Mining strategy optimization method based on random variable and NSGA algorithm

Abstract

The invention belongs to the technical field of mining, and particularly provides a mining strategy optimization method based on a random variable and an NSGA algorithm, and the method comprises the steps: generating the random variable of ore grade and mining cost through employing a Monte Carlo simulation method, constructing a multi-objective optimization model, and obtaining a first solution set of the model through employing an NSGA-I algorithm; introducing the market price fluctuation constraint into the multi-objective optimization model to generate a second solution set under the market price fluctuation condition; and adopting a weighted grey correlation analysis method, an entropy weight method and an analytic hierarchy process to screen an optimal production plan of the second solution set in different market price fluctuation directions. According to the method, uncertainty caused by fluctuation of ore grade, mining cost and market price in the strip mine production process can be effectively handled, scientificity and economic benefits of a production plan are improved, and meanwhile, dynamic optimization of the mine production plan is realized; and an important reference is provided for a mine enterprise to make a flexible and feasible production plan in a complex market environment.

Description

Technical Field

[0001] The present invention relates to the field of mining technology, and in particular to a mining strategy optimization method based on random variables and NSGA algorithm. Background Art

[0002] The production plan of open-pit mines is a crucial link in the mining production process. Reasonable production plans can not only improve the economic benefits of mines, but also play an important role in the long-term sustainable development of mining enterprises. However, in the mining production process, the fluctuations in ore grade, mining costs and market prices often lead to increased uncertainty in production plans, making it difficult for traditional production plans to cope with complex market environments. Most existing technologies only consider geological uncertainty, while relatively little research is done on economic uncertainty, which cannot effectively solve the problems caused by market price fluctuations.

[0003] In the existing technology, deterministic methods are usually used to prepare mine production plans. These methods assume that all input parameters are fixed values, so it is difficult to make reasonable adjustments and responses when facing fluctuations in ore grade, mining costs and market prices. In recent years, in response to geological uncertainties, some studies have adopted a combination of Monte Carlo simulation and intelligent optimization algorithms, but there are still deficiencies in comprehensively considering the uncertainty of economic factors.

[0004] Existing optimization methods include linear programming, dynamic programming, and heuristic algorithms. These methods are usually suitable for simple mining planning problems, but when faced with complex multi-objective, multi-constraint conditions, and multiple uncertain factors, the solution effect is not ideal, and it is difficult to ensure the global optimality and stability of the solution. Therefore, an optimization method that can comprehensively consider geological and economic uncertainties and has good solution capabilities is needed to meet the actual needs of modern open-pit mine production. Summary of the invention

[0005] In view of this, the present invention proposes a mining strategy optimization method based on random variables and NSGA algorithm to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention proposes a mining strategy optimization method based on random variables and NSGA algorithm, comprising:

[0007] Monte Carlo simulation method is used to generate random variables of ore grade and mining cost for the mining point, and a multi-objective optimization model is constructed;

[0008] Using NSGA-II algorithm to obtain a first solution set of the multi-objective optimization model;

[0009] The ore market price fluctuation constraint equation is introduced into the multi-objective optimization model, and a non-dominated sorting genetic algorithm is used to generate a second solution set under different market price fluctuation conditions;

[0010] The weighted grey correlation analysis method, entropy weight method and hierarchical analysis method are used to screen the optimal production plan of the second solution set under different market price fluctuation directions.

[0011] Furthermore, the process of using the Monte Carlo simulation method to generate random variables of ore grade and mining cost for the mining point includes:

[0012] Set initial parameters and boundary conditions;

[0013] A random number generator is used to simulate the changes in ore grade and mining cost of each mining point, and the random numbers are normalized to obtain random variables of ore grade and mining cost of each mining point;

[0014] The probability distribution of ore grade and cost is obtained based on the random variables.

[0015] Furthermore, the objective function of the multi-objective optimization model includes minimizing the ore mining cost and maximizing the ore market value; the constraint conditions include ore grade, ore output, plan completion rate, and mining equipment capacity.

[0016] Furthermore, the minimum objective function of ore mining cost is as follows:

[0017]

[0018] Where minf 1 Indicates that the cost of ore mining is minimal, E is the expectation operator, x i represents the quarterly planned output of the ith ore output point, C i represents the ore mining cost of the i-th mining point, the ore mining cost C i is a random variable.

