Complex equipment-oriented multi-component production process combination optimization method

Abstract

The invention relates to a multi-component production process combination optimization method for complex equipment, and belongs to the technical field of machining process optimization. The method comprises the following specific steps: step 1, establishing an objective function by minimizing processing cost, time cost, environment and human damage cost, and establishing processing process constraint conditions; step 2, establishing a representation mode of the uncertainty set; 3, selecting the number of available equipment and / or process time as an uncertain variable, representing the uncertain variable based on the representation mode in the step 2, and establishing an equipment number and / or process time uncertain robust optimization model in combination with the target function and the constraint condition established in the step 1; and 4, carrying out iterative optimization on the robust optimization model to obtain an optimal process combination.

Description

Technical Field

[0001] The invention relates to a method for optimizing the combination of production processes for multiple components of complex equipment, and belongs to the technical field of processing technology optimization. Background Art

[0002] At present, there are the following problems in the selection of process routes for component production:

[0003] In terms of process route selection and process scheduling: Most of the existing technical solutions first carry out process scheduling for a single component, and then conduct centralized scheduling. There is little research on the integrated collaborative scheduling of multiple components.

[0004] Uncertainty research: Existing technologies for researching uncertain production in workshops use some box-type uncertainty sets to describe processing time, product quantity requirements, etc. This results in overly conservative models and high production costs.

[0005] In terms of decision-making objectives: existing technologies mostly adopt a single objective, such as focusing on production cost or production time cost; when some technologies adopt multiple objectives, they simply add multiple objectives linearly, and the final design points obtained are relatively simple, and the scheduling scheme is less robust. Summary of the invention

[0006] In view of this, the present invention provides a method for optimizing the combination of production processes for complex equipment with multiple components, which performs process selection and production scheduling for the multi-component processing of complex equipment products through problem analysis, mathematical model construction, uncertainty factor characterization, and solution algorithm design.

[0007] The technical solution for implementing the present invention is as follows:

[0008] A method for optimizing the production process combination of multiple components of complex equipment, the specific process is as follows:

[0009] Step 1: Establish the objective function and the constraints of the processing process by minimizing the processing cost, time cost, environment and human damage cost;

[0010] Step 2: Establish a representation model for the uncertain set;

[0011] Step 3: Select the number of available equipment and / or process time as uncertain variables, characterize the uncertain variables based on the characterization mode of step 2, and establish an uncertain robust optimization model for the number of equipment and / or process time by combining the objective function and constraint conditions established in step 1;

[0012] Step 4: Perform iterative optimization on the robust optimization model to obtain the optimal process combination.

[0013] Furthermore, the constraints of the processing process of the present invention are:

[0014] (1) Only one process route can be selected for each component during the entire processing process;

[0015] (2) When a process step is selected, the process is also selected;

[0016] (3) The entire processing process cannot exceed the number of available workers;

[0017] (4) The priority and timing requirements of different components;

[0018] (5) Time requirements for the previous and next steps when processing the same component;

[0019] (6) The maximum time cycle for processing all parts meets the maximum time span requirements.

[0020] Furthermore, the robust optimization model for uncertain equipment quantity of the present invention is:

[0021]

[0022] Among them, λ i is the number of optional process routes for component i; is the processing cost of the j-th process of component i; Y is the environmental and human damage cost of the j-th process of component i; ij The jth process for the i-th component is selected; T span The maximum time span for processing all parts; q ijωm is the number of machines m required for the ωth process of the jth process of component i; X ijωt The ωth process of the jth process of the i-th component starts processing at time t; is the range of the number of devices; Γ m is the uncertain parameter of machine m; φ m and γ m is the introduced dual variable, and φ m ≥0, β m is the disturbance ratio, is the maximum disturbance value of the equipment quantity, and Γ is the parameter of all types of machine uncertainty.

