Scheduling method and device for multi-process parallel locomotives for precious metal detection

Abstract

The invention discloses a scheduling method and device for multi-process parallel locomotives for precious metal detection, and aims at the characteristics of complex steps, diversified equipment and the like in a precious metal alloy detection process, considering resource constraints in an actual detection process and taking minimization of maximum completion time as an optimization target. According to the method, a mathematical model for detecting the scheduling problem between the multi-process parallel locomotives through precious metal is constructed, a high-quality scheduling scheme of the mathematical model is obtained by solving the mathematical model so as to accelerate the convergence speed of the algorithm, multiple neighborhood disturbance strategies are adopted to avoid falling into local optimum, and the global search ability of the algorithm is improved. Through verification of actual detection examples, the method effectively improves the scheduling efficiency and the resource utilization rate in precious metal detection.

Description

Technical Field

[0001] The present invention belongs to the technical field of scheduling of a multi-process parallel machine shop for precious metal alloy detection, and specifically relates to a scheduling method for a multi-process parallel machine shop for precious metal detection, and a scheduling device for a multi-process parallel machine shop for metal detection. Background Art

[0002] my country's manufacturing industry is accelerating its transformation towards intelligence and automation, especially in the fields of new materials and intelligent manufacturing. Improving technological innovation capabilities and production efficiency has become an important part of the national strategy. As a key high-tech material, precious metal alloys are widely used in aerospace, electronics, medical and other fields, and their quality requirements are extremely high. However, the detection process of precious metal alloys faces many challenges due to the multiple complex steps and high precision requirements.

[0003] The detection of precious metal alloys usually includes multiple links such as composition analysis, physical property testing, and structural testing. These detection steps are not only numerous and complex, but also need to be completed in a strictly controlled environment to ensure the accuracy and consistency of the test results. In addition, precious metal detection involves the use of high-precision instruments and equipment, the operation process is cumbersome, and the data processing is complex. Any slight error will have a significant impact on the final test results. Therefore, in the detection process, the connection and coordination of each step is crucial. How to ensure that each step is carried out under optimal conditions and reduce the inefficiency caused by the complexity of the detection steps has become a core problem in the detection of precious metal alloys.

[0004] Traditional precious metal detection methods are mostly manual or semi-automatic, which can easily lead to problems such as long detection cycles, low efficiency, and high error rates. In the face of these challenges, an efficient and accurate scheduling method is urgently needed to simplify the process, improve detection efficiency, and ensure the rational allocation of detection equipment and resources while maintaining high detection accuracy. Summary of the invention

[0005] The main technical problem to be solved by the present invention is to overcome the above-mentioned defects of the prior art and provide a scheduling method and device for a multi-process parallel machine shop for precious metal detection, thereby improving the scheduling efficiency and accuracy.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] According to one aspect of the present disclosure, a scheduling method for a multi-process parallel machine shop for precious metal detection is provided, comprising the following steps:

[0008] S1: Based on the analysis methods, analysis steps and corresponding testing instruments and equipment for precious metal alloy testing, with minimizing the maximum completion time as the optimization goal, a mathematical model for the multi-process parallel machine shop scheduling problem for precious metal testing is constructed, and the constraints of the mathematical model are determined;

[0009] S2: Solve the mathematical model and obtain a high-quality scheduling solution for the mathematical model;

[0010] Wherein, the mathematical model solved in S2 includes:

[0011] S2.1: Initialize the population: including determining the sequence of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of local searches in variable neighborhoods;

[0012] S2.2: Population division: Divide the population into two equal-sized sub-populations, the first sub-population Pop1 and the second sub-population Pop2, where Pop1 focuses on exploration and Pop2 focuses on mining;

[0013] S2.3: Perform exploration operation on Pop1: Calculate the fitness value of each individual in Pop1 according to the individual objective function value and store the best individual in the external memory pool. Use roulette to select two individuals in Pop1 as parent individuals to perform evolution operation;

[0014] S2.4: Perform mining operation on Pop2: Calculate the fitness value of each individual in Pop2 according to the individual objective function value and select two individuals of Pop2 as parent individuals by roulette wheel to perform mining operation based on uniform crossover;

[0015] S2.5: Population update: Use the greedy strategy to update the populations Pop1 and Pop2 respectively. After the update is completed, Pop1 and Pop2 are merged into a new population newPop;

[0016] S2.6: Perform Q-learning-based variable neighborhood search on high-quality individuals: Perform perturbation operations on high-quality individuals and generate perturbation solutions through the Q-learning-based variable neighborhood search algorithm, then use multiple neighborhood structures to perform local search and dynamically update the solution when a better solution is found;

[0017] S2.7: Update Q-table: Update the state of the environment according to the action executed in S2.6. At the same time, according to the superiority relationship between the output new solution and the initial solution, calculate the reward value of the environment and update the Q-table according to the reward value;

[0018] S2.7: Determine whether the iteration termination condition is met. If so, output the high-quality scheduling solution for the precious metal alloy detection multi-process parallel machine shop scheduling problem model. Otherwise, jump to S2.2.

[0019] In one embodiment of the present disclosure, the mathematical model of the multi-process parallel machine shop scheduling problem for precious metal detection is constructed in S1, including:

[0020] The multi-process parallel machine scheduling problem for precious metal detection is described as follows: n precious metal samples A to be detected 1 ,A 2 ,...,A n Requires m instruments and equipment M 1 ,M 2 ,...,M m For testing, each sample contains q i (i=1,2,...,n) detection methods, each detection method consists of O j ,(j=1,2,…,|q i |) detection and analysis steps, where |q i | indicates the detection method q i The total number of assay analysis steps;

[0021] Let O be the total number of detection steps for all precious metal samples to be detected, π = [π 1 ,π 2 ,...,π O ] is the arrangement of the detection and analysis steps of the method to be detected, which determines the order in which the sample detection methods are assigned to specific detectable devices;

[0022] Let O k For device M k The total number of detection steps on , k = 1, 2, ..., m, Equipment M k The above detection method is based on the arrangement of detection analysis steps; Steps for detection and analysis processing time, Steps for detection and analysis The start time of processing, for The equipment used in the previous detection and analysis step, for The position of the previous inspection process on the equipment used, where o = 1, 2, ..., O k ;

[0023] like It means For the first test; if It means For machine M k The first detection and analysis step on the

[0024] The objective function of the multi-process parallel machine scheduling problem for precious metal detection is:

[0025]

[0026] Among them, formula (1) and formula (2) are used to calculate the maximum completion time corresponding to the sequence π, and formula (3) and formula (4) are used to find the optimal order π in all sequence sets π. * , so that C max (π) minimum.

