Workshop scheduling and order delivery success probability prediction method based on improved genetic algorithm

Abstract

The invention discloses a workshop scheduling and order delivery success probability prediction method based on an improved genetic algorithm, and the method comprises the steps: building a workshop scheduling optimization model which comprises the construction of an objective function and the setting of corresponding constraint conditions; and taking the minimum value of the maximum completion time as a target function, solving the model by using an improved genetic algorithm, and solving the minimum maximum completion time of the order so as to evaluate whether the customer order can be completed before the delivery date and evaluate the possibility of successful delivery of the order. Through combination of prediction and improved genetic algorithm optimization, the method can effectively deal with the problems of order demand fluctuation and resource allocation in a complex production environment, remarkably improves the production efficiency, reduces the resource waste, and guarantees the on-time delivery of orders.

Description

Technical Field

[0001] The invention relates to a method for predicting the success probability of workshop scheduling and order delivery based on an improved genetic algorithm. Background Art

[0002] A notable feature of modern manufacturing systems is the uncertainty of order demand. In particular, in the case of sudden large-volume orders or orders with short delivery periods, traditional scheduling systems are difficult to respond in a timely manner, leading to problems such as delivery delays, low production efficiency, and waste of resources. Typical scenarios include industries such as automobile manufacturing and electronic product assembly. When customers temporarily increase order volume or shorten delivery periods, production workshops need to quickly evaluate the capacity of existing resources and adjust equipment use and worker scheduling according to demand.

[0003] Existing methods usually rely on integer programming models or rule-based decision systems. These methods have certain adaptability in simple scenarios, but when faced with complex scheduling problems with multiple processes and multiple machine constraints, they often expose the following shortcomings: (1) High computational complexity: When the problem scale is large, the solution time increases significantly, making it difficult to meet real-time response requirements; (2) Poor dynamic adaptability: Existing systems usually assume fixed resource configurations and lack the flexibility to adjust temporary orders; (3) Low resource utilization: Due to the lack of global optimization, the efficiency of production resource utilization is not maximized.

[0004] In recent years, genetic algorithms, as an optimization method with global search capabilities, have been widely used in shop scheduling problems. By simulating biological evolution mechanisms such as natural selection, crossover, and mutation, genetic algorithms can find approximate optimal solutions in complex search spaces. However, traditional genetic algorithms still have limitations when facing complex production environments, such as being prone to falling into local optimality and slow convergence. Therefore, it is necessary to further optimize the design of genetic algorithms and combine them with prediction models to achieve rapid response to dynamic order demands.

[0005] For example, a study proposed an improved genetic algorithm for multi-objective flexible job shop scheduling, combined with mutation operator optimization, which significantly improved the algorithm's convergence speed and solution quality. Another study applied genetic algorithms to optimize the scheduling problem of multiple processes and multiple machines, and effectively solved the bottleneck problem in production resource allocation through refined fitness function design and local optimization strategies based on neighborhood search.

[0006] Based on the above background, the present invention proposes a method for predicting the success probability of workshop scheduling and order delivery based on an improved genetic algorithm, aiming to solve the production scheduling and order delivery problems under dynamic order demand. The system is particularly suitable for a production environment with multiple products and multiple processes, where each machine can only process one workpiece process, that is, each process of each workpiece can only select one specific machine for processing. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a method for predicting the probability of successful delivery of a job shop and an order based on an improved genetic algorithm in view of the deficiencies in the prior art. The present invention can flexibly select resources according to the load conditions of various resources, improve the sensitivity of production, and propose a job shop scheduling method based on an improved genetic algorithm that is more in line with the current discrete production mode, while achieving the following goals: optimizing the existing scheduling scheme through an improved genetic algorithm under the constraints of multiple processes and multiple machines to minimize the total completion time; efficiently predicting whether the existing resources can meet the needs of customer orders; and providing suggestions for equipment expansion or working time adjustment when it is predicted that the order needs cannot be met.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] A method for predicting the probability of successful delivery of a workshop scheduling and order based on an improved genetic algorithm includes constructing a workshop scheduling optimization model, solving the model using an improved genetic algorithm, and obtaining the minimum maximum completion time of an order to evaluate whether the customer order can be completed before the delivery date and the possibility of successful delivery of the order. The process of the improved genetic algorithm includes encoding, population initialization, fitness calculation, sorting and grouping selection, improved crossover operator, mutation, substitution, iterative optimization and termination.

[0010] Step S1: Mathematical symbol definition, assuming that the workshop has the following parameters and variables:

[0011] J: Workpiece set, J = {1, 2, 3..., n}, a total of n workpieces.

[0012] J j : The jth artifact in the artifact set.

[0013] O: Process set, O = {1, 2, 3, ..., z}, each workpiece has z processes.

[0014] O i : The i-th process in the process set O.

[0015] M: machine set, M = {1, 2, 3, ..., q}, a total of q machines.

[0016] M k : The kth machine in the machine set M;

[0017] t i,j : The processing time of the i-th process of workpiece j.

[0018] C i,j: The completion time of the i-th process of workpiece j, that is, the cumulative time for workpiece j to complete all processes from the first process to the i-th process.

[0019] S i,j : The start time of the i-th process of workpiece j, that is, the time point when the i-th process can be started in the cumulative time span from the first process to the i-th process of workpiece j.

[0020] C j :J j The completion time is the time when all processes are completed.

[0021] Binary decision variables, if the i-th process of workpiece j is assigned to machine k, then Otherwise 0.

[0022] N p :The population has N p chromosomes.

[0023] U x : The xth chromosome in the population.

[0024] The processing machine for each process is fixed and is recorded as Indicates workpiece J j Process O i The only processing machine M k ;

[0025] The processing time matrix T(i,j) represents workpiece J j Process O i Processing time on the corresponding machine.