[0023] Furthermore, the uncertain robust optimization model of processing time of the present invention is:

[0024]

[0025] Among them, λ i is the number of optional process routes for component i; is the processing cost of the j-th process of component i; Y is the environmental and human damage cost of the j-th process of component i; ij The jth process for the i-th component is selected; T span The maximum time span for processing all parts; q ijωm The number of machines m required for the ωth step of the jth process of component i; represents the maximum disturbance value, represents the disturbance ratio; is the explicit value or mean of the processing time, ψ ijω is the uncertain parameter of the processing time of each process, Ω ij is the uncertainty level of the j-th process time of component i.

[0026] Furthermore, the constraint conditions of the present invention: the priority and time sequence requirements between different components are expressed as:

[0027]

[0028] Constraints: The time requirements for the previous and next processes when processing the same component, expressed as:

[0029]

[0030] Among them, Ω ij is the uncertainty level of process processing time.

[0031] Furthermore, in step 4 of the present invention, an improved NSGA-III algorithm is used to solve the optimization model, and the encoding and decoding method of the improved NSGA-III algorithm is:

[0032] Coding method: The first column of the chromosome represents the process route code selected for each component, and the integers in the remaining columns represent whether each process is processed during this time period; when decoding: the first integer in each row of the chromosome represents the selected process code, and the subsequent numbers are 0, which means that the process is not processed during this time period, and greater than or equal to 1, which means that the process is processed during this time period, and the duration of a single process in the chromosome is equal to the original processing time of the process.

[0033] Furthermore, the improved NSGA-III algorithm of the present invention further includes a chromosome correction: during the correction, from the time period T 1 to T dCheck each type of equipment and personnel step by step. If there is surplus equipment and personnel in a time period, increase the processing steps in that time period to shorten the overall processing time, and only consider the surplus processing capacity of equipment or workers once in each time period. If the equipment or personnel in each time period does not meet the constraints, randomly select one or several processes from all processes in that time period to schedule production later to meet the overall constraints of that time period. After performing the above operations for the entire time period, all constraints can be met by individuals.

[0034] Furthermore, the fitness function of the improved NSGA-III algorithm described in the present invention is: let the individual objective function be F, and the maximum value of the group objective function be F max , the new fitness value is F′, then the constructed fitness function is: in To set parameters.

[0035] Furthermore, the probability of elite individual retention in the improved NSGA-III algorithm of the present invention is p′,

[0036]

[0037] Among them, Iter max is the maximum number of iterations, Iter is the current number of iterations, and Iter′ is a hyperparameter.

[0038] Furthermore, in the improved NSGA-III algorithm of the present invention, crossover is performed between chromosomes, i.e., parent crossover, and when the parents cross over, the same component position of the two chromosomes is used to cross over to generate offspring chromosomes;

[0039] After the chromosome crossover, the mutation probability is set to mutate only in the first column of each chromosome, that is, only the process route code of the component is changed; after the crossover and mutation are executed, the chromosome needs to be modified.

[0040] Beneficial effects:

[0041] First, the present invention aims to solve the problems of high cost of multi-component production process of complex equipment products and too many process combination schemes. In order to improve production efficiency and ensure processing quality, it is necessary to select a unique process route for each component of the product, consider the numerous constraints of the production workshop for correct modeling, ensure the effectiveness and practicality of the production and processing plan, and construct an uncertainty set to characterize the uncertain parameters so that the model and the final processing plan have better robustness, that is, to schedule the processes under the constraints of equipment, number of personnel, etc., that is, to determine the start time of each process, so as to complete the production and processing process in an orderly manner.

