Sand dune cat algorithm-based workshop scheduling problem solving method and system

Abstract

The invention discloses a workshop scheduling problem solving method and system based on a sand dune cat algorithm, and belongs to the technical field of production scheduling. The method comprises the following steps: constructing a multi-target flexible workshop scheduling problem model based on workshop working data and setting initial parameters; performing population initialization operation based on the optimized Tent chaotic mapping to generate an initial population, namely an initial scheduling solution; calculating the fitness value of each dune cat individual in the initial population, and performing rapid non-dominated solution sorting according to the fitness values to obtain a local optimal scheduling solution; updating the position of each dune cat individual in the initial population by adopting an optimal neighborhood perturbation strategy and a triangular migration strategy; converting the updated scheduling solution corresponding to the initial population with the updated individual position into a dune cat individual position vector based on a conversion mechanism to obtain a next generation population of the dune cat; and comparing the updated scheduling solution with a local optimal scheduling solution to obtain a current optimal scheduling solution.

Description

Technical Field

[0001] The invention belongs to the technical field of production scheduling, and relates to a method and system for solving workshop scheduling problems based on a SandCat algorithm. Background Art

[0002] As a key link in the automobile manufacturing process, the stamping workshop is responsible for stamping metal sheets into various complex automobile parts, such as body panels, structural parts, etc. through dies. The quality and production efficiency of these parts directly affect the performance, cost and market competitiveness of the whole vehicle. However, with the rapid development of the automobile industry and the increasingly fierce market competition, the high energy consumption problem of the stamping workshop has become increasingly prominent, becoming one of the important factors restricting the improvement of the economic benefits of enterprises. Traditionally, the production scheduling of stamping workshops often relies on manual experience or simple rule systems. This method is powerless in the face of complex and changing production environments, and it is difficult to achieve the optimal balance between energy consumption and production efficiency. Therefore, exploring a scientific and efficient scheduling strategy to optimize the resource allocation of stamping workshops, reduce unnecessary energy consumption, and improve production efficiency has become a technical problem that automobile manufacturers need to solve urgently. In this context, swarm intelligence optimization algorithms have gradually become a powerful tool for solving complex scheduling problems due to their powerful global search capabilities and adaptability. Dune Cat Algorithm (DCA) is a new swarm intelligence algorithm that has emerged in recent years. It simulates the behavior of sand cats in searching for food and habitats in a desert environment, and achieves optimal solution to problems through information exchange and collaboration between individuals.

[0003] However, when applied to actual scheduling problems, the DuneCat algorithm also faces the problems of being easily trapped in local optimal solutions and large randomness in population initialization, which limits its application effect in actual production environments. Summary of the invention

[0004] The purpose of the present invention is to solve the technical problems faced by the prior art Dune Cat algorithm in that it is easy to fall into local optimal solutions and the population initialization has large randomness when applied to actual scheduling problems, and to provide a method and system for solving workshop scheduling problems based on the Dune Cat algorithm.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for solving a workshop scheduling problem based on a dune cat algorithm, comprising:

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

[0008] Performing population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is an initial scheduling solution;

[0009] Calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the fitness value to obtain a local optimal scheduling solution;

[0010] The optimal neighborhood perturbation strategy and triangle wandering strategy are used to update the position of each individual sand dune cat in the initial population.

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

[0012] Starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle;

[0013] A conversion mechanism is used to convert the position vector of the optimal individual into an optimal scheduling solution to complete the solution of the workshop scheduling problem.

