A multi-process route inter-plant automobile mixed flow production optimization method

Abstract

The application discloses a multi-process route single workshop automobile mixed flow production scheduling optimization method, which firstly converts automobile production sequencing problems of each workshop under a multi-process route into a mathematical model problem of combination optimization, analyzes influences of automobile production scheduling sequence changes under the multi-process route on workshop adjustment costs, secondly takes the minimum number of workshop station device adjustment times in automobile production processes as an optimization target, simultaneously considers constraint conditions such as machining start time and completion time and automobile continuous production upper limit, extracts common features of optimization targets and constraint conditions of each workshop, and constructs a general model of automobile mixed flow production scheduling of a single workshop considering the multi-process route; and finally solves the model by using an adaptive genetic algorithm (AGA), and in the solving process, a crossover and mutation operator is designed in combination with an adaptive strategy, so as to improve global and local search capabilities of the algorithm. The production scheduling scheme obtained by the application can effectively solve the automobile mixed flow production scheduling problem of a single workshop considering the multi-process route.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of single-plant automobile mixed flow production optimization with multiple process routes, and particularly relates to a single-plant automobile mixed flow production optimization method with multiple process routes. BACKGROUND

[0002] In order to cope with the rapid changes in the global market and the changing needs of consumers, mixed flow production has become a widely used production mode for automobile manufacturers, in which mode, there are many problems in automobile mixed flow production, such as the change of production sequence in the automobile production process due to the existence of multiple process routes, thereby affecting the normal execution of the production plan and the production cost and efficiency. Therefore, the research on the automobile mixed flow production problem under multiple process routes is of great significance to the automobile manufacturing industry.

[0003] The single-plant automobile mixed flow production problem refers to formulating a reasonable automobile production arrangement sequence for each plant to improve production efficiency and reduce production cost. At present, many scholars have studied the single-plant automobile mixed flow production problem, but it is limited to modeling each welding, painting and assembly plant one by one, and then developing an algorithm to solve these models. The modeling process is complex, and the generalization is not strong, and the operation is not flexible and convenient. How to establish a general model for each plant production and obtain an optimized solution for each plant production by using a unified algorithm can not only simplify the problem modeling and solving process, but also have strong operability in practical application.

[0004] In the algorithm research on the automobile mixed flow production problem, heuristic rules and intelligent optimization algorithms are mostly used for solving. The heuristic rule has fast solving speed and can obtain a solution in a short time, but due to its weak global search ability, the solving precision and quality are poor, and in most cases only a local optimal solution can be obtained. The intelligent optimization algorithm has strong global search ability and can converge to a global optimal solution with a large probability, and its solving precision and quality are often better than that of the heuristic rule, so it is widely used in the solution of the automobile mixed flow production problem. SUMMARY

[0005] In order to overcome the deficiencies of the prior art in solving the automobile mixed flow production problem, the application provides a single-plant automobile mixed flow production optimization method with multiple process routes.

[0006] The single-plant automobile mixed flow production optimization method with multiple process routes comprises the following steps:

[0007] Step 1: determining the description and related assumptions of the single-plant automobile mixed flow production problem with multiple process routes.

[0008] The single workshop mixed-model production sequencing problem with multiple process routes is to determine the optimal production sequence for different types of vehicles, so that the number of times of adjusting the workshop equipment related to the production sequence of vehicles is minimized, thereby reducing the adjustment cost and improving the production efficiency. The multiple process routes mainly include the following two situations, as shown in FIG. 1: Figure 1 The first is to balance the overall production line rhythm, and parallel workstations are set at some workstations with slow production rhythm. The second is that due to different complexity of different types of vehicle processes, parallel workstations are added to meet the production of multiple types of vehicles, or due to special process requirements of some types of vehicles, new workstations need to be designed and laid out for them. In this mode, the production sequence of vehicles will change many times, thereby causing the number of times of adjusting the workshop equipment to change, which directly affects the production efficiency and cost of the workshop. Therefore, when determining the production sequence, the influence of the change of the production sequence on the number of times of adjusting the workstation equipment during the production process also needs to be considered.

[0009] The premise assumptions of the single workshop mixed-model production sequencing problem with multiple process routes include:

[0010] (1) Each vehicle arrives at the shunt before the parallel workstation at equal rhythm intervals.

[0011] (2) If multiple vehicles are simultaneously processed on the parallel workstation, they are discharged from the parallel workstation according to the first-in first-out principle.

[0012] (3) If a vehicle cannot immediately enter the next workstation for processing, it needs to temporarily enter the buffer area between workstations to wait until it is separated from the vehicle that has just entered the next workstation for processing by one rhythm interval.