[0042] Second, complex equipment products have many parts and a long processing cycle, so the parameters and decision variables in the multi-objective robust model are also very large. The improved NSGA-III algorithm is used to optimize and solve the model to obtain the Pareto solution of the model in a short time. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0044] Figure 1 A roadmap for the method of the present invention;

[0045] Figure 2 Schematic diagram of encoding and decoding;

[0046] Figure 3 This is a schematic diagram of chromosome correction;

[0047] Figure 4 Schematic diagram of exponential fitness and linear fitness;

[0048] Figure 5 Parent crossover example diagram;

[0049] Figure 6 Reference point example diagram;

[0050] Figure 7 Flowchart for improving the NSGA-III algorithm. DETAILED DESCRIPTION

[0051] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0052] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0053] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0054] The design concept of the present invention is: the production of complex equipment products often faces problems such as high cost of multi-component production processes and too many process combination schemes. In order to improve production efficiency and ensure processing quality, it is necessary to select a unique process route for each component of the product, and to schedule the process under the constraints of equipment, number of personnel, etc., that is, to determine the start processing time of each process to complete the production process in an orderly manner. At the same time, in order to better evaluate the decision-making plan, a multi-objective model is established from three aspects: processing time cost, expense cost, human factors and environmental friendliness; in order to resist the influence of uncertain factors such as equipment failure and processing time disturbance in reality, it is necessary to characterize the uncertain factors to resist the occurrence of uncertain factors. In order to effectively solve the proposed model, it is necessary to design an improved NSGA-III algorithm to solve the multi-objective robust optimization model to improve decision-making efficiency.

[0055] The present application embodiment provides a robust optimization model construction method for complex equipment multi-component production process combination decision-making. The model constructed by this method can meet the following requirements: Let the set of components required for the production of complex equipment products be I, and each component i (i∈I) has λ i There are q optional process routes, and the processing of each component is independent of each other. The number of m-th machines required for the k-th process of component i is q ijωm , the number of workers of type n required is h ijωn , requiring to determine a unique process from multiple alternative processes for each component under multiple objectives (cost, time, environment and human cost), meeting the priority of component processing, and the number of workshop equipment and personnel, and determine the processing time of all processes in the process, so as to reduce various costs while scheduling production. Figure 1 As shown, the specific process of this method is:

[0056] Step 1: Establish the objective function and constraints;

[0057] S101: process condition setting, parameter definition and decision variable setting;

[0058] Process condition setting: (1) The processing of parts is independent of each other and does not interfere with each other; (2) All processes in the process of all parts are executed sequentially; (3) If two parts have processing priorities, the processing of the other part can only start after all processes of the first part are completed.

[0059] Parameter definition: I: component set, indexed by i; λ i is the number of optional process routes for component i; j is the jth process route; is the total number of processes in the j-th process route of component i; ω is the ω-th process; q ijωm is the number of machines m required for the ωth process of the jth process of component i; h ijωn The number of worker types n required for the ωth process of the jth process of component i; α m is the number of the mth type of machine; α′ is the number of types of machines; δ n is the total number of worker type n; η ijω is the time required for the ωth process of the jth process to process component i (including the time for transportation, etc.); It is a 0-1 parameter, =1, indicating that component i 1 Must be in component i 2 pre-processing; otherwise it is equal to 0; t represents time, dividing the processing process into multiple time periods, T 0 represents the first time period, T d Indicates the last time period; M indicates a large positive number; is the processing cost of the j-th process of component i; is the environmental and human damage cost of the j-th process of component i; T span The maximum time span for machining all parts.

[0060] Decision setting: X ijωt is a 0-1 variable, indicating that the ωth process of the jth process of the i-th component starts processing at time t; Y ij It is a 0-1 variable, indicating that the j-th process of the i-th component is selected.

[0061] S102: Determination of objective function and constraints

[0062] Objective function: The objective function is established by minimizing the processing cost, time cost, environment and human damage cost as follows:

[0063]

[0064] Constraints:

[0065] (1) During the entire processing process, only one process route can be selected for each component:

[0066]

[0067] (2) When a process step is selected, it indicates that the process is also selected:

[0068]

[0069] (3) The available quantity of each processing equipment during the entire processing process cannot exceed:

[0070]

[0071] (4) The entire processing process cannot exceed the number of available workers:

[0072]

[0073] (6) The priority and timing requirements between different components, ω′ 2 Indicates component i 2 Crafts 2 The first process:

[0074]

[0075] (7) Time requirements for the previous and next processes when processing the same component:

