Gradient-guided coevolution algorithm for injection molding process parameters

Abstract

The invention discloses a gradient-guided co-evolutionary algorithm for injection molding process parameters. The gradient-guided co-evolutionary algorithm comprises the steps of data acquisition and sample data set construction; obtaining a sample data set xh according to the workpiece quality data, the forming period and the energy consumption data; determining a process response model, and training the process response model by adopting the sample data set xh; calculating a multi-objective function value; constructing a scaling objective function G (x); obtaining a gradient g of the scaling objective function G (x) through a process response model, and updating a process parameter vector xm of the individual; updating the sparse operator population PGA; bidirectional individual exchange between the gradient population PCG and the sparse operator population PGA; and an environment selection and process scheme output step. The gradient-guided co-evolutionary algorithm for the injection molding process parameters has the advantages that the multi-dimensional injection molding process parameters can be efficiently optimized on multiple targets such as quality, molding period and energy consumption, the mold testing frequency is reduced, the debugging period is shortened, and the comprehensive performance of a workpiece is improved.

Description

Technical Field

[0001] This invention relates to optimization techniques for injection molding process parameters, and in particular to a gradient-guided co-evolutionary algorithm for injection molding process parameters. Background Technology

[0002] Injection molding is a process in which molten raw materials are injected, cooled, and demolded to form semi-finished parts of a specific shape. It is one of the most widely used molding methods in plastic product manufacturing, and is extensively used in the production of automotive parts, electronic product housings, appliance housings, and medical devices. A typical injection molding process includes stages such as plasticizing, injection filling, holding pressure, cooling, and demolding.

[0003] The dimensional accuracy, warpage, shrinkage and sink marks, surface quality, production cycle time, and energy consumption of injection molded parts are closely related to multiple process parameters, including melt temperature, mold temperature, filling time or injection speed, holding pressure and holding time, cooling time, back pressure, and screw speed. These process parameters exhibit significant nonlinear coupling, and different optimization objectives (such as quality, molding cycle time, and energy consumption) often conflict with each other. Therefore, optimizing injection molding process parameters is essentially a complex multi-objective, multi-constraint optimization problem.

[0004] In existing technologies, injection molding simulation software is typically used in conjunction with orthogonal experiments or other experimental design methods to obtain quality indicators and molding cycles under different combinations of process parameters. Then, surrogate models such as neural networks are used to fit the process response relationship. Subsequently, a genetic algorithm is used to globally optimize the surrogate model, thereby obtaining a better process parameter scheme. In addition, some studies have proposed multi-objective evolutionary algorithms based on multi-subpopulation and clustering mechanisms. Through steps such as data preprocessing, population initialization, updating guidance vectors, environment selection, and subpopulation partitioning and adjustment, a superior solution set with multiple modalities and objectives is obtained.

[0005] In terms of multi-objective processing, most existing technologies synthesize multiple quality indicators into a single objective through fuzzy weighting or linear weighting. The weights need to be set empirically, making it difficult to unify them under different products or operating conditions, and failing to fully represent the rich Pareto trade-offs between quality, cycle time, and energy consumption.

[0006] In terms of optimization strategies, existing technologies, such as traditional genetic algorithms and particle swarm optimization, typically treat the injection molding process as a black box system and rely solely on the objective function value for random search. Even when a surrogate model can provide gradient information, it rarely uses the first-order gradient or Jacobian matrix to guide the search direction, resulting in limited convergence speed. In high-dimensional process parameter spaces, a large number of function evaluations are often required to obtain satisfactory results.

[0007] Existing evolutionary algorithms for population structure often employ a single-population structure, simultaneously considering global exploration and local convergence within the same population. This coupling of convergence and diversity can easily lead to problems such as slow convergence in the early stages, insufficient diversity in the later stages, or even premature convergence. This is not conducive to obtaining high-quality and uniformly distributed Pareto solutions in high-dimensional, multi-objective injection molding process optimization. Summary of the Invention

[0008] To avoid the shortcomings of the existing technologies, this invention provides a gradient-guided co-evolutionary algorithm for injection molding process parameters, which can efficiently optimize multi-dimensional injection molding process parameters on multiple objectives such as quality, molding cycle and energy consumption, and reduce the number of trial moldings, shorten the debugging cycle and improve the overall performance of the parts.

[0009] The present invention adopts the following technical solution to solve the technical problem.

[0010] The present invention provides a gradient-guided co-evolutionary algorithm for injection molding process parameters, comprising the following steps:

[0011] Step 1: Data acquisition and sample dataset construction; Collect structural information of the target injection molded part, structural information of the mold, and parameters of the injection molding equipment; obtain part quality data, molding cycle and energy consumption data; and obtain the sample dataset xh based on the part quality data, molding cycle and energy consumption data.

[0012] Step 2: Determine the process response model and train it using the sample dataset xh. ;

[0013] Step 3: Use the trained process response model Calculate the values ​​of multi-objective functions;

[0014] Step 4: Construct the scalarized objective function G(x);

[0015] Step 5: Obtain the gradient g of the scalarized objective function G(x) through the process response model, and update the individual process parameter vector x. m ;

[0016] Step 6: Update the sparse operator population P GA ;

[0017] Step 7: Gradient population P CG and sparse operator population P GA Two-way individual exchange between them;

[0018] Step 8: Environmental selection and process solution output steps.

[0019] The gradient-guided co-evolutionary algorithm for injection molding process parameters of this invention is also characterized by:

[0020] Further, step 1 includes the following steps:

[0021] Step 11: Obtain the process parameter combination xz for injection molding;

[0022] Step 12: Obtain the simulation sample subset xf;

[0023] Step 13: Obtain the measured sample subset xs;

[0024] Step 14: Obtain the sample dataset xh for constructing the injection molding process response model.

