A method for multi-objective robust optimization decision of comprehensive production indexes of ore dressing day

Abstract

The application provides a beneficiation day comprehensive production index multi-objective robust optimization decision method, comprising: obtaining production whole-process data for pretreatment, and constructing decision variable and target variable training data set; according to different disturbance degrees of the decision variable, the decision variable is divided into strong disturbance variable and weak disturbance variable; a sparse search surrogate model is established to obtain an optimal weak disturbance variable non-dominated solution set, which is used for initial population migration of a robust fine search surrogate model; a multi-hidden layer neural network model based on efficient random inactivation is established; a reference point adaptive multi-objective optimization algorithm based on index and a model management strategy based on K-means clustering algorithm are adopted to obtain a robust Pareto solution set and select a new population entering next iteration until an optimal robust solution set is obtained. The problems of mechanism model being unclear, decision variable uncertainty disturbance and the like in the industrial production and operation management process are solved, and the problem that an index robust optimal solution is difficult to find is solved.

Description

Technical Field

[0001] The present invention belongs to the field of industrial artificial intelligence and optimization decision-making technology, and specifically relates to a multi-objective robust optimization decision-making method for comprehensive production indicators of mineral processing day based on a production indicator data-driven agent model. Background Art

[0002] The mineral processing process is a process in which the raw ore is mined from the ground and then separated from the gangue through crushing, grinding and magnetic separation to enrich the useful mineral components, thereby obtaining the concentrate and tailings of qualified grade. The mineral processing production process is a typical complex process industrial process, and its entire production process consists of multiple steps, such as Figure 1 However, currently, decision-making, control, and operational management of the entire manufacturing and production process still rely on human participation in cyber-physical systems. Operators and knowledge workers, drawing on production information obtained from information systems and multi-source, heterogeneous production information acquired through sensory, visual, auditory, and tactile perception, utilize their brain's learning, cognitive, analytical, and decision-making capabilities, relying on experience and knowledge to determine the company's comprehensive production indicators, production indicators for the entire manufacturing and production process, operational indicators, and control system instructions. In the traditional production and operations management model, production operations and planning and scheduling decisions primarily rely on the accumulated experience and relevant process knowledge of enterprise managers. This model fails to organically integrate upper-level production planning and decision-making with lower-level, human-controlled control systems, resulting in the ineffective utilization of a large amount of information and knowledge.

[0003] Production decision makers often use the actual production data of the previous production cycle as a reference value for the grade index and material and energy consumption index of the next production planning cycle. After that, they usually prepare and adjust the production plan according to the "Ore Dressing Plant Production and Operation Plan Management System", such as Figure 2However, when formulating mineral processing production plans, production indicators are often optimized based on a fixed ore grade, failing to consider the uncertainties and fluctuations in ore grade and mill grade caused by varying ore mining locations, variable ore sources, varying ore selectivity, and process fluctuations. This uncertainty in ore grade and intermediate product grade directly impacts the operating conditions of the entire mineral processing process, leading to significant fluctuations in actual concentrate output. For example, when the ore grade is higher than the planned ore grade, the mill grade increases, significantly improving the efficiency of the high-frequency screens and ball mills in the milling and beneficiation stages. While maintaining a qualified concentrate grade, the plant's concentrate production capacity increases significantly. When the ore grade is lower than the planned ore grade, the mill grade decreases, compromising product quality. Conventional production indicator decision-making methods fail to account for these issues, resulting in production plans that deviate significantly from actual production and fail to provide effective guidance. With the development of computer technologies such as industrial cloud, artificial intelligence modeling, and evolutionary computing, the indicator multi-objective optimization decision system designed based on the indicator optimization decision method of the data-driven agent model can greatly improve the decision-making ability of production decision makers and save a lot of time.

[0004] Existing methods for metric optimization decision-making based on data-driven agent models fall into two main categories. One is offline data-driven evolutionary optimization, which cannot actively generate new data during the optimization process. Because this approach cannot actively generate new data, offline data-driven evolutionary optimization focuses on building agent models based on given data to explore the search space. In this case, the agent management strategy and optimization results depend heavily on the quality and quantity of available data.