[0076]

[0077] (8) Linearize equation (3):

[0078]

[0079] (9) Maximum time cycle for all parts processing:

[0080]

[0081] Step 2: Establish a representation model for uncertain sets

[0082] The production of complex equipment products involves many uncertain factors, such as production time, number of equipment failures, etc. These factors will lead to cost changes and uncertainty in production scheduling. If the preset number of machine failures is too low, the model will be too conservative and the cost will be high; if the preset number of machine failures is too high, it will lead to a waste of equipment resources. If the probability distribution of uncertain parameters is clearly known, a random programming model can be established, and the uncertain parameters can be modeled and calculated by taking the mean, etc. However, since it is difficult to obtain the probability distribution of uncertain parameters, it is necessary to establish an uncertainty set and establish a robust optimization model on this basis.

[0083] How to select a suitable uncertainty set to describe the uncertain parameters directly affects the model solution speed, conservatism and optimization results. Therefore, it is necessary to select a suitable uncertainty set according to the characteristics of each uncertainty factor, so as to avoid the uncertainty of the parameters and obtain better robustness.

[0084] The first box uncertainty set

[0085] Box uncertainty sets are widely used in robust optimization, but they are too conservative. Berimas and Sim proposed a robust optimization theory of protection functions: when the left side of the constraints of the linear programming model contains uncertain factors, a protection function is added, and the maximum disturbance term is added to the left side of the inequality. Then, the linear programming strong duality theory is used to transform the model into a linear robust optimization corresponding model.

[0086] Defined as an uncertain parameter in, is a definite value or mean, is the fluctuation range and z uv ∈[-1,1] is a symmetric random variable, and ||z u || 1 ≤Γ u . Define the following constraints:

[0087] Ax≤b,x≥0 (13)

[0088] Where A(U×R) is the coefficient matrix. Assume that the u-th row in the right-hand side term b(R×1) has uncertain parameters. u | represents the number of uncertain parameters in the uth row, parameter Γ u ∈[0,|θ u |] represents the uncertainty level, which is used to adjust the conservativeness of the model. u It is not necessarily an integer. It takes values ​​within the range of the number of uncertain parameters. Not all uncertain parameters are uncertain. The uth row has at most The uncertain parameters vary within their intervals, and the other points are averaged. m The larger the model, the more conservative it is, and vice versa.

[0089] Define the protection function g(θ u ,Γ u ), then formula (13) can be written as the difference between the nominal value and the protection function, that is, formula (13) is equivalent to

[0090]

[0091] in,

[0092]

[0093] Among them, S u represents the set of uncertain parameters in the u-th row of constraints that deviate from the nominal value. u When the value is not an integer, there are at most parameters deviate from their nominal values, in particular, when Γ u When rounding,

[0094]

[0095] In order to transform equation (14) into a more manageable constraint, an auxiliary variable k is introduced v , g(θ u ,Γ u ) is transformed into a linear problem:

[0096]

[0097] Transform equation (19) into the following dual problem:

[0098]

[0099] Among them, φ u and γ uv is a dual variable, so formula (14) can be transformed into formula (24):

[0100]

[0101] When Γ u = 0, that is, no parameter deviates from the nominal value, and the problem is transformed into a deterministic problem. u =θ u When , the problem is a fully robust model, that is, all parameters take the maximum value.

[0102] The second ellipsoid uncertainty set

[0103] As mentioned before, the definition is like an uncertain parameter in is a definite value or mean, is the fluctuation range and z uv ∈[-1,1] is a symmetric random variable, and ||z u || 2 ≤Ω u .

[0104] As constrained by equation (13), the uncertain parameters are in the rows of the coefficient matrix. u ∈[0,|θ u|] represents the uncertainty level, which is used to adjust the conservativeness of the model. According to the theory of Ben-Tal and Nemirovski, The ellipsoid uncertainty set, the robust equation is

[0105]

[0106] Among them, Ω u is the uncertainty, which characterizes the range of uncertainty parameter disturbance.

