A complex equipment multi-component production process combination optimization method

Abstract

The application relates to a complex equipment multi-component production process combination optimization method, and belongs to the technical field of process optimization. The specific process is as follows: step one, a target function is established by taking the minimum processing cost, time cost, environment and human factor damage cost as the target function, and processing process constraint conditions are established; step two, a representation mode of an uncertain set is established; step three, the number of available devices and / or process time are selected as uncertain variables, the uncertain variables are represented based on the representation mode of step two, and an uncertain robust optimization model of the number of devices and / or process time is established by combining the target function and the constraint conditions established in step one; and step four, iterative optimization is carried out on the robust optimization model, and an optimal process combination is obtained.

Description

Technical Field

[0001] The present 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] In terms of uncertainty research: Existing technologies use some box-type uncertainty sets to describe processing time, product quantity requirements, etc. in the study of uncertain production in workshops, which makes the model overly conservative and the production cost relatively high.

[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 plan has poor robustness. 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 solutions for implementing the present invention are 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, environmental and human damage cost;

[0010] Step 2: Establish a representation model for the uncertainty 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 model of step 2, and establish a robust optimization model for the uncertain number of equipment and / or process time by combining the objective function and constraints 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 between different components;

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

[0019] (6) The maximum time period 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 The number of machines m required for the ωth process of component i; X ijωt The ω-th process of the j-th 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 number of devices, and Γ is the parameter of all types of machine uncertainty.

[0023] Furthermore, the processing time uncertainty robust optimization model 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; environmental and human error cost of the jth process of the ith part; Y ij the jth process of the ith part is selected; T span the maximum time span of all parts processing; q ijωm the number of machines m required for the ωth process of the jth process of the ith part; representing the maximum disturbance value, representing the disturbance ratio; the processing time is a nominal value or an average value, ψ ijω the uncertainty parameter of the process time of each process, Ω ij the uncertainty level of the process time of the jth process of the ith part.

[0026] Further, the constraint condition of the present application: the priority and time sequence requirement between different parts is represented as:

[0027]

[0028] Constraint condition: the time requirement of the process before and after the process of the same part is represented as:

[0029]

[0030] wherein, Ω ij the uncertainty level of the process time.

[0031] Further, the fourth step of the present application adopts an improved NSGA-III algorithm to solve the optimization model, and the encoding and decoding mode of the improved NSGA-III algorithm is:

[0032] Encoding mode: the first column of the chromosome represents the process route code selected for each part, and the integer in the remaining columns represents whether each process is processed in the time period; when decoding: the first integer of each row of the chromosome represents the selected process code, and the subsequent numbers are 0, which represents that the process does not process in the time period, and greater than or equal to 1, which represents that the process is processed in the time period, and the duration of a single process in the chromosome is equal to the original processing time of the process.

[0033] Further, the improved NSGA-III algorithm of the present application further includes chromosome correction: when correcting, from the time period T dStep by step, each device and personnel are checked, if there is a surplus of devices and personnel in a time period, the processing procedure of the time period is increased to shorten the overall processing time, and the remaining processing capacity of the number of devices or workers is only considered once in each time period. If the device or personnel in each time period does not meet the constraint, one or more processes in the time period are randomly selected and scheduled later to meet the overall constraint condition of the time period. After the above operation is performed on the entire time period, the individual can meet all the constraint conditions.

[0034] Further, the fitness function of the improved NSGA-III algorithm is: let the individual objective function be F, the maximum value of the population objective function be F max , and the new fitness value be F', then the fitness function is constructed as: Wherein is a set parameter.

[0035] Further, the elite individual retention probability in the improved NSGA-III algorithm is p',

[0036]

[0037] Wherein, Iter max is the maximum iteration number, Iter is the current iteration number, and Iter' is a hyperparameter.

