting the minimization problem into a Hamiltonian, solving the problem by finding the lowest energy state of the Hamiltonian, and then using the system to search for the lowest energy state of the target optimization problem. According to quantum annealing, the following objective function describes how the quantum system should represent the quantum bit q i , through biasing, and then coupling them with other qubits:

[0087]

[0088] Since the objective function is quadratic, it can couple two variables.

[0089] In the context of quantum annealing, the value of the function is often referred to as the energy, since the quantum annealer will find the lowest energy state. In addition to using the objective to find the optimal value, constraints are imposed on the optimization problem. The objective function described above is called quadratic unconstrained binary optimization (QUBO), and the constraints are added using the following equation: QUBO = min(Obj + γ(constraints)) (6)

[0090] According to the question, our objective function is:

[0091]

[0092] The constraints consider the type of excavator and the limited start-up capital. The purchase of at least three types of excavators must be considered, and we consider the purchase cost of the excavator and its corresponding long-term profit discount.

[0093] That is, by comparing the "cost / profit" ratio, the least cost-effective excavator is found and it is not purchased. At this time, the profit can be maximized.

[0094] Therefore, the constraints on the excavator type are:

[0095]

[0096] The constraints for the budget of RMB 24 million are:

[0097]

[0098] In order to transform this problem into a QUBO model, according to relevant principles, the basic QUBO form is:

[0099] minmize / maxmize y=x TQx(10)

[0100] in, [4] Q is the QUBO matrix, x is a problem consisting of binary variables, each variable takes the value {0, 1}, and the goal of QUBO is to find x that minimizes or maximizes y.

[0101] And, the Q matrix is in the form:

[0102]

[0103] Therefore, this paper defines binary variables and quadratic functions to be minimized under binary constraints. In this case, in order to select the profit-maximizing excavator model and its corresponding quantity, we apply the following expression:

[0104]

[0105] Among them, w k represents the number of excavators k, w ki is the binary value of the k-th excavator when the number is i, t ki Indicates that the number of k-th excavators is i.

[0106] Then find a combination of binary variables that maximizes the long-term profit of the excavator, and then use the simulated annealing solver in the Kaiwu SDK to find the combination of binary variables that minimizes the QUBO matrix and corresponds to the maximum long-term profit.

[0107] However, in the QUBO model, the default is to find the lowest energy, so the objective function is negative and inserted into the QUBO model. The objective function can be expressed as:

[0108]

[0109] Among them, for w ki ∈{0,1}, all have w ki 2 =w ki .

[0110] In order to make the model not restricted by this constraint, a penalty factor P = 11000 is introduced, so that the objective function becomes:

[0111]

[0112] To transform the objective function into [5] The QUBO model form makes it possible to use quantum computers to solve it. We can convert all variables into binary variables. Therefore, we replace the binary variables with the corresponding Ising variables and use the following conversion formula:

[0113]

[0114] Among them, z ki Ising variable.

[0115] According to the generated QUBO Hamiltonian, the objective function is transformed into a quadratic form, which can be simplified as follows:

[0116] minW=X T QX+c#(15)

[0117] Where Q is the QUBO symmetric matrix, X T represents the transpose of X, and c represents a constant.

[0118] Next, we solve the Q matrix and then solve the QUBO model based on the working principle of quantum computing. Here we solve the Q matrix as:

[0119]

[0120] In order to solve the corresponding number of excavator types when maximizing profits, we use the simulated annealing solver and CIM simulator built into the Kaiwu SDK. The flowchart of the simulated annealing algorithm solver and the core technology diagram of the CIM simulator are attached to the manual. Figure 3 and Figure 4 ;

[0121] After understanding the working principle of the solver, we set the parameters for the two solvers.

[0122] Parameter settings for the simulated annealing solver: marix (np.ndarray): CIMIsing matrix; T_init (float): initial temperature 100; alpha (float): cooling coefficient 0.5; T_min (float): cutoff temperature 0.1; iterations_per_T (int): iteration depth per temperature 10; size_limit (int): number of solutions returned 10. Parameter settings for the tabu search solver for the CIMIsing model: matrix (np.ndarray): CIMIsing matrix; max_iter (int): maximum number of iterations 10; init (np.ndarray): initial value for iteration, a numpy vector of length len(matrix). If the input is empty, a randomly generated vector is used; t (int): size of the recency tabu table. If the input is empty, 1 / 10 of the matrix side length is used, rounded up; kmax (int): maximum value of the model parameter k. The default value is 3; p1 (int): parameter p1 that affects span changes. The default value is 3; p2 (int): Parameter p2 that affects span changes. The default value is 7.