[0013] The single workshop mixed-model production sequencing problem with multiple process routes is described as follows:

[0014] n vehicles need to pass through m workstations in a workshop for processing, h represents the vehicle index, h={1,2,…,n}, a represents the workstation index, a={1,2,…,m}; I represents the set of vehicle attributes, i represents the i th attribute of the vehicle, i∈I; J i represents the set of characteristics of the i th attribute of the vehicle, j represents the j th characteristic of the i th attribute of the vehicle, j∈J i ; O represents the set of production queues, O=(O 1 ,O 2 ,…,O d ), where d represents the number of production queues; p represents the production queue index, p={1,2,…,d}; O represents the h th vehicle in O p ; T represents the processing time of the h th vehicle in O p at the workstation a; and T represents the processing time of the h th vehicle in Op Start processing time of the hth vehicle at station a; O represents the production queue p Finish processing time of the hth vehicle at station a; Δt represents the interval between the processing start times of two adjacent vehicles; Z a is a 0,1 variable, Z a = 1 if the adjustment of the equipment at station a is affected by the order of the production queue, otherwise Z a = 0; W p,a is a 0,1 variable, W p = 1 if the production queue entering station a is O p,a , otherwise W p,a = 1; is a 0,1 variable, if the attribute features of the vehicles with the sequence numbers h and h+1 in the production queue O p are different, then otherwise

[0015] Step 2: Establish a mathematical model for the mixed production of a single vehicle in a multi-process route.

[0016] The objective function is:

[0017]

[0018] i.e. to minimize the number of adjustments of the equipment at the stations associated with the production sequence.

[0019] The constraint conditions are:

[0020]

[0021]

[0022]

[0023]

[0024] X h,h',p+1 = X h,h',p · Y h,h',p (6)

[0025]

[0026]

[0027] wherein formula (2) ensures that each vehicle in the queue can enter the next station for processing only after the processing at the station is completed; formula (3) indicates that all vehicles are processed at the stations with the same interval; formula (4) determines the finish processing time of each vehicle; and formula (5) indicates that vehicles with the same attribute features are continuously produced G iAfter the last vehicle, the car needs to be forced to switch to another feature; formula (6) and (7) determine the vehicles that are completed at the same time on parallel stations, and the order of the vehicles out of the parallel stations; formula (8) determines the order of vehicles h and h' in the pth queue.

[0028] Step 3: adaptive genetic algorithm optimization solution.

[0029] S31: parameter initialization: set the population size Nind, the generation gap is OPT, the maximum and minimum crossover probability is P c1 , the maximum and minimum mutation probability is M1, M2, and the maximum number of iterations of the algorithm is Maxgen. c2

[0030] S32: population initialization: randomly generate Nind chromosomes using integer coding method, each chromosome corresponds to a vehicle online sequence, and each gene in the chromosome represents a vehicle, and vehicles with the same attribute feature are coded the same.

[0031] S33: fitness function value calculation: take the reciprocal of the objective function 1 / f as the fitness function Fitness, that is, calculate the fitness value of all individuals in the population according to Fitness = 1 / f.

[0032] S34: selection operation: selection operation is performed by roulette method, and selection is performed according to the generation gap OPT and individual fitness function value.

[0033] S35: crossover and mutation operation: according to the adaptive crossover probability and mutation probability, the population after selection operation is subjected to two-point crossover and insertion mutation operation.

[0034] The adaptive crossover probability calculation formula is as follows:

[0035]

[0036] Where P c is the crossover probability, f' is the individual fitness value, f avg is the average fitness value of the population, and f max is the maximum fitness value of the individual in the population.

[0037] The adaptive mutation probability calculation formula is as follows:

[0038]

[0039] Where P m is the mutation probability.

[0040] S36: population merging: adopt the elite reservation strategy, select the top 10% of the elite individuals in the parent population according to the fitness, and combine them with the offspring individuals to form a new population.​

[0041] S37: judging whether the algorithm reaches the iteration termination condition, if yes, outputting the optimal individual, and ending the algorithm, otherwise returning to step S33.

[0042] The beneficial technical effects of the present application are:

[0043] (1) The present application considers the actual situation of multiple process routes in the automobile production process. Due to the existence of multiple process routes, the automobile production sequence will change in the production process, which will disrupt the original production plan of the production management department. However, this problem is often ignored in the existing modeling process of automobile mixed flow production scheduling, resulting in that the production scheduling result does not conform to the actual situation. The present application fully considers the influence of the change of automobile production sequence caused by multiple process routes on the adjustment of workshop station equipment, establishes a single workshop automobile mixed flow production scheduling mathematical model with multiple process routes, so that the production scheduling model conforms to the actual situation and can more accurately guide the actual production.