[0005] Another type is online data-driven evolutionary optimization methods. Compared to offline data-driven evolutionary optimization methods, these methods offer more opportunities to improve algorithm performance. They are particularly effective for solving optimization problems that are expensive to evaluate, solving models with limited training data, and solving complex optimization models that are difficult to accurately establish. Thanks to the rapid development of artificial intelligence technology and the improvement of computing power in recent years, online data-driven evolutionary optimization methods have become an effective approach for solving robust optimization problems with multiple objectives and decision variables.

[0006] However, industrial production processes are characterized by long process flows, unclear mechanisms, strong dynamic nonlinearity, and raw material uncertainty, making it difficult to accurately establish optimization models. Actual industrial production data is large but can be incomplete, unbalanced, or noisy, leading to excessively high computational costs for data processing and data-based function evaluation. The computational cost of building proxy models also increases dramatically with the amount of training data. Furthermore, during the objective function evaluation process, some decision variables, such as ore grade and intermediate product grade, are subject to random interference. This causes the undisturbed decision variables in the evolutionary search process to undergo ineffective evolutionary iterative search processes based on the frequent back-and-forth changes in the objective function. This increases the time required for evolutionary optimization solutions and makes it difficult to find the optimal spatial region in the decision space, leading to local optima and difficulty in finding a robust solution that balances robust performance with optimal performance. Summary of the Invention

[0007] In order to solve the problems that the existing evolutionary optimization methods based on data-driven cannot effectively solve the uncertainty disturbance problem of decision variables, cannot make good use of the disturbance degree of different decision variables to improve the optimization efficiency of evolutionary optimization algorithms, and cannot find robust solutions with low sensitivity to uncertainty interference, the present invention proposes a multi-objective robust optimization decision-making method for mineral processing production indicators based on data-driven proxy models. On the one hand, considering the different degrees of robustness interference suffered by different decision variables, the decision space is divided and the solutions are optimized separately; on the other hand, the model is built using a data-driven proxy model instead of directly using all offline data to build a model. The specific feature of the data-driven proxy model is that it uses part of the data set to model and solve, and then uses actual data to rebuild the sample data set with the optimization results, and then models and solves again, continuously expanding the data sample, improving the solution accuracy and reducing the computational cost.

[0008] To this end, the present invention provides the following technical solutions:

[0009] The present invention provides a multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing, the method comprising:

[0010] Obtain and preprocess the daily production data of the entire process of the mineral processing plant, and divide the preprocessed production data into a decision variable data set and a target variable data set;

[0011] According to the production process and actual production data fluctuations, the decision variables affected by the largest disturbance and the actual disturbance error degree are determined, and then a robust partitioner of the decision variable space is constructed to divide the decision variable data set into a strong disturbance variable data set and a weak disturbance variable data set;

[0012] A sparse search proxy model is established between the weak disturbance variable and the target variable, wherein the sparse search proxy model takes the weak disturbance variable data set as input and the target variable data set as output; a random population is used as the first initialization population, and the sparse search proxy model is subjected to population iterative optimization to obtain a sparse search optimal population, that is, a sparse search optimal weak disturbance variable decision solution set;

[0013] A multi-hidden layer neural network multi-objective robust optimization model based on efficient random dropout is established, wherein the multi-hidden layer neural network multi-objective robust optimization model takes the decision variable data set as input and the target variable data set as output; a random population and the sparse search optimal population are used as the second initialization population to perform population iterative optimization on the multi-hidden layer neural network multi-objective robust optimization model to obtain a robust optimized population; and an optimized decision solution set is obtained based on the robust optimized population.

[0014] Furthermore, the decision variables include: daily ore volume, ore grade, mill grade, dry slag grade, tailings grade and concentrate grade;

[0015] The target variables include: concentrate output, total iron recovery rate of raw ore and grinding ratio, which constitute a multi-objective optimization target; the optimization goal is to maximize the concentrate output, maximize the total iron recovery rate of raw ore and minimize the grinding ratio within the target range of comprehensive production indicators.

[0016] Furthermore, strong disturbance variables include: ore grade and mill grade; weak disturbance variables include: daily ore yield, dry slag grade, tailings grade and concentrate grade.

[0017] Furthermore, performing population iterative optimization on the sparse search proxy model includes: performing population iterative optimization on the sparse search proxy model using an NSGA-II algorithm.