[0123] Results and solutions for Question 1

[0124] According to the above model and two solution methods, the purchase cost of the excavator and the discounted value of the long-term profit are substituted to solve the QUBO problem.

[0125] First, the results of solving the QUBO model using the simulated annealing solver and the CIM simulator are shown below. The maximum value of the Value result indicates that the maximum profit is 580 million yuan.

[0126] Table 3 Results of simulated annealing for solving QUBO problem, see the appendix of the manual Figure 16 .

[0127] Table 4 CIM solution results of QUBO problem, refer to the manual Figure 17 .

[0128] Draw a 3D view of the type and quantity of excavators of interest such as Figure 5 .from Figure 5 As can be seen, Excavator 3 has a higher return on investment than the other three types of excavators, so the number of Excavator 3 purchased may be too large. Based on the enumeration method, we will now calculate the specific excavator type and quantity that can achieve the maximum return.

[0129] In the simulated annealing solver and CIM solver, the maximum gain and error rate are visualized, and the visualization images of the two solution methods are obtained as follows Figure 6 and Figure 7 .

[0130] Based on the image information, we can analyze the maximum profit and error rate of the two solvers. We found that the simulated annealing solver achieved a maximum profit of 580 million yuan at an error rate of 5.2%, while the CIM simulator achieved a maximum profit of 580 million yuan at an error rate of 5.5%. While both solvers achieved a maximum profit of 580 million yuan, the simulated annealing solver achieved a better and lower error rate.

[0131] Furthermore, we also find the type and quantity of excavators that maximize profits. Here, w1 = 1.0, w2 = 2.0, w3 = 10.0, and w4 = 0.0.

[0132] Therefore, the excavator procurement plan with the maximum profit of 580 million yuan is drawn as follows:

[0133] Table 5 Profit-maximizing excavator purchase types and corresponding quantities

[0134]

[0135] Problem 2: Model establishment and solution

[0136] Establishment of a model for maximizing the benefits of combining excavators and mine trucks

[0137] In Problem 2, the matching problem of excavators and mine carts needs to be considered.

[0138] Based on the constraints given in the question, assuming the service life of the excavator and mining cart is 5 years, we consider the model and quantity of excavators to be purchased to maximize profits. We also solve the specific purchase plan based on the matching relationship between the excavator and mining cart and the cost of the mining cart itself. The total profit is calculated as follows:

[0139] Profit = Revenue - Various Costs#(17)

[0140] Therefore, according to the question, we will gradually establish a profit model.

[0141] First, theoretical analysis shows the benefits of mining ore:

[0142] Revenue = Number of excavators of various types × Operating efficiency × Bucket capacity × Working hours × Ore price (18)

[0143] The mathematical expression for ore revenue is:

[0144]

[0145] Among them, Y represents the ore income, z kIndicates the operating efficiency, d k represents the bucket capacity, t1 represents the excavator's operating time, and P represents the ore price. The excavator's operating time for 5 years is 9600 hours.

[0146] The following theoretical analysis shows the cost of the excavator:

[0147] Excavator cost = purchase price + fuel consumption × fuel price × t1 + maintenance cost × t2 + labor cost × t2 (20

[0148] t1 = 5 years × 12 months × 20 days × 8 hours = 9600 hours (21)

[0149] t2 = 5 years × 12 months = 60 months (22)

[0150] The cost of an excavator can be expressed mathematically as follows:

[0151]

[0152] Among them, C1 represents the total cost of the excavator, s k represents the purchase price of the k-th excavator, y k represents the fuel consumption of the k-th excavator, r k represents the maintenance cost of the k-th excavator, p k represents the labor cost of the k-th excavator.