[0026] v: represents the vth process in the total processing sequence (the result of arranging all workpieces in the processing sequence).

[0027] Step S2: Establish a mathematical model, including the objective function and constraints as follows:

[0028] (1) Objective function: the objective function is to minimize the maximum completion time, where C i represents the completion time of job i

[0029] f=min(C max )

[0030] C max It refers to the maximum completion time of all workpieces; that is, the completion time of the last workpiece to be processed among all workpieces.

[0031] (2) The constraints are as follows:

[0032] Process sequence constraint: The processes of each workpiece must be processed in sequence;

[0033]

[0034] Time non-negative constraint: The start time and completion time of each process must be non-negative;

[0035]

[0036] Processing time constraint: completion time equals start time plus processing time;

[0037]

[0038] Machine uniqueness constraint: Each process can only be assigned to one machine;

[0039]

[0040] Machine timing constraints: Only one process can be processed on a machine in the same time period;

[0041] S i,j ≥C p,q or S p,q≥ C i,j , (p,q)∈O and are assigned to the same machine

[0042] Machine processing restriction constraints: Each process must be assigned to a specific machine;

[0043] Only when machine k is the designated machine for the i-th process of job j

[0044] Maximum completion time constraint:

[0045]

[0046] Step S3: Encode the chromosome using a workpiece-based encoding method. The structure of the chromosome consists of multiple lines, and each line represents the execution order of the workpieces of the corresponding process.

[0047] The first part is the workpiece sorting part. The execution order of each process of the workpiece is fixed and generated by randomly arranging the workpiece order. Different chromosomes will have different workpiece orders.

[0048] For example, a randomly generated chromosome is shown in Table 1. The first column reflects the random order of artifacts in the chromosome, for example, J 4 , J 2 , J 7 , J 1 , J 6 , J 8 , J5 , J 3 The other columns reflect the process sequence, and all workpiece processing processes are fixed to O 1 , O 2 , O 3 , O 4 , O 5 , O 6 , O 7 , O 8 .

[0049] Table 1

[0050]

[0051] The second part is the processing machine allocation part: implicit processing, by referring to the processing machine matrix (see Table 2 for examples) during decoding to determine the processing machine corresponding to each process of each workpiece. The processing machine matrix represents the processing machine number that needs to be used for each process of each workpiece during the operation process. Each row corresponds to a workpiece, and each column corresponds to a process of the workpiece. The value in the matrix is ​​the machine number, indicating the machine to which the workpiece needs to be assigned in the corresponding process.

[0052] Table 2

[0053]

[0054] For example, look up Table 2 to get J 1 Follow O 1 The corresponding value is 4, which means workpiece J 1 The first step of O 1 The corresponding machine is M 4 , J 3 Follow O 3 The corresponding one is 5, which is the third process O of J3 3 The corresponding machine is M 5 .

[0055] Step S4: Heuristic population initialization, population initialization includes machine selection initialization and process sorting initialization:

[0056] (1) Machine selection is initialized implicitly using the processing machine matrix. Each process of each workpiece has a uniquely specified machine. The processing machine matrix specifies the processing machine of each process of each workpiece. The processing machine matrix ensures that each process is assigned to the specified processing machine to meet the process constraints.

[0057] (2) The process sequence initialization combines heuristic rules and random strategies, which specifically includes the following steps:

[0058] ① Suppose there are n workpieces in total. Calculate the priority according to the total processing time of each workpiece. The shorter the total processing time of the workpiece, the higher its defined priority (for an example of the total processing time, see Figure 3 ).

[0059] ② Sort the workpieces according to the total processing time. Put the k (k < n) workpieces with higher priorities into the chromosome in the order from the highest to the lowest priority. The execution order of each process of each workpiece itself remains fixed and is put into the chromosome in turn until all processes of each workpiece are allocated;

[0060] ③ Randomly select the remaining n - k workpieces and randomly put them into the chromosome to ensure a certain degree of randomness in the chromosome. The execution order of each process of each workpiece itself remains fixed and is put into the chromosome in turn until all processes of each workpiece are allocated, ensuring a certain degree of randomness in the chromosome.

[0061] ④ Generate the chromosome. The sequential position in the chromosome represents the execution order of the corresponding process.

[0062] For example, suppose there are 8 workpieces in total, each workpiece has 8 processes, and they are all from O 1 to O 8 . First, calculate the priority of the workpieces according to the first step. Second, according to the second step, assume k is 4, then select 4 workpieces with high priorities and put them into the initial chromosome. Sort them according to Figure 3 the total processing time. The four workpieces with the highest priorities are J 1 , J 2 , J 3 , J 5 . Add these four workpieces to the chromosome. The execution order of each process of each workpiece itself remains fixed and is put into the chromosome in turn until all processes of the 4 workpieces are allocated (as shown in Table 3).

[0063] Table 3

[0064]

[0065] Furthermore, according to the third step, randomly select the remaining four workpieces. Suppose the workpieces are randomly arranged as J 7 , J 4 , J 6 , J 8 . The execution order of each process of each workpiece itself remains fixed and is put into the chromosome in turn until all processes of the 4 workpieces are allocated (as shown in Table 4). Finally, generate the chromosome (as shown in Table 5).

[0066] Table 4

[0067]

[0068] Table 5

[0069]

[0070] Step S5: Calculate the fitness. The steps of calculating the fitness are as follows:

[0071] (1) Decode the machine selection part and the process sorting part separately:

[0072] ① The machine selection part reads the gene sequence from the machine selection part of the chromosome. The processing machine for each process is fixed and is recorded as Indicates workpiece J j Process O i The only processing machine M k .