[0107] Step three, select the available number of equipment and / or process time as uncertain variables, characterize the uncertain variables based on the characterization model of step two, and combine the objective function and constraints established in step one to establish an uncertain robust optimization model for the number of equipment and / or process time.

[0108] In the following, we will use the box and ellipsoid uncertainty set method to characterize uncertain parameters, select the number of available equipment and process time as uncertain variables, transform the uncertainty set and deterministic constraints into corresponding robust equations, and use this to establish a robust optimization model. Specifically:

[0109] Model with uncertain number of available devices:

[0110] The number of devices in formula (4) is m is a bounded symmetric random variable, Indicates that

[0111]

[0112] in, represents the maximum disturbance value, β m Represents the disturbance ratio. Since each row has only one uncertain parameter, and Γ m Is a continuous value.

[0113] Therefore, the robust model for the uncertain number of available devices is:

[0114]

[0115] st(2),(5)-(12),

[0116]

[0117] Where Γ represents the parameter of all kinds of machine uncertainty, Γ≤α′, and the uncertainty level Γ and the disturbance ratio β can be set in the decision process m To control the number of failed machines.

[0118] Process time uncertainty model:

[0119] The process time includes the transportation process and has a large uncertainty factor. You can choose the ellipsoid uncertainty set to describe the production time of a single process. It can encompass all possible values ​​within a fixed interval. The construction process uncertain parameters are as follows: represents the maximum disturbance value, Represents the disturbance ratio, in the form of ψ ijω ∈[-1,1],

[0120]

[0121] Among them, U E is the uncertainty set of the process time ellipsoid.

[0122] Formula (6) can be written as

[0123]

[0124] Similarly, formula (7) can be written as

[0125]

[0126] Ω ij is the uncertainty level of process processing time.

[0127] In summary, considering the uncertainty of available processing time, the robust optimization model of the multi-component production process of mechanical products under the ellipsoid uncertainty set is:

[0128]

[0129] st(2),(4),(5),(8)-(12),(32)-(34)

[0130] Step 4: Perform iterative optimization on the robust optimization model to obtain the Pareto solution set of the multi-component processing information of the product, obtain the optimal process combination, and determine the component processing plan.

[0131] In this embodiment, the improved NSGA-III algorithm can be used to solve the optimization model, specifically:

[0132] Due to the large data scale and the fact that the problem is NP-hard, the exact algorithm is inefficient to solve, so the improved NSGA-Ⅲ algorithm is used to solve the problem. NSGA-Ⅲ (Non-dominated Sorting Genetic Algorithm Ⅲ) is an advanced multi-objective evolutionary algorithm designed to handle optimization problems with multiple objectives. It is an improvement on the traditional NSGA-Ⅲ algorithm and is suitable for solving high-dimensional multi-objective optimization models. The following describes the improvements to the traditional NSGA-Ⅲ algorithm:

[0133] (1) Encoding and decoding

[0134] Commonly used encoding methods in genetic algorithms include binary encoding, real number encoding, etc. The encoding method directly affects the operation of genetic operators such as the crossover operator and mutation operator of the genetic algorithm, and therefore determines the efficiency of genetic evolution to a large extent.

[0135] In this embodiment, all variables in the deterministic model are 0-1 variables. If binary encoding is used, additional space is required to record information such as the time sequence of the process. Therefore, integer encoding is used here. Figure 2 As shown, the first column of the chromosome represents the process route code selected for each component, and the integers in the remaining columns represent whether each process is processed in this time period. If it is 0, it means that no process of this process is carried out in this time period. If it is 2, it means that the second process of this process is processed in this time period, and so on for other numbers.

[0136] During decoding, the first integer in each row of the chromosome represents the selected process code. The subsequent digits are 0, which means that the process is not processed during this time period. If they are greater than or equal to 1, they mean that the process is processed during this time period. The duration of a single process in the chromosome is equal to the original processing time of the process.