[0153] Similarly, theoretical analysis shows the cost of minecarts:

[0154] Mining car cost = fuel consumption × fuel price × t1 + maintenance cost × t2 + labor cost × t2 (24)

[0155] Since there are 7, 7, and 3 minecarts in total for minecart 1, minecart 2, and minecart 3, respectively, the cost of minecarts can be expressed mathematically as follows:

[0156]

[0157] Among them, C2 represents the total cost of the minecart, y j ' represents the fuel consumption of the jth mining car, r j ' represents the maintenance cost of the j-th minecart, p j ' represents the labor cost of the j-th minecart.

[0158] Therefore, by simple substitution, we can get the objective function expression of the final profit:

[0159] W=Y-(C1+C2)(26)

[0160] However, in actual operations, there are certain constraints on the matching of excavators and mining trucks: due to the corresponding relationship between the excavator bucket width and the mining truck width, a large excavator cannot be matched with a small mining truck; and to avoid slow loading efficiency, a small excavator will not be matched with an oversized mining truck. The matching relationship between different excavator models and mining trucks is shown in Table 4.

[0161] Table 6 Matching relationship between excavator and mine car

[0162] Mine 1 Mine 2 Mine 3 Excavator 1 1 \ \ Excavator 2 2 1 \ Excavator 3 2 2 1 Excavator 4 \ 2 1

[0163] So assuming k j represents the number of minecarts j, k jk Indicates the number of minecarts j matched by excavator k, for example, k 12 Represents the number of mine carts 1 matched by excavator 2. The constraint matrix of the matching relationship between excavator and mine cart is obtained:

[0164]

[0165] (st)

[0166]

[0167] In addition, there are no less than three types of excavators to be purchased. We assume that there are four types of excavators to be purchased for model construction. That is, the constraints on the types of excavators are:

[0168]

[0169] Solution and optimal solution of QUBO model for Problem 2

[0170] Based on the establishment of the QUBO model in Problem 1, Problem 2 adds constraints on the matching relationship between mining vehicles and excavators to the original model. Therefore, the target profit function under the QUBO model is:

[0171]

[0172] The penalty factor is introduced to make the model not restricted by the constraint condition, so the objective function becomes:

[0173]

[0174] Similar to Problem 1, after converting the objective function into a quadratic form, the QUBO model can be obtained. The QUBO model is then converted into the Hamiltonian of the quantum bit [6]. The minimum energy state of the Hamiltonian is solved using a quantum algorithm. The quantum bit state obtained by solving it with a quantum computer is the optimal solution.

[0175] The answer is searched and solved based on the simulated annealing solver and CIM simulator in the Kaiwu SDK, and finally the optimal solution for the type and number of excavators and the matching of excavators and mining carts to maximize profits is obtained.

[0176] Since the SDK cannot solve problems with more than 100 bits, the number of qubits in the model must be known before solving. In quantum computing, data is stored in qubits. Each qubit has two basic states, represented by |0> and |1>. The qubit can be in a superposition of these two basic states, namely α|0>+β|1>, where α and β are complex numbers and satisfy |α| 2 +|β| 2 =1[7]. In particular, we have simplified the model construction and optimized the algorithm, so the number of quantum bits in the SDK is 93 and 89 respectively.

[0177] Next, we used two solvers to calculate the maximum profit: the CIM simulator achieved a minimum error rate of 5.97%, with a maximum profit of 57,900,3600 yuan; the simulated annealing solver achieved a minimum error rate of 5.58%, with a maximum profit of 57,900,4800 yuan. Compared to the CIM simulator, the simulated annealing solver achieved a lower error rate and greater profit. Using the simulated annealing solver with an initial temperature of 100 degrees Celsius, a decay constant of 0.95, and a stopping criterion of 25 iterations, the curve converged to 57,900,4800 yuan.

[0178] In this mode, when profit reaches its maximum, the excavator type and corresponding quantity for the excavator and mining truck combination can be solved. Here, w1 = 7.0, w2 = 7.0, w3 = 2.0, and w4 = 1.0. Therefore, the excavator procurement plan for a maximum profit of 579,004,800 yuan is as follows:

[0179] Table 7 Profit-maximizing excavator purchase types and corresponding quantities

[0180]

[0181] In addition, according to the matching constraint relationship matrix between excavators and mining vehicles in formula (27), the matching relationship matrix of the number and type of excavators and mining vehicles can be obtained:

[0182]

[0183] The optimal matching solution between excavator and mining car for maximum profit can be obtained:

[0184] Table 8 Optimal matching scheme of excavator and mine car

[0185] model Mine 1 Mine 2 Mine 3 (7 units) Excavator 1 7 0 0 (7 units) Excavators 2 0 7 0 (2 units) Excavator 3 0 0 2 (1 unit) Excavator 4 0 0 1

[0186] For example, for 7 excavators 1, 7 mining vehicles 1 need to be matched, and so on.