[0025] Furthermore, in step 12, the process parameter combination xz from step 11 is input into the simulation software for injection molding process, and the simulation sample subset xf is obtained through the objective function.

[0026] Furthermore, the objective function includes part warpage f1(x), volume shrinkage and shrinkage index f2(x), molding cycle f3(x), and energy consumption per unit qualified part f4(x).

[0027] Furthermore, in step 2, the process response model The expression is shown in the following formula;

[0028] ;

[0029] In the formula, This represents the predicted value of the warpage f1(x) of the part; This represents the predicted value of f2(x), a comprehensive index of volume shrinkage and shrinkage marks. This represents the predicted value of the molding cycle f3(x); This represents the predicted value of energy consumption f4(x) per unit of qualified component.

[0030] Furthermore, in step 3, during the calculation of the multi-objective function value, the VSSPS sparse population initialization method is used to generate two populations: a gradient population P. CG and sparse operator population P GA .

[0031] Furthermore, step 4 includes the following steps:

[0032] Step 41: Generate multiple sets of uniformly distributed reference weight vectors W m ;

[0033] Step 42: Subproblem construction and variable initialization steps;

[0034] Step 43: Calculate the gradient population P CG The m-th individual xm Jacobian matrix J(x) m ).

[0035] Furthermore, step 5 updates the individual's process parameter vector x. m The process includes the following steps:

[0036] Step 51: Calculate the gradient g of the scalarized objective function G(x);

[0037] Step 52: Calculate the optimal step size;

[0038] Step 53: Determine the better solution y.

[0039] Furthermore, step 6 updates the sparse operator population P. GA The process includes the following steps:

[0040] Step 61: Initialize the sparse operator population P GA And evaluate the sparse operator population P GA Individuals;

[0041] Step 62: Crossover Phase;

[0042] Step 63: Mutation phase.

[0043] Furthermore, in step 62, sparse simulated binary crossover S-SBX is used to implement two-phase crossover during the crossover stage.

[0044] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0045] This invention discloses a gradient-guided co-evolutionary algorithm for injection molding process parameters, comprising: data acquisition and sample dataset construction steps; acquiring structural information of the target injection molded part, structural information of the mold, and parameters of the injection molding equipment to obtain part quality data, molding cycle, and energy consumption data, and obtaining a sample dataset xh based on the part quality data, molding cycle, and energy consumption data; determining the process response model, and training the process response model using the sample dataset xh. The trained process response model was used. Calculate the multi-objective function value; construct the scalarized objective function G(x); obtain the gradient g of the scalarized objective function G(x) through the process response model, and update the individual process parameter vector x. m Update the sparse operator population P GA Gradient population P CG and sparse operator population P GA Two-way individual exchange between them; environmental selection and process solution output steps.

[0046] This invention discloses a gradient-guided co-evolutionary algorithm for injection molding process parameters. It directly constructs a multi-objective optimization model with warpage, shrinkage / marking, molding cycle, and energy consumption as components. Combining a uniformly distributed reference weight vector with NSGA-II environment selection, it outputs a Pareto solution set representing various trade-offs between quality, cycle time, and energy consumption, facilitating engineers in selecting process schemes based on different production preferences. Furthermore, it utilizes a feedforward neural network process response model and its Jacobian matrix, achieving gradient-driven optimization of process parameters through FRCG conjugate gradient updates. Relying only on the first-order gradient, it achieves a convergence speed between first-order and second-order methods, significantly reducing the number of function evaluations required in high-dimensional process parameter spaces and improving optimization efficiency across multiple objectives.

[0047] This invention employs a two-population cooperative structure to balance convergence and diversity, with a gradient population P. CG Focusing on fast convergence along the reference weight direction, the sparse operator population P GA By employing S-SBX and S-PM to maintain global exploration and sparse structure optimization, and by periodically exchanging high-quality individuals between the two populations, premature convergence and insufficient diversity issues associated with single-population structures are avoided. This is achieved through VSSPS initialization, S-SBX and S-PM sparse operators, and a df conflict variable mechanism. This invention effectively controls the non-zero parameter dimension in the high-dimensional process parameter space, focusing the search on a few key parameters, thereby reducing the number of trial runs and improving optimization efficiency and solution interpretability.

[0048] The gradient-guided co-evolutionary algorithm for injection molding process parameters of the present invention has the advantages of being able to efficiently optimize multi-dimensional injection molding process parameters on multiple objectives such as quality, molding cycle and energy consumption, and reducing the number of trial moldings, shortening the debugging cycle and improving the overall performance of the parts. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the gradient-guided co-evolutionary algorithm for injection molding process parameters according to the present invention.

[0050] Figure 2 This is a schematic diagram comparing the convergence performance of the algorithm of this invention with that of existing algorithms.

[0051] The present invention will be further described below through specific embodiments and in conjunction with the accompanying drawings. Detailed Implementation

[0052] See Figures 1-2 The present invention provides a gradient-guided co-evolutionary algorithm for injection molding process parameters, comprising the following steps:

[0053] Step 1: Data acquisition and sample dataset construction; Collect structural information of the target injection molded part, structural information of the mold, and parameters of the injection molding equipment; obtain part quality data, molding cycle and energy consumption data; and obtain the sample dataset xh based on the part quality data, molding cycle and energy consumption data.