[0044] (2) The present application extracts the common features of production constraints and optimization objectives of welding, painting and assembly workshops, and establishes a general production scheduling model for each workshop. In the existing modeling process of automobile mixed flow production scheduling, it is usually modeled for welding, painting and assembly workshops one by one, which lacks unified and general model guidance, resulting in a complex modeling process and inflexible and inconvenient operation. The present application reasonably extracts the common features of each workshop and establishes a general model.

[0045] (3) The present application uses an adaptive genetic algorithm to solve the single workshop automobile mixed flow production scheduling mathematical model with multiple process routes. A two-point crossover method and an insertion mutation method based on adaptive crossover and mutation probability are designed to improve the global and local search performance of the algorithm, avoid the algorithm from falling into local optimum, and make it more superior than the standard genetic algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a schematic diagram of multiple process routes;

[0047] Figure 2 is a schematic diagram of the adaptive genetic algorithm (AGA) process;

[0048] Figure 3 is a case 1 of multiple process routes;

[0049] Figure 4 is a case 2 of multiple process routes;

[0050] Figure 5 is a case 3 of multiple process routes. DETAILED DESCRIPTION

[0051] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0052] A multi-process route single workshop automobile mixed flow scheduling optimization method of the application comprises the following steps:

[0053] Step 1: Determine the description and related assumptions of the multi-process route single workshop automobile mixed flow scheduling problem.

[0054] The single workshop automobile mixed flow scheduling problem with multiple process routes is to develop an optimal scheduling sequence for automobiles with different attribute characteristics, so that the number of adjustments of the workshop station equipment related to the automobile scheduling sequence is minimized, thereby reducing the adjustment cost and improving the production efficiency. The multi-process route mainly includes the following two situations, as shown in the following figure: Figure 1 The first is to set parallel stations at some slow production stations in order to balance the overall production line rhythm; the second is to add parallel stations to meet the production of multiple types of automobiles due to different complexity of automobile processes, or to design and layout new stations for automobiles with special process requirements. Under this mode, the automobile scheduling sequence will change many times, thereby causing the number of station equipment adjustments to change, directly affecting the workshop production efficiency and cost. Therefore, when developing the scheduling sequence, the impact of the change of the scheduling sequence on the number of station equipment adjustments during the production process also needs to be considered.

[0055] The assumptions of the single workshop automobile mixed flow scheduling problem with multiple process routes include:

[0056] (1) Each automobile arrives at the shunt before the parallel station at equal rhythm intervals.

[0057] (2) If multiple cars are simultaneously processed on the parallel station, they are discharged from the parallel station according to the first-in, first-out principle.

[0058] (3) If an automobile cannot immediately enter the next station for processing, it needs to temporarily enter the buffer area between stations to wait until it is separated from the previous automobile entering the next station for processing by one rhythm.

[0059] The single workshop automobile mixed flow scheduling problem with multiple process routes is described as follows:

[0060] n automobiles need to pass through m stations in a workshop for processing, h represents the automobile index, h={1,2,…,n}, a represents the station index, a={1,2,…,m}; I represents the set of automobile attributes, i represents the i-th attribute of the automobile, i∈I; J i represents the set of characteristics of automobile attribute i, j represents the j-th characteristic of automobile attribute i, j∈J i ; O represents the set of scheduling queues, O=(O 1 ,O 2 ,…,O d), where d denotes the number of production queue; p denotes the production queue index, p = {1, 2, …, d}; represents the hth vehicle in the production queue O p in the production queue O represents the hth vehicle in the production queue O p in the production queue O represents the hth vehicle in the production queue O p in the production queue O represents the hth vehicle in the production queue O p in the production queue O represents the hth vehicle in the production queue O a is a 0, 1 variable, if the equipment adjustment of station a is affected by the sequence of the production queue, then Z a = 1, otherwise Z a = 0; W p,a is a 0, 1 variable, if the production queue entering station a is O p , then W p,a = 1, otherwise W p,a = 1; is a 0, 1 variable, if the attribute features of the hth and h+1th vehicles in the production queue O p are different, then otherwise

[0061] Step 2: Establish a mathematical model of mixed-model production scheduling for single vehicle in multi-process route.

[0062] The objective function is:

[0063]

[0064] that is, minimizing the number of equipment adjustments of the station associated with the production sequence.