[0018] Furthermore, the NSGA-II algorithm is used to perform population iterative optimization on the sparse search agent model, including:

[0019] Generate a randomly initialized population H0 of size N;

[0020] The fitness value of the population is evaluated by the sparse search agent model, the population is non-dominated sorted, and then the initial population is subjected to binary tournament selection, simulated binary crossover operator and polynomial mutation operator to obtain a new population Q0, and the number of optimization times t=0;

[0021] Forming group R t =H t ∪Q t , for the population R tPerform non-dominated sorting and calculate the crowding degree of the population individuals, and select the N individuals with the highest non-dominated sorting to form the population H t+1 ;

[0022] If the number of optimization attempts is greater than the maximum number of evaluations, the process ends and the population H is output. t+1 , randomly select population H t+1 The N / 2 non-dominated solution set is saved as the sparse search optimal population; otherwise, for the population H t+1 Replication, crossover and mutation to form population Q t+1 , t=t+1, proceed to the next optimization search.

[0023] Furthermore, the multi-hidden layer neural network multi-objective robust optimization model is solved by population iterative optimization, including:

[0024] The AR-MOEA algorithm is used to perform population iterative optimization solution on the multi-hidden layer neural network multi-objective robust optimization model.

[0025] Furthermore, the AR-MOEA algorithm is used to perform population iterative optimization on the multi-hidden layer neural network multi-objective robust optimization model, including:

[0026] Generate a random initialization population A of size N / 2. The initialization population P0 is composed of the random population A and the sparse search agent model optimized population B.

[0027] Generate N uniformly from the unit hyperplane R A fixed reference point W is generated, and the external archive set A0 and the adaptive reference point R0 are generated according to the population P0 and the fixed reference point W. The number of iterations t = 0;

[0028] According to R t Calculate the enhanced inversion generation distance index value of the population individual, from K t The solution is selected to form a mating pool, and the offspring O is formed by simulating the binary crossover operator and the polynomial mutation operator. t ;

[0029] According to population A t , O t and W to generate external archive set A t+1 and adaptive reference point R t+1 ; Then according to R t+1 Calculate K t and O t The enhanced reverse generation distance index value of the individual, from which individuals are selected to form P t+1 ;

[0030] If the number of iterations is greater than the maximum number of iterations, it ends and outputs the population P t+1 ; Otherwise, t=t+1, enter the next iteration.

[0031] Furthermore, performing population iterative optimization to solve the multi-hidden layer neural network multi-objective robust optimization model also includes:

[0032] The decision variables of the robust optimization population are clustered by the K-means clustering method to obtain a cluster population; the cluster population is merged with the second initialized population to serve as the initial population for the next iteration; when the size of the initial population reaches the maximum number of evaluations, the initial population result is output.

[0033] Furthermore, when the size of the initial population does not reach the maximum number of evaluations, the cluster population is added as new data to the mineral processing plant training data set, and the decision variable data set and the target variable data set are updated to perform the next iteration.

[0034] Furthermore, a sparse search proxy model is established between the weak disturbance variable and the target variable, including: sequentially adopting a Gaussian process modeling method to respectively establish sparse search proxy models between multiple weak disturbance variables and multiple target functions.

[0035] Advantages and positive effects of the present invention:

[0036] 1. This invention proposes for the first time an online data-driven proxy model robust optimization algorithm framework based on decision space partitioning. This method fully considers the different degrees of robustness interference experienced by different decision variables. By partitioning the decision space dataset, it fully utilizes the differential characteristics of different datasets and adopts an optimization algorithm based on a data-driven proxy model. During the modeling and solving process, this invention uses a partial dataset to establish an optimization model and solve it. After determining the non-dominated solution, the actual production model is used to expand new sample data, and the next round of modeling and solving is repeated. This reduces computational costs while improving the ability to solve and optimize robust problems.

[0037] 2. The online data-driven agent model robust optimization framework based on decision space partitioning proposed in this invention has good universality and can solve the multi-objective robust optimization problem of indicators under multiple types of uncertainty interference by combining data-driven and optimization methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0039] Figure 1This is the mineral processing production process flow chart;

[0040] Figure 2 Prepare business process diagram for mineral processing production plan;

[0041] Figure 3 This is a flow chart of a multi-objective robust optimization decision-making method for indicators based on a data-driven agent model in an embodiment of the present invention;

[0042] Figure 4 This is a Pareto front comparison diagram of the method of the present invention and the comparative method on the robust optimization problem of daily comprehensive production indicators. DETAILED DESCRIPTION

[0043] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described 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 should fall within the scope of protection of the present invention.