[0014] The present invention is further improved in that:

[0015] The multi-objective flexible workshop scheduling problem model based on workshop work data specifically includes:

[0016] Minimum maximum completion time:

[0017] f1=min{max{C i}},i=1,2,…,n (1)

[0018] The minimum total machine load is:

[0019]

[0020] Maximum machine load minimum:

[0021]

[0022] The model constraints are as follows:

[0023]

[0024] Among them, formula (4) represents the constraint relationship between the processing order of a workpiece between various processes; formula (5) represents that a machine can only process one process at a time; formula (6) represents that any process can be processed by any machine from the available equipment; 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 be processed; M represents the set of stamping machines; O ij represents the jth process of stamping part i; P ijk represents the processing time of the jth process of stamping part i on the kth stamping equipment; S ijk represents the start time of the jth process of stamping part i on the kth stamping equipment; C ijk S represents the processing completion time of the jth process of stamping part i on the kth stamping equipment; ij represents the starting processing time of the jth process of stamping part i; C ij represents the completion time of the jth process of stamping part i; x ijk Indicates whether the j-th process of stamping part i is processed on the k-th stamping equipment. If it is processed, it is 1, otherwise it is 0; C i Represents the completion time of stamping part i.

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

[0026]

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

[0028] The fast non-dominated solution sorting of the initial scheduling solution is specifically as follows:

[0029] In multi-objective optimization, the process of finding the Pareto optimal solution is accompanied by the deterioration of another solution. If at least one objective of individual pi is better than pj, and all objectives of individual pi are not worse than those of pj, then individual pi is said to dominate individual pj, otherwise individual pi cannot dominate individual pj;

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

[0031] Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue to find and assign 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 dominated numbers, and individuals with smaller dominated numbers obtain the local optimal scheduling solution.

[0033] The triangle walking strategy is specifically:

[0034] First, the distance L1 between the best prey position and the current position of the sand cat is calculated. Then, the distance L1 is used to obtain the step length range of the sand cat. The walking direction β is defined according to formula (10). P is the distance between the position obtained after the triangle walk and the prey. The calculation formula for the new position of the sand cat after update 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 disturbance strategy is specifically:

[0041] First determine the optimal position, select a neighborhood range based on the current optimal position, and then perform the perturbation operation in the selected neighborhood range; then repeat the above steps, and gradually approach the current optimal scheduling solution through continuous iterative optimization; the calculation formula is as follows:

[0042]

[0043] Here, 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, the two need to be converted; when encoding, first randomly generate a set of random numbers in a specific interval corresponding to the process sequence, and according to the ROV rule, arrange the random variables in ascending order and rearrange them corresponding to the processes. After the rearrangement, the random number sequence corresponding to the ROV value becomes the value of each element in the individual position vector.

[0046] In a second aspect, the present invention provides a system for solving a workshop scheduling problem based on a dune cat algorithm, comprising:

[0047] Model building module, which builds 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] An initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on an optimized Tent chaotic map to generate an initial population, which is an initial scheduling solution;

[0049] A local optimal scheduling solution acquisition module calculates the fitness value of each individual sand dune cat in the initial population and performs fast non-dominated solution sorting according to the size of the fitness value to obtain a local optimal scheduling solution;

[0050] The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and triangle wandering strategy to update the position of each individual sand dune 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 is updated into the individual position vector of the sand dune cat based on the conversion mechanism to obtain the next generation population of the sand dune cat; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand dune cat individual corresponding to the current optimal scheduling solution as the current optimal individual;

[0052] A loop module, which starts a loop by redistributing the next generation population of the sand dune cat based on an optimized Tent chaotic map, ends the loop when the loop reaches a preset maximum number of iterations, and selects the best individual from the current best individuals obtained in each loop;

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

[0054] In a third aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for solving the workshop scheduling problem based on the Sand Cat algorithm when executing the computer program.

[0055] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for solving the workshop scheduling problem based on the Sand Cat algorithm.