[0054] Based on the structural information of the target injection molded part, the structural information of the mold, and the parameters of the injection molding equipment, determine the process parameters for optimizing the injection molding process, including melt temperature, mold temperature, filling time, injection speed, holding pressure, holding time, cooling time, back pressure, screw speed, and cooling medium temperature, and their value ranges; define each individual x = (x1, x2, ..., x...). d ( ) corresponds to a complete set of process parameter values ​​for the injection molding process, where d is the total number of process parameters in the injection molding process. The process parameter vector x for the injection molding process is defined as: x = (T me ,T mo ,t fill , v inf-1 , …,v inf-b , p hold-1 , …,p hold-q ,t hold-1 ,…,t hold-q , t cool ,P back ,n screw , T cool That is, d = b + 2q + 7; where x1 corresponds to T. me , ......, x d Corresponding to T cool .

[0055] Among them, T me It is the melt temperature; T mo It refers to the mold temperature; t fill It is fill time; v inf-b This refers to the injection speed of segment b; b represents the injection speed (v). inf The number of segments (b) means that during the injection process, the injection speed will be divided into b segments, each with a different speed setting. If b=3, then there will be three injection speed segments v. inf-1 v inf-2 v inf-3 p hold-q This refers to the holding pressure of segment q; t hold-q This refers to the holding time of segment q; q represents the holding pressure (p). hold The number of segments and the holding time (t) hold The number of segments in the injection molding process, particularly the holding pressure stage, plays a crucial role and is typically divided into multiple stages, each with different holding pressures and durations. coolP is the cooling time; back For back pressure; n screw T is the screw speed; cool This refers to the temperature of the cooling medium.

[0056] Then, collect or generate part quality data, molding cycle and energy consumption data under different combinations of process parameters for injection molding processes, and construct a sample dataset xh, as shown in steps 11 to 14 below.

[0057] Step 2: Determine the process response model and train it using the sample dataset xh. ;

[0058] Based on the simulated sample subset xf and the measured sample subset xs, a sample dataset xh is constructed. A process response model is then trained using the sample dataset xh, encompassing the process parameters, part warpage, volume shrinkage and sink mark comprehensive indicators, molding cycle time, and energy consumption per unit of qualified part. The process response model It supports calculating the gradient of each objective function G(x) with respect to process parameters.

[0059] Step 3: Use the trained process response model Calculate the values ​​of multi-objective functions;

[0060] Within the allowable range of process parameters, the process parameter vector x of the injection molding process is represented by real number encoding. Two populations are randomly generated: gradient population P. CG and sparse operator population P GA For the gradient population P CG and sparse operator population P GA Each individual x in the process response model is called to calculate the multi-objective function value, that is, the target value of each objective function is calculated according to formulas (5) to (6) below.

[0061] Step 4: Construct the scalarized objective function G(x);

[0062] Generate multiple sets of uniformly distributed reference weight vectors W in the target space. m , gradient population P CG Each individual element in the algorithm corresponds one-to-one with a reference weight vector. A scalarized objective function G is constructed for the m-th subproblem. m (x).

[0063] Step 5: Obtain the gradient g of the scalarized objective function G(x) through the process response model, and update the individual process parameter vector x. m ;

[0064] For gradient population P CG For each individual sub-problem, the process response model is used. Calculate the gradient g of the scalarized objective function G(x), and update the process parameter vector x of the m-th individual based on the conjugate gradient method. m The updated individuals are then projected into the feasible domain of the process constraints.

[0065] Step 6: Update the sparse operator population P GA ;

[0066] In the sparse operator population P GA Individual selection is performed based on multi-objective fitness and crowding distance, and sparse crossover and sparse mutation operators are used to generate offspring individuals. The multi-objective function value f(x) of the offspring individuals is calculated using the process response model and used to update the sparse operator population P. GA .

[0067] Step 7: Gradient population P CG and sparse operator population P GA Two-way individual exchange between them;

[0068] During the evolutionary process, every predetermined generation t, in the gradient population P... CG and sparse operator population P GA Perform a bidirectional individual exchange operation between them.

[0069] Step 8: Environmental selection and process solution output steps.

[0070] Step 81: Transfer the gradient population P CG and sparse operator population P GA Individuals in the pool are merged into the current candidate population, and the NSGA-II environment selection process is executed. First, considering constraint feasibility, the candidate population is subjected to a fast non-dominated sort to obtain the Pareto front set {F1, F2, ..., F...}. Z-1}, and label the frontier level to which each individual belongs, where F1 is the completely non-dominated solution set and Z is the total number of levels.

[0071] Step 82: Starting from F1, sequentially accumulate the number of individuals in the Pareto front set {F1, F2, ...} in hierarchical order. When the accumulated number of individuals first exceeds or equals N (where N is the population size), the corresponding front is recorded as the critical front F. Z Then the front-end F1...F will be able to fit completely. Z-1 The entire layer is added to the next generation population as the first group of individuals.

[0072] Step 83: For the critical frontier F LFor individuals within the target space, the crowding distance value is calculated using the above formula (8) according to the NSGA-II crowding distance calculation method, in order to measure the sparsity and diversity of the solution, and individuals are selected in descending order of crowding distance to fill the remaining quota until the number of individuals in the next generation population reaches N.

[0073] Step 84: Merge the individuals obtained in Step 82 and Step 83 to form the next generation population, and take the non-dominated solutions in F1 or their cumulative set in multiple generations of iteration as the non-dominated solution set; when the termination condition is reached, select one or more sets of injection molding process parameter solutions from the non-dominated solution set according to the user's preference for part quality, molding cycle and energy consumption as the process scheme output.

[0074] In practice, step 1 includes the following steps:

[0075] Step 11: Obtain the process parameter combination xz for injection molding;

[0076] Then, orthogonal experiments and Latin hypercube experiments were used to process the sample dataset xh to generate several sets of process parameter combinations xz for injection molding.