[0044] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0045] The following describes in detail a multi-objective robust optimization decision-making method for comprehensive daily production indicators of a mineral processing plant in combination with a full-process production data set of two different process periods of a mineral processing plant.

[0046] like Figure 3 As shown, the multi-objective robust optimization decision-making method for comprehensive production indicators of mineral processing day based on the data-driven agent model in the embodiment of the present invention specifically includes the following steps:

[0047] Step 1: After obtaining the daily production data of the ore dressing plant, perform data preprocessing. L is the length of the sample data. Construct a training data loader for decision variables and target variables. The decision variables include six variables: daily ore volume, ore grade, mill grade, dry slag grade, tailings grade, and concentrate grade. The target variables are concentrate output f1, ore total iron recovery rate f2, and mill selection ratio f3. They form a multi-objective optimization target {f1, f2, f3}. The optimization goal is to maximize the concentrate output, maximize the ore total iron recovery rate, and minimize the mill selection ratio within the target range of the comprehensive production indicators.

[0048] The full-process production data set of the concentrator includes production data sets from two different process periods. The decision variables and target variables of different process production periods are consistent. The decision variables include daily raw ore quantity, raw ore grade, grinding grade, dry slag grade, tailings grade, and concentrate grade. The target variables are concentrate output, raw ore total iron recovery rate, and grinding selection ratio.

[0049] The robust optimization decision problem for the entire production process data is established as follows:

[0050] Decision variables X=[x1,x2,…,x D ], there are r decision variables with a large degree of disturbance, which constitute the strong disturbance variable set X SR =[x1,…,x r ], and is affected by the disturbance variable δ i The remaining decision variables constitute the weak disturbance variable set X WR =[x r+1 ,…,x D ], and other parameters remain unchanged.

[0051] The constructed multi-objective robust optimization test problem is as follows:

[0052] minimize F(x)=(f1(X′ SR ,X WR ),…,f M (X′ SR ,X WR )) T

[0053] with X′ SR =[x1+δ1,…,x r +δ r ] T

[0054] X WR =[x r+1 ,…,x D ] T

[0055] subject to x∈Ω,δi ∈Ω δ ;

[0056] Where Ω represents the decision space, δ The optimization goal is to maximize the concentrate output, maximize the total iron recovery rate of the ore, and minimize the grinding ratio within the target range of comprehensive production indicators.

[0057] The whole process data set of the beneficiation plant used in this paper has a total of 1095 sets of valid data. In order to improve the effectiveness of the implementation, all data sets are evenly divided into 5 groups, and the implementation experiment is carried out five times. The average value of the evaluation index of the 5 results is taken as the final implementation result. Among them, the dimension of each decision variable data set is The target variable dataset dimension is The parameters of the evolutionary algorithm involved are set as follows: maximum number of evaluations FE = 10000, initial population P size N = 200.

[0058] After obtaining the decision variable data set and the target variable data set, outliers and null values ​​in the original data are removed or interpolated, and the data are mapped to the interval [0, 1] using the min-max normalization method. The normalization properties of the original data set are recorded for the final data denormalization.

[0059] Construct a training data generator, divide the pre-processed production data into target variable datasets M according to the optimization objectives, decision variables and constraints of the production index optimization model data and decision variable dataset D data , M data The dimension is D data The dimension is Where L = 219 is the length of sample data, M = 3 is the number of target variables, and D = 6 is the number of decision variables.

[0060] Step 2: According to the production process and actual production data fluctuations, determine the decision variables affected by larger disturbances and the actual disturbance error degree, and then construct a decision variable space robust partitioner to divide the decision variable data set into a strong disturbance variable data set and a weak disturbance variable data set.