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

[0057] The invention discloses a method for solving a workshop scheduling problem based on a dune cat algorithm. The invention proposes to use an optimized Tent chaotic map to redistribute the initial state position of the population. The strategy combines the Tent chaotic map and the Logistic chaotic map, and has the characteristics of high traversability, strong deep search capability, and uniform distribution. The population is initialized by this strategy, which solves the problems of high randomness of population distribution, repeated initial values, and the algorithm being prone to premature. Secondly, a triangle wandering strategy is adopted to improve the search behavior of the dune cat. It is reflected in that the dune cat does not directly contact the prey, but increases the randomness of the individual position of the dune cat through wandering behavior, which can avoid unnecessary repeated search space, improve search efficiency, and accelerate the convergence speed of the algorithm. The optimal neighborhood perturbation strategy is adopted to improve the mobility of the dune cat and the global search capability of the algorithm. It is reflected in that the dune cat first determines the optimal position, selects a domain range based on the current optimal position, and performs perturbation operations within the range. This innovation improves the population diversity and the convergence accuracy of the algorithm. In summary, the Sand Cat Algorithm with three improved strategies overcomes the problems of large randomness of population initialization, small population diversity, slow algorithm convergence, and the algorithm is easy to fall into local optimality. When the improved Sand Cat Algorithm is applied to the stamping shop scheduling problem, the solution is significantly better than the original Sand Cat Algorithm, and is better than the Sparrow Algorithm and the Capuchin Algorithm in more than 90% of the results.

[0058] The present invention discloses a system for solving workshop scheduling problems based on the SandCat algorithm. The system aims to enhance the global search capability of the algorithm, avoid premature convergence, and improve the convergence speed and solution quality of the algorithm by introducing new initialization strategies, optimized search mechanisms, and adaptive parameter adjustment methods. In addition, according to the specific characteristics of stamping workshop scheduling, the present invention also 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. The present invention is not only an important improvement to the SandCat algorithm, but also an innovative exploration of the scheduling problem of stamping workshops in the field of automobile manufacturing, and provides new ideas and methods for solving the production bottleneck problems of high energy consumption and low efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0060] Figure 1 It is a flow chart of a method for solving a workshop scheduling problem based on the SandCat algorithm in the present invention;

[0061] Figure 2 A coding schematic diagram of a method for solving a workshop scheduling problem based on a sand cat algorithm in the present invention;

[0062] Figure 3 It is a schematic diagram of ROV rule conversion of a method for solving a shop scheduling problem based on the SandCat algorithm in the present invention;

[0063] Figure 4 It is a Gantt chart of the MK02 example of a method for solving the workshop scheduling problem based on the SandCat algorithm in the present invention;

[0064] Figure 5 It is a convergence diagram of the MK02 example of a method for solving the workshop scheduling problem based on the SandCat algorithm in the present invention; Figure 5 (a) is the maximum completion time relationship diagram; Figure 5 (b) is the total load relationship diagram; Figure 5 (c) is the relationship diagram of the minimum load of the machine;

[0065] Figure 6 It is a module schematic diagram of a system for solving the shop scheduling problem based on the SandCat algorithm in the present invention;

[0066] Figure 7 This is a module diagram of an electronic device in the present invention. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0068] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0069] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0070] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0071] See also Figure 1 The present invention discloses a method for solving a workshop scheduling problem based on a dune 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, performing a population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on an optimized Tent chaotic map to generate an initial population, which is an initial scheduling solution;

[0074] S3, calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the fitness value to obtain a local optimal scheduling solution;

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

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

[0077] S6, starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle;

[0078] S7, using a conversion mechanism to convert the position vector of the optimal individual into an optimal scheduling solution, thereby solving the workshop scheduling problem.

