Digital workshop scheduling method and system based on PSC-IGA algorithm and storage medium

Abstract

The embodiment of the application provides a digital workshop scheduling method and system based on a PSC-IGA algorithm and a storage medium, and belongs to the technical field of digital workshop scheduling. Through the technical scheme, the digital workshop scheduling method and system based on the PSC-IGA algorithm and the storage medium provided by the application adopt the PSC-IGA algorithm (Polychromatic Sets Constraints of improved Genetic Algorithm, genetic algorithm based on polychromatic set constraints), solve the distribution problem of the digital workshop station through the improved genetic algorithm first, determine the distribution scheme with the highest distribution efficiency, establish a two-layer Boolean enclosure matrix based on the determined distribution scheme and the distribution characteristics of the inventory and the station of the digital workshop, and finally further solve the established model by using the improved genetic algorithm, so that the best warehouse integration scheme is quickly and efficiently obtained, and the production efficiency is improved, and the convergence speed of the algorithm is also improved.

Description

Technical Field

[0001] This invention relates to the field of scheduling technology for digital workshops, and more specifically to a digital workshop scheduling method, system, and storage medium based on the PSC-IGA algorithm. Background Technology

[0002] The construction of a digital workshop (DS) is the starting point for manufacturing enterprises to move towards intelligent manufacturing. Digital workshops typically adopt assembly line production, and the corresponding production logistics mainly involves material distribution and warehousing. This article takes the digital workshop of Anhui Boyi Fluid Transmission Co., Ltd. (hereinafter referred to as BY) as an example. Each workstation on the production line is responsible for different processes, and the material requirements are also different. Timely delivery of materials is particularly important. If it is too early, it will occupy the space along the line and cause congestion; if it is too late, it will delay working hours and reduce efficiency. Timely delivery of materials also depends on the cooperation of the automated warehouse inside the workshop. If materials are not matched with timely entry and exit from the warehouse, the task of timely delivery within the time window cannot be completed, which will affect the entire production process.

[0003] In recent years, experts and scholars have conducted extensive research in these two areas. In material distribution, research mainly focuses on the problem of delivery route optimization. The vehicle routing problem (VRP) has a long history, and since the 1960s, many variations have emerged. The material distribution route optimization problem is a classic variation of the VRP problem. Gao et al. considered vehicle load balancing and used a hybrid multi-objective evolutionary algorithm to effectively reduce the total travel distance of material distribution; Chen Guangsheng et al. studied this problem with delivery time and the number of workers as optimization objectives. None of the above literature considered the influence of time windows. The vehicle routing problem with time window (VRPTW) was proposed by Solomon in 1979. Scholars have constructed many different VRPTW optimization models, such as the vehicle routing optimization model with hybrid time windows, the vehicle routing optimization model with soft time windows, and the vehicle routing optimization model with simultaneous pickup and delivery with time windows. Regarding material storage issues, digital workshops are generally equipped with automated storage and retrieval systems (AS / RS). There is also considerable research on automated storage and retrieval systems (AS / RS). Boysen conducted a review and analysis of AS / RS systems, Deng Aimin et al. used genetic algorithms to solve multi-objective location optimization problems, Li Pengfei et al. and Jin Meng et al. also established multi-objective optimization models. The former considered inbound / outbound efficiency and shelf stability, using a virus-cooperative genetic algorithm, while the latter considered material turnover rate and correlation, using a Pareto-based hold-and simulated annealing algorithm. Liu Chenqi et al. proposed an improved ant colony algorithm for location picking path optimization. All of the above literature has done extensive work on material distribution optimization and AS / RS optimization, but rarely considers the coordination of warehousing and distribution, i.e., the issue of integration.

[0004] Existing literature primarily analyzes the characteristics of integrated warehousing and distribution models, continuously proposing new development ideas using algorithms and big data. However, overall, there is still a lack of systematic theoretical support, and the focus is mainly on warehousing and distribution issues in the e-commerce sector. Currently, there is limited research on integrated warehousing and distribution in manufacturing logistics. Manufacturing logistics differs significantly from e-commerce logistics, and integrated warehousing and distribution solutions for e-commerce logistics are not entirely applicable to manufacturing logistics. Therefore, the integrated warehousing and distribution problem in manufacturing logistics requires further research. In the production process, ensuring production is paramount, and the warehousing and distribution of production materials are key factors, inseparable from each other. Optimizing only one aspect is insufficient. Summary of the Invention

[0005] The purpose of this invention is to provide a digital workshop scheduling method, system, and storage medium based on the PSC-IGA algorithm. This method, system, and storage medium can efficiently determine the scheduling scheme of the digital workshop, thereby improving the work efficiency of the digital workshop.