[0027] In one embodiment of the present disclosure, in S1, the constraints include:

[0028] 1) Any instrument or equipment is available at time 0;

[0029] 2) Any precious metal sample can be tested at time 0;

[0030] 3) Each detection and analysis step can be completed by at least one instrument;

[0031] 4) Once the detection and analysis steps are started, they are not allowed to be interrupted;

[0032] 5) Each instrument can only perform one detection and analysis step at a time;

[0033] 6) Precious metal samples can only undergo one testing step at a time;

[0034] In one embodiment of the present disclosure, S2.3 and S2.4 select the parent individuals according to formulas (5)-(6), including:

[0035]

[0036] Among them, C max (π i ) is the i-th individual π in the subpopulation i The corresponding maximum completion time is is the maximum completion time of all individuals in the subpopulation, popsize is the population size, fitness i is the fitness value of the individual with index i in the population, P i is the probability that the i-th individual in the subpopulation is selected as the parent individual; formula (4) represents the calculation of the fitness value of each individual, and formula (5) represents the calculation of the probability that each individual is selected.

[0037] In one embodiment of the present disclosure, in S2.5, a greedy strategy is adopted to update the sub-population and merge the sub-population to complete the population update, including:

[0038]

[0039] newPop=Pop1∪Pop2(9)

[0040] Among them, π i is the i-th individual in the population, π i ' is π i The offspring individuals generated by crossover mutation, C max (π i ) and C max (π i ') represent π i and π i 'The corresponding maximum completion time; Formula (7)-(8) indicates that if the new solution π i If the completion time of ' is not inferior to the old solution, the old solution is replaced by the new solution, otherwise the old solution is retained; Formula (9) indicates that the new population newPop is obtained by merging Pop1 and Pop2 to enter the next iteration.

[0041] In one embodiment of the present disclosure, the Q-learning-based variable neighborhood search in S2.6 includes:

[0042] According to the fitness, a certain proportion of individuals are selected as high-quality individuals to perform local search operations. According to the state determined by the Q table in the current environment, the corresponding perturbation strategy action is selected, and the corresponding perturbation operation is performed on the high-quality individuals to generate perturbation solutions. There are three types of perturbation strategies: exchange, flip and insertion;

[0043] Among them, for the generated perturbation solution, a variable neighborhood local search is performed, starting from the first neighborhood structure, a local search operation is performed on the perturbation solution until an improved solution is found or a predetermined number of times is reached. In each search, a corresponding local search strategy is selected according to different neighborhood structures. When a better solution is found, the current solution is updated and the local search is stopped. If the current improved solution is better than the initial high-quality solution, the solution replaces the initial solution, otherwise the perturbation and variable neighborhood operations are continued;

[0044] In the Q-learning algorithm, both states and actions represent local search strategies. The number of states and actions is equal to the number of local search strategies. The current state is determined by the local search strategy currently used, and the corresponding execution action is selected in the Q table by the ε-greedy strategy in the current state.

[0045]

[0046] Among them, a represents the action taken, Q(St ,a t ) indicates that in the current state S t Take action a t The Q value, arg{Q(S t ,a t )}→max represents the action that maximizes the Q value; rand represents a random number between 0 and 1 that satisfies the normal distribution, and ε represents a very small positive number.

[0047] In one embodiment of the present disclosure, the perturbation operator and the variable neighborhood search operation operator in S2.6 include:

[0048] The search operations for the perturbation strategy performed by individuals include Shake 1-Shake 3:

[0049] Shake 1: Randomly select two different detection and analysis step positions in the detection sequence and exchange the detection and analysis steps at these two positions;

[0050] Shake2: Randomly select two different detection analysis step positions in the detection sequence; if the first selected position is the first in the sequence, adjust the step in the second position to the first in the sequence, and keep the relative order of the remaining steps unchanged; if the first position is not the first, first keep the order of the steps before this position, insert the step in the second position before this position, and rearrange the steps between the two selected positions, and then keep the order of the remaining steps unchanged;

[0051] Shake 3: Randomly select two different detection and analysis step positions in the detection sequence, and flip all the steps between the two positions so that the order of the steps in this interval is reversed;

[0052] The variable neighborhood local search operations performed on the solution generated after the perturbation are NS1-6:

[0053] NS1: Take the perturbed solution as the perturbed solution and generate a new solution through the insertion operation; compare the completion time of the new solution and the perturbed solution. If the new solution is better than the perturbed solution, keep the new solution and discard the perturbed solution; if the insertion operation fails to find a better solution, continue to perform the exchange operation, generate another new solution and compare it with the current solution again, and finally output the optimal solution found in this process;

[0054] NS2: Starting from the perturbed solution, first perform a swap operation to generate a new solution and compare its completion time with that of the original perturbed solution. If the solution generated by the swap operation is better than the original solution, the new solution is retained; otherwise, perform an insert operation to generate a new solution and compare it with the old solution, and finally output the optimal solution after the swap and insert operations;

[0055] NS3: First, a new solution is generated through the swap operation and compared with the completion time of the original perturbed solution. If the new solution performs better than the original perturbed solution, the new solution is retained; if the swap operation fails to improve the quality of the solution, a further flip operation is performed to generate a new solution and compare it with the current solution, and finally the optimal solution is selected as the output;

[0056] NS4: Starting from the perturbed solution, first perform an insertion operation and generate a new solution, compare its completion time with the perturbed solution, and if the new solution is better than the perturbed solution, update the solution; if no improvement is produced, perform a flip operation, generate a new solution and compare the performance of the two, and finally output the optimal solution;

[0057] NS5: Starting from the perturbed solution, first perform a flip operation and generate a new solution, then compare its completion time with the perturbed solution. If the new solution performs better, it is updated. If no better solution is found, perform a swap operation, also generate a new solution and compare it with the current solution, and finally output the optimal solution.