[0073] ② The process sorting part randomly reads the gene sequence P from the process sorting part of the chromosome under the constraints to represent the processing order of the workpiece; in the total processing order of the gene sequence P, the process arrangement of different workpieces is random, but the order of the process arrangement of the same workpiece itself is fixed;

[0074] The processing order of the workpiece represented by the gene sequence P is as follows:

[0075] P={(i 1 ,j 1 ),(i 2 ,j 2 ),…,(i v ,j v )}

[0076] j v : Indicates the workpiece J belonging to the vth process in the total processing sequence j .

[0077] i v :Indicates the workpiece J j The i-th process in .

[0078] v: represents the vth process in the total processing sequence;

[0079] Each v corresponds to a specific workpiece and its process, which are decoded in sequence and a scheduling plan is generated.

[0080] For example, suppose P = {(1 1 ,1 1 ),(1 2 ,3 2 ),(1 3 ,2 3 ),(2 4 ,2 4 ),(25 ,3 5 )}

[0081] (1 1 ,1 1 ) indicates that the first process in the total processing sequence corresponds to workpiece J 1 The first step.

[0082] (1 2 ,3 2 ) indicates that the second process in the total processing sequence corresponds to workpiece J 3 The first step.

[0083] (1 3 ,2 3 ) indicates that the third process in the total processing sequence corresponds to workpiece J 2 The first step.

[0084] (2 4 ,2 4 ) indicates that the fourth process in the total processing sequence corresponds to workpiece J 2 The second process.

[0085] (2 5 ,3 5 ) indicates that the fifth process in the total processing sequence corresponds to workpiece J 3 The second process.

[0086] (2) Generate a scheduling plan

[0087] ① Initialization schedule

[0088] Initialize the idle time F of all machines M :

[0089]

[0090] Initialize the completion time of the previous process of all workpieces A i,j , A i,j represents the completion time of the previous process, the completion time of the i-1th process of workpiece j, that is, the cumulative time for the completion of all processes from the 1st process to the i-1th process of workpiece j;

[0091]

[0092] ② Arrange the processes in order

[0093] According to the gene sequence P in the chromosome, for each process (i v ,j v ) performs the following calculation:

[0094] The only processing machine that reads the process and processing time t i,j

[0095] Calculation process (i v ,j v ) start time

[0096]

[0097] If i v =1(first process), then otherwise

[0098] Process (i v ,j v ) corresponds to the idle time of the processing machine, that is, workpiece J i The idle time of the processing machine corresponding to the i-th process in , and the idle time is the earliest acceptable time.

[0099] Calculation process (i v ,j v ) completion time

[0100]

[0101] Update the machine's idle time

[0102]

[0103] Update the completion time of the artifact Dependency for subsequent processes.

[0104] ③Calculate the completion time of each workpiece

[0105] Workpiece J j Completion time C j is the completion time of all processes:

[0106] C j =max Ci ,j , i∈O

[0107] ④Calculate the total completion time

[0108] The total completion time is the latest completion time of all workpieces:

[0109] C max =max C j , i∈O

[0110] (3) Calculate the fitness value

[0111] The objective function f(C) minimizes the total completion time:

[0112] f(C)=min C max

[0113] The fitness value F is the inverse of the objective function:

[0114]

[0115] Step S6: sorting and grouping selection. The operation steps of the sorting and grouping selection are as follows: adopt the fitness-based roulette selection method to select parent individuals according to the fitness value probability, and give priority to chromosomes with higher fitness values.

[0116] (1) Calculate the selection probability

[0117] ① Calculate the sum of fitness of all chromosomes:

[0118]

[0119] ② Calculate the probability P of each chromosome being selected x

[0120]

[0121] ③Calculate the cumulative selection probability Q x , where Q x ∈[0,1], used to divide the roulette interval:

[0122]

[0123] (2) Selecting chromosomes based on random numbers

[0124] ①Generate random numbers: Generate N p A random number R x ∈[0,1], where x=1,2,…,N p

[0125] ②Chromosome selection: For each random number R x , according to the cumulative selection probability Q x Select chromosome

[0126] If Q x-1 <<R x x , then select chromosome U x

[0127] ③ Repeat the above steps: Repeat N p times until the parent chromosome set is selected.

[0128] ​Step S7: The improved crossover operator includes the crossover of the machine selection part and the crossover of the process sorting part:

[0129] (1) Define crossover probability

[0130] ①Crossover probability P c Used to control whether chromosomes in the population perform crossover operations, and the value range is [0,1].

[0131] ② For each pair of chromosomes in the population, a random number [0,1] is generated independently. If the random number is less than or equal to the crossover probability, a crossover operation is performed on the pair of chromosomes; otherwise, no crossover is performed.

[0132] (2) Machine selection, implicitly using the processing machine matrix, in which each workpiece and each process is assigned to a designated processing machine, without the need for direct crosstalk of genetic data;

[0133] (3) Partial matching crossover (PMX) is used in the process sorting part to ensure the consistency of the workpiece sequence.

[0134] In the process sorting part, the partial matching crossover method is used for crossover operation. According to the crossover probability, two chromosomes are randomly selected from the population. If the crossover condition is met, the partial matching crossover operation is performed. The start and end positions of the exchanged gene fragments are randomly selected, and the gene fragments at the corresponding start and end positions of the chromosomes are exchanged. The conflicting gene points are replaced with each other, and then two new offspring are generated. If the offspring fitness is higher than the parent generation, that is, the crossed chromosome, it will replace the parent generation to enter the next generation population, otherwise no replacement will be performed;

[0135] For example, if the two chromosomes are P1 = [264|7358|1] and P2 = [452|1876|3], if the crossover positions are 3 and 7, then: fragments (7358) and (1876) will be exchanged. For the remaining genes, since 2 does not conflict with (1876), it will be filled in. 6 has a conflict, and the mapping gene of 6 is 8, which still has a conflict. The mapping gene of 8 is 3, which does not have a conflict, so 3 will be filled in the corresponding position of the offspring individual of C1 (see the example). Figure 4 ).