[0019] Furthermore, the objective function for maximizing the market value of the ore is as follows:

[0020]

[0021] In the formula, maxf 2 Indicates that the ore market value is the largest, P 0 represents the initial market price of the ore, G i The ore grade of calcium oxide at the i-th mining point is G i is a random variable, and γ is the rate of change of market price fluctuations.

[0022] Furthermore, the process of solving the multi-objective optimization model using the NSGA-II algorithm includes:

[0023] A group of populations are randomly generated, and the objective function values ​​of mining cost and market value are calculated for each individual in the population;

[0024] Perform non-dominated sorting on individuals in a population, divide the population into different levels, and determine the dominance relationship between individuals;

[0025] Calculate the crowding distance of each individual to obtain the crowding degree of each individual;

[0026] A tournament selection mechanism is used to select individuals of the next generation based on non-dominated sorting and crowding. During the selection process, individuals with lower non-dominated sorting levels and higher crowding are given priority.

[0027] Perform crossover and mutation operations on the selected parent individuals to generate new offspring individuals;

[0028] Merge the parent generation with the child generation, and select a new population from the merged population based on non-dominated sorting and crowding;

[0029] When the maximum number of generations is reached or the convergence condition is met, the iteration stops and the final solution set is output.

[0030] Furthermore, the ore market price fluctuation constraint equation is as follows:

[0031]

[0032] In the formula, x i (t+1) represents the planned output of each platform after market price fluctuations, x i (t) represents the planned output of each platform without being affected by market price fluctuations, α i Represents x i (t) is the sensitivity coefficient to market price changes, ΔP represents the rate of change of the current market price relative to the initial price P0, and τ represents the lag effect coefficient of market price changes.

[0033] Furthermore, the process of selecting the optimal production plan of the second solution set under different market price fluctuation directions includes:

[0034] The weighted grey correlation analysis method is used to calculate the grey correlation coefficient of each solution in the second solution set, and different solutions are compared;

[0035] The entropy weight method and the hierarchical analysis method are used to assign weights to the objective function of the multi-objective optimization model to obtain a comprehensive weight.

[0036] The comprehensive score of each solution is calculated based on the comprehensive weight and the grey correlation coefficient, and the optimal production plan is screened out based on the comprehensive score.

[0037] Furthermore, the comprehensive weight is as follows:

[0038]

[0039] Where W j represents the final weight of objective function j, a j It is represented as the weight of objective function j calculated by analytic hierarchy process, b j The objective function j is represented by the weight calculated by the entropy weight method, n represents the total number of objective functions, and j represents the objective function.

[0040] Furthermore, the optimal production plan is as follows:

[0041]

[0042] In the formula, γ i represents the weighted sum of the correlation coefficient of each indicator and its comprehensive weight, m ​​represents the total number of indicators, r ij Represents grey relational degree.

[0043] Compared with the prior art, the beneficial effects of the present invention include:

[0044] 1. Comprehensive consideration of multiple uncertainties: The present invention comprehensively considers the uncertainties in ore grade, mining cost and market price fluctuations, and uses Monte Carlo simulation to generate random variables, thus ensuring the scientificity and rationality of the model.

[0045] 2. Multi-objective optimization and dynamic adjustment: The dual-objective optimization of mining cost and market value is achieved through the NSGA-II algorithm. At the same time, constraints on market price fluctuations are introduced into the model to ensure that the model can dynamically adapt to changes in market conditions.

[0046] 3. Refined solution screening: Use weighted grey correlation analysis to evaluate and screen the solution results with multiple indicators, and use entropy weight method and analytic hierarchy process to calculate weights to ensure that the final selected solution has the best performance in all aspects.

[0047] 4. Strong applicability: The method provided by the present invention is not only applicable to the optimization of production plans under current market conditions, but can also be adjusted in real time when the market environment fluctuates. It is suitable for medium- and long-term planning and daily scheduling of open-pit mine production. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0049] Figure 1 It is a flowchart of a mining strategy optimization method based on random variables and NSGA algorithm of the present invention;

[0050] Figure 2 is a Pareto front graph obtained in the first iteration in an embodiment of the present invention;

[0051] Figure 3 This is a 3D graph of the Pareto front obtained by the second iteration in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] This embodiment proposes a mining strategy optimization method based on random variables and NSGA algorithm, such as Figure 1 As shown, including:

[0054] Firstly, random variables of ore grade and mining cost are generated by Monte Carlo simulation to simulate the uncertainty in mine production. Then, the NSGA-II algorithm is used to solve the preliminarily constructed multi-objective optimization model to obtain the Pareto front solution set between different objectives. Next, the ore market price fluctuation constraint is introduced into the model, and the solution set is solved by secondary iteration to fully consider the impact of market price fluctuations. Finally, the weighted grey correlation analysis is used to evaluate and screen the solution results to obtain the optimal production plan under different market price conditions.

