Intelligent ore blending method based on CEALA algorithm

Abstract

The invention discloses an intelligent ore blending method based on a CEALA algorithm. According to the invention, the co-evolution ALA algorithm is applied to an intelligent ore blending scene. The population scale is dynamically adjusted according to the population evolution condition in the optimization process through a cyclic population attenuation mechanism, the calculation cost is reduced, and convergence is accelerated while the population diversity is guaranteed. Meanwhile, the algorithm provides a co-evolution mechanism, based on a self-adaptive exploration mechanism and a self-adaptive development mechanism, individuals are dynamically allocated to different evolution mechanisms, the influence of parameter setting on the optimization performance of the algorithm is reduced, exploration and development are balanced, population diversity is increased, and local optimum is avoided. A parameter adaptive mechanism is introduced into the algorithm to capture beneficial information in a population iteration process, so that the influence of parameter setting on the optimization performance of the algorithm is reduced, and the robustness of the algorithm is enhanced. And finally, the algorithm is based on external archiving, beneficial information of abandoned solutions is mined, and the optimization performance of the algorithm is improved.

Description

Technical Field

[0001] This invention belongs to the field of ore blending technology, specifically a smart ore blending method based on the CEALA algorithm. Background Technology

[0002] With increasingly scarce ore resources and persistently high iron ore prices, optimizing ore blending schemes to reduce costs while ensuring product quality is particularly important. Simultaneously, the variety of selectable ores is gradually increasing, and prices are fluctuating significantly, making the traditional method of manually determining ore blending schemes increasingly difficult. Therefore, using advanced optimization algorithms to optimize ore blending schemes is becoming a trend. Currently, optimization algorithms used for ore blending can be broadly divided into two categories: traditional optimization algorithms and intelligent optimization algorithms. Traditional algorithms, such as the Lagrange method and gradient descent, are prone to getting trapped in local optima when dealing with complex nonlinear problems, resulting in less than ideal optimization effects. In contrast, intelligent optimization algorithms, when dealing with complex multimodal problems such as nonlinearity and non-differentiability, can effectively avoid local extrema and discover globally optimal or near-optimal solutions in complex solution spaces through their global search capabilities, multi-strategy fusion mechanisms, and adaptive characteristics.

[0003] The Artificial Lemming Algorithm (ALA) is a novel metaheuristic optimization algorithm proposed in January 2025 based on the group behavior of lemmings in nature. It is particularly suitable for solving complex multimodal problems such as high-dimensional, non-convex, and multimodal problems.

[0004] However, the traditional ALA algorithm has drawbacks such as high parameter sensitivity and easy getting trapped in local optima, and its optimization effect is not ideal when solving such optimization problems. Summary of the Invention

[0005] The purpose of this invention is to provide an intelligent ore blending method based on the CEALA algorithm in order to solve the problems mentioned above.

[0006] The technical solution adopted in this invention is as follows: an intelligent ore blending method based on the CEALA algorithm, the method comprising the following steps: S1. Obtain raw material ore data; S2. Construct a mathematical model; S3. The CEALA algorithm is used for optimization and solution. S4, Output Proportioning Scheme; In step S3, during the iteration process, the population size is linearly varied to reduce the population size and accelerate convergence. The calculation formula is as follows: (1) In the formula, Indicates the maximum population size; denotes the minimum population size, with a magnitude of ; trest represents the iteration number of the remaining iteration times; Trest represents the remaining iteration times; In step S3, the solutions discarded due to population decay are stored in the external archive. Meanwhile, the number of successfully updated individuals in the current iteration is recorded. In the next iteration, it is determined whether to increase the population size based on a random number to maintain the global exploration ability of the algorithm. If the random number rand(0,1) < flag, the population size is restored to , randomly select individuals from the external archive for filling, and then perform population decay again according to formula (1); otherwise, the population decays according to the original formula. In addition, the size of the external archive is , when the archive size exceeds the maximum limit, randomly delete individuals to ensure that the archive size is always .

[0007] In a preferred embodiment, in step S1, raw material library information is obtained, including information such as single ore name, price, Fe, S, Cu, P, TiO2, SiO2, Al2O3, Zn, etc. Constraint conditions such as upper and lower limits of element content constraints and single ore usage limits are set and passed to the algorithm side for optimization and solution. With the goal of minimizing cost, under the condition of meeting various constraint conditions, the optimal proportioning scheme is determined.

