A workshop scheduling method and system based on the Sand Cat algorithm

Abstract

This invention discloses a workshop scheduling method and system based on the Sandcat algorithm, belonging to the field of production scheduling technology. The method includes: constructing a multi-objective flexible workshop scheduling problem model based on workshop work data and setting initial parameters; performing population initialization operations based on optimized Tent chaotic mapping to generate an initial population, which is the initial scheduling solution; calculating the fitness value of each Sandcat individual in the initial population and sorting the solutions using fast non-dominated methods according to the fitness values ​​to obtain a locally optimal scheduling solution; updating the position of each Sandcat individual in the initial population using an optimal neighborhood perturbation strategy and a triangle walk strategy; converting the updated scheduling solution corresponding to the updated initial population into a Sandcat individual position vector based on a transformation mechanism to obtain the next generation of Sandcat population; and comparing the updated scheduling solution with the locally optimal scheduling solution to obtain the current optimal scheduling solution.

Description

Technical Field

[0001] This invention belongs to the field of production scheduling technology, and relates to a workshop scheduling method and system based on the Sand Cat algorithm. Background Technology

[0002] As a crucial link in the automotive manufacturing process, the stamping workshop is responsible for stamping sheet metal into various complex automotive parts, such as body panels and structural components, using molds. The quality and production efficiency of these parts directly affect the performance, cost, and market competitiveness of the entire vehicle. However, with the rapid development of the automotive industry and increasingly fierce market competition, the high energy consumption of stamping workshops has become increasingly prominent, becoming one of the important factors restricting the improvement of enterprise economic efficiency. Traditionally, production scheduling in stamping workshops often relies on manual experience or simple rule systems. This method is inadequate when facing complex and ever-changing production environments, making it difficult to achieve an optimal balance between energy consumption and production efficiency. Therefore, exploring a scientific and efficient scheduling strategy to optimize resource allocation in stamping workshops, reduce unnecessary energy consumption, and improve production efficiency has become a pressing technical challenge for automotive manufacturing enterprises. Against this backdrop, swarm intelligence optimization algorithms, due to their powerful global search capabilities and adaptability, have gradually become a powerful tool for solving complex scheduling problems. The Dune Cat Algorithm (DCA), a newly emerging swarm intelligence algorithm in recent years, simulates the behavior of dune cats searching for food and habitat in the desert environment. Through information exchange and cooperation among individuals, it achieves optimized solutions to problems.

[0003] However, when applied to real-world scheduling problems, the Sandcat algorithm also faces the challenges of easily getting trapped in local optima and having a high degree of randomness in population initialization, which limits its effectiveness in real-world production environments. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problems of the Sand Cat algorithm in the prior art, which is prone to getting trapped in local optima and has large randomness in population initialization when applied to actual scheduling problems, and to provide a workshop scheduling method and system based on the Sand Cat algorithm.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a workshop scheduling method based on the Sand Cat algorithm, comprising:

[0007] A multi-objective flexible workshop scheduling problem model is constructed based on workshop work data, and initial parameters are set, including population size and maximum number of iterations.

[0008] The multi-objective flexible stamping workshop scheduling problem model is initialized by optimizing the Tent chaotic mapping to generate an initial population, which is then used as the initial scheduling solution.

[0009] The fitness value of each sand cat individual in the initial population is calculated, and the non-dominated solutions are sorted according to the fitness value to obtain the local optimal scheduling solution.

[0010] The position of each individual sand cat in the initial population is updated using the optimal neighborhood perturbation strategy and the triangle walk strategy;

[0011] Based on the transformation mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the sand cat individual position vector to obtain the next generation of sand cat population; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual;

[0012] The loop begins by redistributing the next generation of sand cats based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends, and the best individual is selected from the current best individuals obtained in each loop.

[0013] A transformation mechanism is used to convert the position vector of the optimal individual into the optimal scheduling solution.

[0014] A further improvement of the present invention is as follows:

[0015] The specific steps of constructing a multi-objective flexible workshop scheduling problem model based on workshop work data include:

[0016] Minimum maximum completion time:

[0017] f1=min{max{C i}}, i=1,2,…,n (1)

[0018] The minimum total load of the machine is:

[0019]

[0020] Minimum maximum machine load:

[0021]

[0022] The model constraints are as follows:

[0023]

[0024] Wherein, equation (4) represents the constraint relationship of the processing sequence of a workpiece among various processes; equation (5) represents that a machine can only process one process at a certain time; equation (6) represents that any process can be processed by any available machine; i represents the processing number of the stamping workpiece; j represents the process number; k represents the processing machine number; m represents the total number of stamping machines that can process; M represents the set of stamping machines; O ij P represents the j-th process of stamping part i; ijk S represents the processing time of the j-th process of stamping part i on the k-th stamping machine; ijk C represents the start time of the j-th process of stamping part i on the k-th stamping machine; ijk S represents the processing time of the j-th process of stamped part i on the k-th stamping machine; ij C represents the start time of the j-th process of stamping part i; ij Indicates the completion time of the j-th process of stamping part i; x ijk This indicates whether the j-th process of stamping part i is processed on the k-th stamping machine; 1 indicates processing, 0 indicates otherwise. i This indicates the completion time of stamped part i.