[0077] Step 12: Obtain the simulation sample subset xf;

[0078] Step 13: Obtain the measured sample subset xs;

[0079] Representative batches were selected from the production site, and the set values ​​of the actual injection molding process parameters and their stable operating ranges were recorded. Simultaneously, parameters such as part quality inspection results, actual molding cycle, and energy consumption data corresponding to the simulation indicators were collected and compiled to form a measured sample subset xs. The compilation process includes field / unit normalization, stable window aggregation, target caliber unification, key pairing, anomaly / missing data handling, unified scaling, (optional) simulation-to-measurement linear calibration, deduplication, and source domain annotation.

[0080] Step 14: Obtain the sample dataset xh for constructing the injection molding process response model;

[0081] The simulated sample subset xf and the measured sample subset xs undergo data cleaning, outlier removal, missing value handling, and normalization preprocessing. They are then merged under unified process parameters and target index definitions to obtain the sample dataset xh used for process response modeling in injection molding. This merging process involves standardizing fields and units, aggregating stable windows, unifying target calibers, pairing keys, handling outliers and missing values, and calibrating the source domain. The simulated and measured subsets are then merged under unified variable naming and a unified scale (while retaining source domain identifiers and sample weights) to form the final sample dataset for process response modeling.

[0082] In specific implementation, in step 12, the process parameter combination xz from step 11 is input into the simulation software for injection molding process, and the simulation sample subset xf is obtained through the objective function.

[0083] In specific implementation, the objective function includes part warpage f1(x), volume shrinkage and shrinkage mark index f2(x), molding cycle f3(x), and energy consumption per unit qualified part f4(x).

[0084] The process parameters xz of the injection molding process are sequentially input into the injection molding process simulation software. In the virtual environment of the simulation software, the filling, holding pressure, cooling and warpage analysis are completed. The function values ​​of the objective functions corresponding to the process parameters of each injection molding process, such as part warpage f1(x), volume shrinkage and shrinkage mark index f2(x), molding cycle f3(x) and energy consumption per unit qualified part f4(x), are recorded to form a simulation sample subset xf. The expressions of the four objective functions are as follows.

[0085] The expression for the warpage f1(x) of the part is shown in the following formula (1);

[0086] (1)

[0087] In formula (1), x is the above process parameter vector; u(p;x) is the warping displacement vector of sampling point p under parameter x. Let p be the set of sampling points; For the set of sampling points The number of sampling points p in the middle.

[0088] The expression for the volume shrinkage and shrinkage index f2 (x) is shown in the following formula (2);

[0089] (2)

[0090] In formula (2), This is the dimensionless value of the volume shrinkage rate. This is the dimensionless value of the average line contraction. Let α1, α2, and α3 be the dimensionless values ​​of the shrinkage index. , and The weighting coefficients α1, α2 and α3 satisfy the following conditions: 0≤α1≤1, 0≤α2≤1, 0≤α3≤1, α1+α2+α3=1.

[0091] The expression for the molding cycle f3(x) is shown in the following formula (3);

[0092] (3)

[0093] In formula (3), t fill It is the fill time; t hold-k This refers to the holding time of the kth segment; t cool For cooling time; 0 ≤ k ≤ q.

[0094] The expression for the molding cycle f4(x) is shown in the following formula (4);

[0095] (4)

[0096] In formula (4), P(t;x) is the power curve of the injection molding machine, which changes with time t and process parameter vector x; Q(x) is the pass rate, which is calculated based on the proportion of qualified parts under the process parameter vector x, and 0≤Q(x)≤1. This represents the total energy consumption of the injection molding machine in a single cycle within the molding cycle duration f3(x).

[0097] In specific implementation, in step 2, the process response model The expression is shown in the following formula (5);

[0098] (5);

[0099] In formula (5), This represents the predicted value of the warpage f1(x) of the part; This represents the predicted value of f2(x), a comprehensive index of volume shrinkage and shrinkage marks. This represents the predicted value of the molding cycle f3(x); This represents the predicted value of energy consumption f4(x) per unit of qualified component.

[0100] Training is based on the sample dataset with process parameter vector x = (T) me ,T mo ,t fill , v inf-1 , …,v inf-b , p hold-1 ,…,p hold-q , t hold-1 ,…,t hold-q ,t cool ,P back ,n screw ,T cool A differentiable process response model that takes f(x) as input and outputs a multi-objective function value f(x). , To provide a predictive approximation of the multi-objective function f(x), which includes four objective functions f1(x) to f4(x), the Jacobian matrix J(x) of the multi-objective function f(x) with respect to the process parameters is calculated using analytical differentiation or numerical difference methods, as shown in formula (11) below. Given a reference weight vector W, according to g(x) = J(x)... T W, obtains the gradient vector g(x) of the scalarized objective function G(x), and provides the objective function value f(x) and the gradient vector g(x) to the gradient population P. CG The optimization module is used to update the solution.

[0101] First, a sample dataset xh is constructed based on the simulated sample subset xf and the measured sample subset xs, with the process parameter vector x∈R. d Using the part warpage f1(x), the combined index of volume shrinkage and sink mark f2(x), the molding cycle f3(x), and the energy consumption per unit qualified part f4(x) as outputs, a process response model from process parameters to a multi-objective function is trained. ,

[0102] In practical implementation, the process response model The preferred feedforward neural network model is FNN, whose network structure satisfies the following formula (6).