[0055] The present invention can provide a scientific and reasonable production plan under the circumstances of market price fluctuations, mining cost changes and ore grade fluctuations, thereby maximizing the economic benefits and production efficiency of the mine. The method of the present invention is simple and easy to operate, and is suitable for medium- and long-term planning and short-term scheduling decisions of open-pit mines.

[0056] Data preparation: Collect data on ore grade, mining cost and market price, and use Monte Carlo simulation to generate random variables to simulate the fluctuation of these data at each mining point. Monte Carlo simulation uses linear congruential method to generate uniform random numbers. The specific formula is:

[0057] X t+1 =(aX t +c)mod m

[0058] Among them, the initial value X 0 is called the seed, a, c and m (all positive integers) are called the multiplier, increment and modulus respectively, X n Represents the nth pseudo-random number. Through normalization operation, a uniform random number sequence can be obtained:

[0059]

[0060] By normalizing the random numbers, we can get the random variables of ore grade and mining cost at each mining point. By repeatedly simulating and generating a large amount of data, we can ensure that reasonable predictions can be obtained under various geological conditions and cost changes. These generated uniform random numbers are approximately the true sequence of consistent random variables. Sequence X 0 ,X 1 ,X 2 , ... will repeat after at most m steps, so the sequence is periodic, with a period not exceeding m. In this study, the 'rand' function in MATLAB is used to generate a uniformly distributed random number sequence in the interval [0,1], and then these random numbers are adjusted to the fluctuation range of the ore grade and mining cost of each mining point through linear scaling transformation. The pseudo code is as follows:

[0061] C i,s =C i,ub +(C i,lb -C i,ub )×rand(num s ,1)

[0062] G i,s =G i,ub +(G i,lb -G i,ub )×rand(num s ,1)

[0063] Among them, C i,s , G i,s The random numbers representing the ore grade and mining cost of each mining point, C i,ub , G i,ub They represent the upper bound of the ore grade and mining cost of each mining point, and the corresponding C i,lb , G i,lb Indicates its lower bound, nums represents the number of random samples generated. This approach provides a basis for dynamic simulation of uncertainties involved in the model.

[0064] Model establishment: Establish a multi-objective optimization model including minimizing mining costs and maximizing market value, and set relevant constraints. The objective function is: minimizing ore mining costs and maximizing ore market value:

[0065] Since the distance from each mining point to the unloading point is different, the transportation cost varies. In addition, geological factors such as the complexity of the geological structure, the burial depth of the ore body and the hardness of the rock also lead to differences in the mining costs of each mining point. Therefore, the goal is to reduce the overall mining cost. At the same time, considering that the mining cost of each mining point is a random variable that changes under different conditions, it is necessary to effectively deal with these uncertainties in the planning process. The minimum objective function of ore mining cost is as follows:

[0066]

[0067] Where minf 1 Indicates that the cost of ore mining is minimal, E is the expectation operator, x i represents the quarterly planned output of the ith ore output point, C i represents the ore mining cost of the i-th mining point, the ore mining cost C i is a random variable.

[0068] In order to improve the economic output and economic benefits of the mine and ensure that the production decision is financially optimal, it is necessary to reasonably plan the ore grade of each ore output point, consider market factors such as market demand and price fluctuations while meeting production requirements, and flexibly respond to market changes to dynamically adjust the mine production strategy. The goal is to increase the market value of the ore. The maximum objective function of the ore market value is as follows:

[0069]

[0070] In the formula, maxf 2 Indicates that the ore market value is the largest, P 0 represents the initial market price of the ore, G i The ore grade of calcium oxide at the i-th mining point is G i is a random variable, and γ is the rate of change of market price fluctuations.

[0071] Constraints include ore grade constraints, ore output constraints, planned completion rate constraints and equipment capacity constraints. The model is established based on the actual situation of the mine production process to ensure that the optimization plan is realistic and feasible, as shown below:

[0072] (1) Ore grade constraint equation:

[0073]

[0074] In the formula, G min Indicates the lower limit of calcium oxide ore grade, G max V represents the upper limit of calcium oxide ore grade, and Gi represents the ore grade of calcium oxide. min Indicates the lower limit of magnesium oxide ore grade, V max represents the upper limit of magnesium oxide ore grade, and Vi represents the magnesium oxide grade of each platform.