[0061] According to the actual disturbance error degree of the six decision variables, the mean and variance of the decision variable data after normalization are calculated and compared. The raw ore grade and mill grade data with large variance have a greater disturbance effect. In the actual mineral processing production process, the raw ore grade often has an uncertain disturbance degree due to the geological differences in the raw ore mining area. The mill grade is greatly affected by the properties of the raw ore, and there are inevitable human test errors. Therefore, the six decision variables are divided into two strong disturbance variables (raw ore grade and mill grade) and four weak disturbance variables (daily raw ore volume, dry slag grade, tailings grade, concentrate grade), and then the decision variable data set is divided into a strong disturbance variable data set. and weakly disturbed variable datasets

[0062] Step 3: Weakly perturb the variable dataset A sparse search proxy model is proposed as the model input, and the three target variables are concentrate output f1, ore total iron recovery f2, and grinding selection ratio f3. The sparse search proxy model is optimized by the NSGAII algorithm to obtain the optimal Pareto front of the sparse search proxy model. N / 2 non-dominated solution sets are randomly selected and saved as the sparse search optimal population B, that is, the sparse search optimal weak disturbance variable decision solution set, which is used for the initial population migration of the robust fine search proxy model.

[0063] Step three specifically includes:

[0064] Step C1: Daily ore volume, dry slag grade, tailings grade, and concentrate grade data sets As the model input, the concentrate production, ore total iron recovery rate, grinding ratio dataset M data As the model output, the Gaussian process modeling method is used in turn to establish a sparse search proxy model Model1 between the four weak disturbance variables and the three objective functions.

[0065] Step C2: Perform population iterative optimization and solving process on the sparse search agent model. First, generate a random initialization population H0 of size N. The dimension of population H0 is The maximum number of evaluations is FE. The fitness value of the population is evaluated by Model1, and then the population is fast non-dominated sorted.

[0066] The idea of ​​fast non-dominated sorting is to find an individual x from the population P0 as a comparison object each time, and compare the M fitness values ​​of individual x with the fitness values ​​of other individuals according to the dominance relationship. In fact, if the fitness value of each dimension of some individuals is smaller than x, then the individual must be a dominated individual and will no longer be considered in the next round of sorting; the other part is individuals larger than x or unrelated to x. If x is not dominated by all these individuals, then x is a non-dominated individual of the population and x is incorporated into the non-dominated set.

[0067] This process is repeated until a non-dominated hierarchy is found, where all individuals at each level do not dominate each other. The initial population is then subjected to binary tournament selection, simulated binary crossover operators, and polynomial mutation operators to obtain a new population Q0, where t = 0.

[0068] Step C3: Form a new group R t =H t ∪Q t , for the population R t Perform non-dominated sorting and calculate the crowding degree of the population individuals, and select the N individuals with the highest non-dominated sorting to form the population H t+1 Among them, the crowding degree of the population is used to estimate the density of other solutions around a solution. For each solution i of the objective function matrix, the average side length of the M-dimensional cube composed of solutions i-1 and i+1 is calculated as the crowding distance i of the solution. instance The crowding distance of the boundary solution is infinite.

[0069]

[0070] Among them, f j () represents the j-th dimension objective function value of the individual.

[0071] Step C4: If the termination condition t>FE is met, then end and output population H t+1 , randomly select population H t+1 The N / 2 non-dominated solution set is saved as the sparse search optimal population B; otherwise, for population H t+1 Replicate, crossover and mutation to form a new population Q t+1 , t=t+1, go to step C3.

[0072] Step 4: Set the maximum number of evaluations, FE, and the size of the initial population, P, to N. Initialize the population P to consist of a random population, A, and a sparse search agent model optimization population, B. Using six decision variable datasets as model input and three target variable datasets as model output, a multi-objective robust optimization model based on a multi-hidden-layer neural network with efficient random dropout is established. An indicator-based reference point adaptive multi-objective optimization algorithm is used for optimization, and the resulting optimal Pareto front is saved as the robust optimization population result.

[0073] Step 4 specifically includes:

[0074] Step D1, set the maximum number of evaluations FE, the initial population P size is N. Take the disturbance variable data set D data As the model input, the target variable dataset M dataAs the model output, a multi-hidden layer neural network model Model2 based on efficient dropout is established. During training and testing, this network weakens the co-adaptation between neurons by randomly dropping hidden layer nodes. Dropout can be interpreted as adding noise during model training to enhance the robustness of the model. The scale of the neural network is selected according to the size of the data dimension, and a two-layer fully connected neural network with L = 2 is chosen. Assume that d l is a row vector of the l-th (l ∈ [1, L]) layer of the neural network, and each of its elements follows a Bernoulli distribution, that is

[0075]

[0076] where 0.5 < p < 1. After using the dropout method, the output of the l-th layer can be expressed as

[0077]

[0078] where denotes the Hadamard product, and g l is the activation function of the l-th layer. x l , W l , and b l are the input vector, weight matrix, and bias vector of the l-th layer respectively.