[0025] The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map; the calculation formula for the optimized Tent chaotic map is as follows:

[0026]

[0027] Where k = 0, 1, 2 represents the number of mappings, and t represents the current iteration number.

[0028] The specific steps of performing fast non-dominated solution sorting on the initial scheduling solution are as follows:

[0029] In multi-objective optimization, the process of finding the Pareto optimal solution is always accompanied by the variation of another solution. If individual pi is better than individual pj in at least one objective and no individual pi is worse than individual pj in any objective, then individual pi is said to dominate individual pj; otherwise, individual pi cannot dominate individual pj.

[0030] First, calculate the dominance set of each individual in the population and the number of individuals it is dominated by, i.e., the number of dominated individuals. The dominance set refers to the set of all individuals that are completely superior to a particular individual, while the number of dominated individuals reflects the relative superiority or inferiority of that individual in the population. After identifying those individuals that are not dominated by any other individuals, place them in the first level of the non-dominated hierarchy.

[0031] Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue searching for and assigning new non-dominated levels until all individuals are classified into the corresponding levels.

[0032] Finally, within each non-dominated level, individuals are further sorted according to their number of dominated individuals, and the individuals with smaller number of dominated individuals obtain the locally optimal scheduling solution.

[0033] The triangle walking strategy is specifically as follows:

[0034] First, calculate the distance L1 between the optimal prey position and the sand cat's current position. Then, use this distance L1 to determine the sand cat's stride range. Define its walking direction β according to formula (10). P is the distance between the position obtained after the triangular walk and the prey. The formula for calculating the sand cat's updated position is as follows:

[0035] L1 = pos b (t)-pos c (t) (8)

[0036]

[0037] β=2×π×rand() (10)

[0038] P = L1 2 +L2 2 -2×L1×L2×cos(β) (11)

[0039] Pos new =pos b (t)+r×P (12).

[0040] The optimal neighborhood perturbation strategy is specifically as follows:

[0041] First, determine the optimal location. Based on the current optimal location, select a neighborhood range, and then perform a perturbation operation within the selected neighborhood range. Then, repeat the above steps, gradually approaching the current optimal scheduling solution through continuous iterative optimization. The calculation formula is as follows:

[0042]

[0043] Where t represents the number of iterations.

[0044] The conversion mechanism is specifically as follows:

[0045] Since the individual position is a continuous value and the scheduling solution is a discrete value, it is necessary to convert between the two. During encoding, a set of random numbers in a specific interval based on the process order is first generated. According to the ROV rule, the random variables are rearranged in ascending order and the process is rearranged. After rearrangement, the order of the random numbers corresponding to the ROV values ​​becomes the value of each element in the individual position vector.

[0046] Secondly, the present invention provides a workshop scheduling system based on the Sand Cat algorithm, comprising:

[0047] The model building module constructs a multi-objective flexible workshop scheduling problem model based on workshop work data and sets initial parameters, including population size and maximum number of iterations.

[0048] The initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping workshop scheduling problem model based on the optimized Tent chaotic mapping to generate an initial population, which is the initial scheduling solution.

[0049] The local optimal scheduling solution acquisition module calculates the fitness value of each sand cat individual in the initial population and sorts the non-dominated solutions quickly according to the size of the fitness value, and uses the initial population as the initial scheduling solution;

[0050] The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and the triangle walking strategy to update the position of each individual sand cat in the initial population;

[0051] The current optimal individual acquisition module converts the updated scheduling solution corresponding to the initial population after the individual position update into a sand cat individual position vector based on the conversion mechanism to obtain the next generation of sand cat population; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand cat individual corresponding to the current optimal scheduling solution as the current optimal individual;

[0052] The loop module starts by redistributing the next generation of the sand cat population based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends. In each loop, the best individual is selected from the current best individuals.

[0053] The optimal scheduling solution acquisition module uses a conversion mechanism to convert the position vector of the optimal individual into the optimal scheduling solution.

[0054] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described workshop scheduling method based on the Sand Cat algorithm.