[0038] Further, the improved NSGA-III algorithm crosses between chromosomes, i.e. parent crossing, when the parent crossing, the same part position of the two chromosomes is crossed to produce offspring chromosomes;

[0039] After the chromosomes are crossed, the mutation probability is set to only mutate in the first column of each chromosome, i.e. change only the process route code of the part; after the crossing and mutation are performed, the chromosomes need to be corrected.

[0040] Beneficial effects:

[0041] First, the present application aims at the problems of high cost of complex equipment product multi-component production process and too many process combination schemes. In order to improve production efficiency and ensure processing quality, a unique process route needs to be selected for each part of the product, the numerous constraints of the production workshop are considered for correct modeling, the effectiveness and practicality of the production processing scheme are ensured, and the uncertain set is constructed to represent the uncertain parameter, so that the model and the final processing scheme have good robustness, i.e. the start processing time of each process is determined to complete the production processing process in order under the constraint conditions of equipment, number of personnel, etc.

[0042] Second, complex equipment products have many parts and long processing cycles, 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 following briefly introduces the drawings required for use in the embodiments. 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 any 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 Schematic diagram of chromosome correction;

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

[0048] Figure 5 Example diagram of parental crossover;

[0049] Figure 6 Example diagram of reference points;

[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, in the absence of conflict, the following embodiments and features in the embodiments may be combined with each other; and, based on the embodiments in this disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative work are within the scope of protection of this 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 can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0054] The design concept of the present invention is as follows: the production of complex equipment products often faces problems such as high costs in the multi-component production process 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 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 embodiment of the present application 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 complex equipment product production 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 step of the j-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 limitations of workshop equipment and personnel, and to determine the processing time of all steps 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 collection, 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 The number of machines m required for the ωth process of component i; h ijωn The number of worker types n required for the ωth step 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 staff type n; η ijω The time required for the ωth step of the jth process to process component i (including the time for transportation, etc.); is a 0-1 parameter, =1, indicating that component i1 must be processed before component i2; otherwise it is equal to 0; t represents time, dividing the processing process into multiple time periods, T0 represents the first time period, T d Indicates the last time period; M represents 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 jth process of component i; T span The maximum time span for machining all parts.

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

[0061] S102: Determine the objective function and constraints

[0062] Objective function: The objective function is established by minimizing 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 shall not exceed:

[0070]

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

[0072]

[0073] (6) Priority and timing requirements between different parts. ω′2 represents the first step of process j2 of part i2:

[0074]

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

[0076]

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

[0078]

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

[0080]

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

[0082] The production of complex equipment involves numerous uncertainties, such as production time and the number of equipment failures. These factors can lead to cost fluctuations and uncertainty in production scheduling. Predicting too low a number of machine failures can lead to an overly conservative model and high costs; however, setting too high a number can waste equipment resources. If the probability distribution of uncertain parameters is clearly known, a stochastic programming model can be established, using methods such as averaging the uncertain parameters for modeling and calculation. However, since obtaining the probability distribution of uncertain parameters is difficult, it is necessary to establish an uncertainty set and, based on this, a robust optimization model.

[0083] How to select the appropriate uncertain set to describe the uncertain parameters directly affects the model solving speed, the degree of conservation and optimization results. Therefore, we need to select the appropriate uncertain set according to the characteristics of each uncertain factor, to avoid the uncertainty of the parameters while obtaining better robustness.

[0084] The first box-type uncertain set

[0085] Box-type uncertain set is widely used in robust optimization, but it is too conservative. Berimas and Sim proposed the robust optimization theory of protection function: when the linear programming model constraint condition contains uncertain factors on the left side, increase the protection function, increase the maximum disturbance term on the left side of the inequality, and then use the linear programming strong duality theory to convert the model into a linear robust optimization corresponding model.