[0008] In a preferred embodiment, in step S2, a mathematical model is established as follows: Objective function: Constraint conditions: In the formula, E and k respectively represent the comprehensive cost and the number of raw ore; and respectively represent the cost and proportion corresponding to the i th raw ore; and represent the maximum and minimum values of the finished ore content constraint; [[ID=​​​​​​​​​​​​​​​​​

[0010] Then make a judgment, if If the value is greater than 1, the adaptive exploration mechanism is executed; otherwise, the adaptive development mechanism is executed.

[0011] In a preferred embodiment, the roulette wheel selection in the adaptive exploration mechanism is a probability-based selection method that simulates the roulette wheel process. Roulette wheel selection helps select individuals with higher fitness and increases the probability of these individuals being selected. The algorithm employs a roulette wheel mechanism to replace the fixed-value settings in the original algorithm, reducing the impact of parameter settings on algorithm performance and improving algorithm robustness. Based on the fitness value of each individual, its selection probability is calculated. As shown in the following formula: (3) In the formula, Represents an individual i The fitness value.

[0012] (1) If rand < P ( i If the individual executes the improved hole-digging strategy, the update formula is as follows: (4) In the formula, Indicates the first t In this iteration, the top performers are ranked based on their fitness values. p Individuals randomly selected from % of the individuals, This refers to an individual randomly selected from the population. a ≠ i ; Indicates the first t The individual randomly selected from the external archive in the next iteration; This represents the disturbance parameter.

[0013] (2) If rand≥ P ( i If an individual implements an improved long-distance migration strategy, the individual update formula is as follows: (5) In the formula, The random number vector represents Brownian motion, utilizing dynamic and uniform step sizes to explore potential regions of the search space. The standard Brownian motion step size is obtained based on the probability density of a normal distribution with variance of 1 and mean of 0. , This refers to an individual randomly selected from the population. a , b , c and i They are not equal.

[0014] In a preferred embodiment, the adaptive development mechanism calculates the individual selection probability and makes a judgment based on the roulette wheel strategy, and then executes different evolutionary strategies accordingly.

[0015] (1) If rand < P ( i If the individual executes an improved foraging strategy, the update formula is as follows: (6) (2) If rand≥ P ( i If the individual implements an improved predator avoidance strategy, the individual update formula is as follows: (7) In the formula, and Represents a random number between 0 and 1. The constant representing 1.5.

[0016] In a preferred embodiment, in step S3, the fitness value of an individual is calculated, and the population is updated based on greedy selection. The discarded solutions are stored in an external archive, and the global optimum is updated.

[0017] In a preferred embodiment, in step S3, the parameters are updated. For the disturbance parameters An adaptive strategy is adopted.

[0018] First, initialize the parameters. ; Then, the individual perturbation parameters are expressed as follows: Update; Finally, during the iteration process, based on the number of successful individual evolutions... ,renew , adopting the formula Update, among which The Lehmer mean is calculated using the following formula: .

[0019] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention proposes an improved ALA algorithm, the Co-evolutionary ALA algorithm, and applies it to intelligent ore blending scenarios. Through a cyclical population decay mechanism, the algorithm dynamically adjusts the population size based on population evolution during optimization, reducing computational costs and accelerating convergence while maintaining population diversity. Simultaneously, the algorithm proposes a co-evolutionary mechanism, dynamically assigning individuals to different evolutionary mechanisms based on adaptive exploration and adaptive exploitation mechanisms. This reduces the impact of parameter settings on the algorithm's optimization performance, balancing exploration and exploitation, increasing population diversity, and avoiding getting trapped in local optima. The algorithm introduces a parameter adaptive mechanism to capture useful information during population iteration, further reducing the impact of parameter settings on optimization performance and enhancing the algorithm's robustness. Finally, based on external archives, the algorithm mines useful information from discarded solutions, improving its optimization performance. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the optimization solution process using the CEALA algorithm in this invention; Figure 3 This is a diagram illustrating the intelligent ore blending results of this invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0022] Example: Reference Figure 1-3 , A smart ore blending method based on the CEALA algorithm. The implementation steps are as follows: 1. Obtain raw ore data; 2. Construct a mathematical model; 3. The CEALA algorithm is used for optimization and solution. 4. Output the mixing ratio scheme.