[0058] NS6: First, a new solution is generated by flipping the operation, and the completion time is compared with the perturbed solution. If the solution generated by the flipping operation is better, it is retained; if there is no improvement, the insertion operation is continued to generate and compare new solutions, and finally the optimal solution is selected for output.

[0059] In one embodiment of the present disclosure, the reward value after the action is calculated in S2.7 and the Q table is updated. The specific operations are:

[0060] After performing a variable neighborhood local search based on Q-learning on the initial solution, the initial solution is compared with the new solution according to formula (11) to calculate the reward value obtained by the action, and then the corresponding Q(S) is updated according to formula (12). t ,a t )value;

[0061]

[0062]

[0063] Among them, reward t Indicates that the agent is in state S t Next, perform action a t The reward value obtained, C max (π i ) and C max (π i ') respectively represent π i and π i ' and the maximum completion time of the solution obtained after performing variable neighborhood search; Q(S t ,a t ) indicates the state S tExecute action a t The Q value, a represents the learning rate, g represents the discount factor, Indicates state S t+1 The maximum Q value obtained by executing all actions under the same condition, A represents the action set.

[0064] According to another aspect of the present disclosure, the present disclosure also provides a scheduling device for a multi-process parallel machine shop for precious metal detection, comprising:

[0065] Model building module, which is used to build a mathematical model for the multi-process parallel machine shop scheduling problem of precious metal detection based on the analysis method, analysis steps and corresponding detection instruments and equipment for precious metal alloy detection, with minimizing the maximum completion time as the optimization goal, and determine the constraints of the mathematical model;

[0066] Model solving module, used to solve the mathematical model and obtain the high-quality scheduling solution of the mathematical model;

[0067] The model solving module includes: parameter initialization module, population division module, population exploration module, population mining module, population update module, variable neighborhood search module, Q table update module, iterative update module, among which,

[0068] The parameter initialization module is used to initialize the population: including determining the order of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of local searches in variable neighborhoods;

[0069] The population division module is used to divide the population into two sub-populations of the same size, the first sub-population Pop1 and the second sub-population Pop2, where Pop1 focuses on exploration and Pop2 focuses on mining;

[0070] The population exploration module is used to perform exploration operations on Pop1: the fitness value of each individual in Pop1 is calculated according to the individual objective function value and the optimal individual is stored in the external memory pool. Two individuals in Pop1 are selected as parent individuals by roulette to perform evolution operations;

[0071] Population mining module, used to perform mining operations on Pop2: calculate the fitness value of each individual in Pop2 according to the individual objective function value and use roulette to select two individuals of Pop2 as parent individuals to perform mining operations based on uniform crossover;

[0072] Population update module, used for population update: adopt greedy strategy to update the populations Pop1 and Pop2 respectively, and merge Pop1 and Pop2 into a new population newPop after the update is completed;

[0073] The variable neighborhood search module is used to perform Q-learning-based variable neighborhood search on high-quality individuals: the variable neighborhood search algorithm based on Q-learning is used to perform perturbation operations on high-quality individuals and generate perturbation solutions, and then a variety of neighborhood structures are used to perform local searches, and the solutions are dynamically updated when a better solution is found;

[0074] Q-table update module, used to update the Q-table: update the state in the environment according to the action executed in S2.6, and calculate the reward value of the environment and update the Q-table according to the superiority relationship between the output new solution and the initial solution;

[0075] The iterative update module is used to determine whether the iteration termination condition is met. If so, it outputs a high-quality scheduling solution for the multi-process parallel machine shop scheduling problem model for precious metal alloy detection. Otherwise, it jumps to the population division module for another iteration.

[0076] The beneficial effect of the present invention is that by optimizing the step connection and resource allocation in the detection process, combined with an intelligent scheduling algorithm, effective scheduling of multiple parallel detection equipment is achieved, aiming to improve the overall efficiency and accuracy of precious metal detection. An appropriate modeling method is used to dynamically schedule multiple processes in the precious metal detection process, and the scheduling problem is solved by a dual-population variable neighborhood search algorithm based on Q-learning, which can avoid the problems of low efficiency and easy errors in existing methods. This method can effectively shorten the detection time, improve the utilization rate of detection equipment, and ensure accurate result output in complex processes. Through the scheduling method of the present invention, the resource scheduling of the precious metal detection workshop is more flexible, and the production efficiency and detection quality are significantly improved, meeting the strict requirements of the high-tech manufacturing industry for precious metal alloy detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0078] Figure 1 A flow chart of a scheduling method for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention is shown.

[0079] Figure 2 A schematic diagram of a Pop1 population POX crossover operation according to an embodiment of the present invention is shown.

[0080] Figure 3 Schematic diagram of Pop1 population mutation operation according to an embodiment of the present invention.

[0081] Figure 4 Schematic diagram of Pop2 population UX crossover operation according to an embodiment of the present invention.

[0082] Figure 5The present invention is a flowchart showing an example of a scheduling method for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention.

[0083] Figure 6 It is an iterative decline curve diagram of an example of a scheduling method for a multi-process parallel machine shop for precious metal detection in an embodiment of the present invention.

[0084] Figure 7 The present invention is a schematic diagram of the structure of a scheduling device for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification, but the present invention is not limited in any form. It should be pointed out that for those of ordinary skill in the art, several changes and improvements can be made without departing from the idea of ​​the present invention. These all belong to the protection scope of the present invention.