[0075] (2) Ore output constraint equation:

[0076]

[0077] Where D T,max Indicates the total upper limit of mining output of all platforms, η i Indicates the completion rate of the ore mining plan of each platform.

[0078] (3) Plan completion rate constraint equation:

[0079]

[0080] In the formula, C min represents the upper limit of the completion rate of the ore mining plan, C max Indicates the lower limit of the ore mining plan completion rate.

[0081] (4) Mining equipment capacity constraint equation:

[0082]

[0083] Where N s represents the number of mining equipment, W s Indicates the rated mining capacity of the mining equipment during the planning period; N t Indicates the number of devices, W s It represents the rated capacity of the equipment during the planning period; α and β represent the actual working coefficients of the equipment.

[0084] Preliminary solution: Use the NSGA-II algorithm to solve the multi-objective optimization model and obtain the Pareto front solution set between different objectives. The main steps of the NSGA-II algorithm include:

[0085] Population initialization: Randomly generate the initial population, each individual represents a possible solution, and the population size is. The initial population ensures the diversity of solutions by randomly assigning values ​​to the output of each mining point.

[0086] Objective function calculation: Calculate the mining cost and market value of each individual to determine its position in the target space. The objective function calculation process involves estimating and predicting the mining cost and market value to ensure that each individual solution has an accurate objective function value.

[0087] Fast non-dominated sorting: Sort the individuals in the population according to the non-dominated relationship and divide the individuals into different levels. When sorting, it is necessary to traverse all individuals in the population and compare each pair of individuals to determine the dominance relationship and stratify them.

[0088] Crowding estimation: Calculate the crowding distance of each individual to measure the distribution density of individuals in the Pareto layer to which they belong. When calculating crowding, the minimum and maximum values ​​of each objective function in the layer are calculated to obtain the relative positions of individuals.

[0089] Selection operation: Individual selection is performed based on non-dominated sorting and crowding, and a tournament selection mechanism is used to retain solutions with greater diversity and ensure that the selected individuals are evenly distributed in the Pareto front.

[0090] Crossover and mutation: Perform crossover and mutation operations on the selected individuals to generate new offspring individuals. The crossover operation randomly selects crossover points to synthesize part of the genome of two parent individuals into a new individual; the mutation operation randomly changes some gene values ​​of an individual to introduce new genetic information.

[0091] Population merging and updating: Merge the parent generation with the child generation, and select a new population based on non-dominated sorting and crowding to ensure that the population size remains unchanged and retains high-quality solutions.

[0092] Termination condition: When the maximum number of generations is reached or the Pareto front solution set no longer changes significantly, the iteration is terminated and the final solution set is output.

[0093] The Pareto front image of the first iteration is as follows: Figure 2 As shown in , the obtained frontier has good uniformity and dispersion. Then, based on the initial solution, the ore market price fluctuation constraint is added and a second iteration is performed. Due to the addition of new constraints, 7 new solutions are generated for the original solution according to the market price fluctuation range, as shown in Figure 3 shown.

[0094] Introduction of market price fluctuations and secondary solution:

[0095] Simulate the impact of price fluctuations on production: Through parameter sensitivity analysis, simulate the impact of market price fluctuations on mining plans, and introduce market price fluctuation constraint equations:

[0096]

[0097] In the formula, xi (t+1) represents the planned output of each platform after market price fluctuations, x i (t) represents the planned output of each platform without being affected by market price fluctuations, α i Represents x i (t) is the sensitivity coefficient to market price changes, ΔP represents the rate of change of the current market price relative to the initial price P0, and τ represents the lag effect coefficient of market price changes.

[0098] Secondary update of solution set: The solution set obtained in the initial solution is updated and solved twice iteratively using the NSGA-II algorithm to cope with the impact of market price fluctuations on the optimal solution set, and finally the optimized production plan under different price fluctuation conditions is obtained.

[0099] Screening and evaluation of the optimal solution:

[0100] Weighted grey correlation analysis: Use weighted grey correlation analysis to evaluate the solution results, and compare different schemes by calculating the grey correlation coefficient of each scheme.