[0137] (2) Create an initial population

[0138] When creating the initial population, it is necessary to ensure that each chromosome represents a feasible solution, and to maximize the uniform distribution of all initial solutions in space to increase population diversity and help the algorithm obtain the best global optimization effect. Therefore, during initialization, the lowest component can be randomly initialized according to the component priority, and then the next level of components can be encoded under the condition of ensuring the order of component processing time.

[0139] After initializing the population random code, each individual needs to be modified to ensure the feasibility of the solution. Figure 3 As shown, the correction time is from time period T 1 to T dCheck each type of equipment and personnel step by step. If there is surplus equipment and personnel in a time period, increase the processing steps in that time period to shorten the overall processing time, and only consider the surplus processing capacity of equipment or workers once in each time period. If the equipment or personnel in each time period does not meet the constraints, randomly select one or several processes from all processes in that time period to schedule production later to meet the overall constraints of that time period. After performing the above operations for the entire time period, all constraints can be met by individuals.

[0140] (3) Calculate fitness

[0141] Each chromosome is an individual. The fitness of an individual is a measure of the degree of advantage of the individual in the survival of the population, which is used to distinguish the "good and bad" of individuals. The fitness is calculated using the fitness function. The fitness function can be obtained through the value of the individual objective function. This embodiment is to minimize the objective function. If a linear change is used, the probability of being abandoned is very high when the individual fitness is small, and the potential for continued optimization is reduced, which makes it easy to fall into a local optimal solution. Therefore, an exponential change can be used instead of a linear change, so that the individual still maintains a certain probability of being selected when the fitness is small, thereby making it easier to obtain the global optimal solution.

[0142] The index changes as follows: If the objective function of an individual is F, the maximum value of the group objective function is F max , the new fitness value is F′, then the constructed fitness function is: in To set the parameters, F max =100, the function graph is as follows Figure 4 shown.

[0143] It can be seen that even when the objective function is near the maximum value, its fitness is still not too low. Therefore, compared with linear changes, the probability of inheritance to the next generation is higher, which helps to enhance the diversity of the population.

[0144] (4)Select

[0145] When performing the selection operation, the traditional roulette method can be used for selection, that is, the probability of an individual being selected is proportional to its fitness. The specific operation will not be repeated here.

[0146] In the traditional crossover genetic algorithm, the optimal fitness of each generation before iteration is quite different. Therefore, in order to increase the search direction and avoid falling into the local optimal solution, the elite individuals are retained to the next generation, and a certain scale of individuals with poor fitness are selected to be inherited to the next generation to increase the search space. If the elite retention probability is p′, then

[0147]

[0148] Among them, Iter max is the maximum number of iterations, Iter is the current number of iterations, Iter′ is a hyperparameter. As the number of iterations increases, the probability of elite retention also increases, and the remaining individuals are composed of performance crossover individuals. When Iter′=0.2, as the iterations proceed, the probability of elite retention gradually approaches 1.

[0149] (5) Crossover and mutation

[0150] Crossover can be performed between chromosomes, i.e., parental crossover. When parental crossover is performed, the same parts of two chromosomes are used to cross over and produce offspring chromosomes, such as Figure 5 shown.

[0151] After the chromosome crossover, the mutation probability is set to mutate only in the first column of each chromosome, that is, to change only the process route code of the component. After the crossover and mutation are completed, the chromosome needs to be corrected. Since the process time of different processes is not exactly the same, it is necessary to ensure that the duration of each process is equal to the original processing time based on the original correction strategy.