[0023] This invention proposes an intelligent ore blending method based on an improved ALA algorithm (CollaborationEvolution ALA, CEALA). Under various constraints, it determines the cost-optimal blending scheme to improve mineral resource utilization, thereby enhancing product quality and overall efficiency. Therefore, this invention proposes a CEALA algorithm for optimized ore blending, providing theoretical guidance and technical basis for reducing blending costs while ensuring product ore quality. Based on the original ALA algorithm, the CEALA algorithm introduces a cyclic population decay mechanism to accelerate convergence while maintaining population diversity. Simultaneously, the individual evolution formula in the algorithm is improved by proposing a co-evolution mechanism. Individual evolution employs an adaptive exploration mechanism and an adaptive exploitation mechanism, dynamically adjusting the individual evolution task during iteration to balance exploration and exploitation. Finally, the algorithm introduces a parameter adaptive mechanism and an external archiving mechanism to capture useful information during population iteration, reducing the impact of parameter settings on the algorithm's optimization performance, enhancing the algorithm's robustness, and improving its optimization performance.

[0024] Flowchart as follows Figure 1 As shown: Obtain information from the raw material library, including the name and price of individual ores, and information on Fe, S, Cu, P, TiO2, SiO2, Al2O3, Zn, etc. Set upper and lower limits for element content and restrictions on the use of individual ores, and input them into the algorithm for optimization. With the goal of minimizing costs, determine the optimal ratio scheme while satisfying all constraints.

[0025] The mathematical model is established as follows: Objective function: Constraints: In the formula, E and k These represent the total cost and the quantity of raw ore, respectively. and They represent the first i The cost and proportion of each type of raw material ore; and Indicates the maximum and minimum values ​​of the finished ore content constraint; Indicates the first i The elemental content of each type of raw material ore; and They represent the first i The lower and upper limits for the use of certain raw materials.

[0026] This invention proposes an intelligent ore blending method based on an improved ALA algorithm, the implementation steps of which are as follows: 1. Population initialization.

[0027] The population is initialized randomly.

[0028] In the formula, and These represent the lower and upper limits of the search range, respectively.

[0029] 2. Cyclic population decline mechanism In nature, r-strategy and k-strategy are two different survival and reproduction patterns developed during biological evolution. The core difference lies in their environmental adaptation methods and the focus of their reproductive investment. Therefore, this algorithm proposes a cyclic population decay strategy to maintain population diversity while accelerating convergence. Typically, during iteration, the population size is linearly varied to reduce the population size and accelerate convergence. The calculation formula is as follows: (1) In the formula, Indicates the maximum population size; This represents the minimum population size, which is . ; t rest The iteration number representing the remaining iterations; T rest Indicates the number of remaining iterations.

[0030] Meanwhile, to avoid excessive population decay and the neglect of potential solutions, the algorithm incorporates a feedback mechanism and an external archiving mechanism. Solutions discarded due to population decay are stored in an external archive, while the number of successfully updated individuals in the current iteration is recorded. In the next iteration, a random number is used to determine whether to increase the population size to maintain the algorithm's global exploration capability. rand (0,1)< flag Then the population size will be restored to Individuals are randomly selected from the external archive to fill the population, and then population decline is performed again according to formula (1); otherwise, population decline is performed according to the original formula. Furthermore, the size of the external archive is... When the archive size exceeds the maximum limit, individuals will be randomly deleted to ensure that the archive size remains constant. .

[0031] 3. Calculate the energy factor E Calculate according to the following formula E : (2) In the formula, t Indicates the current iteration number; T This indicates the maximum number of iterations.

[0032] Then make a judgment, if If the value is greater than 1, proceed to step 4; otherwise, proceed to step 5.

[0033] 4. Adaptive exploration mechanism Roulette wheel selection is a probability-based selection method that simulates the roulette wheel process. It helps select individuals with higher fitness and increases the probability of these individuals being selected. This algorithm uses a roulette wheel mechanism to replace the fixed-value settings in the original algorithm, reducing the impact of parameter settings on algorithm performance and improving robustness. The selection probability is calculated based on each individual's fitness value. As shown in the following formula: (3) In the formula, Represents an individual i The fitness value.