[0055] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described workshop scheduling method based on the Sand Cat algorithm.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] This invention discloses a workshop scheduling method based on the Sand Cat algorithm. The invention proposes to redistribute the initial state positions of the population using an optimized Tent chaotic map. This strategy combines Tent and Logistic chaotic maps, exhibiting high ergodicity, strong depth-search capability, and uniform distribution. Initializing the population with this strategy solves the problems of high population distribution randomness, repeated initial values, and premature convergence. Secondly, a triangle walking strategy is adopted to improve the Sand Cat's search behavior. Instead of directly contacting prey, the Sand Cat increases the randomness of its individual position through wandering behavior, avoiding unnecessary repeated search space, improving search efficiency, and accelerating the algorithm's convergence speed. An optimal neighborhood perturbation strategy is employed to improve the Sand Cat's mobility and the algorithm's global search capability. The Sand Cat first determines its optimal position, then selects a neighborhood based on this optimal position, and performs perturbation operations within this range. This innovation improves population diversity and the algorithm's convergence accuracy. In summary, the Sand Cat algorithm with three improved strategies overcomes the problems of large randomness in population initialization, low population diversity, slow convergence speed, and easy getting trapped in local optima. When the improved Sand Cat algorithm is applied to the stamping workshop scheduling problem, the solution results are significantly better than the original Sand Cat algorithm, and it outperforms the Sparrow algorithm and the Curly-tailed Monkey algorithm in more than 90% of the results.

[0058] This invention discloses a workshop scheduling system based on the Sandcat algorithm. This system enhances the algorithm's global search capability and avoids premature convergence by introducing a new initialization strategy, optimizing the search mechanism, and adaptively adjusting parameters, while simultaneously improving the algorithm's convergence speed and solution quality. Furthermore, considering the specific characteristics of stamping workshop scheduling, this invention designs corresponding encoding methods, fitness functions, and decoding strategies to ensure that the algorithm can accurately and efficiently solve practical problems in stamping workshop scheduling, bringing significant economic and social benefits to enterprises. This invention is not only a significant improvement to the Sandcat algorithm but also an innovative exploration of stamping workshop scheduling problems in the automotive manufacturing field, providing new ideas and methods for solving the bottleneck problem of high energy consumption and low efficiency in production. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart of a workshop scheduling method based on the Sand Cat algorithm in this invention;

[0061] Figure 2 This is a schematic diagram of the coding of a workshop scheduling method based on the Sand Cat algorithm in this invention;

[0062] Figure 3 This is a schematic diagram of ROV rule transformation in a workshop scheduling method based on the Sand Cat algorithm in this invention;

[0063] Figure 4 This is a Gantt chart of the MK02 example of a workshop scheduling method based on the Sand Cat algorithm in this invention;

[0064] Figure 5 This is the convergence diagram of the MK02 example of a workshop scheduling method based on the Sand Cat algorithm in this invention; Figure 5 (a) is a diagram showing the relationship between maximum completion time; Figure 5 (b) is the total load diagram; Figure 5 (c) is a diagram showing the minimum load relationship of the machine;

[0065] Figure 6 This is a schematic diagram of a workshop scheduling system based on the Sand Cat algorithm in this invention;

[0066] Figure 7 This is a block diagram of the electronic device in this invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0068] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0069] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0070] The present invention will now be described in further detail with reference to the accompanying drawings:

[0071] See Figure 1 This invention discloses a workshop scheduling method based on the Sand Cat algorithm, comprising:

[0072] S1. Construct a multi-objective flexible workshop scheduling problem model based on workshop work data and set initial parameters, including population size and maximum number of iterations;

[0073] S2, perform population initialization operation on the multi-objective flexible stamping workshop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, and use the initial population as the initial scheduling solution;

[0074] S3, calculate the fitness value of each sand cat individual in the initial population and sort the non-dominated solutions according to the fitness value to obtain the local optimal scheduling solution;

[0075] S4, the optimal neighborhood perturbation strategy and the triangle walking strategy are used to update the position of each individual sand cat in the initial population;

[0076] S5, based on the conversion mechanism, the updated scheduling solution corresponding to the initial population after the individual position update is converted into the sand cat individual position vector to obtain the next generation of sand cat population; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual;

[0077] S6, start the loop by redistributing the next generation of sand cats based on the optimized Tent chaotic map, and end the loop when the loop reaches the preset maximum number of iterations. Select the best individual from the current best individuals obtained in each loop.

[0078] S7, a transformation mechanism is used to convert the position vector of the optimal individual into the optimal scheduling solution.