[0079] The invention discloses a method for solving a workshop scheduling problem based on a dune cat algorithm. The invention proposes to use an optimized Tent chaotic map to redistribute the initial state position of the population. The strategy combines the Tent chaotic map and the Logistic chaotic map, and has the characteristics of high traversability, strong deep search capability, and uniform distribution. The population is initialized by this strategy, which solves the problems of high randomness of population distribution, repeated initial values, and the algorithm being prone to premature. Secondly, a triangle wandering strategy is adopted to improve the search behavior of the dune cat. It is reflected in that the dune cat does not directly contact the prey, but increases the randomness of the individual position of the dune cat through wandering behavior, which can avoid unnecessary repeated search space, improve search efficiency, and accelerate the convergence speed of the algorithm. The optimal neighborhood perturbation strategy is adopted to improve the mobility of the dune cat and the global search capability of the algorithm. It is reflected in that the dune cat first determines the optimal position, selects a domain range based on the current optimal position, and performs perturbation operations within the range. This innovation improves the population diversity and the convergence accuracy of the algorithm. In summary, the Sand Cat Algorithm with three improved strategies overcomes the problems of large randomness of population initialization, small population diversity, slow algorithm convergence, and the algorithm is easy to fall into local optimality. When the improved Sand Cat Algorithm is applied to the stamping shop scheduling problem, the solution is significantly better than the original Sand Cat Algorithm, and is better than the Sparrow Algorithm and the Capuchin Algorithm in more than 90% of the results.

[0080] The embodiment of the present invention discloses a method for solving a workshop scheduling problem based on a sand cat algorithm. The content of the present invention is described in detail below in conjunction with specific embodiments:

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

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

[0083] Table 1 Parameter definition

[0084]

[0085] Based on this, the multi-objective flexible job shop scheduling model constructed is as follows:

[0086] Minimum maximum completion time:

[0087] f1=min{max{C i}},i=1,2,…,n(

[0088] 1) The minimum total load of the machine is:

[0089]

[0090] Maximum machine load minimum:

[0091]

[0092] The model constraints are as follows:

[0093]

[0094] Among them, formula (4) represents the constraint relationship between the processing order of a workpiece between various processes; formula (5) means that a machine can only process one process at a time; formula (6) means that any process can be processed by any machine from the available equipment;

[0095] In particular, the problem studied in the patent of this invention mainly includes two sub-problems: process sorting and machine sorting. Therefore, an equal-length double-chain real number coding method is adopted. The coding length is twice the total number of processes and the lengths of the two segments of coding are equal. Assuming that the process length is L, the coding length is 2L, the machine code and the process code are both 2L, the element value range of the individual position vector is [-3, 3], Oij represents the j-th process of workpiece i, the first L codes represent the machine codes selected for the process, and the last L codes represent the sorting of the processes. The specific method is as follows Figure 2 shown.

[0096] Step 2: performing population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is an initial scheduling solution;

[0097] The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map. The calculation formula of the optimized Tent chaotic map is as follows:

[0098]

[0099] Wherein, k=0, 1, 2, represents the number of mappings, and t represents the current number of iterations.

[0100] At the same time, for each machine allocation scheme, multiple sets of candidate schemes for process sorting are randomly generated, and these process sorting schemes are combined with machine allocation schemes one by one, and the objective function value of each combination is evaluated. By comparing the objective function values ​​of different combinations, the best combination is selected as the initial solution. This process is repeatedly applied to all generated machine allocation schemes to complete the construction of the entire initial population, ensuring population diversity and solution quality.

[0101] Step 3, calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the size of the fitness value to obtain a local optimal scheduling solution;

[0102] In multi-objective optimization, the process of finding the Pareto optimal solution is accompanied by the deterioration of another solution. If at least one objective of individual pi is better than pj, and all objectives of individual pi are not worse than those of pj, then individual pi is said to dominate individual pj, otherwise individual pi cannot dominate individual pj;

[0103] First, calculate the dominating set of each individual in the population and the number of individuals it is dominated by, i.e., the dominated number; the dominating solution set refers to the set of all individuals that are completely superior to a particular individual, while the dominated number reflects the relative superiority of the individual in the population; after identifying those individuals that are not dominated by any other individual, place them in the first layer of the non-dominated hierarchy;

[0104] Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue to find and assign new non-dominated levels until all individuals are classified into the corresponding levels;

[0105] Finally, within each non-dominated level, individuals are further sorted according to their dominated number, and individuals with smaller dominated numbers obtain the local optimal scheduling solution. Individuals with smaller dominated numbers mean that they have higher competitiveness and better solution quality in the population. This method can comprehensively and systematically evaluate the pros and cons of individuals in the population, providing strong support for subsequent decision-making and optimization.