[0103] (6);

[0104] In formula (6), l = 2, 3, ... L-1, where L is the total number of layers in the FNN; W l and b l Let be the weight matrix and bias vector of the l-th layer of the FNN, respectively; σ(·) is the non-linear activation function; θ = This refers to the set of network parameters; the feedforward neural network model (FNN) consists of three layers: an input layer, hidden layers, and an output layer; among them, As the first hidden layer, the This represents the l-th hidden layer; Indicates the output layer.

[0105] By minimizing the loss function The feedforward neural network model FNN is trained as shown in the following formula (7).

[0106] (7);

[0107] In formula (7), This represents the predicted value of the k-th objective function (obtained through the process response model), where 1 ≤ k ≤ 4; γ represents the k-th objective function value of the i-th sample in the sample dataset xh, where N is the total number of samples in the sample dataset xh; i This represents the weight of each sample, set according to the sample's source (the difference between simulated and experimental samples); β k This represents the weight of each objective function, set according to the importance of the objective; λ represents the L2 regularization coefficient, used to prevent the model from overfitting. This represents the L2 regularization term, which penalizes excessively large values ​​of model parameters.

[0108] The process of training a process response model is to minimize the loss function. The optimization process includes the following steps:

[0109] 1. Initialize network parameters: Randomly initialize network weights θ= , l=1,…, L, where L is the total number of layers in the FNN.

[0110] 2. Forward Propagation: For each sample x, the output is calculated through a feedforward neural network. .

[0111] 3. Calculate the loss: Calculate the loss for each sample. And sum the results over the entire training set.

[0112] 4. Backpropagation: The backpropagation algorithm is used to calculate the gradient of the loss function with respect to the weight parameter θ.

[0113] 5. Parameter update: Update the network parameters θ using the gradient descent method.

[0114] 6. Iterative optimization: Repeat steps 2-5 until the loss function is reached. It converges to the minimum value.

[0115] The feedforward neural network model FNN is trained such that, given any process parameter vector x, the process response model... It can output the predicted values ​​of each objective function f1(x) to f4(x). ~ It supports calculating the gradient of each objective function with respect to the process parameters through finite difference, and calculating the search direction vector s of the solution to be updated based on the calculated gradient g and the gradient g0 obtained in the previous iteration, as shown in the following formula (8).

[0116] (8)

[0117] In formula (8), s represents the search direction vector of the solution to be updated; g represents the gradient of the solution x to be updated (expressed as a vector) calculated by scalarizing the objective function G(x), and the specific calculation process is shown in step 51 below; g0 and s0 represent the gradient and search direction vector of the solution obtained in the previous iteration, respectively; K is a counter that increments by 1 at the end of each iteration; d is the dimension of the decision variable (i.e., the total number of process parameters in the injection molding process), d = b + 2q + 7. The mod function is used to calculate the remainder after dividing two integers.

[0118] In specific implementation, during step 3, the calculation of the multi-objective function value uses the VSSPS sparse population initialization method to generate two populations: a gradient population P. CG and sparse operator population P GA .

[0119] The feedforward neural network model FNN is trained such that, given any process parameter vector x, the process response model... It can output the predicted values ​​of each objective function f1(x) to f4(x). ~ The '^' symbol represents the predicted value of the objective function obtained by the process response model, and is used to approximate the true objective function f1(x)~f4(x).

[0120] During training, a real sample dataset xh is first obtained, and then the feedforward neural network model FNN is trained; subsequent calls during training are... We don't always do realistic simulations.

[0121] Step 31: Within the allowable range of process parameters, represent the injection molding process parameter vector using real number encoding, where each individual x = (x1, x2, ..., x...). d This directly corresponds to a complete set of process parameter values;

[0122] Step 32: Divide the value range of each process parameter dimension into several stripe sub-ranges according to the preset stripe width, and set variable sampling probability or sampling density for different stripes.

[0123] Step 33: Using the Variable Stripe Sparse Population Sampling (VSSPS) method, sample points are extracted non-uniformly and sparsely from different stripes in each dimension of the process parameter. The samples extracted from each dimension are combined to form individuals, and a gradient population P is generated sequentially. CG and sparse operator population P GA .

[0124] Step 34: In the sampling process of the variable stripe sparse population, instead of using a two-layer encoding scheme to represent the sparsity of the solution set, a single-layer real number encoding is used to directly represent the process parameters, thereby avoiding additional encoding and decoding overhead and achieving higher computational efficiency; for the gradient population P CG and sparse operator population P GA Each individual in the process response model is invoked. Calculate the multi-objective function value to inform the subsequent gradient population P. CG and sparse operator population P GA The evolutionary update provides initial evaluation results.

[0125] Steps 31-34 constitute the population initialization process, where real-number encoding is used to represent the process parameter vector x of the injection molding process, with each individual corresponding to a complete set of process parameter values. For the gradient population P... CG and sparse operator population P GA Each population has a set of solutions. The decision variables of a solution are a set of injection molding process parameter vectors. The objective value of each solution in the population is calculated in order to prepare for the calculation of gradient g in step 5 below.

[0126] In practice, step 4 includes the following steps:

[0127] Step 41: Generate multiple sets of uniformly distributed reference weight vectors W m ;

[0128] Given an objective dimension (number of objective functions) of M, the Das and Dennis method generates N numbers of functions on an M-dimensional unit simplex. CG The uniformly distributed reference weight vector W is shown in the following formula (9).

[0129] (9);

[0130] In formula (9), m = 1, 2, ..., N CG N CG It is a gradient population P CG The number of solutions; The superscript m indicates the nth solution, i.e., the mth subproblem; the subscript 1 indicates the first objective function f1(x). This invention includes four objective functions f1(x) to f4(x), i.e., M=4. In specific implementation, the number of weight vectors corresponds to the number of solutions to the objective function. This invention includes four objective functions, so one W... m It's a 4-dimensional vector, for example. = (0.1, 0.3, 0.5, 0.1). Gradient population P CG The number of solutions equals the number of Ws.m .