[0079] This invention discloses a workshop scheduling method based on the Sand Cat algorithm. The invention proposes to redistribute the initial state positions of the population using an optimized Tent chaotic map. This strategy combines Tent and Logistic chaotic maps, exhibiting high ergodicity, strong depth-search capability, and uniform distribution. Initializing the population with this strategy solves the problems of high population distribution randomness, repeated initial values, and premature convergence. Secondly, a triangle walking strategy is adopted to improve the Sand Cat's search behavior. Instead of directly contacting prey, the Sand Cat increases the randomness of its individual position through wandering behavior, avoiding unnecessary repeated search space, improving search efficiency, and accelerating the algorithm's convergence speed. An optimal neighborhood perturbation strategy is employed to improve the Sand Cat's mobility and the algorithm's global search capability. The Sand Cat first determines its optimal position, then selects a neighborhood based on this optimal position, and performs perturbation operations within this range. This innovation improves population diversity and the algorithm's convergence accuracy. In summary, the Sand Cat algorithm with three improved strategies overcomes the problems of large randomness in population initialization, low population diversity, slow convergence speed, and easy getting trapped in local optima. When the improved Sand Cat algorithm is applied to the stamping workshop scheduling problem, the solution results are significantly better than the original Sand Cat algorithm, and it outperforms the Sparrow algorithm and the Curly-tailed Monkey algorithm in more than 90% of the results.

[0080] This invention discloses a workshop scheduling method based on the Sand Cat algorithm. The following detailed description of the invention is provided in conjunction with specific embodiments:

[0081] Step 1: Construct a multi-objective flexible workshop scheduling problem model based on workshop work data and set initial parameters, including population size and maximum number of iterations;

[0082] The initial population size is set to 200, and the maximum number of iterations is set to 500. Based on the problem being solved, the following parameters are defined:

[0083] Table 1 Parameter Definitions

[0084]

[0085]

[0086] Based on this, the constructed multi-objective flexible job shop scheduling model is as follows:

[0087] Minimum maximum completion time:

[0088] f1=min{max{C i}}, i=1,2,…,n (1)

[0089] The minimum total load of the machine is:

[0090]

[0091] Minimum maximum machine load:

[0092]

[0093] The model constraints are as follows:

[0094]

[0095] Equation (4) represents the constraint relationship of the processing sequence of a workpiece among various processes; Equation (5) represents that a machine can only process one process at a certain time; Equation (6) represents that any process can be processed by any available machine.

[0096] Specifically, the problem studied in this invention patent mainly includes two sub-problems: process sequencing and machine sequencing. Therefore, an equal-length double-chain real number encoding method is adopted, with the encoding length being twice the total number of processes and the two code segments having equal lengths. Assuming the process length is L, then the encoding length is 2L. Both the machine code and the process code are 2L. The element values ​​of the individual position vector range from [-3, 3]. Oij represents the j-th process of workpiece i. The first L codes represent the machine code for process selection, and the last L codes represent the sequence of processes. The specific method is as follows: Figure 2 As shown.

[0097] Step 2: Perform population initialization operation on the multi-objective flexible stamping workshop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is the initial scheduling solution;

[0098] The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map; the calculation formula for the optimized Tent chaotic map is as follows:

[0099]

[0100] Where k = 0, 1, 2 represents the number of mappings, and t represents the current iteration number.

[0101] Simultaneously, for each machine allocation scheme, multiple candidate schemes for process ordering are randomly generated. These process ordering schemes are then combined with the machine allocation scheme one by one, and the objective function value of each combination is evaluated. By comparing the objective function values ​​of different combinations, the optimal combination is selected as the initial solution. This process is repeated for all generated machine allocation schemes, completing the construction of the entire initial population and ensuring population diversity and solution quality.

[0102] Step 3: Calculate the fitness value of each sand cat individual in the initial population and sort the non-dominated solutions according to the fitness value to obtain the local optimal scheduling solution;

[0103] In multi-objective optimization, the process of finding the Pareto optimal solution is always accompanied by the variation of another solution. If individual pi is better than individual pj in at least one objective and no individual pi is worse than individual pj in any objective, then individual pi is said to dominate individual pj; otherwise, individual pi cannot dominate individual pj.

[0104] First, calculate the dominance set of each individual in the population and the number of individuals it is dominated by, i.e., the number of dominated individuals. The dominance set refers to the set of all individuals that are completely superior to a particular individual, while the number of dominated individuals reflects the relative superiority or inferiority of that individual in the population. After identifying those individuals that are not dominated by any other individuals, place them in the first level of the non-dominated hierarchy.

[0105] Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue searching for and assigning new non-dominated levels until all individuals are classified into the corresponding levels.