[0136] Step S8: mutation operation, the operation steps of the mutation operation are as follows:

[0137] (1) Define mutation probability: W p ∈[0,1] represents the probability of each chromosome in the population mutating.

[0138] ①Assume the current population size is N p , the chromosome set of the population in generation t:

[0139] ② For each chromosome U in the population x, independently generate a random number R x ∈[0,1]. If R x <<W p , then select chromosome U x Mutate; otherwise, do not mutate.

[0140] (2) Selection of mutant genes: For the mutated chromosome, the positions of two genes are randomly selected from its task sequence to ensure that the two positions meet the requirements of being within the task sequence range and not adjacent.

[0141] (3) Exchange gene positions: swap the position contents of the two selected genes. After the exchange, update the chromosome task sequence to form a new mutant chromosome.

[0142] (4) All mutated chromosomes and the remaining unmutated chromosomes form a new generation of population and serve as the basis for the next genetic operation.

[0143] Step S9: Alternative operation, the operation steps of the alternative operation are as follows:

[0144] (1) Let the population size after crossover and mutation be N p , check whether there are duplicate chromosomes in the population.

[0145] (2) If there are identical chromosomes, only one is retained and the remaining duplicate chromosomes are removed; finally, a randomly generated new chromosome is added to ensure that the population size remains at N. p .

[0146] Step S10: iterative optimization and termination. The steps of iterative optimization and termination are as follows:

[0147] (1) According to the fitness value, record the optimal solution of each generation and update the population.

[0148] (2) When the maximum number of generations is reached or the optimal solution is no longer significantly improved, the final scheduling plan is output, including the minimum completion time, the optimal Gantt chart, and the convergence chart.

[0149] As a further optimization scheme of the method for predicting the success probability of workshop scheduling and order delivery based on the improved genetic algorithm of the present invention, an order delivery and scheduling system based on prediction and improved genetic algorithm including multiple modules (see Figure 1 ): It includes input module X1, prediction module X2, optimization comparison module X3 and output module X4, and the most important improved genetic algorithm module called by X1-X3 modules. In the improved genetic algorithm module, the improved genetic algorithm is started to solve the workshop scheduling optimization model to obtain the minimum maximum completion time of the order, so as to evaluate whether the customer order process can be completed before the delivery date. The content is as follows:

[0150] (1) Input module X1: The input module consists of two parts: the first part is to receive customer order information (such as product type, process requirements, product quantity and delivery time); the second part is to input the operation information of the target workshop, such as the optional machine information for each process, the number of machines, the processing time of each process of each machine, the idle time of the machine, etc.

[0151] (2) Prediction module X2: The prediction module can extract customer order information (such as product type, process requirements, product quantity and delivery date), call the improved genetic algorithm module in the prediction module, use the improved genetic algorithm to solve the workshop scheduling optimization model, and find the minimum maximum completion time for completing customer order information under the conditions of the target workshop's operating information. Compare the minimum maximum completion time with the delivery date to evaluate whether the customer order can be completed before the delivery date under the existing resource conditions of the target workshop. If it can, directly enter the output module to output the order delivery success, otherwise enter the optimization comparison module.

[0152] (3) Optimization comparison module X3: The optimization comparison module can detect the output result of the prediction module. If the prediction module outputs that the customer order cannot be completed on time, the customer order information in the input module and the data of the target workshop's operation information are extracted and input into the optimization comparison module. The production personnel need to increase the production resources in the optimization comparison module. The production resources include increasing the number of machines, reducing the idle time of the machines, and adjusting the daily working hours of the workers. The improved genetic algorithm module is called in the optimization comparison module, and the workshop scheduling optimization model is solved by using the improved genetic algorithm to obtain the minimum maximum completion time of the customer order information under the condition of increasing the production resources. The production resources are increased multiple times and the improved genetic algorithm is run multiple times to solve, and the delivery time is evaluated until the output can meet the customer's delivery date, and the production resources that meet the customer's delivery date are output in the output module. If the adjustment of production resources such as machine and labor time has exceeded the maximum constraint of the target workshop, the output module outputs the order delivery failure.

[0153] (4) The improved genetic algorithm module called by the X1-X3 modules (see Figure 2 ), the contents of which are as follows:

[0154] 4.1) Constructed workshop scheduling optimization model

[0155] 4.2) Genetic algorithm module:

[0156] ① Coding module A: responsible for encoding the decision variables of the production scheduling problem.

[0157] ② Population heuristic initialization module B: Initialize the population using heuristic rules and random strategies.

[0158] ③Fitness evaluation module C: calculates population fitness.

[0159] ④ Sorting and grouping roulette module D: select according to the fitness value.

[0160] ⑤ Improve the crossover operator module E: Optimize the crossover operator to improve the quality of the optimal solution.

[0161] ⑥ Mutation module F: Increase the diversity of the population to avoid premature convergence and failure to obtain the global optimal solution.

[0162] ⑦Replacement module G: Check and remove duplicate chromosomes in the offspring, which is crucial to maintain the diversity of the population and improve the coverage of the search space.

[0163] ⑧ Iterative optimization and termination module H: Iterative optimization according to the fitness value until the termination condition is reached.

[0164] (5) Output module X4: The output module can output the final result and give optimization suggestions. If the minimum completion time can meet the delivery date, the final scheduling plan is output: ① Output the optimized production scheduling plan, including the optimal Gantt chart, convergence diagram, machine allocation, process sequence, workpiece completion time, etc. ② Output the final scheduling plan, including the processing sequence, assigned machines, and estimated completion time of all orders. If the minimum completion time cannot meet the delivery date, the order delivery failure is output, and the optimization suggestions are output: ① The delivery date needs to be renegotiated with the customer. ② Pre-set emergency response plans, such as acceleration plans and spare resource allocation when production is delayed.