[0131] Weight vector The kth component is used This means that each weighted component satisfies: Ensure that all reference weight vectors are approximately uniformly distributed in the target space to distinguish the gradient population P. CG The convergence direction of each solution.

[0132] For example = (0.1, 0.3, 0.5, 0.1), where =0.1, =0.3......; The sum of the four components of this vector is equal to 1; Because the objective function has four components, each component must be greater than or equal to 0.

[0133] Step 42: Subproblem construction and variable initialization steps;

[0134] The gradient population P CG The m-th individual x m (i.e., the m-th solution) and the m-th reference weight vector W m A one-to-one correspondence is established to construct a scalarized objective function G for the m-th subproblem. m (x), see formula (10) below.

[0135] (10)

[0136] Then, initialize the external archive A, design the restart counter K, gradient cache G, and search direction cache S; the external archive A stores the gradient population P. CG and sparse operator population P GA That is, A is the gradient population P CG and sparse operator population P GA The set of gradients. Restart the counter K, incrementing it by 1 at the end of each iteration. The gradient cache G stores all gradients g (expressed as vectors), which is the set of g; the search direction cache S stores all search directions s, which is the set of s; these parameters are all related to calculating the conjugate gradient. k represents the k-th objective function, 1≤k≤M=4.

[0137] Step 43: Calculate the gradient population P CG The m-th individual x m Jacobian matrix J(x) m ).

[0138] In each iteration, the m-th individual x in the gradient population m The gradient g is calculated based on the Jacobian matrix J(x) mJacobian matrix J(x) m See formula (11) below.

[0139] (11);

[0140] In formula (11), f(x) m ) is through process response model The multi-objective function vector is calculated; ∂ represents the partial derivative.

[0141] In the above steps, step 41 generates a uniform reference vector, which is equivalent to decomposition. The number of reference vectors generated corresponds to the number of solutions. Step 42 constructs a scalarized objective function for each subproblem, which is to calculate the gradient. Step 43 calculates the Jacobian matrix. These are all preparatory steps for calculating the gradient g in the next step, 5.

[0142] In specific implementation, step 5 updates the individual process parameter vector x. m The process includes the following steps:

[0143] Step 51: Calculate the gradient g of the scalarized objective function G(x);

[0144] The Jacobian matrix J(x) of the multi-objective function is calculated based on the process response model, and the scalarized objective function G(x) is constructed according to the reference weight vector. The gradient of the scalarized objective function G(x) is then used. For input, w is calculated as shown in formula (9) above. The search direction vector s is calculated using the Fletcher–Reeves conjugate gradient (FRCG) method, as shown in formula (8) above.

[0145] The FRCG conjugate gradient method relies only on first-order gradient information, and its convergence speed is between that of the first-order gradient method and the second-order Newton method. It balances efficiency and effectiveness when solving large-scale optimization problems.

[0146] Step 52: Calculate the optimal step size;

[0147] To determine a suitable step size, an exponential line search strategy is adopted, with the step size factor set at 0.9. e and 0.2 e The form decreases, where e is the step size, and a new solution y is generated at each candidate step size. The i-th variable of the new solution y is y_i. i Calculate according to the following formula (12).

[0148] (12)

[0149] In formula (12), and Let A represent two solutions to the i-th decision variable randomly selected from external file A. , There are two randomly selected solutions, each consisting of d decision variables. , There are only two decision variables for two random solutions; d i =1 indicates that the decision variable y i It belongs to the sparse conflicting variable set df, meaning that the signs of its first-order partial derivatives on each objective are significantly different; when d i =0 indicates that the decision variable y i It does not belong to df. Therefore, d i When =0, the i-th variable y i Searching along the conjugate gradient direction s i Update to improve population convergence; d i When =1, the i-th variable y i Using differential evolution differential vectors To increase population diversity.

[0150] Step 53: Determine the better solution y.

[0151] If the calculated G(x) is smaller than the original G(x), then the solution y is better, and the original gradient population's current solution x is replaced. Given a step size e, if the new solution y is better than the current solution x on the scalarized objective function G(x), then the new solution y is accepted, and the original gradient population P is replaced by the new solution y. CG The current solution x is stored in the archive, and a better solution y is added to the archive, overwriting the current solution x, and the process waits for the next environment selection. Otherwise, e is increased and the step size is decreased until a better solution is found or the preset maximum number of line search steps is reached.

[0152] In step 5, for each individual in the gradient population, the gradient of the scalar objective function is calculated using the process response model, the process parameter vector of the individual is updated based on the conjugate gradient method, and the updated individual is projected into the process constraint feasible region.

[0153] In specific implementation, step 6 updates the sparse operator population P. GA The process includes the following steps:

[0154] Step 61: Initialize the sparse operator population P GA And evaluate the sparse operator population P GA Individuals;

[0155] When the sparse operator population P GA After initialization, the sparse operator population P is... GAThe individuals in the process are evaluated using the standard NSGA-II fast nondominated sorting plus crowding distance, in preparation for the crossover mutation in step 62.

[0156] Step 62: Crossover Phase;

[0157] Step 63: Mutation phase.