[0065] The constraint conditions are:

[0066]

[0067]

[0068]

[0069]

[0070] X h,h',p+1 = X h,h',p · Y h,h',p (6)

[0071]

[0072]

[0073] Wherein, formula (2) guarantees each car in the queue can enter the next station for processing after the processing in the station is completed; formula (3) all cars are put into each station for processing at the same time interval; formula (4) determines the completion time of each car; formula (5) represents that the cars with the same attribute feature are continuously produced G i after one car is produced, the car needs to be forcibly switched to another feature car; formula (6) and (7) determine the cars that are simultaneously processed in the parallel stations and the order of the cars going out of the parallel stations; formula (8) determines the order of the cars h and h' in the pth queue.

[0074] Step 3: adaptive genetic algorithm optimization solution.

[0075] The algorithm flow chart of the adaptive genetic algorithm is shown in Figure 2 , and specifically is as follows:

[0076] S31: parameter initialization: set the population size Nind, the generation gap is OPT, the maximum and minimum crossover probabilities are P c1 , P c2 , the maximum and minimum mutation probabilities are M1 and M2, and the maximum iteration number of the algorithm is Maxgen.

[0077] S32: population initialization: Nind chromosomes are randomly generated by using the integer coding method, each chromosome corresponds to a car online sequence, each gene in the chromosome represents a car, and the cars with the same attribute feature are coded in the same way.

[0078] S33: fitness function value calculation: the reciprocal of the objective function 1 / f is taken as the fitness function Fitness, that is, the fitness values of all individuals in the population are calculated according to Fitness=1 / f.

[0079] S34: selection operation: the selection operation is performed by using the roulette method, and the selection is performed according to the generation gap OPT and the individual fitness function value.

[0080] S35: crossover and mutation operation: according to the adaptive crossover probability and the mutation probability, the population after the selection operation is subjected to two-point crossover and insertion mutation operation.

[0081] The adaptive crossover probability calculation formula is as follows:

[0082]

[0083] Wherein, P c is the crossover probability, f' is the individual fitness value, f avg is the average fitness value of the population, and f max is the maximum fitness value of the individual in the population.

[0084] The adaptive mutation probability calculation formula is as follows:

[0085]

[0086] wherein P m is the mutation probability.

[0087] S36: Population merging: the top 10% of the elite individuals in the parent population are selected by the elite preservation strategy, combined with the offspring individuals to form a new population.

[0088] S37: Determine whether the algorithm reaches the iteration termination condition. If yes, output the optimal individual, and the algorithm ends. Otherwise, return to step S33.

[0089] Embodiment:

[0090] Taking a painting workshop as an application background, examples are constructed for various process routes. The multi-process routes are shown in Figure 3 , Figure 4 , Figure 5 , and the experimental examples constructed in the three cases are respectively recorded as Case01-T, Case02-T, and Case03-T. For the painting workshop, the main workstations that affect the workshop adjustment cost are the topcoat workstations. The switching of the spray gun pigment on this workstation will directly affect the production cost of the painting workshop. It is assumed that 4 types of vehicles and 4 colors of automobiles can be produced in mixed flow on the production line of the painting workshop. The daily output of the painting workshop is set to 100, 200, and 400 vehicles. The vehicle type, color, and quantity under each scale are shown in Tables 1, 2, and 3.

[0091] Table 1 Vehicle type, color, and quantity table (total amount 100 vehicles)

[0092]

[0093] Table 2 Vehicle type, color, and quantity table (total amount 200 vehicles)

[0094]

[0095] Table 3 Vehicle type, color, and quantity table (total amount 400 vehicles)

[0096]

[0097] The mathematical model of the example is established according to formulas (1)-(8), and the model is solved by using an adaptive genetic algorithm (AGA). Numerical experiments are performed through a Python 3.7 platform, and the AGA and a traditional genetic algorithm (GA) are compared. In each example, 10 runs are performed, and the optimal solution Best and the average value Avg of the 10 run results are compared. The experimental results are shown in Table 4.

[0098] Table 4: Solution results of three examples

[0099]

[0100] The experimental results show that, under different process routes and different vehicle scales, the solution results of the adaptive genetic algorithm are better than those of the traditional genetic algorithm. From the comparison results of the average value row optimal solution Best, in the examples Case01-T, Case02-T and Case03-T, the AGA is improved by 15.47%, 14.85% and 17.72% compared with the GA, respectively. From the comparison results of the average value row average value Avg, in the examples Case01-T, Case02-T and Case03-T, the AGA is improved by 15.50%, 17.51% and 17.78% compared with the GA, respectively. It can be seen that the multi-process route single vehicle mixed flow scheduling problem model and the solving method proposed in the present application are superior to the prior art.