[0165] Working principle of the present invention:

[0166] (1) Forecasting and evaluation: First, the forecasting module is used to estimate the order delivery time and evaluate whether the existing resources can meet the demand.

[0167] (2) Scheduling optimization: When the prediction results show that the existing resources cannot meet the order requirements, the system optimizes the production schedule by improving the genetic algorithm and generates the optimal resource allocation plan.

[0168] (3) Execution and feedback: The optimized scheduling plan is output and executed. If new situations arise during the production process, the system will provide real-time feedback and make dynamic adjustments to ensure that orders are delivered on time.

[0169] Compared with the prior art, the beneficial effects achieved by the present invention are: by combining prediction with improved genetic algorithm optimization, the present invention can effectively cope with order demand fluctuations and resource allocation problems in complex production environments, significantly improve production efficiency, reduce resource waste, and ensure on-time delivery of orders. BRIEF DESCRIPTION OF THE DRAWINGS

[0170] Figure 1 It is the overall flow chart of the order delivery and scheduling system of the present invention;

[0171] Figure 2 It is the flow chart of the optimized improved genetic algorithm of the present invention;

[0172] Figure 3 The heuristic initialization is sorted by total processing time;

[0173] Figure 4 It is a schematic diagram of the crossover algorithm;

[0174] Figure 5 is a convergence diagram of the optimal processing time in Example 1 of the present invention;

[0175] Figure 3 and Figure 5 The unit of the vertical axis time is seconds. DETAILED DESCRIPTION

[0176] A method for predicting the success probability of shop scheduling and order delivery based on an improved genetic algorithm (see Figure 1 ), the specific implementation is as follows:

[0177] Step S1: Input data. The module required is input module X1, and the content is as follows:

[0178] (1) Receive customer order information:

[0179] ① Collect customer order information, including product type, required processes, product quantity, delivery date, etc.

[0180] ② For each order, extract the required process requirements (such as processing time and equipment requirements for each process) and delivery time requirements.

[0181] (2) Enter customer order information and existing production resource information in the input module:

[0182] ① Enter the required process requirements (such as processing time for each process, processing machine requirements, etc.) and delivery time requirements required for the order.

[0183] ② Input the data of existing production resources, including the number of machines, the processing time of each process of each machine, the idle time of the machine, etc.

[0184] Step S2: Order demand forecasting and resource evaluation. The module required is the forecasting module X2, and the content is as follows:

[0185] (1) Based on historical order data and production capacity, a predictive model is used to estimate the processing time and required production resources (such as the number of machines, workers’ daily working hours, etc.) for each order.

[0186] (2) Call the improved genetic algorithm module to estimate the shortest completion time of the order and determine whether the existing resources can meet the order delivery time.

[0187] (3) If satisfied, the production resources that meet the requirements are output. If not satisfied, the subsequent optimization comparison module is entered.

[0188] Step S3: Optimize the comparison module X3, the content of which is as follows:

[0189] The optimization comparison module aims to dynamically adjust the production resource configuration by improving the genetic algorithm according to the gap between order demand and existing resources until the delivery date and output required by the customer are met. Through the optimization module, the system can dynamically adjust resource configuration, efficiently generate scheduling plans that meet customer needs, and improve production flexibility and resource utilization. The specific steps are as follows:

[0190] (1) Input resource adjustment information:

[0191] ① Based on the resource assessment results, enter the number of machines that need to be added or the number of hours that need to be extended.

[0192] ② Consider the actual production constraints (such as the maximum number of machines, worker scheduling restrictions, etc.) and use resource adjustment information as the initial condition for improving the genetic algorithm.

[0193] (2) Improved genetic algorithm optimization:

[0194] ① Call the improved genetic algorithm module to minimize the order completion time as the optimization goal.

[0195] ② In the calculation process of the improved genetic algorithm, combined with the new resource allocation, dynamically adjust the process sequence and equipment allocation.

[0196] ③ Evaluate the optimization plan through the fitness function, record the optimal solution of each generation, and gradually approach the scheduling plan that meets the delivery time requirements.

[0197] (3) Output optimization results:

[0198] ① When the minimum completion time can meet the customer's delivery date, the production resources that meet the customer's delivery date will be output in the output module.

[0199] ② If the optimization result still fails to meet the customer's requirements, the order delivery failure will be output in the output module.

[0200] Step S4: Improved genetic algorithm module called by X1-X3 modules (see example Figure 2 ), the contents of which are as follows:

[0201] (1) Chromosome coding: The process sequence and machine allocation coding of the workpiece are used to transform the production scheduling problem into a chromosome representation in the improved genetic algorithm. The process sequence coding is to randomly generate the processing sequence of the workpiece; the machine allocation coding is to automatically allocate the processing machine according to the implicit processing of the processing machine matrix.

[0202] (2) Population initialization: Generate the initial population, including the machine selection part and the process sorting part. Initialization is completed through a heuristic strategy combined with a randomization method to ensure the diversity of the population and the quality of the initial solution, providing a better starting point for the algorithm.

[0203] (3) Fitness evaluation: For each chromosome in the population, decode it according to its process order and machine selection, and calculate the total completion time as the fitness value. The fitness is used to evaluate the quality of individuals and provide a basis for the selection operation.

[0204] (4) Selection operation, the content of which is as follows: adopting a probability selection mechanism based on the roulette method, preferentially selecting chromosomes with higher fitness values ​​as parent individuals. This operation increases the chances of excellent individuals being retained and participating in reproduction, thereby improving optimization efficiency.

[0205] (5) Crossover operation: Since the machine selection part is implicitly processed, the gene data does not need to be directly crossed. Partial matching crossover (PMX) is performed on the process sorting part of the offspring, and the crossover points are randomly selected, the fragments are exchanged, and the conflicting genes are processed through the mapping rules to generate new offspring chromosomes. This operation increases the solution space coverage ability of the population and explores better solutions.