[0101] Calculation of weights by entropy weight method and analytic hierarchy process: Taking into account the importance of each evaluation index, objective and subjective weights are assigned to the indexes through entropy weight method and analytic hierarchy process respectively to improve the accuracy of the evaluation.

[0102] Calculation of comprehensive correlation coefficient: Combine the weight and correlation coefficient to calculate the comprehensive score of each solution, finally sort the solutions and select the best solution. The best solution should have advantages in all aspects (economic benefits, production costs, anti-fluctuation ability, etc.). The specific process is as follows:

[0103] Weighted grey correlation analysis to select the best solution

[0104] Data normalization: Normalize the various indicators in the solution set obtained by solving the model to eliminate the influence of the dimensions of each indicator so as to make a unified comparison.

[0105] Correlation coefficient calculation: Calculate the correlation coefficient between the reference sequence and the comparison sequence. The formula is:

[0106]

[0107] Among them, Δ ij It represents the absolute difference between the jth element of the reference sequence and the ith element of the comparison sequence. ρ is the resolution coefficient, which is generally 0.5.

[0108] Entropy weight method and analytic hierarchy process weight calculation: The entropy weight method and analytic hierarchy process are used to calculate the weight of each indicator respectively. The entropy weight method calculates the objective weight through the information entropy of each indicator to measure the importance of the indicator; the analytic hierarchy process determines the subjective weight by constructing a judgment matrix and performing a consistency test. After calculating the weights of each objective function of the uncertain multi-objective optimization model using the entropy weight method and analytic hierarchy process, they are combined into a comprehensive weight using the following formula.

[0109]

[0110] Calculation of comprehensive correlation coefficient: Combine the correlation coefficient with the weight to calculate the comprehensive score of each solution, and finally sort the solutions according to the comprehensive score to select the best solution under different market conditions. The formula is:

[0111]

[0112] The distribution of weights reflects the relative importance of each indicator in the decision-making problem.

[0113] The optimization method provided in this embodiment has the following advantages:

[0114] Comprehensive consideration of multiple uncertainties: The present invention comprehensively considers the uncertainties in ore grade, mining cost and market price fluctuations, and uses Monte Carlo simulation to generate random variables, thus ensuring the scientificity and rationality of the model.

[0115] Multi-objective optimization and dynamic adjustment: The dual-objective optimization of mining cost and market value is achieved through the NSGA-II algorithm. At the same time, the constraints of market price fluctuations are introduced into the model to ensure that the model can dynamically adapt to changes in market conditions.

[0116] Refined solution screening: Multi-index evaluation and screening of solution results are carried out through weighted grey correlation analysis, and weights are calculated by combining entropy weight method and hierarchical analysis method to ensure that the final selected solution has the best performance in all aspects.

[0117] Strong applicability: The method provided by the present invention is not only applicable to the optimization of production plans under current market conditions, but can also be adjusted in real time when the market environment fluctuates. It is suitable for medium- and long-term planning and daily scheduling of open-pit mine production.

[0118] The mine uses computer-aided production scheduling when compiling the annual plan, while the monthly and quarterly plans are mainly determined by manual experience, and a rough range is determined through experience and then executed. In addition, both the annual plan and the monthly plan do not take into account the uncertainty problems in the production process, such as: changes in ore grade, mining and transportation costs, and price fluctuations of ore in the market. To this end, this embodiment uses an algorithm combining NSGA-II with weighted grey correlation analysis to optimize this problem. Table 1 is the parameters of the optimization algorithm, and Table 2 is the basic parameters of each mining point stope.

[0119] Table 1

[0120]

[0121] For the constraints of market price fluctuations on output, the parameter value of sensitivity α should follow the increase or decrease with the amplitude of market price fluctuations. If the market price fluctuates greatly, the value of α should be larger to reflect the high sensitivity of output to price changes; if the production cost is relatively stable, the value of α can be appropriately reduced because the sensitivity of output to price fluctuations is relatively low. Finally, combined with the historical data of the mine, regression analysis is used to fit the relationship between market price and output, determine the actual impact of price changes on output, and calibrate the value of α. Table 3 shows the value of the sensitivity parameter.