[0106] Finally, within each non-dominated level, individuals are further ranked according to their number of dominated individuals. Individuals with smaller dominated numbers yield locally optimal scheduling solutions. Individuals with smaller dominated numbers indicate higher competitiveness and superior solution quality within the population. This method allows for a comprehensive and systematic evaluation of the quality of individuals in the population, providing strong support for subsequent decision-making and optimization.

[0107] Step 4: Update the position of each individual sand cat in the initial population using the optimal neighborhood perturbation strategy and the triangle walk strategy;

[0108] The addition of a triangle walking learning strategy enables the algorithm to converge faster. First, the distance L1 between the optimal prey position and the sand cat's current position is calculated. Then, the sand cat's step size range is obtained using this distance L1. Its walking direction β is defined according to formula (10), and P is the distance between the position obtained after the triangle walking and the prey. The formula for calculating the sand cat's updated position is as follows:

[0109] L1 = pos b (t)-pos c (t) (8)

[0110]

[0111] β=2×π×rand() (10)

[0112] P = L1 2 +L2 2 -2×L1×L2×cos(β) (11)

[0113] Pos new=pos b (t)+r×P (12).

[0114] Secondly, an optimal neighborhood perturbation strategy is introduced to further improve the Sand Cat's mobility and the algorithm's global exploration capability, preventing the algorithm from getting trapped in local optima. This involves moderately perturbing the Sand Cat's position during the global search phase. Specifically, the optimal neighborhood perturbation strategy is as follows:

[0115] First, determine the optimal location. Based on the current optimal location, select a neighborhood range, and then perform a perturbation operation within the selected neighborhood range. Then, repeat the above steps, gradually approaching the current optimal scheduling solution through continuous iterative optimization. The calculation formula is as follows:

[0116]

[0117] Where t represents the number of iterations.

[0118] This perturbation can enrich population diversity, improve convergence accuracy, better escape local optima during global search, find the global optimum, improve the convergence speed of the algorithm, and avoid premature convergence.

[0119] Step 5: Based on the conversion mechanism, the updated scheduling solution corresponding to the initial population after the individual position update is converted into a sand cat individual position vector to obtain the next generation of sand cats; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual; the conversion mechanism is specifically as follows:

[0120] Since the individual position is a continuous value and the scheduling solution is a discrete value, it is necessary to convert between the two. During encoding, a set of random numbers in a specific interval based on the process order is first generated. According to the ROV rule, the random variables are rearranged in ascending order and the process is rearranged. After rearrangement, the order of the random numbers corresponding to the ROV values ​​becomes the value of each element in the individual position vector.

[0121] Step 6: Start the loop by redistributing the next generation of sand cats based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends. Select the best individual from the current best individuals obtained in each loop.

[0122] Step 7: Use a conversion mechanism to convert the position vector of the optimal individual into the optimal scheduling solution to complete the workshop scheduling.

[0123] Verification of the beneficial effects of the present invention:

[0124] To evaluate the performance of the improved algorithm, the improved Sandcat algorithm was compared with the original Sandcat algorithm, the Curly-tailed Monkey algorithm, and the Sparrow algorithm on the same problem. The Inverse Gaussian Dispersion (IGD) and Highest Gaussian Value (HV) metrics were used to measure the improved algorithm's performance in terms of diversity and convergence. The formulas for calculating IGD and HV are shown below:

[0125] The formula for calculating the inverse generation distance (IGD) is as follows:

[0126]

[0127] Among them, |Ω * |D represents the number of elements in the Pareto front obtained by the algorithm. i (Ω * ,Ω) refers to Ω * The shortest Euclidean distance between the i-th element in Ω and the elements in Ω. The smaller the IGD value, the better the convergence performance of the algorithm.

[0128] The formula for calculating the hypervolume HV is as follows:

[0129]

[0130] Where δ is the Lebesgue measure. i HV represents the volume of the region enclosed by the non-dominated solution i and the reference point. The larger the HV value, the better the diversity of the algorithm.

[0131] Four algorithms were used to solve ten cases MK01-MK10, and each was run independently 20 times. The average value was taken, and the data in Table 2 below was obtained.

[0132] Table 2 IGD and HV

[0133]

[0134] As shown in Table 2, in 10 sets of examples, the improved Sand Cat algorithm outperformed other algorithms in 90% of the performance metrics. This result strongly demonstrates that the proposed improvement strategy can effectively enhance the algorithm's performance.

[0135] In addition, the optimization results for three optimization indicators—maximum completion time, total machine load, and maximum machine load—were statistically analyzed. The bold text in the tables represents the optimal results, as shown in Tables 3, 4, and 5.