[0106] Step 4: Use the optimal neighborhood perturbation strategy and triangle walk strategy to update the position of each individual sand dune cat in the initial population;

[0107] The learning strategy of adding triangle walk enables the algorithm to converge faster. First, the distance L1 between the best prey position and the current position of the sand cat is calculated, and then the step range of the sand cat is obtained by using the distance L1. The walking direction β is defined according to formula (10), P is the distance between the position obtained after triangle walk and the prey, and the calculation formula of the new position of the sand cat after update is as follows:

[0108] L1=pos b (t)-pos c (t) (8)

[0109]

[0110] β=2×π×rand() (10)

[0111] P=L1 2 +L2 2 -2×L1×L2×cos(β) (11)

[0112] Pos new =pos b(t)+r×P (12).

[0113] Secondly, the optimal neighborhood perturbation strategy is introduced to further improve the mobility of the sand cat and the global exploration ability of the algorithm, prevent the algorithm from falling into the local optimal solution, and moderately perturb the position of the sand cat in the global search stage. The optimal neighborhood perturbation strategy is specifically:

[0114] First determine the optimal position, select a neighborhood range based on the current optimal position, and then perform the perturbation operation in the selected neighborhood range; then repeat the above steps, and gradually approach the current optimal scheduling solution through continuous iterative optimization; the calculation formula is as follows:

[0115]

[0116] Here, t represents the number of iterations.

[0117] This disturbance can enrich the diversity of the population, improve the convergence accuracy, better escape the local optimum during the global search, find the global optimal solution, increase the convergence speed of the algorithm, and avoid premature algorithm maturation.

[0118] Step 5: Based on the conversion mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the individual position vector of the sand dune cat to obtain the next generation population of the sand dune cat; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand dune cat individual corresponding to the current optimal scheduling solution is used as the current optimal individual; the conversion mechanism is specifically:

[0119] Since the individual position is a continuous value and the scheduling solution is a discrete value, the two need to be converted; when encoding, first randomly generate a set of random numbers in a specific interval corresponding to the process sequence, and according to the ROV rule, arrange the random variables in ascending order and rearrange them corresponding to the processes. After the rearrangement, the random number sequence corresponding to the ROV value becomes the value of each element in the individual position vector.

[0120] Step 6, starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle;

[0121] Step seven, using a conversion mechanism to convert the position vector of the optimal individual into an optimal scheduling solution, thereby solving the workshop scheduling problem.

[0122] The beneficial effects of the present invention are verified as follows:

[0123] In the performance evaluation of the improved algorithm, the data obtained by solving the same example by the improved Dune Cat algorithm is compared with the original Dune Cat algorithm, the Capuchin algorithm, and the Sparrow algorithm. The IGD and HV indicators are used to measure the performance of the improved algorithm in terms of diversity and convergence. The calculation formulas of IGD and HV are as follows:

[0124] The inverse generation distance IGD is calculated as follows:

[0125]

[0126] Among them, |Ω * | is the number of elements in the Pareto frontier obtained by the algorithm, D i (Ω * ,Ω) refers to Ω * The shortest Euclidean distance between the i-th element in Ω and the element in Ω. The smaller the IGD value, the better the convergence performance of the algorithm.

[0127] Hypervolume HV, calculated as follows:

[0128]

[0129] Where δ is the Lebesgue measure. V i It represents the volume of the area enclosed by the non-dominated solution i and the reference point. The larger the HV value, the better the diversity of the algorithm.

[0130] The four algorithms are used to solve the ten examples MK01-MK10, and each is run 20 times independently. The average value is taken to obtain the data shown in Table 2.