[0006] To achieve the above objectives, embodiments of the present invention provide a digital workshop scheduling method based on the PSC-IGA algorithm, the method comprising:

[0007] Obtain the workstations in the digital workshop and their corresponding material requirements;

[0008] Multiple chromosomes are randomly generated to complete the delivery tasks at each workstation, forming the initial first population;

[0009] A genetic algorithm is used to iteratively update the first population to obtain a delivery plan;

[0010] The workstations and storage areas of the digital workshop are coded according to the delivery plan and based on a Boolean matrix to form a second group;

[0011] Calculate the fitness of each individual in the second population;

[0012] Determine if the iteration count k satisfies the termination condition;

[0013] If the iteration count k does not meet the termination condition, let the number of individuals m = 0;

[0014] Select the individual with the highest fitness from the second population and put it into the third population p(k+1), and update the number of individuals m = m+1;

[0015] Randomly select the two individuals with the highest fitness from the second population;

[0016] Calculate the crossover probability between the two individuals;

[0017] Determine whether the crossover probability is greater than a preset first probability value;

[0018] If the crossover probability is determined to be greater than the first probability value, a single-point crossover operation is performed on the two individuals.

[0019] Calculate the mutation probability of the two individuals after a single-point crossover operation;

[0020] Determine whether the mutation probability is greater than a preset second probability value;

[0021] If the crossover probability is determined to be greater than the second probability value, a basic bit mutation operation is performed on the two individuals;

[0022] The two individuals after the basic bit mutation operation are placed into the third population p(k+1), and the number of individuals m = m+2 is updated.

[0023] Determine whether the number of individuals m is less than the preset population capacity;

[0024] If the number of individuals m is determined to be less than the population capacity, the two individuals with the highest fitness are randomly selected from the second population again, and the corresponding steps of the method are executed until the number of individuals m is greater than or equal to the population capacity.

[0025] If the number of individuals m is greater than or equal to the population capacity, the iteration count k is updated, and it is checked again whether the iteration count k meets the termination condition. The corresponding steps of the method are then executed until the iteration count k meets the termination condition.

[0026] If the iteration number k satisfies the termination condition, calculate the fitness of each individual in each of the third population p(k+1);

[0027] The individual with the highest fitness is selected as the final assignment result.

[0028] Optionally, the random generation of multiple chromosomes to complete the delivery task at each workstation to form the initial first population specifically includes:

[0029] The initial position of the delivery vehicle in the digital workshop is represented by the number 0;

[0030] Each workstation is represented by a number from 1 to z, where z is the number of workstations;

[0031] Determine the number of delivery vehicles.

[0032] Optionally, the step of iteratively updating the first population using a genetic algorithm to obtain a delivery plan specifically includes:

[0033] Calculate the fitness of each chromosome;

[0034] The two chromosomes with the highest fitness in the first population are selected using a roulette wheel selection method.

[0035] Perform crossover and mutation operations on the two selected chromosomes;

[0036] Determine whether the first population satisfies the preset iteration termination condition;

[0037] If the first population satisfies the iteration termination condition, the first population is used as the delivery scheme; if the first population does not satisfy the iteration termination condition, the fitness of each chromosome is recalculated, and the corresponding steps of the method are executed until the first population satisfies the iteration termination condition.

[0038] Optionally, calculating the fitness of each chromosome specifically includes:

[0039] The fitness of each chromosome is calculated according to formula (1).

[0040]

[0041] Where F1 is the fitness of the chromosome, m is the total number of workstations i, and T i For the delivery time of workstation i, y ik y is a variable used to indicate whether workstation i is delivered by delivery tool k. ik =1 indicates that workstation i is delivered by delivery tool k, y ik =0 indicates that workstation i was not delivered by delivery tool k, T w For the cleaning time of the material, z i z is a variable used to indicate whether a material needs to be cleaned. i =1 indicates that the material needs to be cleaned, z i =0 indicates that the material does not need to be cleaned, T ij x is the time it takes for the delivery vehicle to travel from workstation i to workstation j. ijk Let x be a variable used to indicate whether delivery tool k moves from workstation i to workstation j. ijk =1 indicates that the delivery tool k moves from workstation i to workstation j, x ijk =0 indicates that the delivery tool k did not move from workstation i to workstation j, s i Let i be the unloading time at workstation i. Penalty time for deliveries that do not fall within the service time window.

[0042] Optionally, the step of encoding the workstations and warehouse areas of the digital workshop according to the delivery scheme and based on a Boolean matrix to form a second group specifically includes:

[0043] A first-level matrix is ​​established with the workstations as column vectors and the required materials as row vectors, wherein the elements in the first-level matrix are used to indicate whether the workstation needs to deliver the materials;

[0044] A second-level matrix is ​​established, with the material as the row vector and the storage area containing the material as the column vector. The elements in the second-level matrix indicate whether the storage area contains the material.

[0045] Multiple individuals are randomly generated based on the first-layer matrix and the second-layer matrix to form the second population.