[0034] (1) If rand < P ( i If the individual executes the improved hole-digging strategy, the update formula is as follows: (4) In the formula, Indicates the first t In this iteration, the top performers are ranked based on their fitness values. p Individuals randomly selected from % of the individuals, This refers to an individual randomly selected from the population. a ≠ i ; Indicates the first t The individual randomly selected from the external archive in the next iteration; This represents the disturbance parameter.

[0035] (2) If rand≥ P ( i If an individual implements an improved long-distance migration strategy, the individual update formula is as follows: (5) In the formula, The random number vector represents Brownian motion, utilizing dynamic and uniform step sizes to explore potential regions of the search space. The standard Brownian motion step size is obtained based on the probability density of a normal distribution with variance of 1 and mean of 0. , This refers to an individual randomly selected from the population. a , b , c and i They are not equal.

[0036] 5. Adaptive development mechanism As mentioned earlier, the individual selection probability is calculated, and a judgment is made based on the roulette wheel strategy, and different evolutionary strategies are executed accordingly.

[0037] (1) If rand < P ( i If the individual executes an improved foraging strategy, the update formula is as follows: (6) (2) If rand≥ P ( i If the individual implements an improved predator avoidance strategy, the individual update formula is as follows: (7) In the formula, and Represents a random number between 0 and 1. The constant representing 1.5.

[0038] 6. Greedy Choice Calculate the fitness value of each individual, update the population based on greedy selection, store the discarded solutions in an external archive, and update the global optimum.

[0039] 7. Parameter Update For the disturbance parameters An adaptive strategy is adopted.

[0040] First, initialize the parameters. ; Then, the individual perturbation parameters are expressed as follows: Update; Finally, during the iteration process, based on the number of successful individual evolutions... ,renew , adopting the formula Update, among which The Lehmer mean is calculated using the following formula: .

[0041] From the above, we can conclude that: This invention proposes an intelligent ore blending method based on the CEALA algorithm. The innovation lies in proposing an improved ALA algorithm, the Collaboration Evolution ALA (CEALA), and applying it to intelligent ore blending scenarios. The algorithm proposes a cyclical population decay mechanism, dynamically adjusting the population size based on population evolution during optimization to reduce computational costs and accelerate convergence while maintaining population diversity. Simultaneously, the algorithm proposes a co-evolutionary mechanism, dynamically assigning individuals to different evolutionary mechanisms based on adaptive exploration and adaptive exploitation mechanisms. This reduces the impact of parameter settings on the algorithm's optimization performance, balancing exploration and exploitation, increasing population diversity, and avoiding getting trapped in local optima. The algorithm introduces a parameter adaptive mechanism to capture useful information during population iteration, reducing the impact of parameter settings on the algorithm's optimization performance and enhancing its robustness. Finally, the algorithm utilizes external archives to mine useful information from discarded solutions, further improving its optimization performance.

[0042] The results of this invention are shown as follows Figure 3 As shown, the horizontal axis represents the ore blending sequence number, and the vertical axis represents the ore blending cost (yuan / ton). The red line represents the ore blending cost of the method of this invention, and the blue line represents the cost of manual ore blending. The results show that, compared with the cost of manual ore blending, the ore blending scheme optimized by the CEALA algorithm in this invention has a lower cost, providing theoretical guidance and technical basis for reducing ore blending costs and improving the overall efficiency of enterprises.

[0043] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0044] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A smart ore blending method based on the CEALA algorithm, characterized in that: The method includes the following steps: S1. Obtain raw material ore data; S2. Construct a mathematical model; S3. The CEALA algorithm is used for optimization and solution. S4, Output Proportioning Scheme; In step S3, during the iteration process, the population size is linearly varied to reduce the population size and accelerate convergence. The calculation formula is as follows: （1） In the formula, Indicates the maximum population size; This represents the minimum population size, which is . ;trest represents the iteration number of the remaining iterations; Trest represents the number of remaining iterations; In step S3, the solutions discarded due to population decay are stored in an external archive. Meanwhile, the number of successfully updated individuals in the current iteration is recorded. In the next iteration, it is judged whether to increase the population size based on a random number to maintain the global exploration ability of the algorithm. If the random number rand(0, 1) < flag, the population size is restored to , and individuals are randomly selected from the external archive for filling, and then the population decay is carried out again according to formula (1); otherwise, the population decays according to the original formula. In addition, the size of the external archive is . When the archive size exceeds the maximum limit, individuals are randomly deleted to ensure that the archive size is always .