[0152] (6) Sorting based on reference points and individual selection

[0153] This step is to select N (number of populations) individuals from the merged population according to the result of fast non-dominated sorting. If the total number of individuals in the first l-1 layers is exactly N after fast non-dominated sorting, then these N individuals can be directly selected. If the total number of individuals in the first l-1 layers is less than N, and the total number of individuals in the first l layers is greater than N, then individuals need to be selected from the individuals in the lth layer so that the total number of selected individuals is N. The specific process is:

[0154] First, non-dominated sorting

[0155] If the objective function has two or more dimensions, when the objective values ​​of all dimensions of a solution are better than the objectives of the corresponding dimensions of another solution, the former solution is said to dominate the other solution. Non-dominated sorting is to decompose the solution set into different levels of Pareto frontiers, that is, to divide a set of solutions into multiple sets, all solutions in each set do not dominate each other, but any solution in the higher level dominates any solution in the lower level. The non-dominated sorting process is as follows:

[0156] Step 1: Determine the number of solutions n dominated by each solution p p And the solution set S dominated by solution p p , set layer = 0

[0157] Step 2: Set n p = 0 are classified into the Pareto solution set F of one level layer middle.

[0158] Step 3: Traverse F layer S for each solution p in p , S p The n of each solution in p Minus 1.

[0159] Step4: layer=layer+1.

[0160] Step 5: Repeat steps 2-4 until all individuals are classified into the Pareto solution set at a certain level.

[0161] Secondly, reference point generation

[0162] In order to make the final Pareto solution evenly distributed, NSGA-Ⅲ adopts a reference point sorting method, first constructing evenly distributed reference points, then establishing a connection between the solution and the reference point, and finally generating a uniformly distributed solution, providing users with multiple balanced solutions. Figure 6 The following are examples of reference points for three quartered targets. After the quartering operation is performed on each side, the intersection points of the parallel quartering points on each side are connected, and the intersection points of the quartering points and the original quartering points are both reference points.

[0163] Finally, linking reference points to individual choices

[0164] The above reference points are evenly distributed in the target space, but if the scale of each objective function is different, resulting in different biases in the solution, for example, the ranges of the two objective functions are [0,10] and [0,100] respectively, then when the solution and the reference point are connected, the distribution of the final solution will be affected. In specific operations, conventional normalization or adaptive normalization can be used. The difference is that the denominator of the scaling formula of the former is the extreme value difference of each objective function, while the latter is the difference between the intercept of each coordinate axis and the minimum value of the corresponding objective function.

[0165] After normalization, it is necessary to establish the connection between the normalized individuals and the reference points to ensure that the reference points are widely distributed throughout the target space. Based on the matching relationship between the individuals and the reference points, the number of individuals connected to each reference point is confirmed, and N individuals are selected as the next generation.

[0166] In summary, the basic process of improving NSGA-III is as follows:

[0167] Step 1: Set algorithm parameters, such as population size, mutation probability, etc.

[0168] Step 2: Calculate evenly distributed reference points based on the equal fractions of the target dimension and the number of objective functions.

[0169] Step 3: Set Iter = 0, encode chromosomes and generate the initial population P 0, and calculate the individual fitness.

[0170] Step 4: Generate offspring population Q through selection, crossover, and mutation iter .

[0171] Step 6: Parent and offspring populations are merged into R iter , that is, R iter =P iter ∪Q iter .

[0172] Step 7: R iter The fitness of individuals is calculated and fast non-dominated sorting is performed.

[0173] Step 8: Normalize the individual target values.

[0174] Step 9: Determine the associated reference point corresponding to each individual and iter N individuals are selected to enter the next generation.

[0175] Step 10: Iter = Iter + 1.

[0176] Step 11: Check whether the maximum number of iterations is reached or the update rate of the three objective functions is less than a given minimum value. If so, the algorithm ends; otherwise, return and repeat Step 4 to Step 10.

[0177] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for optimizing the combination of production processes for complex equipment with multiple components, characterized in that: The specific process is: Step 1: Establish the objective function and the constraints of the processing process by minimizing the processing cost, time cost, environment and human damage cost; Step 2: Establish a representation model for the uncertain set; Step 3: Select the number of available equipment and / or process time as uncertain variables, characterize the uncertain variables based on the characterization mode of step 2, and establish an uncertain robust optimization model for the number of equipment and / or process time by combining the objective function and constraint conditions established in step 1; Step 4: Perform iterative optimization on the robust optimization model to obtain the optimal process combination.

2. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 1 is characterized in that: The constraints of the processing are: (1) Only one process route can be selected for each component during the entire processing process; (2) When a process step is selected, the process is also selected; (3) The entire processing process cannot exceed the number of available workers; (4) The priority and timing requirements of different components; (5) Time requirements for the previous and next steps when processing the same component; (6) The maximum time cycle for processing all parts meets the maximum time span requirements.

3. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 2 is characterized in that: The robust optimization model with uncertain equipment quantity is: Among them, λ i is the number of optional process routes for component i; is the processing cost of the j-th process of component i; Y is the environmental and human damage cost of the j-th process of component i; ij The jth process for the i-th component is selected; T span The maximum time span for processing all parts; q ijωm is the number of machines m required for the ωth process of the jth process of component i; X ijωt The ωth process of the jth process of the i-th component starts processing at time t; is the range of the number of devices; Γ m is the uncertain parameter of machine m; φ m and γ m is the introduced dual variable, β m is the disturbance ratio, is the maximum disturbance value of the equipment quantity, and Γ is the parameter of all types of machine uncertainty.

4. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 2 is characterized in that: The robust optimization model for uncertain processing time is: Among them, λ i is the number of optional process routes for component i; is the processing cost of the j-th process of component i; Y is the environmental and human damage cost of the j-th process of component i; ij The jth process for the i-th component is selected; T span The maximum time span for processing all parts; q ijωm The number of machines m required for the ωth step of the jth process of component i; represents the maximum disturbance value, represents the disturbance ratio; is the explicit value or mean of the processing time, ψ ijω is the uncertain parameter of the processing time of each process, Ω ij is the uncertainty level of the j-th process time of component i.

5. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 4 is characterized in that: The constraints: the priority and time sequence requirements between different components are expressed as: Constraints: The time requirements for the previous and next processes when processing the same component, expressed as: Among them, Ω ij is the uncertainty level of process processing time.

6. The method for optimizing the combination of production processes for complex equipment with multiple components according to any one of claims 1 to 5, characterized in that: The step 4 uses the improved NSGA-III algorithm to solve the optimization model. The encoding and decoding method of the improved NSGA-III algorithm is: Coding method: The first column of the chromosome represents the process route code selected for each component, and the integers in the remaining columns represent whether each process is processed during this time period; when decoding: the first integer in each row of the chromosome represents the selected process code, and the subsequent numbers are 0, which means that the process is not processed during this time period, and greater than or equal to 1, which means that the process is processed during this time period, and the duration of a single process in the chromosome is equal to the original processing time of the process.

7. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 6 is characterized in that: The improved NSGA-III algorithm also includes a chromosome correction: when the correction is made, the time period from T1 to T d Check each type of equipment and personnel step by step. If there is surplus equipment and personnel in a time period, increase the processing steps in that time period to shorten the overall processing time, and only need to consider the surplus processing capacity of equipment or workers once in each time period; if the equipment or personnel in each time period does not meet the constraints, randomly select one or several processes from all processes in that time period and schedule them later to meet the overall constraints of that time period. After performing the above operations for the entire time period, all constraints can be met by the individual.

8. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 6 is characterized in that: The fitness function of the improved NSGA-III algorithm is: Let the individual objective function be F and the maximum value of the group objective function be F max , the new fitness value is F′, then the constructed fitness function is: in To set parameters.

9. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 6 is characterized in that: The probability of elite individual retention in the improved NSGA-III algorithm is p′, Among them, Iter max is the maximum number of iterations, Iter is the current number of iterations, and Iter′ is a hyperparameter.

10. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 6, characterized in that: In the improved NSGA-III algorithm, chromosomes are crossed over, i.e., parental crossover, and when parents cross over, the same component position of two chromosomes is used to cross over to generate offspring chromosomes; After the chromosome crossover, the mutation probability is set to mutate only in the first column of each chromosome, that is, only the process route code of the component is changed; after the crossover and mutation are executed, the chromosome needs to be modified.

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