[0086] Figure 1 The flowchart of a scheduling method for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention is shown. Figure 1 As shown, in one embodiment, the scheduling method for a precious metal detection multi-process machine shop provided by the present disclosure mainly includes the following steps:

[0087] S1: Based on the analysis methods, analysis steps and corresponding instruments and equipment required for precious metal alloy detection, with minimizing the maximum completion time as the optimization goal, a mathematical model for the multi-process parallel machine shop scheduling problem of precious metal detection is constructed, and the constraints of the model are determined;

[0088] S2: Solve the mathematical model and obtain a high-quality scheduling solution for the mathematical model;

[0089] Among them, solving the mathematical model in S2 includes the following sub-steps:

[0090] S2.1: Initialize the population: including determining the sequence of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of local searches in variable neighborhoods;

[0091] S2.2: Population division: Divide the population into two sub-populations of equal size, Pop1 and Pop2, where Pop1 focuses on exploration and Pop2 focuses on mining;

[0092] S2.3: Perform exploration operation on Pop1: Calculate the fitness value of each individual in Pop1 according to the individual objective function value and store the best individual in the external memory pool, then use the roulette wheel method to select two individuals in Pop1 as parent individuals to perform evolution operation;

[0093] S2.4: Perform mining operation on Pop2: Calculate the fitness value of each individual in Pop2 according to the individual objective function value and select two individuals of Pop2 as parent individuals by roulette wheel to perform mining operation based on uniform crossover;

[0094] S2.5: Population update: Use the greedy strategy to update the populations Pop1 and Pop2 respectively. After the update is completed, merge Pop1 and Pop2 into a new population newPop;

[0095] S2.6: Perform Q-learning-based variable neighborhood search on high-quality individuals: Through the Q-learning-based variable neighborhood search algorithm, perturbation operations are performed on high-quality individuals and perturbation solutions are generated. Subsequently, local search is performed using multiple neighborhood structures. When a better solution is found, the solution is dynamically updated to improve the global search efficiency and optimization effect.

[0096] S2.7: Update Q-table: Update the state of the environment according to the action performed in S2.6. At the same time, according to the relationship between the output new solution and the initial solution, calculate the reward value of the environment and update the Q-table according to the value;

[0097] S2.7: Determine whether the iteration termination condition is met. If so, output the high-quality scheduling solution under the problem scale, otherwise jump to S2.2.

[0098] The iteration termination condition can be determined according to actual needs, for example, the reward value of the environment is greater than or equal to a preset reward threshold, or the iteration duration exceeds a preset duration threshold, or the number of iterations exceeds a preset number threshold.

[0099] It should be noted that the preset reward threshold, preset duration threshold, and preset number threshold can be pre-configured in the scheduling device. The values ​​of the above thresholds can be determined according to actual needs, and the present disclosure does not make specific limitations on this.

[0100] In the disclosed embodiments, by optimizing the step connection and resource allocation in the detection process, combined with an intelligent scheduling algorithm, effective scheduling of multiple parallel detection equipment is achieved, aiming to improve the overall efficiency and accuracy of precious metal detection. An appropriate modeling method is used to dynamically schedule multiple processes in the precious metal detection process, and the scheduling problem is solved by a dual-population variable neighborhood search algorithm based on Q-learning, which can avoid the problems of low efficiency and easy errors in existing methods. This method can effectively shorten the detection time, improve the utilization rate of detection equipment, and ensure accurate result output in complex processes. Through the scheduling method of the present invention, the resource scheduling of the precious metal detection workshop is more flexible, and the production efficiency and detection quality are significantly improved, meeting the strict requirements of the high-tech manufacturing industry for precious metal alloy detection.

[0101] Furthermore, the mathematical model in the aforementioned step S1 is constructed as follows: The multi-process parallel machine scheduling problem for precious metal detection is described as follows: n precious metal samples A to be detected 1 ,A 2 ,...,A n Requires m instruments and equipment M 1 ,M 2 ,...,M m Each sample contains q i (i=1,2,...,n) detection methods, each of which consists of O j ,(j=1,2,…,|q i |) detection and analysis steps, where |q i | indicates the detection method q i The total number of detection and analysis steps. Let O be the total number of detection steps for all precious metal samples to be detected, π = [π 1 ,π 2 ,...,π O ] is the arrangement of the detection and analysis steps of the detection method to be detected, which determines the order in which the sample detection methods are assigned to specific detectable devices. k For device M k The total number of detection steps on , k = 1, 2, ..., m, Equipment M k The above detection method is based on the arrangement of detection analysis steps; Steps for detection and analysis processing time, Steps for detection and analysis The start time of processing, for The equipment used in the previous detection and analysis step, for The position of the previous inspection process on the equipment used, where o = 1, 2, ..., O k .like It means For the first test; if It means For machine M k The first detection analysis step on the problem. The objective function of this problem is:

[0102]

[0103] Among them, formula (1) and formula (2) are used to calculate the maximum completion time corresponding to the sequence π, and formula (3) and formula (4) are used to find the most ordered π in all sequence sets π. * , so that C max (π) minimum.

[0104] In one embodiment, in S1, the constraints include but are not limited to the following:

[0105] 1) Any instrument or equipment is available at time 0;

[0106] 2) Any precious metal sample can be tested at time 0;

[0107] 3) Each detection and analysis step can be completed by at least one instrument;

[0108] 4) Once the detection and analysis steps are started, they are not allowed to be interrupted;

[0109] 5) Each instrument can only perform one detection and analysis step at a time;

[0110] 6) Precious metal samples can only undergo one testing step at a time;

[0111] like Figure 2-Figure 4 As shown, in one embodiment, in S2.3 and S2.4, the parent individuals are selected according to formulas (5)-(6), as follows:

[0112]

[0113] Among them, C max (π i ) is the i-th individual π in the subpopulation i The corresponding maximum completion time is is the maximum completion time of all individuals in the subpopulation, popsize is the population size, fitness i is the fitness value of the individual with index i in the population, P iis the probability that the i-th individual in the subpopulation is selected as the parent individual; formula (4) represents the calculation of the fitness value of each individual, and formula (5) represents the calculation of the probability that each individual is selected.