[0206] (6) Mutation operation: The mutation operation selects chromosomes by setting the mutation probability and randomly selects some genes in the chromosomes to exchange positions, thereby generating new chromosomes. This can effectively increase population diversity, prevent the algorithm from falling into local optimality, and improve global search capabilities and optimization quality.

[0207] (7) Replacement operation: Check whether there are duplicate chromosomes in the population. If duplicates are found, only one is retained and the other duplicate chromosomes are removed. At the same time, new chromosomes are randomly generated to supplement the population and keep the population size unchanged. By removing duplicate individuals and introducing random chromosomes, the diversity of the population is enhanced and the global search capability is improved.

[0208] (8) Iterative optimization, which is as follows: record the optimal solution in each generation of the population and update the population. When the maximum number of iterations is reached or the optimal solution is no longer significantly improved, output the final scheduling solution, including the minimum completion time, the optimal Gantt chart, and the convergence chart. This step ensures that the algorithm continues to improve during the optimization process and ultimately obtains a high-quality solution.

[0209] Step S5: Optimize the final solution output. The module required is the output module X4, and the content is as follows:

[0210] (1) If the minimum completion time can meet the delivery date, the final scheduling plan is output:

[0211] ① Output the optimized production scheduling plan, including the convergence diagram (see Figure 5 ), optimal Gantt chart, machine allocation, process sequence, workpiece completion time, etc.

[0212] ② Output the final scheduling plan, including the processing sequence of all orders, the assigned machines, and the estimated completion time.

[0213] (2) If the minimum completion time cannot meet the delivery period, output the order delivery failure and output optimization suggestions:

[0214] ①Need to renegotiate the delivery date with the customer

[0215] ② Set up emergency response plans in advance, such as acceleration plans and backup resource allocation when production is delayed.

[0216] Effect of technical solution implementation:

[0217] (1) Dynamic response to demand changes: The system can quickly respond to changes in customer orders, evaluate whether existing resources can meet demand, and optimize scheduling plans as needed.

[0218] (2) Improve resource utilization: Optimize resource allocation by improving genetic algorithms, maximize the utilization of production resources, reduce production bottlenecks, and shorten production cycles.

[0219] (3) Reduce production delays: In the event of sudden large-volume orders or urgent delivery deadlines, the system can quickly adjust production plans to ensure that orders are delivered on time.

[0220] (4) Reduce manual intervention: Through intelligent improved genetic algorithm scheduling, reduce manual scheduling errors and intervention, and improve production efficiency and accuracy.

[0221] (5) Improve the company's flexible production capabilities: Through the intelligent scheduling system, the flexibility of the production line is improved, enabling the company to better respond to changing market demands.

[0222] Example 1: Using the Improved Genetic Algorithm to Solve the Problem of 8 Processes, 8 Machines, and 8 Workpieces In this example, there are eight machines and eight products. Each product has eight processes, and each process of each product has only one unique machine to choose from. The processing schedule is shown in Table 6. For example, J 1 The first step of O 1 In M 1The processing time is 11. The population size N of this example is p =100, the maximum number of iterations is 100, the crossover probability: P c =0.9, mutation probability: W p =0.2, and the optimal solution of this example can be obtained by taking the maximum number of iterations as the termination condition.

[0223] The convergence diagram of the optimal processing time in Example 1 of the present invention is as follows: Figure 5 As shown, according to Figure 5 From the optimal solution iteration diagram, we can see that the objective function value of the improved genetic algorithm gradually decreases during the iteration process, indicating that the algorithm is effectively optimizing the scheduling plan. This optimization not only reduces the idle time of the equipment, but also significantly improves the utilization rate of the equipment. The iteration diagram indirectly reflects the optimization effect of the scheduling plan by showing the convergence process of the algorithm, that is, with the iteration of the algorithm, the production scheduling gradually tends to more efficient resource allocation, thereby improving the overall production efficiency and shortening the production cycle to achieve the goal of minimum processing time.

[0224] Table 6

[0225]