[0079] The neurons retained in x l need to be multiplied by to ensure that has the same output range as the output of the l-th layer without randomly dropping neurons. During forward propagation, for different training data, d l needs to be regenerated. Similar to the standard neural network, in the dropout neural network, W l is also updated through backpropagation. During backpropagation, the weights in W l connected to the dropped neurons are not updated.

[0080] After that, in the uncertainty δ neighboring perturbation space B δ of r strong perturbation variables, the Monte Carlo method is used to randomly select H sampling points within the perturbation neighborhood of each value, and the average effective objective value of Model2 is calculated. The final robust objective optimization function value formula is as follows:

[0081]

[0082] Step D2: Generate a randomly initialized population A with a size of N / 2. The initial population P0 is composed of the random population A and the sparse search surrogate model optimized population B. Generate N uniformly from the unit hyperplane RA fixed reference point W is generated, and the external archive set A0 and the adaptive reference point R0 are generated according to the population P0 and the fixed reference point W, and t=0.

[0083] Step D3: According to R t Calculate the value of the enhanced inverted generational distance index (IGD-NS) of the population individuals, from K t The solution is selected to form a mating pool, and the offspring O is formed by simulating the binary crossover operator and the polynomial mutation operator. t The IGD-NS index can further identify the quality of non-contributing solutions. The contributing solutions and non-contributing solutions in the non-dominated solution set are non-contributing solutions whose Euclidean distance to any reference point is not small. These non-contributing solutions constitute the non-contributing solution set. The IGD-NS index is defined as follows:

[0084]

[0085] Among them, the dis(·) function represents the Euclidean distance between two individuals in the target space, X, X * (X * ∈X) and Y represent the non-dominated solution set, non-contributing solution set and reference point set respectively.

[0086] Step D4: According to population A t , O t and W to generate external archive set A t+1 and adaptive reference point R t+1 ; Then according to R t+1 Calculate K t and O t The value of IGD-NS of the individual, from which the individual is selected to form P t+1 .

[0087] Step D5: If the termination condition t>FE is met, then end and output the population P t+1 ; Otherwise, t=t+1, go to step D3.

[0088] Step 5: Use the K-means clustering method to select k groups of cluster centers of the robust optimization population results as the new non-dominated solution set. After evaluation, the new non-dominated solution set and the corresponding target value are constructed as a new cluster population P. k , and merged with the initial population as the new initial population P = [P, P k ]; Determine whether the size of the new initial population Q reaches the maximum evaluation times FE. If so, output the non-dominated population P and calculate the evaluation index; otherwise, the new cluster population P kAdd as new data to the mineral processing plant training data set, update the decision variable data set D data and target variable dataset M data , skip to step 3.

[0089] Step 5 specifically includes:

[0090] Step E1: Use the K-means clustering algorithm to divide the decision variables of the final population obtained in step D5 into k categories, use the centers of the k categories as the selected individuals, and truly evaluate the objective function values ​​of these individuals. After evaluation, the new non-dominated solution set and the corresponding target value are constructed as the new cluster center population P k , parameter k = 9, the selection of this parameter can be appropriately adjusted according to the population size.

[0091] Step E2: New k cluster center populations P k After merging with the initial population P, the new initial population P for the next iterative evolution is P = [P, P k ]. If the size of the initial population P of the next iterative evolution is greater than the maximum evaluation number FE, the non-dominated population P is output as the final non-dominated solution set, and the hyper-volume (HV) index result is calculated as the evaluation index value.

[0092] The larger the HV value, the better the algorithm performance. Among them, the hypervolume index is used to evaluate the comprehensive performance of the multi-objective optimization algorithm by calculating the hypervolume of the space enclosed by the non-dominated solution set and the reference point.

[0093]

[0094] Where λ represents the Lebesgue measure, v i represents the hypervolume consisting of the reference point and the non-dominated individuals x, and P represents the non-dominated set. Because the calculation process of the hypervolume index does not require the prior determination of the Pareto optimal surface, it has good practicality in actual engineering problems.