[0114] Figure 2 FIG. 2 is a schematic diagram showing a Pop1 population POX crossover operation in an embodiment of the present invention. Figure 2 As shown, the process of POX crossover operation of Pop1 population is shown, and the process of POX crossover operation of parent individual 1 and parent individual 2 is shown to obtain offspring individual 1 and offspring individual 2.

[0115] Figure 3 Schematic diagram of Pop1 population mutation operation in an embodiment of the present invention. Figure 3 As shown, one of the elements in the parent individual can be moved to the insertion position to obtain the mutated population.

[0116] Furthermore, in S2.5, the greedy strategy is adopted to update the sub-population and merge the sub-population to complete the population update, specifically:

[0117]

[0118] newPop=Pop1∪Pop2(9)

[0119] Among them, π i is the i-th individual in the population, π i ' is π i The offspring individuals generated by crossover mutation, C max (π i ) and C max (π i ') represent π i and π i 'The corresponding maximum completion time; Formula (7)-(8) indicates that if the new solution π i If the completion time of ' is not inferior to the old solution, the old solution is replaced by the new solution, otherwise the old solution is retained; Formula (9) indicates that the new population newPop is obtained by merging Pop1 and Pop2 to enter the next iteration.

[0120] Furthermore, in the variable neighborhood search based on Q-learning in S2.6, the specific operations are as follows:

[0121] According to the fitness, a certain proportion of individuals are selected as high-quality individuals to perform local search operations. According to the state determined by the Q table in the current environment, the corresponding perturbation strategy action is selected, and then the high-quality individuals are subjected to corresponding perturbation operations to generate perturbation solutions. There are three types of perturbation strategies: exchange, flip and insertion. For the generated perturbation solution, the present invention performs a variable neighborhood local search. First, a local search operation is performed on the perturbation solution starting from the first neighborhood structure until an improved solution is found or a predetermined number of times is reached. Each time a search is performed, a corresponding local search strategy is selected according to a different neighborhood structure. When a better solution is found, the current solution is updated and the local search is stopped. If the current improved solution is better than the initial high-quality solution, the solution replaces the initial solution, otherwise the perturbation and variable neighborhood operations continue to be performed;

[0122] In the designed Q-learning algorithm, both states and actions represent local search strategies, and the number of states and actions is equal to the number of local search strategies. The current state is determined by the local search strategy currently used, and the corresponding execution action is selected in the Q table by the ε-greedy strategy in the current state. The specific contents are shown in Table 1 and formula (10):

[0123] Table 1 Q table

[0124]

[0125]

[0126] Among them, a represents the action taken, Q(S t ,a t ) indicates that in the current state S t Take action a t The Q value, arg{Q(S t ,a t )}→max represents the action that maximizes the Q value; rand represents a random number between 0 and 1 that satisfies the normal distribution, and ε represents a very small positive number.

[0127] Furthermore, the perturbation operator and the variable neighborhood search operation operator in S2.6 are specifically:

[0128] The search operation for the perturbation strategy performed by the individual is Shake 1-3:

[0129] Shake 1: In the detection sequence, two different detection and analysis step positions are randomly selected and the steps at these two positions are swapped. This operation reconstructs the process path by swapping the order of steps, thereby exploring the potential impact of different step orders on overall performance optimization.

[0130] Shake 2: Randomly select two different detection and analysis step positions in the detection sequence. If the first selected position is the first in the sequence, adjust the step of the second position to the first in the sequence, and keep the relative order of the remaining steps unchanged; if the first position is not the first, first keep the order of the steps before this position, insert the step of the second position before this position, and rearrange the steps between the two selected positions, and then keep the order of the remaining steps unchanged. This strategy further explores the impact of local adjustments on the overall process efficiency by reorganizing the order of steps within the sequence.

[0131] Shake 3: In the detection sequence, two different detection and analysis step positions are randomly selected, and all steps between the two positions are flipped, that is, the order of the steps in this interval is reversed. This operation changes the direction of local step execution to explore the impact of different process orders on the final performance indicators.

[0132] The variable neighborhood local search operations performed on the solution generated after the perturbation are NS1-6:

[0133] NS1: Take the perturbed solution as the initial solution and generate a new solution through the insertion operation. Then, compare the completion time of the new solution with the original perturbed solution. If the new solution is better than the original solution, keep the new solution and discard the old solution. If the insertion operation fails to find a better solution, continue to perform the exchange operation, generate another new solution and compare it with the current solution again, and finally output the optimal solution found in this process.

[0134] NS2: Starting from the perturbed solution, first perform a swap operation to generate a new solution and compare its completion time with that of the original perturbed solution. If the solution generated by the swap operation is better than the original solution, the new solution is retained; otherwise, perform an insertion operation to generate a new solution and compare it with the old solution. Finally, output the optimal solution after the swap and insertion operations.

[0135] NS3: First, a new solution is generated through the swap operation and compared with the completion time of the original perturbed solution. If the new solution performs better than the original solution, the new solution is retained; if the swap operation fails to improve the quality of the solution, a further flip operation is performed to generate a new solution and compare it with the current solution, and finally the optimal solution is selected as the output.

[0136] NS4: Starting from the perturbed solution, first perform an insertion operation and generate a new solution, and compare its completion time with the perturbed solution. If the new solution is better than the perturbed solution, update the solution; if no improvement is produced, perform a flip operation, generate a new solution and compare the performance of the two, and finally output the optimal solution.

[0137] NS5: Starting from the perturbed solution, first perform a flip operation and generate a new solution, then compare its completion time with the perturbed solution. If the new solution performs better, it is updated. If no better solution is found, perform a swap operation, also generate a new solution and compare it with the current solution, and finally output the optimal solution.

[0138] NS6: First, a new solution is generated by flipping the operation, and the completion time is compared with the perturbed solution. If the solution generated by the flipping operation is better, it is retained; if there is no improvement, the insertion operation is continued to generate and compare new solutions, and finally the optimal solution is selected for output.