2. The intelligent ore blending method based on the CEALA algorithm as described in claim 1, characterized in that: In step S1, raw material library information is obtained, including single ore name, price, Fe, S, Cu, P, TiO2, SiO2, Al2O3, and Zn information. Upper and lower limits of element content and single ore usage restrictions are set and passed to the algorithm for optimization. With the goal of minimizing cost, the optimal ratio scheme is determined under the condition of satisfying all constraints.

3. The intelligent ore blending method based on the CEALA algorithm as described in claim 1, characterized in that: In step S2, the mathematical model is established as follows: Objective function: Constraints: In the formula, E and k These represent the total cost and the quantity of raw ore, respectively. and They represent the first i The cost and proportion of each type of raw material ore; and Indicates the maximum and minimum values ​​of the finished ore content constraint; Indicates the first i The elemental content of each type of raw material ore; and They represent the first i The lower and upper limits for the use of certain raw materials.

4. The intelligent ore blending method based on the CEALA algorithm as described in claim 1, characterized in that: In step S3, the energy factor E is calculated according to the following formula: （2） In the formula, t represents the current iteration number; T represents the maximum number of iterations; Then make a judgment, if If the value is greater than 1, the adaptive exploration mechanism is executed; otherwise, the adaptive development mechanism is executed.

5. The intelligent ore blending method based on the CEALA algorithm as described in claim 4, characterized in that: The adaptive exploration mechanism described uses roulette wheel selection, a probability-based selection method that simulates the roulette wheel process. Roulette wheel selection helps select individuals with higher fitness and increases the probability of these individuals being selected. The algorithm employs a roulette wheel mechanism to replace the fixed-value settings in the original algorithm, reducing the impact of parameter settings on algorithm performance and improving robustness. The selection probability is calculated based on each individual's fitness value. As shown in the following formula: （3） In the formula, Represents an individual i fitness value; (1) If rand < P ( i If the individual executes the improved hole-digging strategy, the update formula is as follows: （4） In the formula, Indicates the first t In this iteration, the top performers are ranked based on their fitness values. p Individuals randomly selected from % of the individuals, This refers to an individual randomly selected from the population. a ≠ i ; Indicates the first t The individual randomly selected from the external archive in the next iteration; Indicates the disturbance parameters; (2) If rand≥ P ( i If an individual implements an improved long-distance migration strategy, the individual update formula is as follows: （5） In the formula, A random number vector representing Brownian motion is used to explore some potential regions of the search space using dynamic and uniform step sizes; The standard Brownian motion step size is obtained based on the probability density of a normal distribution with variance of 1 and mean of 0. , This refers to an individual randomly selected from the population. a , b , c and i They do not interact with each other.

6. The intelligent ore blending method based on the CEALA algorithm as described in claim 4, characterized in that: In the adaptive development mechanism, the individual selection probability is calculated, and a judgment is made based on the roulette wheel strategy, and different evolutionary strategies are executed accordingly. (1) If rand < P ( i If the individual executes an improved foraging strategy, the update formula is as follows: （6） (2) If rand≥ P ( i If the individual implements an improved predator avoidance strategy, the individual update formula is as follows: （7） In the formula, and Represents a random number between 0 and 1. The constant representing 1.

5.

7. The intelligent ore blending method based on the CEALA algorithm as described in claim 1, characterized in that: In step S3, the fitness value of an individual is calculated, and the population is updated based on greedy selection. The discarded solutions are stored in an external archive, and the global optimum is updated.

8. The intelligent ore blending method based on the CEALA algorithm as described in claim 1, characterized in that: In step S3, the parameter is updated. For the disturbance parameters An adaptive strategy is adopted. First, initialize the parameters. ; Then, the individual perturbation parameters are expressed as follows: Update; Finally, during the iteration process, based on the number of successful individual evolutions... ,renew , adopting the formula Update, among which The Lehmer mean is calculated using the following formula: .

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