[0187] Problem 3: Model establishment and solution

[0188] Establishment of optimal matching model for complex combination of excavator and mining truck

[0189] Based on the considerations in question 2, the smart mine underwent further upgrades. The number of mining vehicles and excavators was increased to 10, the initial capital was raised to 40 million yuan, and the purchase of at least five types of excavators was required.

[0190] Problem 3 is more complex in terms of quantity combinations. To maximize profits, we still use equation (17) Profit = Revenue - Various Costs to construct the model. In this case, the binary unconstrained quadratic optimization model is still applicable, and the binary decision variable is whether to purchase the corresponding quantity of the excavator type.

[0191] For question 3, the theoretical expression of ore revenue is as shown in equation (18), and its mathematical expression is:

[0192]

[0193] Among them, Y represents the ore income, z k Indicates the operating efficiency, d k represents the bucket capacity, t1 represents the working time of the excavator, and P represents the ore price.

[0194] The following theoretical analysis shows that the cost of the excavator is Equation (20), and its mathematical expression represents the cost of the excavator:

[0195]

[0196] Among them, C1 represents the total cost of the excavator, s k represents the purchase price of the k-th excavator, y k represents the fuel consumption of the k-th excavator, r k represents the maintenance cost of the k-th excavator, p k represents the labor cost of the k-th excavator.

[0197] Similarly, the specific value of the cost generated by the mine cart can be analyzed by theoretical formula (24).

[0198] Table 9 Cost of different types of mine cars

[0199] model Cost (yuan) Mine 1 1008000 Mine 2 3264000 Mine 3 4056000 Mine 4 4896000 Mine 5 5784000 Mine 6 4032000 Mine 7 4680000 Mine 8 5184000 Mine 9 5803200 Mine 10 6516000 total 45223200

[0200] Therefore, by simple substitution, we can get the objective function expression of the final profit:

[0201] W=Y-(C1+452232000)(34)

[0202] However, in actual operations, there are certain constraints on the matching of excavators and mining vehicles. In order to construct a quadratic unconstrained optimization equation, we need to first find the constraints in the problem.

[0203] Excavator and mine car matching constraints: Table 6 shows the matching relationship table of different types of excavators and mine cars, among which Table 10 shows the matching relationship of ten types of excavators and mine cars. For details, please refer to the appendix of the manual. Figure 9 .

[0204] According to the definition of mathematical symbols in Question 2, assuming k j represents the number of minecarts j, k kj represents the number of mine carts j matched by excavator k, and the constraint matrix of the ten excavator-mine cart matching relationships is obtained:

[0205]

[0206] (st)

[0207]

[0208]

[0209] Excavator purchase constraints: No less than 5 types must be considered, that is, the constraints on the excavator types are:

[0210]

[0211] Budget constraint: The initial capital for purchasing the excavator is 40 million yuan, so the budget constraint is:

[0212]

[0213] Among them, Price k is the unit price of the k-th excavator, w k is the number of excavators k

[0214] Solution of subQUBO model

[0215] The above objective function is expressed in binary using the QUBO model, and the objective function expression for profit maximization is obtained as follows:

[0216]

[0217] In order to make the objective function free from constraints, we introduce a penalty factor and obtain the unconstrained profit maximization objective function as follows:

[0218]

[0219] After using the Kaiwu SDK to solve the problem, we discovered that the solver was unable to operate properly due to the increasing number of excavators and mine carts in the model and the increasing complexity of the combination, resulting in the number of qubits far exceeding 100. As suggested in the problem, we can try the subQUBO model method for solving the problem.

[0220] subQUBO stands for Sub Quadratic Unconstrained Binary Optimization (SQUBO), commonly used to solve optimization problems with binary variables. It is an extension of QUBO (quadratic unconstrained binary optimization) and is used for decomposition and parallelization of large-scale problems.