[0095] If the size of the initial population P of the next iterative evolution is not greater than the maximum evaluation times FE, the new clustering population P of step E1 will be k Add to the ore dressing plant training data set and update the decision variable data set D data and target variable dataset M data , skip to step 3.

[0096] The evolutionary algorithms used in this paper are the currently popular multi-objective evolutionary algorithms NSGA-II and AR-MOEA. The core concept of the NSGA-II algorithm is to combine a parent population with its resulting offspring population, allowing them to compete to produce the next generation. This algorithm boasts fast execution speed and strong versatility. The algorithm utilizes crowding distance to ensure population diversity, fast non-dominated sorting to reduce computational complexity, and an elitist strategy to improve algorithm performance. This helps ensure that high-quality individuals from the parent generation enter the next generation in optimization problems, ensuring that the best individuals are not lost. The steps of the NSGA-II algorithm are shown in Table 1.

[0097] Table 1

[0098]

[0099] AR-MOEA is an indicator-based, reference-point-adaptive multi-objective evolutionary algorithm. During the selection phase, the algorithm uses the enhanced inverse generation distance metric (IGD-NS) as a selection criterion, capable of distinguishing individuals from populations that do not contribute to the metric. During the calculation of IGD-NS, a set of reference points is adaptively retained and updated. The proposed reference-point adaptation method not only utilizes a uniformly sampled hyperplane of points from a unit but also adaptively adjusts the distribution of reference points based on the contribution of candidate solutions from the external archive in IGD-NS. This method is more robust in capturing Pareto fronts of varying shapes and can accelerate the population's evolution toward the Pareto front. The AR-MOEA algorithm steps are shown in Table 2.

[0100] Table 2

[0101]

[0102] It is understandable that, in specific implementations, the modeling phase and the meta-heuristic optimization algorithm phase can find parallel replacement algorithms based on the particularity of the optimization problem data.

[0103] The above-described embodiments address the high computational costs of data processing, data-based function evaluation, and proxy model construction, existing in the prior art, from two perspectives: 1. Considering the varying degrees of robustness interference experienced by different decision variables, the decision space is partitioned and optimized separately; 2. Modeling is done using a data-driven proxy model approach, rather than directly building a model using all offline data. Data-driven proxy models are a technical term that refers to the use of a partial dataset for modeling and solving, followed by the use of actual data to reconstruct a sample dataset from the optimization results, and then performing modeling and solving again. This continuously expands the data sample, improves solution accuracy, and reduces computational costs.

[0104] The experimental results are as follows Figure 4 As shown in Table 3, Figure 4 Table 3 is a Pareto front comparison diagram of the method of the present invention and the comparative method in the robust optimization problem of the comprehensive production indicators on the mineral processing day. Table 4 is the HV index results of the robust optimization decision population of the comprehensive production indicators on the mineral processing day by the method of the present invention and the comparative method. The larger the HV value, the better the algorithm performance.

[0105] Table 3

[0106] Method of the present invention Conventional data-driven approach Problems with this Example 3.9315e+2 3.8318e+2

[0107] As shown in the table above, the proposed method significantly improves the hypervolume evaluation metric in solving the robust optimization decision-making problem for comprehensive production indicators in a mineral processing plant compared to conventional data-driven methods. Experiments demonstrate that the proposed method offers excellent performance, achieving superior evaluation metric results for both application-specific problems and multi-class robust testing, demonstrating state-of-the-art performance.

[0108] 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, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing, characterized by: The method comprises: Obtain and preprocess the daily production data of the entire process of the mineral processing plant, and divide the preprocessed production data into a decision variable data set and a target variable data set; According to the production process and actual production data fluctuations, the decision variables affected by the largest disturbances and the actual degree of disturbance error are determined, and then a robust partitioner for the decision variable space is constructed to divide the decision variable data set into a strong disturbance variable data set and a weak disturbance variable data set. A sparse search proxy model is established between the weak disturbance variable and the target variable, wherein the sparse search proxy model takes the weak disturbance variable data set as input and the target variable data set as output; a random population is used as the first initialization population, and the sparse search proxy model is subjected to population iterative optimization to obtain a sparse search optimal population, that is, a sparse search optimal weak disturbance variable decision solution set; A multi-hidden layer neural network multi-objective robust optimization model based on efficient random dropout is established, wherein the multi-hidden layer neural network multi-objective robust optimization model takes the decision variable data set as input and the target variable data set as output; a random population and the sparse search optimal population are used as the second initialization population to perform population iterative optimization on the multi-hidden layer neural network multi-objective robust optimization model to obtain a robust optimized population; and an optimized decision solution set is obtained based on the robust optimized population.