[0139] Furthermore, the calculation of the reward value after executing the action and updating the Q table in the aforementioned step S2.7 is specifically performed as follows:

[0140] After performing a variable neighborhood local search based on Q-learning on the initial solution, the initial solution is compared with the new solution according to formula (11) to calculate the reward value obtained by the action, and then the corresponding Q(S) is updated according to formula (12). t ,a t )value;

[0141]

[0142] Among them, reward t Indicates that the agent is in state S t Next, perform action a t The reward value obtained, C max (π i ) and C max (π i ') respectively represent π i and π i ' and the maximum completion time of the solution obtained after performing variable neighborhood search; Q(S t ,a t ) indicates the state S t Execute action a t The Q value, a represents the learning rate, g represents the discount factor, Indicates state S t+1 The maximum Q value obtained by executing all actions under the same condition, A represents the action set.

[0143] Figure 5 FIG. 1 is an example flow chart of a scheduling method for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention. Figure 5 As shown, the scheduling method for a multi-process parallel workshop for precious metal detection disclosed in the present invention includes:

[0144] Initialize the population: Initialize algorithm parameters including but not limited to: popsize, α, γ, ε, etc.;

[0145] The population is divided into sub-population Pop1 and sub-population Pop2;

[0146] Perform a POX-based crossover operation on the subpopulation Pop1, perform an insertion-based mutation operation on the generated offspring solution, and use a greedy strategy to update individuals;

[0147] Perform a UX-based crossover operation on the subpopulation Pop2, perform an insertion-based mutation operation on the generated offspring solution, and update the individuals based on the greedy strategy;

[0148] Merge new subpopulations;

[0149] Perform Q-learning-based variable neighborhood search for high-quality individuals;

[0150] Update status and Q table;

[0151] Determine whether the iteration termination condition is met. If so, output the most optimal scheduling solution. If not, g=g+1, return to the step of dividing the population into sub-populations Pop1 and sub-populations Pop2, and iterate again.

[0152] Figure 6 FIG. 1 is an iterative decline curve diagram of an example of a scheduling method for a multi-process parallel machine shop for precious metal detection according to an embodiment of the present invention. Figure 6 As shown in Figure 2, as the number of iterations increases, makespan gradually decreases and tends to be stable.

[0153] Figure 7 FIG. 1 is a schematic diagram showing a scheduling device for a multi-process parallel machine shop for precious metal detection provided by an embodiment of the present disclosure. Figure 7 As shown, in one embodiment, a scheduling device for a multi-process parallel machine shop for precious metal detection disclosed in the present invention includes:

[0154] Model building module 710, for building a mathematical model of the multi-process parallel machine shop scheduling problem for precious metal detection based on the analysis method, analysis steps and corresponding detection instruments and equipment for precious metal alloy detection, with minimizing the maximum completion time as the optimization goal, and determining the constraints of the mathematical model;

[0155] The model solving module 720 is used to solve the mathematical model and obtain a high-quality scheduling solution of the mathematical model;

[0156] The model solving module 720 includes: a parameter initialization module 721, a population division module 722, a population exploration module 733, a population mining module 724, a population update module 725, a variable neighborhood search module 726, a Q table update module 727, and an iterative update module 728, wherein:

[0157] Parameter initialization module 721, used to initialize the population: including determining the sequence of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of variable neighborhood local searches;

[0158] A population division module 722 is used to divide the population into two equal-sized first sub-populations Pop1 and second sub-populations Pop2, wherein Pop1 focuses on exploration and Pop2 focuses on mining;

[0159] The population exploration module 723 is used to perform an exploration operation on Pop1: calculate the fitness value of each individual in Pop1 according to the individual objective function value and store the best individual in the external memory pool, and select two individuals in Pop1 as parent individuals by roulette to perform evolution operation;

[0160] The population mining module 724 is used to perform a mining operation on Pop2: calculate the fitness value of each individual in Pop2 according to the individual objective function value and select two individuals of Pop2 as parent individuals by a roulette wheel method to perform a mining operation based on uniform crossover;

[0161] The population updating module 725 is used for population updating: the greedy strategy is used to update the populations Pop1 and Pop2 respectively, and after the updating is completed, Pop1 and Pop2 are merged into a new population newPop;

[0162] A variable neighborhood search module 726 is used to perform a variable neighborhood search based on Q-learning on high-quality individuals: a perturbation operation is performed on the high-quality individuals and a perturbation solution is generated through a variable neighborhood search algorithm based on Q-learning, and then a local search is performed using a variety of neighborhood structures, and the solution is dynamically updated when a better solution is found;

[0163] Q table update module 727, used to update the Q table: update the state of the environment according to the action executed in S2.6, and calculate the reward value of the environment according to the superiority relationship between the output new solution and the initial solution and update the Q table according to the reward value;

[0164] The iterative update module 728 is used to determine whether the iteration termination condition is met. If so, it outputs a high-quality scheduling solution for the precious metal alloy detection multi-process parallel machine shop scheduling problem model, otherwise it jumps to the population division module 722 for another iteration.

[0165] According to another aspect of an embodiment of the present invention, a solution system for a dual-population variable neighborhood search based on Q-learning applied to the precious metal alloy detection scheduling problem is also provided, comprising: 1. A construction module, which is used to minimize the total detection time as an optimization goal, including a model construction method for a type of precious metal alloy detection multi-process parallel machine shop scheduling problem. 2. An execution module, which further searches for high-quality solutions through a global search process based on dual-population co-evolution and combines an effective variable neighborhood search based on Q-learning with local search to improve the quality of the solution, thereby achieving an effective solution to the problem.