Claims

1. A method for predicting the success probability of workshop scheduling and order delivery based on an improved genetic algorithm, characterized in that: The method includes constructing a workshop scheduling optimization model, solving the model using an improved genetic algorithm, and obtaining the minimum maximum completion time of an order to evaluate whether a customer order can be completed before the delivery date and the possibility of successful order delivery; For mathematical symbol definition, assume that the workshop has the following parameters and variables: J: Workpiece set, J = {1, 2, 3, ..., n}, a total of n workpieces; J j : The jth artifact in the artifact set; O: process set, O = {1, 2, 3, ..., z}, each workpiece has z processes; O i : the i-th process in the process set O; M: machine set, M = {1, 2, 3, ..., q}, a total of q machines; M k : The kth machine in the machine set M; t i,j : The processing time of the i-th process of workpiece j; C i,j : The completion time of the i-th process of workpiece j, that is, the cumulative time for workpiece j to complete all processes from the first process to the i-th process; S i,j : The start time of the i-th process of workpiece j, that is, the time point at which the i-th process can be started in the cumulative time span from the first process to the i-th process of workpiece j; C j : The completion time of job j, that is, the time when all processes are completed; Binary decision variables, if the i-th process of workpiece j is assigned to machine k, then Otherwise, 0; N p :The population has N p chromosomes; U x : the xth chromosome in the population; The processing machine for each process is fixed and is recorded as Indicates workpiece J j Process O i The only processing machine M k ; The processing time matrix T(i,j) represents workpiece J j Process O i Processing time on the corresponding machine; The scheduling optimization model includes constructing the objective function and setting the corresponding constraints; the minimum value of the maximum completion time is taken as the objective function, where C i represents the completion time of job i: f=min(C max ) C max Refers to the maximum completion time of all workpieces; that is, the completion time of the last workpiece to be processed among all workpieces; The scheduling optimization model is solved by using an improved genetic algorithm, and the improved genetic algorithm includes the following steps: 1) The chromosome is encoded using an artifact-based encoding method. The structure of the chromosome consists of multiple lines, each of which represents the execution order of the artifacts of the corresponding process; The first part is the workpiece sorting part. The execution order of each process of the workpiece is fixed. The chromosome is generated by randomly arranging the workpiece order. Different chromosomes will have different workpiece orders. The second part is the processing machine allocation part: implicit processing, by referring to the processing machine matrix during decoding to determine the processing machine corresponding to each process of each workpiece; wherein the processing machine matrix represents the processing machine number that needs to be used for each process of each workpiece during the operation process, each row of the processing machine matrix corresponds to a workpiece, each column corresponds to a process of the workpiece, and the value in the matrix is ​​the machine number, indicating the machine that the workpiece needs to be assigned to in the corresponding process; 2) Heuristic population initialization, population initialization includes machine selection initialization and process sorting initialization: The machine selection initialization implicitly uses the processing machine matrix, in which the unique designated processing machine for each workpiece and each process is clearly specified; through the processing machine matrix, it is ensured that each workpiece and each process is assigned to the designated unique processing machine to meet the process constraints; The process sequence initialization combines heuristic rules and random strategies, and specifically includes the following steps: ① Assuming there are n workpieces in total, the priority is calculated based on the total processing time of each workpiece. The shorter the total processing time of the workpiece, the higher its priority is defined; ② Sort the workpieces by total processing time, and put the k workpieces with higher priority into the chromosome in descending order of priority. The execution order of each process of each workpiece remains unchanged and is put into the chromosome in sequence until all processes of each workpiece are allocated; k <n; ③ Randomly select the remaining nk workpieces and randomly put them into the chromosome to ensure that the chromosome has a certain degree of randomness. The execution order of each process of each workpiece itself is fixed and put into the chromosome in sequence until all processes of each workpiece are assigned; ④ Generate chromosomes. The sequential position in the chromosomes indicates the execution order of the corresponding processes; 3) Calculate the fitness. The steps are as follows: 3.1) Decode the machine selection part and the process sorting part respectively: ① The machine selection part reads the gene sequence from the machine selection part of the chromosome. The processing machine for each process of a workpiece is unique and fixed, denoted as Indicates workpiece J j Process O i The only processing machine M k ; ② The process sorting part randomly reads the gene sequence P from the process sorting part of the chromosome under the constraints to represent the processing order of the workpiece; in the total processing order of the gene sequence P, the process arrangement of different workpieces is random, but the order of the process arrangement of the same workpiece itself is fixed; The processing order of the workpiece represented by the gene sequence P is as follows: P={(i1,j1),(i2,j2),…,(i v ,j v )} j v : represents the workpiece J belonging to the vth process in the total processing sequence of the gene sequence P j ; i v :Indicates the workpiece J j The i-th process in ; v: represents the vth process in the total processing sequence, and the result of arranging all workpieces in the processing sequence; Each v corresponds to a specific workpiece and its process, which are decoded in sequence and a scheduling plan is generated later; 3.2) Generate a scheduling plan ① Initialization schedule Initialize the idle time F of all machines M : Initialize the completion time of the previous process of all workpieces A i,j , A i,j represents the completion time of the previous process, the completion time of the i-1th process of workpiece j, that is, the cumulative time for the completion of all processes from the 1st process to the i-1th process of workpiece j; ② Arrange the processes in order According to the gene sequence P in the chromosome, for each process (i v ,j v ) performs the following calculation: The only processing machine that reads the process and processing time t i,j Calculation process (i v ,j v ) start time If i v =1 means the first process, then otherwise Process (i v ,j v ) corresponds to the idle time of the processing machine, that is, workpiece J j The idle time of the processing machine corresponding to the i-th process in , the idle time is the earliest acceptable time; Calculation process (i v ,j v ) completion time Update the machine's idle time Update the completion time of the artifact Dependencies for subsequent processes; ③Calculate the completion time of each workpiece Workpiece J j Completion time C j is the completion time of all processes: C j =max C i,j ,i∈O ④Calculate the total completion time The total completion time is the latest completion time of all workpieces: C max =max C j ,i∈O 3.3) Calculate the fitness value The objective function f(C) is to minimize the total completion time: f(C)=min C max The fitness value F is the inverse of the objective function: 4) Sorting and grouping selection, wherein the steps of sorting and grouping selection are as follows: adopting a roulette wheel selection method based on fitness, selecting parent individuals according to the fitness value probability, and giving priority to chromosomes with higher fitness values; 5) Then improve the crossover operator, including the crossover of the machine selection part and the crossover of the process sorting part; 5.1) Define crossover probability ①Crossover probability P c Used to control whether the chromosomes in the population perform crossover operations, the value range is [0,1]; ② For each pair of chromosomes in the population, a random number [0,1] is independently generated. If the random number is less than or equal to the crossover probability, the pair of chromosomes is crossovered; otherwise, no crossover is performed. 5.2) The machine selection part implicitly uses the processing machine matrix, in which each workpiece and each process is assigned to a specified processing machine. Since the machine selection part is implicitly processed, the gene data does not need to be directly crossed; 5.3) In the process sorting part, the partial matching crossover method is used for crossover operation. According to the crossover probability, two chromosomes are randomly selected from the population. If the crossover condition is met, the partial matching crossover operation is performed. The starting and ending positions of the exchanged gene fragments are randomly selected, and the gene fragments at the corresponding starting and ending positions of the chromosomes are exchanged. The conflicting gene points are replaced with each other, and two new offspring are generated. If the offspring fitness is higher than the parent generation, that is, the crossed chromosome, it replaces the parent generation and enters the next generation population. Otherwise, no replacement is performed. 6) Then, the process is sequentially subjected to the operations of mutation and substitution; 7) Iterative optimization and termination, the steps of iterative optimization and termination are as follows: ① According to the fitness value, record the optimal solution of each generation and update the population; ② When the maximum number of algebraic solutions is reached or the optimal solution gradually converges, the final scheduling plan is output, including the minimum completion time, the optimal Gantt chart and the convergence chart.