Claims

1. A method for optimizing mixed-flow production scheduling in a single workshop for automobile manufacturing with multiple process routes, characterized in that, Includes the following steps: Step 1: Determine the description and relevant assumptions of the multi-process route single-workshop mixed-flow automotive production scheduling problem; The underlying assumptions for mixed-flow automotive production scheduling in a single workshop with multiple process routes include: (1) Each car arrives at the branch point before the parallel workstation at equal intervals; (2) If multiple cars are processed simultaneously at a parallel workstation, the cars shall be taken out from the parallel workstation according to the first-in-first-out principle; (3) Cars that cannot immediately enter the next workstation for processing must temporarily enter the buffer zone between workstations and wait until there is a one-beat interval between them and the previous car entering the next workstation for processing. The problem of mixed-flow scheduling for single-workshop automotive production with multiple process routes is described as follows: n cars need to be processed through m workstations in a certain workshop. Let h represent the car index, h = {1, 2, ..., n}, and a represent the workstation index, a = {1, 2, ..., m}. Let I represent the set of car attributes, and i represent the i-th attribute of the car. J i Let represent the feature set of car attribute i, and j represent the j-th feature of car attribute i. O represents the set of production scheduling queues, O = (O 1 O 2 ,…,O d ), where d represents the number of production queues; p represents the index of the production queue, p={1,2,…,d}; Indicating the production scheduling queue The hth car in the middle; Representative production queue The processing time of the hth car at workstation a; Representative production queue The start time of processing of the hth car at workstation a; Representative production queue The completion time of the hth car at workstation a; Z represents the time interval between the production launches of two adjacent vehicles; a Let Z be a variable of 0 or 1. If the equipment adjustment at workstation a is affected by the automobile production queue order, then Z... a =1, otherwise Z a =0; W p,a The variables are 0 and 1. If they enter the production queue of workstation a, it is... Then W p,a =1, otherwise W p,a =0; If the production queue is a variable of 0 or 1, If the car attributes with sequential serial numbers h and h+1 are different, then... ,otherwise ; Step 2: Establish a mathematical model for mixed-flow production scheduling of automobiles in a single workshop with multiple process routes; The objective function is: （1） That is, to minimize the number of times workshop workstation equipment is adjusted in relation to the production scheduling sequence; The constraints are: （2） （3） （4） （5） （6） （7） （8） Equation (2) ensures that each car in the queue can only enter the next workstation for processing after it has been processed at the current workstation; Equation (3) ensures that all cars are put into processing at each workstation at the same time interval; Equation (4) determines the completion time of each car; Equation (5) indicates that cars with the same attribute characteristics are continuously scheduled for production. i After a vehicle is completed, it needs to be forcibly switched to a vehicle with a different characteristic; Equations (6) and (7) determine the order in which vehicles that are processed simultaneously at the parallel workstations exit the parallel workstations; Equation (8) determines the order in which the vehicles exit the parallel workstations. and The order of the p-th queue; Step 3: Optimize and solve using an adaptive genetic algorithm; S31: Parameter initialization: Set the population size Nind, generation gap to OPT, and maximum and minimum crossover probabilities to P. c1 P c2 The maximum and minimum mutation probabilities are P. m1 P m2 The maximum number of iterations for the algorithm is Maxgen; S32: Population initialization: Nind chromosomes are randomly generated using an integer encoding method. Each chromosome corresponds to a car online sequence. Each gene in the chromosome represents a car. Cars with the same attribute characteristics have the same code. S33: Fitness function value calculation: The fitness function is calculated using the reciprocal of the objective function, 1 / f. That is, the fitness value of all individuals in the population is calculated based on Fitness = 1 / f. S34: Selection Operation: The selection operation is performed using a roulette wheel method, based on the generation gap OPT and the individual fitness function value; S35: Crossover and mutation operations: Based on the adaptive crossover and mutation probabilities, the selected population will undergo two-point crossover and insertion mutation operations. The adaptive crossover probability calculation formula is as follows: （9） Among them, P c For crossover probability, f is the individual fitness value. avg f is the average fitness value of the population. max This represents the maximum fitness value of an individual in the population. The formula for calculating the adaptive mutation probability is as follows: （10） Among them, P m The mutation probability; S36: Population Merging: Using an elite preservation strategy, select the top 10% of the most fit individuals from the parent population and combine them with offspring individuals to form a new population. S37: Determine whether the algorithm has reached the iteration termination condition. If it has, output the optimal individual and the algorithm ends; otherwise, return to step S33.

Images