[0136] Table 3 Maximum Completion Time

[0137]

[0138] Table 4 Total Machine Load

[0139]

[0140]

[0141] Table 5. Maximum Machine Load Results Data

[0142]

[0143] As shown in the three tables above, the improved Sand Cat algorithm significantly outperforms the other three algorithms in all ten calculation examples across the three optimization metrics.

[0144] Since instance MK02 outperforms other instances in terms of results and running time, it is selected for in-depth analysis to further explore the performance of the improved Sand Cat Algorithm (ISCSO). Figure 4 The image shows the Gantt chart for solving example MK02 using the improved Sand Cat algorithm. Figure 5 The convergence process of the maximum completion time under the MK02 instance is clearly illustrated. As can be seen from the figure, ISCSO not only significantly accelerates the convergence speed but also obtains a higher-quality scheduling solution. This significant advantage strongly demonstrates the feasibility and effectiveness of the ISCSO improvement strategy.

[0145] This invention addresses the problems of the Sand Cat algorithm, such as its tendency to get trapped in local optima and the significant randomness in population initialization. It proposes a hybrid chaotic mapping strategy during the population initialization stage to improve the uniformity of population distribution and avoid the generation of duplicate solutions. Furthermore, by adding a triangle walking strategy and an optimal neighborhood perturbation strategy to change the global position of the Sand Cat, the algorithm's convergence speed and search efficiency are accelerated. Finally, the improved algorithm is evaluated using two key metrics, IGD and HV, through solving the stamping workshop examples MK01-MK10. The optimized values ​​for maximum completion time, total machine load, and maximum machine load are output. Numerically, the improved Sand Cat algorithm outperforms the comparative algorithms, demonstrating the effectiveness and superiority of the improved Sand Cat algorithm presented in this invention.

[0146] See Figure 6 This invention provides a workshop scheduling system based on the Sand Cat algorithm, comprising:

[0147] The model building module constructs a multi-objective flexible workshop scheduling problem model based on workshop work data and sets initial parameters, including population size and maximum number of iterations.

[0148] The initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping workshop scheduling problem model based on the optimized Tent chaotic mapping to generate an initial population, and uses the initial population as the initial scheduling solution.

[0149] The local optimal scheduling solution acquisition module calculates the fitness value of each sand cat individual in the initial population and sorts the non-dominated solutions quickly according to the size of the fitness value to obtain the local optimal scheduling solution;

[0150] The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and the triangle walking strategy to update the position of each individual sand cat in the initial population;

[0151] The current optimal individual acquisition module converts the updated scheduling solution corresponding to the initial population after the individual position update into a sand cat individual position vector based on the conversion mechanism to obtain the next generation of sand cat population; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand cat individual corresponding to the current optimal scheduling solution as the current optimal individual;

[0152] The loop module starts by redistributing the next generation of the sand cat population based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends. In each loop, the best individual is selected from the current best individuals.

[0153] The optimal scheduling solution acquisition module uses a conversion mechanism to convert the position vector of the optimal individual into the optimal scheduling solution.

[0154] This invention discloses a workshop scheduling system based on the Sandcat algorithm. This system enhances the algorithm's global search capability and avoids premature convergence by introducing a new initialization strategy, optimizing the search mechanism, and adaptively adjusting parameters, while simultaneously improving the algorithm's convergence speed and solution quality. Furthermore, considering the specific characteristics of stamping workshop scheduling, this invention designs corresponding encoding methods, fitness functions, and decoding strategies to ensure that the algorithm can accurately and efficiently solve practical problems in stamping workshop scheduling, bringing significant economic and social benefits to enterprises. This invention is not only a significant improvement to the Sandcat algorithm but also an innovative exploration of stamping workshop scheduling problems in the automotive manufacturing field, providing new ideas and methods for solving the bottleneck problem of high energy consumption and low efficiency in production.

[0155] See Figure 7 A third objective of this invention is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the workshop scheduling method based on the Sand Cat algorithm.

[0156] The workshop scheduling method based on the Sand Cat algorithm includes the following steps:

[0157] A multi-objective flexible workshop scheduling problem model is constructed based on workshop work data, and initial parameters are set, including population size and maximum number of iterations.

[0158] The multi-objective flexible stamping workshop scheduling problem model is initialized by optimizing the Tent chaotic mapping to generate an initial population, which is then used as the initial scheduling solution.

[0159] The fitness value of each sand cat individual in the initial population is calculated, and the non-dominated solutions are sorted according to the fitness value to obtain the local optimal scheduling solution.