2. The method for predicting the success probability of workshop scheduling and order delivery based on an improved genetic algorithm as claimed in claim 1, characterized in that: The constraints set by the scheduling optimization model are as follows: Process sequence constraint: The processes of each workpiece must be processed in sequence; Time non-negative constraint: The start time and completion time of each process must be non-negative; Processing time constraint: completion time equals start time plus processing time; Machine uniqueness constraint: Each process can only be assigned to one machine; Machine timing constraints: Only one process can be processed on a machine in the same time period; S i,j ≥C p,q or and assigned to the same machine Machine processing restriction constraints: Each process must be assigned to a specific machine; Only when machine k is the designated machine for the i-th process of job j Maximum completion time constraint:

3. A method for controlling the probability of successful workshop scheduling and order delivery based on an improved genetic algorithm as claimed in claim 1, characterized in that The specific steps of step 4) of improving the genetic algorithm are as follows: (1) Calculate the selection probability ① Calculate the sum of fitness of all chromosomes: N p :The population has N p Chromosomes; U x : the xth chromosome in the population; ② Calculate the probability P of each chromosome being selected x ③Calculate the cumulative selection probability Q x , where Q x ∈[0,1], used to divide the roulette interval: (2) Selecting chromosomes based on random numbers ①Generate random numbers: Generate N p A random number R x ∈[0,1], where x=1,2,…,N p ②Chromosome selection: For each random number R x , according to the cumulative selection probability Q x Select chromosome If Q x-1 <<R x x , then select chromosome U x ​ ③ Repeat the above steps: Repeat N p times until the parent chromosome set is selected.

4. A method for controlling the probability of successful workshop scheduling and order delivery based on an improved genetic algorithm as claimed in claim 1, characterized in that In step 6) of the improved genetic algorithm, the mutation operation steps are as follows: (1) Define mutation probability: W p ∈[0,1] represents the probability of each chromosome in the population mutating; ①Assume the current population size is N p , the chromosome set of the population in generation t: ② For each chromosome U in the population x , independently generate a random number R x ∈[0,1], if R x <<W p , then select chromosome U x Make a mutation; otherwise, do not mutate; (2) Selection of mutant genes: For a mutated chromosome, two gene positions are randomly selected from its task sequence to ensure that the two positions meet the requirements of being within the task sequence range and not adjacent; (3) Exchange gene positions: swap the positions of the two selected genes. After the exchange, update the chromosome task sequence to form a new variant chromosome. (4) All mutated chromosomes and the remaining unmutated chromosomes form a new generation of population and serve as the basis for the next genetic operation.

5. The method for controlling the probability of successful workshop scheduling and order delivery based on an improved genetic algorithm as claimed in claim 1, characterized in that In step 6) of the improved genetic algorithm, the alternative operation steps are as follows: (1) Let the population size after crossover and mutation be N p , check whether there are duplicate chromosomes in the population. (2) If there are identical chromosomes, only one is retained and the remaining duplicate chromosomes are removed; finally, a randomly generated new chromosome is added to ensure that the population size remains at N. p .

6. The method for workshop scheduling and order delivery success probability based on improved genetic algorithm as claimed in claim 1, characterized in that The process of using the workshop scheduling optimization model and the improved genetic algorithm to obtain the minimum maximum completion time of the order to evaluate whether the customer order can be completed before the delivery date includes the following steps: Step S1, receiving customer order information, including product type, process requirement, product quantity and delivery date; and obtaining the operation information of the target workshop, including: information of each process of each pending order of the target workshop, information of the available machines for each process, the number of machines, and the processing time of each process of each machine, and the idle time of the machine; Inputting the customer order information and the target workshop's operation information into an input module; Step S2, extracting the customer order information and the target workshop's operation information data in the input module, inputting them into the prediction module, calling the workshop scheduling optimization model in the prediction module, and solving the workshop scheduling optimization model using the improved genetic algorithm, obtaining the minimized maximum completion time for completing the customer order information under the target workshop's operation information, comparing the minimized maximum completion time with the delivery date, and evaluating whether the target workshop can complete the customer order before the delivery date under the existing resource conditions. If so, directly enter the output module, otherwise enter the optimization comparison module; Step S3, the optimization comparison module can detect the output result of the prediction module. If the prediction module outputs that the customer order cannot be completed on time, the customer order information in the input module and the data of the operation information of the target workshop are extracted and input into the optimization comparison module. In the optimization comparison module, production resources are added to the operation information of the target workshop. The production resources include increasing the number of machines and reducing the idle time of machines. The workshop scheduling optimization model is called in the optimization comparison module, and the workshop scheduling optimization model is solved by using the improved genetic algorithm to obtain the minimum maximum completion time of the customer order information under the condition of increasing the production resources. The production resources are increased multiple times and the improved genetic algorithm is run multiple times for solving until the output result can meet the customer's delivery date and is output in the output module, or the increased production resources have exceeded the maximum constraint of the target workshop, then the order delivery failure is output in the input module; Step S4: Output module, which can output the final result of the prediction module or the optimization comparison module and give optimization suggestions; minimize the maximum completion time to meet the customer's delivery period, and output the optimized production scheduling plan; if the minimized maximum completion time cannot meet the delivery period, output the order delivery failure and give optimization suggestions: the delivery period needs to be renegotiated with the customer, and emergency response plans are pre-set, including acceleration plans when production is delayed, spare resource allocation or output order delivery failure.

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