[0131] Table 2IGD and HV

[0132]

[0133]

[0134] As can be seen from Table 2, in 10 groups of examples, 90% of the operating indicators of the improved DuneCat algorithm are better than those of other algorithms. This result strongly proves that the proposed improvement strategy can effectively improve the algorithm performance.

[0135] In addition, the optimization results of the three optimization indicators of maximum completion time, total machine load, and maximum machine load were statistically analyzed. The bold fonts in the table are the best results, as shown in Table 3, Table 4, and Table 5:

[0136] Table 3 Maximum completion time

[0137]

[0138] Table 4 Total machine load

[0139]

[0140]

[0141] Table 5 Maximum machine load result data

[0142]

[0143] As shown in the above three tables, in terms of the three optimization indicators, the results obtained by the improved SandCat algorithm on ten examples are significantly better than those of the other three algorithms.

[0144] Since the example MK02 has better results and a moderate running time than other examples, in order to analyze the performance of the improved sand cat algorithm (ISCSO) in more detail, the example MK02 is selected for in-depth discussion. Figure 4 The Gantt chart of the improved DuneCat algorithm solution example MK02 is shown. Figure 5 The convergence process of the maximum completion time under the MK02 instance is clearly shown. From the figure, it can be seen that ISCSO not only converges significantly faster, but also can obtain a better scheduling solution. This significant advantage strongly proves the feasibility and effectiveness of the ISCSO improvement strategy.

[0145] In view of the problems that the Sand Cat algorithm is prone to fall into local optimality and the population initialization has great randomness, the present invention proposes a hybrid chaotic mapping strategy in the population initialization stage, which improves the uniformity of population distribution and avoids the generation of repeated solutions; the global position of the Sand Cat is changed by adding a triangle walk strategy and an optimal field perturbation strategy, so as to accelerate the convergence speed and search efficiency of the algorithm; finally, by solving the stamping workshop examples MK01-MK10, the improved algorithm is evaluated using the two major indicators of IGD and HV, and the optimized values ​​of the maximum completion time, the total machine load and the maximum machine load are output. From a numerical point of view, the improved Sand Cat algorithm is better than the comparison algorithm, which reflects the effectiveness and superiority of the improved Sand Cat algorithm of the present invention.

[0146] See also Figure 6 The present invention provides a system for solving a workshop scheduling problem based on a dune cat algorithm, comprising:

[0147] Model building module, which builds 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] An initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on an optimized Tent chaotic map to generate an initial population, which is an initial scheduling solution;

[0149] A local optimal scheduling solution acquisition module calculates the fitness value of each individual sand dune cat in the initial population and performs fast non-dominated solution sorting according to the size of the fitness value to obtain a local optimal scheduling solution;

[0150] The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and triangle wandering strategy to update the position of each individual sand dune 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 is updated into the individual position vector of the sand dune cat based on the conversion mechanism to obtain the next generation population of the sand dune cat; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand dune cat individual corresponding to the current optimal scheduling solution as the current optimal individual;

[0152] A loop module, which starts a loop by redistributing the next generation population of the sand dune cat based on an optimized Tent chaotic map, ends the loop when the loop reaches a preset maximum number of iterations, and selects the best individual from the current best individuals obtained in each loop;

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

[0154] The present invention discloses a system for solving workshop scheduling problems based on the SandCat algorithm. The system aims to enhance the global search capability of the algorithm, avoid premature convergence, and improve the convergence speed and solution quality of the algorithm by introducing new initialization strategies, optimized search mechanisms, and adaptive parameter adjustment methods. In addition, according to the specific characteristics of stamping workshop scheduling, the present invention also 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. The present invention is not only an important improvement to the SandCat algorithm, but also an innovative exploration of the scheduling problem of stamping workshops in the field of automobile manufacturing, and provides new ideas and methods for solving the production bottleneck problems of high energy consumption and low efficiency.