[0160] The position of each individual sand cat in the initial population is updated using the optimal neighborhood perturbation strategy and the triangle walk strategy;

[0161] Based on the transformation mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the sand cat individual position vector to obtain the next generation of sand cat population; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual;

[0162] The loop begins by redistributing the next generation of sand cats based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends, and the best individual is selected from the current best individuals obtained in each loop.

[0163] A transformation mechanism is used to convert the position vector of the optimal individual into the optimal scheduling solution.

[0164] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the workshop scheduling method based on the Sand Cat algorithm.

[0165] The workshop scheduling method based on the Sand Cat algorithm includes the following steps:

[0166] A multi-objective flexible workshop scheduling problem model is constructed based on workshop work data, and initial parameters are set, including population size and maximum number of iterations.

[0167] The multi-objective flexible stamping workshop scheduling problem model is initialized by optimizing the Tent chaotic mapping to generate an initial population, which is then used as the initial scheduling solution.

[0168] The fitness value of each sand cat individual in the initial population is calculated, and the non-dominated solutions are sorted according to the fitness value to obtain the local optimal scheduling solution.

[0169] The position of each individual sand cat in the initial population is updated using the optimal neighborhood perturbation strategy and the triangle walk strategy;

[0170] Based on the transformation mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the sand cat individual position vector to obtain the next generation of sand cat population; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual;

[0171] The loop begins by redistributing the next generation of sand cats based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends, and the best individual is selected from the current best individuals obtained in each loop.

[0172] A transformation mechanism is used to convert the position vector of the optimal individual into the optimal scheduling solution.

[0173] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A workshop scheduling method based on the Sand Cat algorithm, characterized in that, include: A multi-objective flexible workshop scheduling problem model is constructed based on workshop work data, and initial parameters are set, including population size and maximum number of iterations. The specific steps of constructing a multi-objective flexible workshop scheduling problem model based on workshop work data include: Minimum maximum completion time: The minimum total load of the machine is: Minimum maximum machine load: The model constraints are as follows: Wherein, equation (4) represents the constraint relationship of the processing sequence of a workpiece among various processes; equation (5) represents that a machine can only process one process at a certain time; equation (6) represents that any process can be processed by any available machine; i represents the processing number of the stamping workpiece; j represents the process number; k represents the processing machine number; m represents the total number of stamping machines that can process; M represents the set of stamping machines; O ij P represents the j-th process of stamping part i; ijk S represents the processing time of the j-th process of stamping part i on the k-th stamping machine; ijk C represents the start time of the j-th process of stamping part i on the k-th stamping machine; ijk S represents the processing time of the j-th process of stamped part i on the k-th stamping machine; ij C represents the start time of the j-th process of stamping part i; ij Indicates the completion time of the j-th process of stamping part i; x ijk This indicates whether the j-th process of stamping part i is processed on the k-th stamping machine; 1 indicates processing, 0 indicates otherwise. i Indicates the completion time of stamped part k; The multi-objective flexible stamping workshop scheduling problem model is initialized by optimizing the Tent chaotic mapping to generate an initial population, which is then used as the initial scheduling solution. The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map; the calculation formula for the optimized Tent chaotic map is as follows: Where k = 0, 1, 2 represents the number of mappings, and t represents the current iteration number; The fitness value of each sand cat individual in the initial population is calculated, and the non-dominated solutions are sorted according to the fitness value to obtain the local optimal scheduling solution. The position of each individual sand cat in the initial population is updated using the optimal neighborhood perturbation strategy and the triangle walk strategy; Based on the transformation mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the sand cat individual position vector to obtain the next generation of sand cat population; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand cat individual corresponding to the current optimal scheduling solution is taken as the current optimal individual; The loop begins by redistributing the next generation of sand cats based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends, and the best individual is selected from the current best individuals obtained in each loop. A transformation mechanism is used to convert the position vector of the optimal individual into the optimal scheduling solution.

2. The workshop scheduling method based on the Sand Cat algorithm according to claim 1, characterized in that, The fitness value of each sand cat individual in the initial population is calculated, and the fast non-dominated solutions are sorted according to the fitness value to obtain the local optimal scheduling solution. In multi-objective optimization, the process of finding the Pareto optimal solution is always accompanied by the variation of another solution. If individual pi is better than individual pj in at least one objective and no individual pi is worse than individual pj in any objective, then individual pi is said to dominate individual pj; otherwise, individual pi cannot dominate individual pj. First, calculate the dominance set of each individual in the population and the number of individuals it is dominated by, i.e., the number of dominated individuals. The dominance set refers to the set of all individuals that are completely superior to a particular individual, while the number of dominated individuals reflects the relative superiority or inferiority of that individual in the population. After identifying those individuals that are not dominated by any other individuals, place them in the first level of the non-dominated hierarchy. Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue searching for and assigning new non-dominated levels until all individuals are classified into the corresponding levels. Finally, within each non-dominated level, individuals are further sorted according to their number of dominated individuals, and the individuals with smaller number of dominated individuals obtain the locally optimal scheduling solution.