[0166] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A scheduling method for a multi-process parallel machine shop for precious metal detection, characterized in that: The following steps are involved: S1: Based on the analysis methods, analysis steps and corresponding testing instruments and equipment for precious metal alloy testing, with minimizing the maximum completion time as the optimization goal, a mathematical model for the multi-process parallel machine shop scheduling problem for precious metal testing is constructed, and the constraints of the mathematical model are determined; S2: Solve the mathematical model and obtain a high-quality scheduling solution for the mathematical model; Wherein, the mathematical model solved in S2 includes: S2.1: Initialize the population: including determining the sequence of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of local searches in variable neighborhoods; S2.2: Population division: Divide the population into two equal-sized sub-populations, the first sub-population Pop1 and the second sub-population Pop2, where Pop1 focuses on exploration and Pop2 focuses on mining; S2.3: Perform exploration operation on Pop1: Calculate the fitness value of each individual in Pop1 according to the individual objective function value and store the best individual in the external memory pool. Use roulette to select two individuals in Pop1 as parent individuals to perform evolution operation; S2.4: Perform mining operation on Pop2: Calculate the fitness value of each individual in Pop2 according to the individual objective function value and select two individuals of Pop2 as parent individuals by roulette wheel to perform mining operation based on uniform crossover; S2.5: Population update: Use the greedy strategy to update the populations Pop1 and Pop2 respectively. After the update is completed, Pop1 and Pop2 are merged into a new population newPop; S2.6: Perform Q-learning-based variable neighborhood search on high-quality individuals: Perform perturbation operations on high-quality individuals and generate perturbation solutions through the Q-learning-based variable neighborhood search algorithm, then use multiple neighborhood structures to perform local search and dynamically update the solution when a better solution is found; S2.7: Update Q-table: Update the state of the environment according to the action executed in S2.

6. At the same time, according to the superiority relationship between the output new solution and the initial solution, calculate the reward value of the environment and update the Q-table according to the reward value; S2.7: Determine whether the iteration termination condition is met. If so, output the high-quality scheduling solution for the precious metal alloy detection multi-process parallel machine shop scheduling problem model. Otherwise, jump to S2.

2.

2. The method according to claim 1, characterized in that The mathematical model of the multi-process parallel machine shop scheduling problem for precious metal detection is constructed in S1, including: The multi-process parallel machine scheduling problem for precious metal detection is described as follows: n precious metal samples A1, A2, ..., A n It requires m instruments and equipment M1, M2, ..., M m For testing, each sample contains q i (i=1,2,…,n) detection methods, each detection method consists of O j ,(j=1,2,…,|q i |) detection and analysis steps, where |q i | indicates the detection method q i The total number of assay analysis steps; Let O be the total number of detection steps for all precious metal samples to be detected, π=[π1,π2,...,π O ] is the arrangement of the detection and analysis steps of the method to be detected, which determines the order in which the sample detection methods are assigned to specific detectable devices; Let O k For device M k The total number of detection steps on , k = 1, 2, ..., m, Equipment M k The above detection method is based on the arrangement of detection analysis steps; Steps for detection and analysis processing time, Steps for detection and analysis The start time of processing, for The equipment used in the previous detection and analysis step, for The position of the previous inspection process on the equipment used, where o = 1, 2, ..., O k ; like It means For the first test; if It means For machine M k The first detection and analysis step on the The objective function of the multi-process parallel machine scheduling problem for precious metal detection is: Among them, formula (1) and formula (2) are used to calculate the maximum completion time corresponding to the sequence π, and formula (3) and formula (4) are used to find the optimal order π in all sequence sets π. * , so that C max (π) minimum.

3. The method according to claim 1, characterized in that: In S1, the constraints include: 1) Any instrument or equipment is available at time 0; 2) Any precious metal sample can be tested at time 0; 3) Each detection and analysis step can be completed by at least one instrument; 4) Once the detection and analysis steps are started, they are not allowed to be interrupted; 5) Each instrument can only perform one detection and analysis step at a time; 6) Precious metal samples can only undergo one testing step at a time.

4. The method according to claim 1, characterized in that S2.3 and S2.4 select parent individuals according to formulas (5)-(6), including: Among them, C max (π i ) is the i-th individual π in the subpopulation i The corresponding maximum completion time is is the maximum completion time of all individuals in the subpopulation, popsize is the population size, fitness i is the fitness value of the individual with index i in the population, P i is the probability that the i-th individual in the subpopulation is selected as the parent individual; formula (4) represents the calculation of the fitness value of each individual, and formula (5) represents the calculation of the probability that each individual is selected.

5. The method according to claim 1, characterized in that In S2.5, the greedy strategy is used to update the sub-population and merge the sub-population to complete the population update, including: newPop=Pop1∪Pop2(9) Among them, π i is the i-th individual in the population, π i ' is π i The offspring individuals generated by crossover mutation, C max (π i ) and C max (π i ') represent π i and π i 'The corresponding maximum completion time; Formula (7)-(8) indicates that if the new solution π i If the completion time of ' is not inferior to the old solution, the old solution is replaced by the new solution, otherwise the old solution is retained; Formula (9) indicates that the new population newPop is obtained by merging Pop1 and Pop2 to enter the next iteration.

6. The method according to claim 1, characterized in that The Q-learning-based variable neighborhood search in S2.6 includes: According to the fitness, a certain proportion of individuals are selected as high-quality individuals to perform local search operations. According to the state determined by the Q table in the current environment, the corresponding perturbation strategy action is selected, and the corresponding perturbation operation is performed on the high-quality individuals to generate perturbation solutions. There are three types of perturbation strategies: exchange, flip and insertion; Among them, for the generated perturbation solution, a variable neighborhood local search is performed, starting from the first neighborhood structure, a local search operation is performed on the perturbation solution until an improved solution is found or a predetermined number of times is reached. In each search, a corresponding local search strategy is selected according to different neighborhood structures. When a better solution is found, the current solution is updated and the local search is stopped. If the current improved solution is better than the initial high-quality solution, the solution replaces the initial solution, otherwise the perturbation and variable neighborhood operations are continued; In the Q-learning algorithm, both states and actions represent local search strategies. The number of states and actions is equal to the number of local search strategies. The current state is determined by the local search strategy currently used, and the corresponding execution action is selected in the Q table by the ε-greedy strategy in the current state. Among them, a represents the action taken, Q(S t ,a t ) indicates that in the current state S t Take action a t The Q value, arg{Q(S t ,a t )}→max represents the action that maximizes the Q value; rand represents a random number between 0 and 1 that satisfies the normal distribution, and ε represents a very small positive number.