2. A multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 1, characterized in that: The decision variables include: daily ore volume, ore grade, mill grade, dry slag grade, tailings grade and concentrate grade; The target variables include: concentrate output, total iron recovery rate of raw ore and grinding ratio, which constitute a multi-objective optimization goal; the optimization goal is to maximize the concentrate output, maximize the total iron recovery rate of raw ore and minimize the grinding ratio within the target range of comprehensive production indicators.

3. The multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 2 is characterized in that: Strong disturbance variables include: ore grade and mill grade; weak disturbance variables include: daily ore yield, dry slag grade, tailings grade and concentrate grade.

4. The multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 1 is characterized in that: Performing population iterative optimization on the sparse search proxy model includes: performing population iterative optimization on the sparse search proxy model using an NSGA-II algorithm.

5. A multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 4, characterized in that: The sparse search agent model is solved by population iterative optimization using the NSGA-II algorithm, including: Generate a randomly initialized population H0 of size N; The fitness value of the population is evaluated by the sparse search agent model, the population is non-dominated sorted, and then the initial population is subjected to binary tournament selection, simulated binary crossover operator and polynomial mutation operator to obtain a new population Q0, and the number of optimization times t=0; Forming group R t =H t ∪Q t , for the population R t Perform non-dominated sorting and calculate the crowding degree of the population individuals, and select the N individuals with the highest non-dominated sorting to form the population H t+1 ; If the number of optimization attempts is greater than the maximum number of evaluations, the process ends and the population H is output. t+1 , randomly select population H t+1 The N / 2 non-dominated solution set is saved as the sparse search optimal population; otherwise, for the population H t+1 Replication, crossover and mutation to form population Q t+1 , t=t+1, proceed to the next optimization.

6. The multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 1 is characterized in that: Performing population iterative optimization to solve the multi-hidden layer neural network multi-objective robust optimization model, including: The AR-MOEA algorithm is used to perform population iterative optimization solution on the multi-hidden layer neural network multi-objective robust optimization model.

7. A multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 6, characterized in that: The AR-MOEA algorithm is used to perform population iterative optimization on the multi-hidden layer neural network multi-objective robust optimization model, including: Generate a random initialization population A of size N / 2. The initialization population P0 is composed of the random population A and the sparse search agent model optimized population B. Generate N uniformly from the unit hyperplane R A fixed reference point W is generated, and the external archive set A0 and the adaptive reference point R0 are generated according to the population P0 and the fixed reference point W. The number of iterations t = 0; According to R t Calculate the enhanced inversion generation distance index value of the population individual, from K t The solution is selected to form a mating pool, and the offspring O is formed by simulating the binary crossover operator and the polynomial mutation operator. t ; According to population A t , O t and W to generate external archive set A t+1 and adaptive reference point R t+1 ; Then according to R t+1 Calculate K t and O t The enhanced reverse generation distance index value of the individual, from which individuals are selected to form P t+1 ; If the number of iterations is greater than the maximum number of iterations, it ends and outputs the population P t+1 ; Otherwise, t=t+1, enter the next iteration.

8. The multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 6 is characterized in that: Performing population iterative optimization to solve the multi-hidden layer neural network multi-objective robust optimization model also includes: The decision variables of the robust optimization population are clustered by the K-means clustering method to obtain a cluster population; the cluster population is merged with the second initialized population to serve as the initial population for the next iteration; when the size of the initial population reaches the maximum number of evaluations, the initial population result is output.

9. A multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 8, characterized in that: When the size of the initial population does not reach the maximum number of evaluations, the cluster population is added as new data to the mineral processing plant training data set, and the decision variable data set and the target variable data set are updated to perform the next iteration.

10. The multi-objective robust optimization decision-making method for comprehensive daily production indicators of mineral processing according to claim 1, characterized in that: A sparse search proxy model is established between a weak disturbance variable and a target variable, including: sequentially adopting a Gaussian process modeling method to respectively establish sparse search proxy models between a plurality of weak disturbance variables and a plurality of target functions.

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