[0046] Optionally, calculating the fitness of each individual in the second population specifically includes:

[0047] The fitness of each individual is calculated according to formulas (2) to (6).

[0048] F2=1 / {(0.5f1′+1)+(0.5f2′+1)}, (2)

[0049] f'=(ff min ) / (f max -f min (3)

[0050]

[0051]

[0052]

[0053] Where F2 is the fitness function for each individual, f' is the dimensionless function, and f' is the fitness function for each individual. min Let f be the minimum value of the function f. max Let f be the maximum value of function f, f1′ and f2′ be the dimensionless values ​​of f1 and f2 respectively, r be the location number, n be the number of the locations, V1 be the horizontal speed of the stacker crane, P be the traction power of the stacker crane, and b be the maximum value of function f. r This represents the storage location r in column b, where L is the width of each storage location, M is the mass of the material, g is the acceleration due to gravity, and a r Let r represent the storage location at level a, H be the height of the storage location, V2 be the vertical speed of the stacker crane, m be the total number of workstations i, and T be the total number of workstations i. i For the delivery time of workstation i, y ik y is a variable used to indicate whether workstation i is delivered by delivery tool k. ik =1 indicates that workstation i is delivered by delivery tool k, y ik =0 indicates that workstation i was not delivered by delivery tool k, T w For the cleaning time of the material, z i z is a variable used to indicate whether a material needs to be cleaned. i =1 indicates that the material needs to be cleaned, z i =0 indicates that the material does not need to be cleaned, T ij x is the time it takes for the delivery vehicle to travel from workstation i to workstation j. ijk Let x be a variable used to indicate whether delivery tool k moves from workstation i to workstation j. ijk=1 indicates that the delivery tool k moves from workstation i to workstation j, x ijk =0 indicates that the delivery tool k did not move from workstation i to workstation j, s i Let i be the unloading time at workstation i. Penalty time for deliveries that do not fall within the service time window.

[0054] Optionally, calculating the crossover probability between the two individuals specifically includes:

[0055] The crossover probability is calculated according to formula (7).

[0056]

[0057] Where c is the crossover probability, c1 and c2 are preset constants, and F 2max F1 is the maximum fitness value in the second population, and F2′ is the larger fitness value between the two individuals. 2avg This represents the average fitness of the second population.

[0058] Optionally, calculating the mutation probability of the two individuals after a single-point crossover operation specifically includes:

[0059] The mutation probability is calculated according to formula (8).

[0060]

[0061] Where d is the mutation probability, d1 and d2 are preset constants, and F 2max F represents the maximum fitness value in the second population. 2avg F1 is the average fitness of the second population, and F2″ is the larger fitness value among the two individuals.

[0062] On the other hand, the present invention also provides a digital workshop scheduling system based on the PSC-IGA algorithm, the scheduling system including a processor for executing any of the methods described above.

[0063] In another aspect, the present invention also provides a storage medium storing instructions for being read by a machine to cause the machine to perform any of the methods described above.

[0064] Through the above technical solution, the digital workshop scheduling method, system, and storage medium based on the PSC-IGA algorithm provided by this invention first solves the delivery problem of digital workshop workstations using the improved genetic algorithm to determine the delivery scheme with the highest delivery efficiency. Then, based on the determined delivery scheme and the distribution characteristics of inventory and workstations in the digital workshop, a two-layer Boolean enclosing matrix is ​​established. Finally, the improved genetic algorithm is used to solve the established model, quickly and efficiently obtaining the optimal integrated warehouse scheme, which improves production efficiency and the convergence speed of the algorithm.

[0065] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0066] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0067] Figure 1 This is a flowchart of a digital workshop scheduling method based on the PSC-IGA algorithm according to an embodiment of the present invention;

[0068] Figure 2 This is a schematic diagram of an encoding rule according to an embodiment of the present invention;

[0069] Figure 3 This is a flowchart of a genetic algorithm according to one embodiment of the present invention;

[0070] Figure 4 This is a schematic diagram of crossover and mutation operations according to one embodiment of the present invention;

[0071] Figure 5 This is a trend graph showing the changes in the population mean and the optimal solution when the number of delivery vehicles is 1.

[0072] Figure 6 This is a trend graph showing the changes in the population mean and the optimal solution when the number of delivery vehicles is 1.

[0073] Figure 7 This is a trend graph showing the changes in the population mean and the optimal solution when the number of delivery vehicles is 1; and

[0074] Figure 8This is a trend graph showing the changes in the population mean and the optimal solution obtained by the model according to one embodiment of the present invention. Detailed Implementation

[0075] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0076] In embodiments of the present invention, unless otherwise stated, directional terms such as "upper," "lower," "top," and "bottom" are generally used to describe the relative positional relationships of components in relation to the directions shown in the accompanying drawings or in relation to the vertical, perpendicular, or gravitational directions.