[0122] Table 2

[0123]

[0124] Table 3

[0125]

[0126] This implementation can effectively deal with the uncertainty caused by ore grade, mining cost and market price fluctuations in the open-pit mine production process, and improve the scientificity and economic benefits of production planning. By combining Monte Carlo simulation, NSGA-II algorithm and weighted grey correlation analysis, the dynamic optimization of mine production plan is achieved, which provides an important reference for mining enterprises to formulate flexible and feasible production plans in a complex market environment.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A mining strategy optimization method based on random variables and NSGA algorithm, characterized in that: include: Monte Carlo simulation method is used to generate random variables of ore grade and mining cost for the mining point, and a multi-objective optimization model is constructed; Using NSGA-II algorithm to obtain a first solution set of the multi-objective optimization model; The ore market price fluctuation constraint equation is introduced into the multi-objective optimization model, and a non-dominated sorting genetic algorithm is used to generate a second solution set under different market price fluctuation conditions; The weighted grey correlation analysis method, entropy weight method and hierarchical analysis method are used to screen the optimal production plan of the second solution set under different market price fluctuation directions.

2. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 1, characterized in that: The process of using the Monte Carlo simulation method to generate random variables of ore grade and mining cost for the mining point includes: Set initial parameters and boundary conditions; A random number generator is used to simulate the changes in ore grade and mining cost of each mining point, and the random numbers are normalized to obtain the random variables of ore grade and mining cost of each mining point; The probability distribution of ore grade and cost is obtained based on the random variables.

3. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 1, characterized in that: The objective function of the multi-objective optimization model includes minimizing the ore mining cost and maximizing the ore market value; the constraint conditions include ore grade, ore output, plan completion rate, and mining equipment capacity.

4. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 3 is characterized in that: The minimum objective function of ore mining cost is as follows: In the formula, minf1 means the minimum cost of ore mining, E is the expectation operator, and x i represents the quarterly planned ore output of the ith ore output point, C i represents the ore mining cost of the i-th mining point, the ore mining cost C i is a random variable.

5. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 3 is characterized in that: The objective function for maximizing the market value of the ore is as follows: In the formula, maxf2 represents the maximum market value of the ore, P0 represents the initial market price of the ore, and G i The ore grade of calcium oxide at the i-th mining point is G i is a random variable, and γ is the rate of change of market price fluctuations.

6. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 1, characterized in that: The process of solving the multi-objective optimization model using the NSGA-II algorithm includes: A group of populations are randomly generated, and the objective function values ​​of mining cost and market value are calculated for each individual in the population; Perform non-dominated sorting on individuals in a population, divide the population into different levels, and determine the dominance relationship between individuals; Calculate the crowding distance of each individual to obtain the crowding degree of each individual; A tournament selection mechanism is used to select individuals of the next generation based on non-dominated sorting and crowding. During the selection process, individuals with lower non-dominated sorting levels and higher crowding are given priority. Perform crossover and mutation operations on the selected parent individuals to generate new offspring individuals; Merge the parent generation with the child generation, and select a new population from the merged population based on non-dominated sorting and crowding; When the maximum number of generations is reached or the convergence condition is met, the iteration stops and the final solution set is output.

7. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 1, characterized in that: The ore market price fluctuation constraint equation is as follows: In the formula, x i (t+1) represents the planned output of each platform after market price fluctuations, x i (t) represents the planned output of each platform without being affected by market price fluctuations, α i Represents x i (y) The sensitivity coefficient to market price changes, ΔP represents the rate of change of the current market price relative to the initial price P0, and τ represents the lag effect coefficient of market price changes.

8. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 1, characterized in that: The process of selecting the optimal production plan of the second solution set under different market price fluctuation directions includes: The weighted grey correlation analysis method is used to calculate the grey correlation coefficient of each solution in the second solution set, and different solutions are compared; The entropy weight method and the hierarchical analysis method are used to assign weights to the objective function of the multi-objective optimization model to obtain a comprehensive weight. The comprehensive score of each solution is calculated based on the comprehensive weight and the grey correlation coefficient, and the optimal production plan is screened out based on the comprehensive score.

9. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 8, characterized in that: The combined weights are as follows: Where W j represents the final weight of objective function j, a j It is represented as the weight of objective function j calculated by analytic hierarchy process, b j The objective function j is represented by the weight calculated by the entropy weight method, n represents the total number of objective functions, and j represents the objective function.

10. The mining strategy optimization method based on random variables and NSGA algorithm according to claim 8, characterized in that: The optimal production plan is as follows: In the formula, γ i represents the weighted sum of the correlation coefficient of each indicator and its comprehensive weight, m ​​represents the total number of indicators, r ij Represents grey relational degree.

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