[0086] Define the uncertain parameter Where, is the nominal value or mean value, is the fluctuation range and z uv ∈[-1,1] is a random variable with symmetric distribution, and ||z u ||1≤Γ u . Define the constraint as follows:

[0087] Ax≤b, x≥0 (13)

[0088] Where, A(U×R) is the coefficient matrix, assuming that the u-th row of the right side term b(R×1) in the constraint has uncertain parameters, |θ u | represents the number of uncertain parameters in the u-th row, and parameter Γ u ∈[0,|θ u |] represents the uncertainty level, which is used to adjust the degree of model conservation. Γ u is not necessarily an integer, taking value within the range of the number of uncertain parameters, not all uncertain parameters are uncertain, and the u-th row has at most uncertain parameters varying within its interval, and the other points taking the mean value. Therefore, the larger Γ m , the more conservative the model, and vice versa.

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

[0090]

[0091] Where,

[0092]

[0093] Among them, S u represents the set of uncertain parameters in the u-th row of constraints that deviate from their nominal values. 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 Equation (14) can be transformed into Equation (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. When Γ 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 above, the definition is like the uncertain parameter in is a definite value or mean, The fluctuation range and z uv ∈[-1,1] is a symmetrically distributed 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 form 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 number of available 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] The following is a method based on the box and ellipsoid uncertainty set to represent uncertain parameters. We 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 them to establish a robust optimization model. Specifically:

[0109] Model with uncertain number of available devices:

[0110] The number of devices α in formula (4) 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 process of transportation and so on, which 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 for 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 size and the NP-hard nature of the problem, exact algorithms are inefficient. Therefore, an improved NSGA-III algorithm was used to solve the problem. NSGA-III (Non-dominated Sorting Genetic Algorithm III) is an advanced multi-objective evolutionary algorithm designed to handle multi-objective optimization problems. 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] Common encoding methods used 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 largely determines the efficiency of genetic evolution.

[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. Subsequent numbers of 0 represent that the process is not processed in this time period. Numbers greater than or equal to 1 represent that the process is processed in this time period, and 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 that all initial solutions are evenly distributed in space to increase population diversity and facilitate the algorithm's optimal global optimization. Therefore, during initialization, the lowest priority components can be randomly initialized, and then the next level of components can be encoded while maintaining the order of component processing time.

[0139] After initializing the random coding of the population, each individual needs to be modified to ensure the feasibility of the solution. Figure 3 As shown, the correction time is from time period T1 to T d Each type of equipment and personnel is checked step by step. If there is excess equipment and personnel in a time period, additional processing steps are added to that time period to shorten the overall processing time. The remaining equipment or worker capacity only needs to be considered once in each time period. If the equipment or personnel in each time period does not meet the constraints, one or more steps are randomly selected from all steps in that time period and scheduled to meet the overall constraints of the time period. After performing the above operation for the entire time period, all constraints are met.

[0140] (3) Calculating fitness

[0141] Each chromosome is an individual. The fitness of an individual is a measure of the degree of advantage of the individual in surviving in the population and is used to distinguish between "good" and "bad" individuals. Fitness is calculated using a fitness function. The fitness function can be obtained through the value of the individual objective function. This embodiment minimizes the objective function. If a linear change is used, the probability of being abandoned when the individual fitness is small is very high, 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, 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 fitness function is constructed as: 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 traditional crossover genetic algorithms, the optimal fitness of each generation before iteration varies greatly. Therefore, in order to increase the search direction and avoid falling into the local optimal solution, elite individuals are retained to the next generation, while a certain number 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, and 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 chromosome crossover, the mutation probability is set to mutate only the first column of each chromosome, changing only the process routing code of the component. After executing crossover and mutation, the chromosome needs to be modified. Because the process times of different processes are not exactly the same, based on the original modification strategy, it is necessary to ensure that the duration of each process is equal to the original processing time.