[0158] In the mutation phase: Sparse Polynomial Mutation (S-PM) is used, employing a combination of numerical fine-tuning and sparsity mutation. This not only fine-tunes the real values ​​at non-zero positions but also treats the overall sparsity of an individual as a variable parameter. After a single scalar mutation, several bits are flipped in batches, allowing the individual sparsity to adaptively adjust with generational evolution, thus enhancing the global exploration capability of the search. Finally, the generated offspring are merged with the parent generation into the external file A.

[0159] Steps 61-63 are the sparse operator population P GA The goal of crossover and mutation of individuals in the population is also to update the sparse operator population P. GA In the solution, steps 5 and 6 are respectively updating the gradient population P. CG and sparse operator population P GA The process of solving the problem.

[0160] In specific implementation, in step 62, the two-phase crossover is achieved by using sparse simulated binary crossover S-SBX in the crossover stage.

[0161] During the crossover phase, Sparse Simulated Binary Crossover (S-SBX) is employed to achieve a crossover method that preserves sparsity by performing two-phase crossover and position swapping. The core idea is to retain the numerical processing of traditional SBX while handling inconsistent dimensions between parents at zero / non-zero positions through random mask swapping. This allows the genetic information at "non-zero positions" to be propagated as inheritable features, ensuring that the overall sparsity of the offspring is close to that of the parents and preventing the search space from becoming denser.

[0162] Two parent individuals were selected during the crossover phase. and By comparing parental individuals and The zero / non-zero states across all dimensions divide gene locations into two cases: one is the parent individual. and One type is the set of matching locations where all gene positions are zero or all are non-zero; the other type is the set of matching locations in the parent individual. and The gene positions are a set of mismatched positions consisting of zero and non-zero values. For matched positions, this invention directly applies the traditional simulated binary crossover (SBX) to generate offspring real values ​​near the parent's real value, so that the process parameters that are determined to be non-zero are finely optimized in their neighborhood, while the dimensions of parameters that are simultaneously zero remain at zero or near zero. For mismatched positions, a random exchange mask vector v is generated to determine which parent inherits the gene bit by bit, or to swap it between two offspring.

[0163] Gradient population P CG and sparse operator population P GA During the bidirectional individual exchange process, a bidirectional individual exchange operation is performed every preset algebraic interval t.

[0164] Step 71: GA→CG direction swap; use sparse operator population P GA The individual (solution) replaces the gradient population P CG The individual (solution);

[0165] For the m-th reference weight vector In the sparse operator population P GA Traverse the current population individual x, and quantize the objective function G. m (x), see the following formula (13);

[0166] (13)

[0167] The scalarized objective function G is calculated using formula (13). m The scalarized target value of (x). Selected from this weight vector. The lower has the smallest individual As a candidate individual; if the candidate individual scalarized target value G ( () is superior to gradient population P CG Individual corresponding to the subproblem scalarized target value G ( (Directly compare the target values; the smaller the value, the better the solution), then use Replace gradient population P CG Individual corresponding to the subproblem This will enable the sparse operator population P to... GA The solution that performs better in this direction is the gradient-injected population P. CG At most k can be replaced GA-CG Individual.

[0168] Step 72: Swap the CG→GA directions; use the gradient population P CG The individual (solution) replaces the sparse operator population PGA The individual (solution);

[0169] In the gradient population P CG In this process, the scalarized target value set for all individuals is calculated. Select k CG-GA A set of individuals with better scalar targets As an elite group; calculate the gradient population P CG The scalarized target values ​​of all individuals are used to select the k with the smallest target value from this set. CG-GA Each solution forms a set. As an elite group, the scalarized objective function G is calculated using formula (9). m The scalarized target value of (x). The smaller the scalarized target value, the better the individual. After calculation, the values ​​are sorted, so we choose the smallest target value, k. CG-GA The solution is given.

[0170] In the sparse operator population P GA In the process, the crowding distance value of each individual is calculated according to the multi-objective crowding index, as shown in the following formula (14).

[0171] (14)

[0172] In formula (14), CD i P represents the population of sparse operators. GA The crowding distance of the i-th individual in the equation; M represents the number of objective functions; f k (i+1) represents the value of the i-th individual on the k-th objective function, 1≤k≤M, and M is 4 in this invention; and Let i and i represent the maximum and minimum values ​​of the k-th objective function in the current frontier, respectively. Let i+1 and i-1 represent the individuals preceding and following the i-th individual after sorting by the k-th objective function, respectively.

[0173] Determine the k that minimizes the crowding distance CG-GA Individual Set As the replaced set; the elite set The individuals in the text are replaced in a one-to-one correspondence manner. (Right now Individuals in the ordinary population (P) will be included in the gradient population P. CG The population P of sparse operators injected with solutions that perform well in different reference directions GA To improve the sparse operator population P GA Overall quality and multi-objective distribution performance. The individuals in it are The shortest crowding distance among k CG-GA Each individual is the one that is to be replaced. The individuals in the list are those with poor performance and are to be replaced; there are a total of k individuals. CG-GA Individual.

[0174] like Figure 1 This invention discloses a gradient-guided co-evolutionary algorithm for injection molding process parameters. It acquires structural information about the injection molded part and the mold, and establishes a response model between process parameters and quality indicators based on numerical simulation and historical production data. Real-number encoding is used to initialize the gradient population P. CG and sparse operator population P GA Two populations; the gradient population P CG A uniformly distributed reference weight vector is generated, and based on the gradient information of the process response model, the conjugate gradient method is used to iteratively update each sub-problem; in the sparse operator population P GA The system employs multi-objective genetic operations of sparse crossover and sparse mutation to generate new individuals; bidirectional individual exchange is performed between two populations every preset number of generations, and non-dominated solution sets are maintained through environmental selection, ultimately outputting a set of injection molding process parameter schemes that compromise between quality, cycle time, and energy consumption.