[0077] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0078] like Figure 1 The diagram shows a flowchart of a digital workshop scheduling method based on the PSC-IGA algorithm according to an embodiment of the present invention. Figure 1 In this context, the method may include:

[0079] In step S10, the workstations in the digital workshop and their corresponding material requirements are obtained. Specifically, the workstation and its corresponding material requirements may include the workstation's location, number, and the type of materials that need to be delivered to each workstation.

[0080] In step S11, multiple chromosomes are randomly generated to complete the delivery tasks at each workstation, forming an initial first population. In this embodiment, considering the facilities of a digital workshop, the delivery vehicles need to start from their initial parking position, deliver materials to each workstation, and then return to their initial parking position. Therefore, the initial position of the delivery vehicle in the digital workshop can be represented by the number 0; each workstation can be represented by numbers 1 to z, where z is the number of workstations; finally, the number of delivery vehicles is determined. Based on the above encoding method, a chromosome of the form (0, 3, 5, 0, 8, 7, 2, 0, 1, 4, 6, 0) can be formed. In the chromosome shown in this embodiment, three delivery vehicles execute path 1 (0, 3, 5, 0), path 2 (0, 8, 7, 2, 0), and path 3 (0, 1, 4, 6, 0), respectively, as follows. Figure 2 As shown.

[0081] In this embodiment, further considering that many individuals in the randomly generated chromosomes may not meet the requirements of the actual site, constraints can be pre-set to screen the randomly generated chromosomes before random generation. This can reduce the number of iterations of the algorithm and thus improve the efficiency of the algorithm. Regarding the specific form of these constraints, in a preferred example of this invention, the inventors have designed constraints for the environmental conditions of the digital workshop site as shown in formulas (1) to (5).

[0082] ∑ k y ik =1, (1)

[0083]

[0084]

[0085]

[0086] A i ≤t i ≤B i (5)

[0087] Where i = 1, 2, ..., m; k = 1, 2, ..., q. i is the workstation number, m is the number of workstations, k is the delivery tool number, and q is the number of workstations.

[0088] For formula (1), y ik Let y be a variable used to indicate whether workstation i is delivered by delivery tool k. ik =1 indicates that workstation i is delivered by delivery tool k. ik=0 indicates that workstation i is not delivered by delivery vehicle k. Formula (1) is used to indicate that the material corresponding to workstation i can only be delivered by one delivery vehicle.

[0089] For formulas (2) and (3), x i0k This indicates that the delivery tool k moves from its initial position to workstation i, x 0jk This indicates that the delivery vehicle k moves from workstation j to its initial position. Formulas (2) and (3) are used to indicate that each delivery vehicle performs a transportation task on only one path.

[0090] For formulas (4) and (5), A i B is the earliest time that workstation i receives materials. i Let C be the latest time that workstation i receives materials, and D be the earliest time that A receives materials. i and the latest time to receive materials B i The preset constant. Through this formula (4), a penalty time can be set based on the relationship between the time when the delivery tool k arrives at workstation i and the actual assembly time of workstation i, thereby realizing the evaluation of the delivery time of the delivery tool k. Formula (5) can be used to indicate that the point at which the material arrives at the workstation needs to be within the time window of that workstation, i.e., A i and B i between.

[0091] In step S12, a genetic algorithm is used to iteratively update the first population to obtain a delivery plan. Specifically, the genetic algorithm may include, for example: Figure 3 The steps are shown in the diagram. Figure 3 In this context, the genetic algorithm may include:

[0092] In step S40, the fitness of each chromosome is calculated. The calculation of fitness can take various forms known to those skilled in the art. In a preferred embodiment of the invention, the inventors consider that the standard for evaluating the quality of the generated chromosome is primarily the time it takes for the delivery vehicle to complete the delivery task according to the delivery method corresponding to that chromosome. Therefore, the time to complete the delivery task can be used as the calculation of fitness, i.e., formula (6).

[0093]

[0094] Where minF is the time to complete the delivery task, F1 is the chromosome fitness, m is the total number of workstations i, and T i For the delivery time of workstation i, y ik y is a variable used to indicate whether workstation i is delivered by delivery tool k. ik =1 indicates that workstation i is delivered by delivery tool k, y ik =0 indicates that workstation i was not delivered by delivery tool k, Tw For the cleaning time of the material, z i z is a variable used to indicate whether a material needs to be cleaned. i =1 indicates that the material needs to be cleaned, z i =0 indicates that the material does not need to be cleaned, T ij x is the time it takes for the delivery vehicle to travel from workstation i to workstation j. ijk Let x be a variable used to indicate whether delivery tool k moves from workstation i to workstation j. ijk =1 indicates that the delivery tool k moves from workstation i to workstation j, x ijk =0 indicates that the delivery tool k did not move from workstation i to workstation j, s i Let i be the unloading time at workstation i. Penalty time for deliveries that do not fall within the service time window.