[0221] This is a new hybrid annealing method called sub-QUBO model extraction with multiple solution instances. Based on a strong theoretical background, we extract a sub-QUBO model with a limited size as follows: S (N S <N I ) solution examples, and focus on N S Solve for a specific binary variable x in the example i , if x i The value of N S If the variation among the solution instances is large, it will be included in the subQUBO model;

[0222] Otherwise, it is not included. We use the Ising machine to find the (quasi) ground state solution of the extracted subQUBO model and add it as a new solution instance. By repeating this process, we can eventually obtain the (quasi) ground state solution of the original QUBO model.

[0223] Experimental evaluation confirms that for large QUBO models, the proposed method can obtain better quasi-ground state solutions than existing methods.

[0224] The steps for using the subQUBO method are as follows:

[0225]

[0226] Complex combination results and optimal solutions

[0227] Based on the detailed explanation of the subQUBO method in other documents, as well as debugging and calling the code in the programming environment, we set the initial temperature to 100°C, the decay constant to 0.95, and the stopping criterion to 25 iterations. The subQUBO simulated annealing results are plotted in the figure. The maximum profit from simulated annealing converges to 381,207,899 yuan. Therefore, the maximum profit for the excavator and mine cart in this complex combination is 381,207,899 yuan.

[0228] By solving the problem, we can know the type and quantity of excavators under the combination of excavators and mining trucks when the profit reaches the maximum. The excavator procurement plan when the maximum profit is 381,207,899 yuan is as follows:

[0229] Table 11 Ten profit-maximizing excavator purchase types and their corresponding quantities

[0230]

[0231] In addition, according to the matching constraint relationship between excavators and mining vehicles in formulas (35) and (36), the matching relationship matrix of the number and type of excavators and mining vehicles can be obtained:

[0232]

[0233] The optimal matching solution between the excavator and the mining car at the maximum profit can be obtained.

[0234] Table 12 shows the optimal matching schemes for ten excavators and mining vehicles. Figure 11 .

[0235] For example, for 5 excavators 1, 5 mine carts 1, 5 mine carts 2, 2 mine carts 3, and so on need to be matched.

[0236] Application of the QUBO model for hyperparameter tuning of artificial intelligence models

[0237] The QUBO model is commonly used to solve combinatorial optimization problems where the variables are binary (equal to 0 or 1) and the objective function is a quadratic form. It is suitable for problems that require finding the optimal solution under given constraints, especially when the problem can be transformed into a binary variable and a quadratic objective function. This model has applications in many fields, including but not limited to:

[0238] 1. Circuit design: The QUBO model can be used to optimize the layout of logic gates to minimize delay or power consumption in the circuit.

[0239] 2. Logistics and transportation: used to optimize the delivery routes of goods to minimize costs or maximize efficiency.

[0240] 3. Financial investment: used to optimize investment portfolios to maximize returns or minimize risks.

[0241] 4. Combinatorial optimization: Solve combinatorial optimization problems such as the traveling salesman problem (TSP) and the knapsack problem.

[0242] 5. Artificial Intelligence and Quantum Computing: The QUBO model is closely related to quantum computing and quantum optimization, and can be used to solve problems that are difficult to solve on traditional computers.

[0243] In question 4, we need to give an example of a potential application scenario for decision optimization by building a QUBO model. Based on the above and team discussion, we chose the scenario of "artificial intelligence model hyperparameter tuning" for exploration.

[0244] Currently, artificial intelligence (AI) technology is developing towards large-scale distributed AI and multi-expert collaborative systems, parallel reasoning, various expert system development tools, large-scale distributed AI development environments, and distributed multi-agent collaborative systems. In the field of AI, the performance of machine learning models often depends on the selection and tuning of hyperparameters. Hyperparameters are parameters set before model training, and different hyperparameter combinations can significantly affect model performance. Traditional hyperparameter tuning methods, such as greedy algorithms and grid search, often require multiple experiments, consuming significant time and computing resources. In current deep learning and machine learning research, researchers often face complex model structures and large datasets, which creates a vast hyperparameter search space. Properly selecting hyperparameters can significantly improve model performance, but this also increases the difficulty of hyperparameter tuning. Traditional methods, such as greedy search or grid search, can address this problem, but these methods are less efficient in high-dimensional spaces, especially when complex relationships exist between hyperparameters.