[0175] like Figure 2 This paper presents the convergence performance of various algorithms on the classic sparse multi-objective optimization problem SMOP7 (Sparse Multiobjective Optimization Problem 7). The x-axis represents the number of function evaluations, and the y-axis represents the Inverted Generational Distance (IGD) metric, which reflects the overall difference between the solution set obtained by the algorithm and the true Pareto front. Generally, the smaller the IGD value, the closer the solution set obtained by the algorithm is to the true Pareto front, and the better its distribution; therefore, the faster the curve descends and the lower the final value, the better the convergence performance of the algorithm. Figure 2As can be seen, the IGD of most algorithms gradually decreases with the increase of the number of evaluations, indicating that they are constantly approaching the optimal frontier. Among them, the multi-objective optimization analysis method of this invention (GCEA, Gradient-Guided Coevolutionary Algorithm) is compared with algorithms such as SparseEA (Sparse Evolutionary Algorithm), AFSEA (Adjoint Feature-Selection-based Evolutionary Algorithm), TS-SparseEA (Two-Stage Sparse Evolutionary Algorithm), MOEA / PSL (Pareto-Optimal Subspace Learning-based Evolutionary Algorithm), S-NSGA-II (Sparse Nondominated Sorting Genetic Algorithm II), and DKCA (Dynamic Knowledge-Guided Coevolutionary Algorithm). These are all very specific algorithm abbreviations that have been very representative in recent years. Overall, GCEA consistently maintained the lowest IGD throughout the evolutionary process, demonstrating the fastest and most stable convergence. DKCA and TS-SparseEA also showed relatively fast IGD reduction, ultimately ranking second only to GCEA. AFSEA performed relatively steadily, outperforming SparseEA and S-NSGA-II. MOEA / PSL, however, consistently exhibited high IGD and slow convergence, resulting in the weakest overall performance. In conclusion, this figure illustrates significant performance differences among different algorithms on the classic benchmark problem SMOP7, with the GCEA algorithm of this invention demonstrating the best performance in terms of convergence and solution set quality.

[0176] While maintaining global search capability, this invention improves convergence speed by utilizing gradient information. Through a dual-population collaborative structure, it balances convergence and population diversity, effectively reducing the number of trial moldings, shortening the process debugging cycle, and improving the overall performance of the manufactured parts.

[0177] This invention uses a process response model as an interface, which can be seamlessly connected to existing injection molding simulation platforms and production data acquisition systems. It is integrated into the process design and production optimization process as a software module, which is convenient for migration and application between different parts and molds, and has good prospects for engineering implementation.

[0178] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0179] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A gradient-guided co-evolutionary algorithm for injection molding process parameters, characterized in that, Includes the following steps: Step 1: Data acquisition and sample dataset construction; Collect structural information of the target injection molded part, structural information of the mold, and parameters of the injection molding equipment; obtain part quality data, molding cycle and energy consumption data; and obtain the sample dataset xh based on the part quality data, molding cycle and energy consumption data. Step 2: Determine the process response model and train it using the sample dataset xh. ; Step 3: Use the trained process response model Calculate the values ​​of multi-objective functions; Step 4: Construct the scalarized objective function G(x); Step 5: Obtain the gradient g of the scalarized objective function G(x) through the process response model, and update the individual process parameter vector x. m ; Step 6: Update the sparse operator population P GA ; Step 7: Gradient population P CG and sparse operator population P GA Two-way individual exchange between them; Step 8: Environmental selection and process solution output steps.

2. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, Step 1 includes the following steps: Step 11: Obtain the process parameter combination xz for injection molding; Step 12: Obtain the simulation sample subset xf; Step 13: Obtain the measured sample subset xs; Step 14: Obtain the sample dataset xh for constructing the injection molding process response model.

3. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 2, characterized in that, In step 12, the process parameter combination xz from step 11 is input into the simulation software for injection molding process, and the simulation sample subset xf is obtained through the objective function.

4. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 3, characterized in that, The objective function includes part warpage f1(x), volume shrinkage and shrinkage index f2(x), molding cycle f3(x), and energy consumption per unit qualified part f4(x).

5. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, In step 2, the process response model The expression is shown in the following formula; ； In the formula, This represents the predicted value of the warpage f1(x) of the part; This represents the predicted value of f2(x), a comprehensive index of volume shrinkage and shrinkage marks. This represents the predicted value of the molding cycle f3(x); This represents the predicted value of energy consumption f4(x) per unit of qualified component.

6. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, In step 3, during the calculation of the multi-objective function value, the VSSPS sparse population initialization method is used to generate two populations: the gradient population P. CG and sparse operator population P GA .

7. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, Step 4 includes the following steps: Step 41: Generate multiple sets of uniformly distributed reference weight vectors W m ; Step 42: Subproblem construction and variable initialization steps; Step 43: Calculate the gradient population P CG The m-th individual x m Jacobian matrix J(x) m ).

8. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, Step 5 updates the individual's process parameter vector x. m The process includes the following steps: Step 51: Calculate the gradient g of the scalarized objective function G(x); Step 52: Calculate the optimal step size; Step 53: Determine the better solution y.

9. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 1, characterized in that, Step 6 involves updating the sparse operator population P. GA The process includes the following steps: Step 61: Initialize the sparse operator population P GA And evaluate the sparse operator population P GA Individuals; Step 62: Crossover Phase; Step 63: Mutation phase.

10. The gradient-guided co-evolutionary algorithm for injection molding process parameters according to claim 9, characterized in that, In step 62, sparse simulated binary crossover S-SBX is used to achieve two-phase crossover during the crossover phase.

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