[0095] However, during subsequent calculations, the inventors discovered that directly using this time as the fitness calculation would lead to data overflow, resulting in low algorithm execution efficiency. Therefore, the inventors designed a fitness function as shown in formula (7).

[0096]

[0097] In step S41, a roulette wheel selection method is used to select the two chromosomes with the highest fitness in the first population. Specifically, this roulette wheel selection method can be achieved by first arranging the chromosomes in ascending order of fitness, and then using the fitness value as the probability of each chromosome being selected.

[0098] In step S42, crossover and mutation operations are performed on the selected two chromosomes. These crossover and mutation operations can take many forms known to those skilled in the art. In a preferred embodiment of the invention, considering the poor diversity produced by traditional crossover and mutation operations, and the need for multiple iterations to obtain a suitable chromosome during actual device computation, the inventors designed the following... Figure 4 The crossover and mutation operations are shown. Figure 4 In this process, the gene values ​​on both sides of the non-first and last positions 0 of the two selected chromosomes can be swapped first; then the swapped chromosomes can be legalized according to the preset constraints; next, the two legalized chromosomes can be subjected to sub-path rotation and transposition operations; finally, a second legalization operation can be performed.

[0099] In step S43, it is determined whether the first group satisfies a preset iteration termination condition. Specifically, the iteration termination condition may be, for example, determining whether it is less than a preset number of iterations. If it is less than the preset number of iterations, the condition is satisfied; otherwise, it is not satisfied. The number of iterations may be, for example, 200.

[0100] In step S44, if the first group satisfies the iteration termination condition, the first group is taken as the delivery scheme.

[0101] If the first population does not meet the iteration termination condition, the fitness of each chromosome is recalculated and the corresponding steps of the method are executed until the first population meets the iteration termination condition, i.e., the process returns to step S41.

[0102] In step S13, the workstations and warehouse areas of the digital workshop are encoded according to the delivery plan and based on a Boolean matrix to form a second group. In this embodiment, the inventors considered the characteristics of the actual digital workshop's workstation and warehouse layout and used a two-layer matrix approach for encoding. Specifically, in the first layer, the inventors established a first-layer matrix with workstations as column vectors and required materials as row vectors. The elements in the first-layer matrix are used to indicate whether the workstation needs material delivery. As shown in formula (8),

[0103]

[0104] In the second layer, a matrix can be constructed using materials as row vectors and storage areas as column vectors. The elements in the second-layer matrix indicate whether a storage area contains materials. The constructed second-layer matrix can be as shown in formula (9).

[0105]

[0106] Finally, multiple individuals are randomly generated based on the first-level and second-level matrices to form a second population. For example, as shown in Table 1...

[0107] Table 1

[0108]

[0109] In step S14, the fitness of each individual in the second population is calculated. The calculation of this fitness can take many forms known to those skilled in the art. In this embodiment, the specific method can be, for example, calculating the fitness of each individual according to formulas (10) to (14).

[0110] F2=1 / {(0.5f1′+1)+(0.5f2′+1)}, (10)

[0111] f'=(ff min ) / (fmax -f min (11)

[0112]

[0113]

[0114]

[0115] Where F2 is the fitness function for each individual, and f' is the dimensionless function. min Let f be the minimum value of the function f. max Let f be the maximum value of function f, f1′ and f2′ be the dimensionless values ​​of f1 and f2 respectively, r be the warehouse location number, n be the number of warehouse locations, V1 be the horizontal speed of the stacker crane, P be the traction power of the stacker crane, and b be the maximum value of function f. r This represents the storage location r in column b, where L is the width of each storage location, M is the mass of the material, g is the acceleration due to gravity, and a r Let r represent the storage location at level a, H be the height of the storage location, V2 be the vertical speed of the stacker crane, m be the total number of workstations i, and T be the total number of workstations i. i For the delivery time of workstation i, y ik y is a variable used to indicate whether workstation i is delivered by delivery tool k. ik =1 indicates that workstation i is delivered by delivery tool k, y ik =0 indicates that workstation i was not delivered by delivery tool k, T w For the cleaning time of the material, z i z is a variable used to indicate whether a material needs to be cleaned. i =1 indicates that the material needs to be cleaned, z i =0 indicates that the material does not need to be cleaned, T ij x is the time it takes for the delivery vehicle to travel from workstation i to workstation j. ijk Let x be a variable used to indicate whether delivery tool k moves from workstation i to workstation j. ijk =1 indicates that the delivery tool k moves from workstation i to workstation j, x ijk =0 indicates that the delivery tool k did not move from workstation i to workstation j, s i Let i be the unloading time at workstation i. Penalty time for deliveries that do not fall within the service time window.

[0116] In step S15, it is determined whether the iteration count k satisfies the termination condition. Specifically, the iteration termination condition can be, for example, whether it is less than a preset iteration count. If it is less than the preset iteration count, the condition is satisfied; otherwise, it is not satisfied. The iteration count can be, for example, 500 times.