3. The workshop scheduling method based on the Sand Cat algorithm according to claim 1, characterized in that, The triangle walking strategy is specifically as follows: First, calculate the distance L1 between the optimal prey position and the sand cat's current position. Then, use this distance L1 to determine the sand cat's stride range. Define its walking direction β according to formula (10). P is the distance between the position obtained after the triangular walk and the prey. The formula for calculating the sand cat's updated position is as follows: L1=pos b (t)-pos c (t) (8) β=2×π×rand() (10) P=L1 2 +L2 2 -2×L1×L2×cos(β) (11) Pos new =pos b (t)+r×P (12)。 4. The workshop scheduling method based on the Sand Cat algorithm according to claim 1, characterized in that, The optimal neighborhood perturbation strategy is specifically as follows: First, determine the optimal location. Based on the current optimal location, select a neighborhood range, and then perform a perturbation operation within the selected neighborhood range. Then, repeat the above steps, gradually approaching the current optimal scheduling solution through continuous iterative optimization. The calculation formula is as follows: Where t represents the number of iterations.

5. The workshop scheduling method based on the Sand Cat algorithm according to claim 1, characterized in that, The conversion mechanism is specifically as follows: Since the individual position is a continuous value and the scheduling solution is a discrete value, it is necessary to convert between the two. During encoding, a set of random numbers in a specific interval based on the process order is first generated. According to the ROV rule, the random variables are rearranged in ascending order and the process is rearranged. After rearrangement, the order of the random numbers corresponding to the ROV values ​​becomes the value of each element in the individual position vector.

6. A workshop scheduling system based on the Sand Cat algorithm, characterized in that, include: The model building module constructs a multi-objective flexible workshop scheduling problem model based on workshop work data and sets initial parameters, including population size and maximum number of iterations. The specific steps of constructing a multi-objective flexible workshop scheduling problem model based on workshop work data include: Minimum maximum completion time: f1=min{max{C i ]},i=1,2,…,n (1) The minimum total load of the machine is: Minimum maximum machine load: The model constraints are as follows: Wherein, equation (4) represents the constraint relationship of the processing sequence of a workpiece among various processes; equation (5) represents that a machine can only process one process at a certain time; equation (6) represents that any process can be processed by any available machine; i represents the processing number of the stamping workpiece; j represents the process number; k represents the processing machine number; m represents the total number of stamping machines that can process; M represents the set of stamping machines; O ij P represents the j-th process of stamping part i; ijk S represents the processing time of the j-th process of stamping part i on the k-th stamping machine; ijk C represents the start time of the j-th process of stamping part i on the k-th stamping machine; ijk S represents the processing time of the j-th process of stamped part i on the k-th stamping machine; ij C represents the start time of the j-th process of stamping part i; ij Indicates the completion time of the j-th process of stamping part i; x ijk This indicates whether the j-th process of stamping part i is processed on the k-th stamping machine; 1 indicates processing, 0 indicates otherwise. i Indicates the completion time of stamped part i; The initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping workshop scheduling problem model based on the optimized Tent chaotic mapping to generate an initial population, and uses the initial population as the initial scheduling solution. The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map; the calculation formula for the optimized Tent chaotic map is as follows: Where k = 0, 1, 2 represents the number of mappings, and t represents the current iteration number; The local optimal scheduling solution acquisition module calculates the fitness value of each sand cat individual in the initial population and sorts the non-dominated solutions quickly according to the size of the fitness value to obtain the local optimal scheduling solution; The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and the triangle walking strategy to update the position of each individual sand cat in the initial population; The current optimal individual acquisition module converts the updated scheduling solution corresponding to the initial population after the individual position update into a sand cat individual position vector based on the conversion mechanism to obtain the next generation of sand cat population; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand cat individual corresponding to the current optimal scheduling solution as the current optimal individual; The loop module starts by redistributing the next generation of the sand cat population based on the optimized Tent chaotic map. When the loop reaches the preset maximum number of iterations, the loop ends. In each loop, the best individual is selected from the current best individuals. The optimal scheduling solution acquisition module uses a conversion mechanism to convert the position vector of the optimal individual into the optimal scheduling solution.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the workshop scheduling method based on the Sand Cat algorithm according to any one of claims 1-5.

8. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the workshop scheduling method based on the Sand Cat algorithm according to any one of claims 1-5.

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