[0152] (6) Reference point ranking and individual selection

[0153] This step is to select N (number of populations) individuals from the merged population based on the results of the fast non-dominated sort. If the total number of individuals in the first l-1 layers is exactly N after the fast non-dominated sort, 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, a solution is said to dominate another solution if the objective values ​​of all dimensions of the solution are better than the objectives of the corresponding dimensions of the other solution. Non-dominated sorting decomposes the solution set into different levels of Pareto fronts. In other words, it divides a set of solutions into multiple sets, in which all solutions in each set do not dominate each other, but any solution in a higher level dominates any solution in a 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 a 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] Step 4: 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 points, and finally generating a uniformly distributed solution, providing users with multiple balanced solutions. Figure 6 The following example shows three reference points for a target divided into four equal parts. After the quartering operation is performed on each side, lines are drawn to connect the parallel pairs of points on each side. The intersection of these lines and the original quartering points serve as reference points.

[0163] Finally, linking reference points to individual choices

[0164] The reference points are evenly distributed across the target space. However, if the scales of the objective functions are different, resulting in different biases in the solutions, for example, if the ranges of the two objective functions are [0, 10] and [0, 100], respectively, this can affect the distribution of the final solution when linking the solution and the reference points. Conventional normalization or adaptive normalization can be used. The difference is that the denominator of the scaling formula in the former is the difference between the extreme values ​​of each objective function, while the denominator of the scaling formula in the latter is the difference between the intercepts of each coordinate axis and the minimum value of the corresponding objective function.

[0165] After normalization, it is necessary to establish a 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 the chromosome and generate the initial population P0, and calculate the individual fitness.

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

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

[0172] Step 7: R iter The fitness of individuals in the network is calculated and a 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 scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the production process combination of multiple components of complex equipment, characterized by: The specific process is: Step 1: Establish the objective function and the constraints of the processing process by minimizing the processing cost, time cost, environmental and human damage cost; Step 2: Establish a representation model for the uncertainty set; Step 3: Select the number of available equipment and / or process time as uncertain variables, characterize the uncertain variables based on the characterization model of step 2, and establish a robust optimization model for the uncertain number of equipment and / or process time by combining the objective function and constraints established in step 1; Step 4: Iteratively optimize the robust optimization model to obtain the optimal process combination; 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 The number of machines m required for the ωth process of component i; X ijωt The ω-th process of the j-th 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 number of devices, Γ is the parameter of all types of machine uncertainty; 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 for 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 processing time of component i.

2. The method for optimizing the production process combination of multiple components of complex equipment according to claim 1, 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 between different components; (5) Time requirements for the previous and next steps when processing the same component; (6) The maximum time period for processing all parts meets the maximum time span requirements.

3. The method for optimizing the production process combination of multiple components for complex equipment according to claim 1, characterized in that: The constraints are the priority and time sequence requirements between different components, which can be expressed as: Constraints: The time requirements for the previous and next steps when processing the same component are expressed as: Among them, Ω ij is the uncertainty level of process processing time.

4. The method for optimizing the production process combination of multiple components for complex equipment according to any one of claims 1 to 3, 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 in this time period; when decoding: the first integer in each row of the chromosome represents the selected process code, and the subsequent numbers 0 represent that the process is not processed in this time period, and numbers greater than or equal to 1 represent that the process is processed in this time period, and the duration of a single process in the chromosome is equal to the original processing time of the process.

5. The method for optimizing the production process combination of multiple components for complex equipment according to claim 4 is characterized in that: The improved NSGA-III algorithm also includes chromosome correction: when correcting, the time period from T1 to T d Check each type of equipment and personnel step by step. If there are 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, then randomly select one or several processes from all processes in that time period and 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 the individual.

6. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 4, 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 fitness function is constructed as: in To set parameters.

7. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 4, 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.

8. The method for optimizing the combination of production processes for complex equipment with multiple components according to claim 4, characterized in that: In the improved NSGA-III algorithm, crossover is performed between chromosomes, i.e., parental crossover. When the parents cross over, the same component position of the two chromosomes is used to cross over to generate offspring chromosomes; After the chromosomes cross, 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 cross and mutation are executed, the chromosomes need to be modified.

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