[0117] In step S16, if the iteration number k does not meet the termination condition, the number of individuals m is set to 0.

[0118] In step S17, the individual with the highest fitness is selected from the second population and placed into the third population p(k+1), and the number of individuals m = m+1 is updated.

[0119] In step S18, the two individuals with the highest fitness are randomly selected from the second population.

[0120] In step S19, the crossover probability between the two individuals is calculated. Specifically, this crossover probability can be calculated according to formula (15).

[0121]

[0122] Where c is the crossover probability, c1 and c2 are preset constants, and F 2max F1 represents the maximum fitness value in the second population, and F2′ represents the larger fitness value between the two individuals. 2avg This represents the average fitness of the second population.

[0123] In step S20, it is determined whether the crossover probability is greater than a preset first probability value.

[0124] In step S21, if the crossover probability is greater than the first probability value, a single-point crossover operation is performed on the two individuals.

[0125] In step S22, the mutation probability of the two individuals after the single-point crossover operation is calculated. Specifically, this mutation probability can be calculated according to formula (16).

[0126]

[0127] Where d is the mutation probability, d1 and d2 are preset constants, and F 2max F represents the maximum fitness value in the second population. 2avg F2″ represents the average fitness of the second population, and F2″ represents the larger fitness value between the two individuals.

[0128] In step S23, it is determined whether the mutation probability is greater than a preset second probability value.

[0129] In step S24, if the crossover probability is determined to be greater than the second probability value, a basic bit mutation operation is performed on the two individuals.

[0130] In step S25, the two individuals after the basic bit mutation operation are placed into the third population p(k+1), and the number of individuals m = m+2 is updated.

[0131] In step S26, it is determined whether the number of individuals m is less than the preset population capacity.

[0132] If the number of individuals m is less than the population capacity, the two individuals with the highest fitness are randomly selected from the second population again, and the corresponding steps of the method are executed, i.e., return to step S18, until the number of individuals m is greater than or equal to the population capacity.

[0133] In step S27, if the number of individuals m is greater than or equal to the population capacity, the iteration count k is updated, the iteration count k is checked again to see if the termination condition is met, and the corresponding steps of the method are executed, i.e., the process returns to step S15 until the iteration count k meets the termination condition.

[0134] In step S28, if the iteration number k satisfies the termination condition, the fitness of each individual in each third population p(k+1) is calculated.

[0135] In this embodiment, the inventors discovered that although the encoding rules set in step S13 can adapt to the special conditions of workstations and storage locations in a digital workshop, each encoded individual is in matrix form, resulting in a large memory footprint for a single individual. During iteration and calculation, as the number of generated individuals increases, the memory usage also increases, leading to excessive system memory consumption. To address this technical problem, the inventors adopted a method of setting a third population p(k+1). After generating a certain number of individuals (population capacity) in each iteration, the generated portion is grouped into a third population and stored, and a new third population is established, thereby releasing memory.

[0136] In step S29, the individual with the highest fitness is selected as the final assignment result.

[0137] On the other hand, the present invention also provides a digital workshop scheduling system based on the PSC-IGA algorithm, which may include a processor that can be used to execute any of the methods described above.

[0138] In another aspect, the present invention also provides a storage medium that can store instructions that can be read by a machine to cause the machine to perform any of the methods described above.

[0139] Through the above technical solution, the digital workshop scheduling method, system, and storage medium based on the PSC-IGA algorithm provided by this invention first solves the delivery problem of digital workshop workstations using the improved genetic algorithm to determine the delivery scheme with the highest delivery efficiency. Then, based on the determined delivery scheme and the distribution characteristics of inventory and workstations in the digital workshop, a two-layer Boolean enclosing matrix is ​​established. Finally, the improved genetic algorithm is used to solve the established model, quickly and efficiently obtaining the optimal integrated warehouse scheme, which improves production efficiency and the convergence speed of the algorithm.

[0140] In one embodiment of the present invention, the method provided by the present invention can be applied to a BY digital workshop. Based on on-site investigation, it is known that the digital workshop includes one automated warehouse, eight workstations, and a cleaning time T. w The loading time is fixed at 1 minute, the unloading time is negligible, and the unloading time is s. i The time limit is fixed at 1.5 minutes. The early arrival penalty factor C for delivery vehicles arriving at the workstation early is 60 minutes, and the late arrival penalty factor D is 90 minutes. Specific workstation information can be found in Table 2.

[0141] Table 2

[0142]

[0143] Adopting such Figure 1 The method shown is based on the above data, with the genetic algorithm parameters set as follows: initial population size of 50, crossover probability of 0.9, and mutation probability of 0.1. The number of iterations and the optimal solution change as the number of delivery vehicles is 1, 2, and 3, respectively, as shown below. Figures 5 to 7 As shown.

[0144] Figures 5 to 7 The results of the optimal solution are shown in Table 3.