7. The method according to claim 1, characterized in that The perturbation operator and the variable neighborhood search operation operator in S2.6 include: The search operations for the perturbation strategy performed by individuals include Shake 1-Shake 3: Shake 1: Randomly select two different detection and analysis step positions in the detection sequence and exchange the detection and analysis steps at these two positions; Shake 2: Randomly select two different detection analysis step positions in the detection sequence; if the first selected position is the first in the sequence, adjust the step at the second position to the first in the sequence, and keep the relative order of the remaining steps unchanged; if the first position is not the first, first keep the order of the steps before this position, insert the step at the second position before this position, and rearrange the steps between the two selected positions, and then keep the order of the remaining steps unchanged; Shake 3: Randomly select two different detection and analysis step positions in the detection sequence, and flip all the steps between the two positions so that the order of the steps in this interval is reversed; The variable neighborhood local search operations performed on the solution generated after the perturbation are NS1-6: NS1: Take the perturbed solution as the perturbed solution and generate a new solution through the insertion operation; compare the completion time of the new solution and the perturbed solution. If the new solution is better than the perturbed solution, keep the new solution and discard the perturbed solution; if the insertion operation fails to find a better solution, continue to perform the exchange operation, generate another new solution and compare it with the current solution again, and finally output the optimal solution found in this process; NS2: Starting from the perturbed solution, first perform a swap operation to generate a new solution and compare its completion time with that of the original perturbed solution. If the solution generated by the swap operation is better than the original solution, the new solution is retained; otherwise, perform an insert operation to generate a new solution and compare it with the old solution, and finally output the optimal solution after the swap and insert operations; NS3: First, a new solution is generated through the swap operation and compared with the completion time of the original perturbed solution. If the new solution performs better than the original perturbed solution, the new solution is retained; if the swap operation fails to improve the quality of the solution, a further flip operation is performed to generate a new solution and compare it with the current solution, and finally the optimal solution is selected as the output; NS4: Starting from the perturbed solution, first perform an insertion operation and generate a new solution, compare its completion time with the perturbed solution, and if the new solution is better than the perturbed solution, update the solution; if no improvement is produced, perform a flip operation, generate a new solution and compare the performance of the two, and finally output the optimal solution; NS5: Starting from the perturbed solution, it first performs a flip operation and generates a new solution, then compares its completion time with the perturbed solution. If the new solution performs better, it is updated; if no better solution is found, it performs a swap operation, also generates a new solution and compares it with the current solution, and finally outputs the optimal solution; NS6: First, a new solution is generated by flipping the operation, and the completion time is compared with the perturbed solution. If the solution generated by the flipping operation is better, it is retained; if there is no improvement, the insertion operation is continued to generate and compare new solutions, and finally the optimal solution is selected for output.

8. The method according to claim 1, characterized in that The reward value after the action is calculated in S2.7 and the Q table is updated. The specific operations are: After performing a variable neighborhood local search based on Q-learning on the initial solution, the initial solution is compared with the new solution according to formula (11) to calculate the reward value obtained by the action, and then the corresponding Q(S) is updated according to formula (12). t ,a t )value; Among them, reward t Indicates that the agent is in state S t Next, perform action a t The reward value obtained, C max (π i ) and C max (π i ') respectively represent π i and π i ' and the maximum completion time of the solution obtained after performing variable neighborhood search; Q(S t ,a t ) indicates the state S t Execute action a t The Q value, a represents the learning rate, g represents the discount factor, Indicates state S t+1 The maximum Q value obtained by executing all actions under Represents an action set.

9. A scheduling device for a multi-process parallel machine shop for precious metal detection, characterized in that: include: Model building module, which is used to build a mathematical model for the multi-process parallel machine shop scheduling problem of precious metal detection based on the analysis method, analysis steps and corresponding detection instruments and equipment for precious metal alloy detection, with minimizing the maximum completion time as the optimization goal, and determine the constraints of the mathematical model; Model solving module, used to solve the mathematical model and obtain the high-quality scheduling solution of the mathematical model; The model solving module includes: parameter initialization module, population division module, population exploration module, population mining module, population update module, variable neighborhood search module, Q table update module, iterative update module, among which, The parameter initialization module is used to initialize the population: including determining the order of detection and analysis steps; determining the detection instruments and equipment selected for each analysis step; determining the detection completion time; setting parameters, including population size, maximum number of iterations, Q table, and number of local searches in variable neighborhoods; The population division module is used to divide the population into two sub-populations of the same size, the first sub-population Pop1 and the second sub-population Pop2, where Pop1 focuses on exploration and Pop2 focuses on mining; The population exploration module is used to perform exploration operations on Pop1: the fitness value of each individual in Pop1 is calculated according to the individual objective function value and the optimal individual is stored in the external memory pool. Two individuals in Pop1 are selected as parent individuals by roulette to perform evolution operations; Population mining module, used to perform mining operations on Pop2: calculate the fitness value of each individual in Pop2 according to the individual objective function value and use roulette to select two individuals of Pop2 as parent individuals to perform mining operations based on uniform crossover; Population update module, used for population update: adopt greedy strategy to update the populations Pop1 and Pop2 respectively, and merge Pop1 and Pop2 into a new population newPop after the update is completed; The variable neighborhood search module is used to perform Q-learning-based variable neighborhood search on high-quality individuals: the variable neighborhood search algorithm based on Q-learning is used to perform perturbation operations on high-quality individuals and generate perturbation solutions, and then a variety of neighborhood structures are used to perform local searches, and the solutions are dynamically updated when a better solution is found; Q-table update module, used to update the Q-table: update the state in the environment according to the action executed in S2.6, and calculate the reward value of the environment and update the Q-table according to the superiority relationship between the output new solution and the initial solution; The iterative update module is used to determine whether the iteration termination condition is met. If so, it outputs a high-quality scheduling solution for the multi-process parallel machine shop scheduling problem model for precious metal alloy detection. Otherwise, it jumps to the population division module for another iteration.

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