[0245] Quantum computing offers many potential advantages over traditional computing. Although the technology is still in its developmental stages, its potential has already garnered widespread attention. Quantum computing leverages the properties of quantum superposition and entanglement. Its parallelism allows for faster processing of large-scale problems, significantly improving algorithmic efficiency. Furthermore, quantum computing is highly effective for solving certain types of problems, such as combinatorial optimization. Therefore, leveraging the advantages of quantum computing to accelerate the hyperparameter tuning process of AI models has become a promising research topic.

[0246] Research Methodology:

[0247] Problem definition: We hope to accelerate the hyperparameter tuning process of artificial intelligence models through the advantages of quantum computing. Specifically, we use hyperparameters as decision variables and the performance measure of the model (such as accuracy) as the objective function. QUBO model construction: We introduce each hyperparameter into a binary variable and construct a QUBO model. Based on the relationship between hyperparameters, the objective function aims to maximize or minimize the performance measure. Application of CoherentIsing Machines (CIM): Utilize the parallel computing and high connectivity of CIM to more efficiently search the hyperparameter space in quantum computing. The quantum advantage of CIM can improve search efficiency and find better hyperparameter combinations.

[0248] Ideas and technical routes: Select key hyperparameters: First, we need to carefully select key hyperparameters that have a significant impact on model performance. This may include learning rate, number of layers, number of nodes, etc., depending on the machine learning model and task being used.

[0249] QUBO model design:

[0250] Introduction of decision variables: For each selected hyperparameter, a binary variable is introduced to represent its value.

[0251] Objective Function Design: Design an objective function that maximizes or minimizes the model's performance metric, forming a quadratic objective function. Then, explore the constraints of the function and introduce a penalty factor to make the objective function unaffected by the constraints, forming a binary, unconstrained, binary function.

[0252] Simulated annealing or CIM simulation: A QUBO model is constructed using the simulated annealing algorithm or CIM. These algorithms leverage the advantages of quantum computing and can efficiently solve high-dimensional and complex problems.

[0253] Performance evaluation: Use the obtained optimal hyperparameter combination to train the machine learning model and evaluate its performance on the validation set or test set. Compare the performance of the hyperparameter combinations obtained using quantum computing methods and traditional methods. Through this technical route, we hope to give full play to the advantages of quantum computing in the hyperparameter tuning of artificial intelligence models and improve the efficiency of the optimization process to better support research and application in the field of artificial intelligence. Therefore, a technical roadmap is drawn based on the QUBO model of artificial intelligence hyperparameter tuning. For details, please refer to the attached manual. Figure 12 .

[0254] Expected research results:

[0255] By introducing quantum computing into the hyperparameter tuning process of AI models, we expect to achieve the following:

[0256] Faster optimization speed: Quantum optimization algorithms are parallel and efficient, which can speed up the process of hyperparameter search, thereby reducing the time required for tuning. More accurate hyperparameter adjustment: Quantum optimization algorithms may be able to find the optimal solution for hyperparameters more accurately, thereby improving the performance and generalization ability of the model. Solving high-dimensional space problems: Traditional optimization algorithms may be limited when dealing with high-dimensional hyperparameter spaces, while quantum optimization algorithms may be more suitable for dealing with optimization problems in high-dimensional spaces, which is particularly useful for complex artificial intelligence models. Overcoming local optimal solution problems: Quantum optimization algorithms generally have better global search capabilities, which can help models avoid falling into the local optimal solution of traditional algorithms, thereby improving the performance and stability of the model.

[0257] Application to multiple AI models: Quantum optimization algorithms are not only applicable to specific types of models, but can also be applied to various types of AI models, including supervised learning, unsupervised learning, reinforcement learning, etc.

[0258] QUBO model algorithm and expression: refer to the instruction manual for details Figure 13 .