[0145] Table 3

[0146]

[0147] As can be seen from Table 3, the actual delivery time is the shortest when the number of delivery vehicles is 2, that is, the optimal solution can be achieved when the number of delivery vehicles is 2.

[0148] Once the delivery plan is determined, the method following step S13 is executed, which involves first coding the workstations and warehouse areas to obtain the second group. Data obtained from the field shows the correspondence between the materials requiring delivery to the workstations and the materials stored in the warehouse areas, as shown in Table 4.

[0149] Table 4

[0150]

[0151]

[0152] Based on the method provided by this invention, the above data can be solved to determine that the material outbound sequence is: 21-81-71-61-51-11-31-41-22-82-72-62-52-12-32-42. Based on this sequence, storage areas are selected and coded, constraints are established, and a model solving algorithm based on these constraints is selected and designed.

[0153] Assume the horizontal travel speed of the stacker crane in the automated warehouse is V1 = 60 m / min, the vertical lifting speed is V2 = 40 m / min, the width of each storage location is L = 0.8 m, the height is H = 0.56 m, the energy consumption of the stacker crane is P = 200 kW, g = 9.8 m / s², and M = 2 kg. Based on the constraints in the Boolean enclosure matrix, the allocation of material storage locations and the picking path of the stacker crane are planned. Let the I / O number be 1, and the coordinates be (0, 1). Set some parameters for the genetic algorithm: initial population size is 50, chromosome length is 17, crossover probability is 0.7, and mutation probability is 0.05. Substitute these parameters into the MATLAB program, and after multiple experiments, determine that the number of genetic iterations is 500. The changes in the optimal solution and the population mean are as follows: Figure 8 As shown.

[0154] As shown in the figure, the genetic algorithm achieves good optimization results for this objective, converging after approximately 400 iterations and finally obtaining the optimal solution. The optimal objective function value decreased from 0.2729 before optimization to 0.1310 after optimization, a reduction of approximately 52%. The optimized location allocation and picking path are shown in Table 5.

[0155] Table 5

[0156]

[0157]

[0158] This solution achieves a globally optimal state in reducing stacker crane operating time and energy consumption. The optimization results show that generating the outbound order based on the delivery route results, and then establishing constraints to solve the location allocation problem based on these results, leads to a globally optimal state for stacker crane operating time and energy consumption. The results prove that the method is effective and feasible, ensuring delivery needs while improving the efficiency and operating cost of automated warehouse operations. Table 6 shows the comparison results of the constraint-based genetic algorithm used in this section after 10 runs with the traditional genetic algorithm.

[0159] Table 6

[0160]

[0161] As can be seen from Table 6, the genetic algorithm based on multi-color set constraints used in this paper effectively accelerates the convergence speed.

[0162] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0163] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0164] Those skilled in the art will understand that all or part of the steps in the methods described above can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device, such as a microcontroller, chip, or processor, to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0165] Furthermore, various different embodiments of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the embodiments of the present invention, they should also be regarded as the content disclosed by the embodiments of the present invention.

Claims

1. A digital shop floor scheduling method based on the PSC-IGA algorithm, characterized in that, The scheduling method includes: Obtain the workstations in the digital workshop and their corresponding material requirements; Multiple chromosomes are randomly generated to complete the delivery tasks at each workstation, forming the initial first population; A genetic algorithm is used to iteratively update the first population to obtain a delivery plan; The workstations and storage areas of the digital workshop are coded according to the delivery plan and based on a Boolean matrix to form a second group; Calculate the fitness of each individual in the second population; Determine the number of iterations Does the termination condition meet? Determining the number of iterations If the termination condition is not met, let the number of individuals be... ; Select the individual with the highest fitness from the second population and add it to the third population. And update the number of individuals. ; Randomly select the two individuals with the highest fitness from the second population; Calculate the crossover probability between the two individuals; Determine whether the crossover probability is greater than a preset first probability value; If the crossover probability is determined to be greater than the first probability value, a single-point crossover operation is performed on the two individuals. Calculate the mutation probability of the two individuals after a single-point crossover operation; Determine whether the mutation probability is greater than a preset second probability value; If the crossover probability is determined to be greater than the second probability value, a basic bit mutation operation is performed on the two individuals; The two individuals after the basic bit mutation operation are placed into the third population. And update the number of individuals. ; Determine the number of individuals Is the population size less than the preset population capacity? In determining the number of individuals If the population size is less than the stated population capacity, the two individuals with the highest fitness are randomly selected from the second population again, and the corresponding steps of the method are executed until the number of individuals reaches the stated population capacity. Greater than or equal to the population size; In determining the number of individuals If the population size is greater than or equal to the population size, the number of update iterations is... Check the iteration count again. Check if the termination condition is met, and execute the corresponding steps of the method until the specified number of iterations is reached. The termination conditions are met; In determining the number of iterations If the termination condition is met, calculate the values ​​for each of the third groups. The fitness of each individual; The individual with the highest fitness is selected as the final assignment result; The step of encoding the workstations and warehouse areas of the digital workshop according to the delivery plan and based on a Boolean matrix to form a second group specifically includes: A first-level matrix is ​​established with the workstations as column vectors and the required materials as row vectors, wherein the elements in the first-level matrix are used to indicate whether the workstation needs to deliver the materials; A second-level matrix is ​​established with the material as the row vector and the storage area of ​​the material as the column vector, wherein the elements in the second-level matrix are used to indicate whether the storage area stores the material; Multiple individuals are randomly generated based on the first-layer matrix and the second-layer matrix to form the second population.