[0155] See also Figure 7 The third object of the present invention is to provide an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method for solving the workshop scheduling problem based on the Sand Cat algorithm are implemented.

[0156] The method for solving the workshop scheduling problem based on the SandCat algorithm comprises the following steps:

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

[0158] Performing population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is an initial scheduling solution;

[0159] Calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the fitness value to obtain a local optimal scheduling solution;

[0160] The optimal neighborhood perturbation strategy and triangle wandering strategy are used to update the position of each individual sand dune cat in the initial population.

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

[0162] Starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle;

[0163] A conversion mechanism is used to convert the position vector of the optimal individual into an optimal scheduling solution to complete the solution of the workshop scheduling problem.

[0164] The fourth object of the present invention is to provide a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for solving the workshop scheduling problem based on the Sand Cat algorithm are implemented.

[0165] The method for solving the workshop scheduling problem based on the SandCat algorithm comprises the following steps:

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

[0167] Performing population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is an initial scheduling solution;

[0168] Calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the fitness value to obtain a local optimal scheduling solution;

[0169] The optimal neighborhood perturbation strategy and triangle wandering strategy are used to update the position of each individual sand dune cat in the initial population.

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

[0171] Starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle;

[0172] A conversion mechanism is used to convert the position vector of the optimal individual into an optimal scheduling solution to complete the solution of the workshop scheduling problem.

[0173] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented 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] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0175] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0176] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0177] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for solving the workshop scheduling problem based on the SandCat algorithm, characterized in that: include: A multi-objective flexible workshop scheduling problem model is constructed based on the workshop work data and initial parameters are set, including the population size and the maximum number of iterations; Performing population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on optimized Tent chaotic mapping to generate an initial population, which is an initial scheduling solution; Calculating the fitness value of each individual sand dune cat in the initial population and performing fast non-dominated solution sorting according to the fitness value to obtain a local optimal scheduling solution; The optimal neighborhood perturbation strategy and triangle wandering strategy are used to update the position of each individual sand dune cat in the initial population. Based on the conversion mechanism, the updated scheduling solution corresponding to the initial population after the individual position is updated is converted into the individual position vector of the sand dune cat to obtain the next generation population of the sand dune cat; the updated scheduling solution is compared with the local optimal scheduling solution to obtain the current optimal scheduling solution, and the sand dune cat individual corresponding to the current optimal scheduling solution is used as the current optimal individual; Starting a cycle by redistributing the next generation population of the sand dune cat based on the optimized Tent chaotic map, ending the cycle when the cycle reaches a preset maximum number of iterations, and selecting the best individual from the current best individuals obtained in each cycle; A conversion mechanism is used to convert the position vector of the optimal individual into an optimal scheduling solution to complete the solution of the workshop scheduling problem.

2. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 1 is characterized in that: The multi-objective flexible workshop scheduling problem model based on workshop work data specifically includes: Minimum maximum completion time: f1=min{max{C i }},i=1,2,…,n (1) The minimum total machine load is: Maximum machine load minimum: The model constraints are as follows: Among them, formula (4) represents the constraint relationship between the processing order of a workpiece between various processes; formula (5) represents that a machine can only process one process at a time; formula (6) represents that any process can be processed by any machine from the available equipment; 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 be processed; M represents the set of stamping machines; O ij represents the jth process of stamping part i; P ijk represents the processing time of the jth process of stamping part i on the kth stamping equipment; S ijk represents the start time of the jth process of stamping part i on the kth stamping equipment; C ijk S represents the processing completion time of the jth process of stamping part i on the kth stamping equipment; ij represents the starting processing time of the jth process of stamping part i; C ij represents the completion time of the jth process of stamping part i; x ijk Indicates whether the j-th process of stamping part i is processed on the k-th stamping equipment. If it is processed, it is 1, otherwise it is 0; C i Represents the completion time of stamping part i.

3. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 2 is characterized in that: The optimized Tent chaotic map is a combination of the Tent chaotic map and the Logistic chaotic map. The calculation formula of the optimized Tent chaotic map is as follows: Wherein, k=0, 1, 2, represents the number of mappings, and t represents the current number of iterations.

4. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 2 is characterized in that: The fast non-dominated solution sorting of the initial scheduling solution is specifically as follows: In multi-objective optimization, the process of finding the Pareto optimal solution is accompanied by the deterioration of another solution. If at least one objective of individual pi is better than pj, and all objectives of individual pi are not worse than those of pj, then individual pi is said to dominate individual pj, otherwise individual pi cannot dominate individual pj; First, calculate the dominating set of each individual in the population and the number of individuals it is dominated by, i.e., the dominated number; the dominating solution set refers to the set of all individuals that are completely superior to a particular individual, while the dominated number reflects the relative superiority of the individual in the population; after identifying those individuals that are not dominated by any other individual, place them in the first layer of the non-dominated hierarchy; Subsequently, these classified individuals are removed from the population, and the above process is repeated to continue to find and assign 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 dominated numbers, and individuals with smaller dominated numbers obtain the local optimal scheduling solution.

5. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 2 is characterized in that: The triangle walking strategy is specifically: First, the distance L1 between the best prey position and the current position of the sand cat is calculated. Then, the distance L1 is used to obtain the step length range of the sand cat. The walking direction β is defined according to formula (10). P is the distance between the position obtained after the triangle walk and the prey. The calculation formula for the new position of the sand cat after update 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)。 6. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 2 is characterized in that: The optimal neighborhood disturbance strategy is specifically: First determine the optimal position, select a neighborhood range based on the current optimal position, and then perform the perturbation operation in the selected neighborhood range; then repeat the above steps, and gradually approach the current optimal scheduling solution through continuous iterative optimization; the calculation formula is as follows: Here, t represents the number of iterations.

7. The method for solving the workshop scheduling problem based on the SandCat algorithm according to claim 2 is 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, the two need to be converted; when encoding, first randomly generate a set of random numbers in a specific interval corresponding to the process sequence, and according to the ROV rule, arrange the random variables in ascending order and rearrange them corresponding to the processes. After the rearrangement, the random number sequence corresponding to the ROV value becomes the value of each element in the individual position vector.

8. A system for solving workshop scheduling problems based on the SandCat algorithm, characterized in that: include: Model building module, which builds 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; An initial scheduling solution acquisition module performs a population initialization operation on the multi-objective flexible stamping shop scheduling problem model based on an optimized Tent chaotic map to generate an initial population, which is an initial scheduling solution; A local optimal scheduling solution acquisition module calculates the fitness value of each individual sand dune cat in the initial population and performs fast non-dominated solution sorting according to the size of the fitness value to obtain a local optimal scheduling solution; The current optimal scheduling solution acquisition module uses the optimal neighborhood perturbation strategy and triangle wandering strategy to update the position of each individual sand dune 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 is updated into the individual position vector of the sand dune cat based on the conversion mechanism to obtain the next generation population of the sand dune cat; compares the updated scheduling solution with the local optimal scheduling solution to obtain the current optimal scheduling solution, and takes the sand dune cat individual corresponding to the current optimal scheduling solution as the current optimal individual; A loop module, which starts a loop by redistributing the next generation population of the sand dune cat based on an optimized Tent chaotic map, ends the loop when the loop reaches a preset maximum number of iterations, and selects the best individual from the current best individuals obtained in each loop; The optimal scheduling solution acquisition module uses a conversion mechanism to convert the position vector of the optimal individual into an optimal scheduling solution to solve the workshop scheduling problem.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for solving the workshop scheduling problem based on the SandCat algorithm as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for solving the shop scheduling problem based on the SandCat algorithm according to any one of claims 1 to 7.

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