[0259] Exploring the QUBO model for AI hyperparameter tuning examples:

[0260] With this data, we employed quantum computing to conduct a preliminary exploration of AI hyperparameters. Assuming N_i is the number of qubits, N_e is the energy level, and N_s is the number of solvable problems, we calculated the accuracy distribution of the QUBO solver under different parameter configurations, for example: N_i = 20, N_e = 5, and N_s = 10.

[0261] Reference Manual Figure 14 This figure is a box plot showing the accuracy distribution of the QUBO solver under different parameter configurations. Each box represents the statistical distribution of the algorithm's accuracy under a specific set of parameters. The box plot illustrates the dispersion of the data by displaying a five-number summary of the data (minimum, first quartile, median, third quartile, and maximum) as well as possible outliers. We found that the median accuracy varied across different parameter settings, but overall it was almost always above 0.80, indicating high accuracy. The interquartile range represents the variability of the accuracy, with shorter boxes indicating more consistent results and longer boxes indicating greater variability. The results show that for N_i60, N_e7, and N_s6, some parameter settings have longer boxes, indicating greater variability in accuracy under these settings, while some shorter boxes indicate more stable accuracy under these settings.

Claims

1. The mine combination optimization method based on QUBO is characterized by: Includes the following methods: Obtain data on the type, quantity, procurement cost, operating efficiency, and matching relationships of mining equipment to construct an initial data set; Based on the initial data set, a mathematical model is established with maximizing total profit as the objective function and budget constraints and equipment matching relationships as constraints; Convert the objective function and constraints into a QUBO model, solve the QUBO model using a quantum computer or simulated annealing algorithm, and obtain the optimal equipment procurement plan and equipment matching relationship; The subQUBO method is used to decompose and iteratively solve large-scale quantum bit problems, generating dynamic optimization results in complex combination scenarios.

2. The mine combination optimization method based on QUBO according to claim 1, characterized in that: The construction of the QUBO model includes: Define the equipment quantity decision variable as a binary variable and replace the binary variable with the Ising variable; The constraints are embedded into the objective function through the penalty factor to form an unconstrained quadratic optimization model; Generate the QUBO Hamiltonian matrix, whose expression is: minW=X T QX+c Where Q is the QUBO symmetric matrix, X T represents the transpose of X, and c represents a constant.

3. The mine combination optimization method based on QUBO according to claim 1, characterized in that: The modeling of device matching relationships includes the following: According to the bucket width compatibility between the excavator and the mining truck, a multi-dimensional matching constraint matrix is constructed; The matching relationship is converted into linear or nonlinear constraints and integrated into the QUBO model through penalty factors.

4. The QUBO-based mine combination optimization method according to claim 1, characterized in that: The subQUBO method consists of the following steps: Decompose the original QUBO model into multiple sub-QUBO problems; Use the simulated annealing algorithm to solve each sub-problem separately, and obtain the global optimal solution by iteratively integrating the sub-problem solutions; Dynamically adjust the size of subproblems to adapt to the limit on the number of quantum bits.

5. The mine combination optimization method based on QUBO according to claim 1, characterized in that: The solution process adopts a hybrid optimization strategy, including: Use the simulated annealing algorithm to perform preliminary solution and generate a candidate solution set; Perform secondary optimization on the candidate solution set through CIM to reduce the error rate; The results of different solvers were compared, and the optimal solution with an error rate lower than 5.5% was selected.

6. The QUBO-based mine combination optimization method according to claim 1, characterized in that: It also includes the sensitivity analysis steps: Conduct multiple value tests on the penalty factor to verify the stability of the model under different constraint strengths; By balancing the error rate and profit maximization, the optimal penalty factor range is determined to be 7700-50000.

7. The QUBO-based mine combination optimization method according to claim 1, characterized in that: This method is further extended to AI model hyperparameter tuning, including: Convert the hyperparameter selection problem into a QUBO model; Quantum computing can be used to accelerate the hyperparameter search process and improve model training efficiency.

8. The QUBO-based mine combination optimization system according to any one of claims 1 to 7, characterized in that: Includes the following: Data collection module: used to obtain equipment type, cost, efficiency and matching relationship data; Modeling module: used to construct objective functions and constraints and convert them into QUBO models; Solving module: Integrates simulated annealing algorithm, CIM solver and subQUBO method to solve QUBO model; Output module: Generate equipment procurement plan, matching relationship table and profit maximization report.

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