2. The method according to claim 1, characterized in that, The random generation of multiple chromosomes to complete the delivery tasks at each workstation to form the initial first population specifically includes: The initial position of the delivery vehicle in the digital workshop is represented by the number 0; Each workstation is represented by a number from 1 to z, where z is the number of workstations; Determine the number of delivery vehicles.

3. The method according to claim 1, characterized in that, The step of iteratively updating the first population using a genetic algorithm to obtain a delivery plan specifically includes: Calculate the fitness of each chromosome; The two chromosomes with the highest fitness in the first population are selected using a roulette wheel selection method. Perform crossover and mutation operations on the two selected chromosomes; Determine whether the first population satisfies the preset iteration termination condition; If the first population satisfies the iteration termination condition, the first population is used as the delivery scheme; if the first population does not satisfy the iteration termination condition, the fitness of each chromosome is recalculated, and the corresponding steps of the method are executed until the first population satisfies the iteration termination condition.

4. The method according to claim 3, characterized in that, The calculation of the fitness of each chromosome specifically includes: The fitness of each chromosome is calculated according to formula (1). ，（1） in, The fitness of the chromosome. For workstation Total quantity For workstation Delivery time, For use as an indicator station Whether by delivery vehicle Variables in delivery Indicates workstation By delivery tool delivery, Indicates workstation Not delivered by delivery tool delivery, For the cleaning time of the materials, This is a variable used to indicate whether a material needs to be cleaned. This indicates that the material needs to be cleaned. This indicates that the material does not need to be cleaned. For delivery tools from the workstation Arrive at workstation Time, For use in indicating delivery vehicles From workstation Move to workstation variables, Indicates delivery tool From workstation Move to workstation , Indicates delivery tool Not from workstation Move to workstation , For workstation The unloading time, Penalty time for deliveries that do not fall within the service time window.

5. The method according to claim 1, characterized in that, The calculation of the fitness of each individual in the second population specifically includes: The fitness of each individual is calculated according to formulas (2) to (6). ，（2） ，（3） ，（4） ，（5） ，（6） in, The fitness function for each individual. For dimensionless functions, For function The minimum value, For function The maximum value, and Dimensionless and The value, This is the location number. The number of storage locations. The speed of the stacker crane in the horizontal direction. This refers to the traction power of the stacker crane. Indicates the first Column storage location , Width of each storage location, For the quality of materials, It is the acceleration due to gravity. Indicates the first Layer storage location , The height of the storage location. The speed at which the stacker crane moves in the vertical direction. For workstation Total quantity For workstation Delivery time, For use as an indicator station Whether by delivery vehicle Variables in delivery Indicates workstation By delivery tool delivery, Indicates workstation Not delivered by delivery tool delivery, For the cleaning time of the materials, This is a variable used to indicate whether a material needs to be cleaned. This indicates that the material needs to be cleaned. This indicates that the material does not need to be cleaned. For delivery tools from the workstation Arrive at workstation Time, For use in indicating delivery vehicles From workstation Move to workstation variables, Indicates delivery tool From workstation Move to workstation , Indicates delivery tool Not from workstation Move to workstation , For workstation The unloading time, Penalty time for deliveries that do not fall within the service time window.

6. The method according to claim 1, characterized in that, The calculation of the crossover probability between the two individuals specifically includes: The crossover probability is calculated according to formula (7). ，（7） in, The crossover probability is... , As a preset constant, This represents the maximum fitness value in the second population. The larger of the two individuals' fitness values. This represents the average fitness of the second population.

7. The method according to claim 1, characterized in that, The calculation of the mutation probability of the two individuals after a single-point crossover operation specifically includes: The mutation probability is calculated according to formula (8). ，（8） in, The mutation probability is... , As a preset constant, This represents the maximum fitness value in the second population. This represents the average fitness of the second population. The larger of the two individuals is the fitness value.

8. A digital workshop scheduling system based on the PSC-IGA algorithm, characterized in that, The scheduling system includes a processor for performing the method as described in any one of claims 1 to 7.

9. A storage medium, characterized in that, The storage medium stores instructions that are read by a machine to cause the machine to perform the method as described in any one of claims 1 to 7.

Images