Multi-target welding beam design method based on adaptive evolutionary algorithm
By combining adaptive evolutionary algorithms and state split trees, the design of welded beams is optimized, solving the problem of balancing performance and cost in the design of welded beams, and realizing the efficient and stable design of welded beams.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-29
- Publication Date
- 2026-04-03
AI Technical Summary
Existing multi-objective welded beam design methods struggle to effectively reduce manufacturing costs while ensuring the performance of welded beams, especially under complex buckling load and shear stress constraints, making it difficult to obtain design schemes with good convergence and uniform distribution.
An adaptive evolutionary algorithm is adopted. By constructing a multi-objective function and using a state split tree as a Q-function approximator, the evolutionary operator is dynamically selected. Combined with supervised learning of the experience buffer pool, the geometric design parameters of the welded beam are optimized to ensure that the design scheme meets physical constraints and achieves a balance between performance and cost.
This approach achieves both safety and stability in welded beam structures while effectively reducing manufacturing costs, and obtains a Pareto optimal solution set that is sufficiently convergent and uniformly distributed, thereby improving the engineering practical value of the design scheme.
Smart Images
Figure CN121787263A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of welded beam technology, and in particular to a multi-objective welded beam design method based on an adaptive evolutionary algorithm. Background Technology
[0002] In modern industrial manufacturing, welded beams, as a key structural component, are widely used in bridges, buildings, and mechanical engineering. To meet diverse engineering requirements, the design of welded beams necessitates the comprehensive consideration of multiple objectives. Traditional single-objective welded beam design methods typically focus solely on minimizing the total cost of the welded beam. While this approach can effectively reduce manufacturing costs, it may lead to poor performance of the welded beam in practical applications.
[0003] In contrast, multi-objective welded beam design methods place particular emphasis on balancing total cost with beam end deflection under specific loads. Multi-objective evolutionary algorithms (MOEA) are a common solution for multi-objective problems; however, multi-objective welded beam design problems are characterized by strong nonlinearity and stringent constraints. In particular, the complex coupling between buckling capacity constraints and shear stress constraints leads to a narrow, irregular, or even disconnected feasible domain. This makes it difficult to obtain high-quality welded beam designs with good convergence and uniform distribution when applying existing MOEAs to multi-objective welded beam design scenarios. Summary of the Invention
[0004] To address the aforementioned problems and technical requirements, this application proposes a multi-objective welded beam design method based on an adaptive evolutionary algorithm. The technical solution of this application is as follows: A multi-objective welded beam design method based on an adaptive evolutionary algorithm, comprising: Using multiple geometric design parameters of the welded beam as decision variables, a method is constructed based on these decision variables to minimize the manufacturing cost of the welded beam and to optimize its performance under load. A multi-objective function is used to minimize the deflection at the beam end under action, and the physical constraints of the welded beam are determined. generate A uniformly distributed weight vector is initialized randomly. A design scheme for a welded beam was constructed. Sub-problems, any number of sub-problems Size problem Corresponding welded beam design scheme and weight vector Each welded beam design scheme includes the design values of various decision variables. Represents the weight vector China's preference for trade-offs in manufacturing costs Represents the weight vector The trade-off preference regarding beam end deflection; Initialize the operator pool containing multiple evolution operators, the state split tree, and an empty experience buffer pool; In each iteration round, for any i... Size problem Perform the following steps (1) to (4): (1) Extracting subproblems Multidimensional feature vectors Multidimensional feature vectors Used to characterize welded beam design schemes The degree of approximation to the boundary of physical constraints and the optimization potential; (2) Using the state split tree as a Q-function approximator for multidimensional feature vectors Select the best-matching evolution operator from the operator pool. Using evolution operators Design scheme for welded beams and sub-problems Modify the existing welded beam design schemes within the adjacent area to generate a new welded beam design scheme. ; (3) Utilizing the new welded beam design scheme Update the design scheme for welded beams and sub-problems Design schemes for welded beams within the neighborhood range, and calculate and execute evolutionary operators. The resulting improvement in the engineering performance of welded beams will serve as an immediate reward. ; (4) When detected When the physical validity-based indicators are met, it is considered a high-quality experience group. Store in the experience buffer pool; Complete the current iteration round After processing each subproblem, the state split tree is reconstructed through supervised learning using all high-quality experience groups in the experience buffer pool. Based on the updated state split tree and subproblems, the next iteration round is entered until the maximum number of iterations is reached. Then, the Pareto optimal solution set is output to obtain multiple sets of welded beam design schemes under different trade-off preferences.
[0005] A further technical solution involves reconstructing the state split tree through supervised learning using high-quality experience groups from the experience buffer pool, including: For any _th_ in the experience buffer pool A high-quality experience group Design scheme for welded beams Extracting multidimensional feature vectors Utilize the current state to split the tree Calculate multidimensional feature vectors Maximum Q value And obtain the Bellman objective value. , It is a discount factor. Indicates splitting the tree using the current state. Multidimensional feature vectors Evolution operators selected from the operator pool Q value at that time; by As input features, with Bellman objective values To output the labels, a new binary regression tree is trained using all the high-quality experience groups in the experience buffer pool as the updated state split tree based on the fitting Q-iteration algorithm.
[0006] A further technical solution involves reconstructing the state split tree through supervised learning using high-quality experience groups from the experience buffer pool, and also includes: In the process of training a new binary regression tree using the fitting Q-iteration algorithm based on various high-quality experience groups: When the number of high-quality experience groups within a node is less than When, or when the mean squared error of the Bellman objective values of all high-quality experience groups within a node is below a threshold. When, or when the variance of the input features of a high-quality experience group within a node is 0 within the potential split range, continue splitting the current node; where, This indicates the minimum number of samples allowed by the terminal node; Candidate split points are found by sorting, deduplicating, and calculating the median across all dimensions, and then maximized. The optimal split point is located from the candidate split points and splitting is performed; where... It is the sum of squared errors of the Bellman objective values of all high-quality empirical groups within the node before the split. It is the sum of the squared errors of the Bellman objective values of all high-quality experience groups within the left and right child nodes after the split; It is the first node within the node before the split. Bellman's target value for high-quality experience groups It refers to all nodes within the node before the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the left child node after the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the right child node after the split. The average of the Bellman target values of the high-quality experience groups.
[0007] A further technical solution involves utilizing a new welded beam design. Update the design scheme for welded beams and sub-problems The design schemes for welded beams within the vicinity include: For the design scheme of welded beams and sub-problems Any welded beam design scheme within the adjacent area ,when At that time, a new welded beam design scheme was used. Replacement welded beam design scheme Otherwise, retain the welded beam design. Unchanged; among them, Subproblems Chebyshev function value, It utilizes a welded beam design scheme. Subtotal problem Design scheme for welded beams in China The Chebyshev function value after that; Among them, sub-problems The design scheme for welded beams within the neighborhood range is related to the weight vector. The design schemes of welded beams corresponding to the subproblems to which several weight vectors within the neighborhood belong, and the weight vectors. The neighborhood range includes the weight vector The nearest weight vectors.
[0008] Its further technical solution is to compute and execute the evolution operator. The resulting improvement in the engineering performance of welded beams will serve as an immediate reward. include: Calculations utilizing the new welded beam design scheme Replacement welded beam design scheme Improvement rate Calculate all new welded beam design schemes The sum of the improvement rates resulting from the replacement welded beam design will be used as an immediate reward. .
[0009] Its further technical solution is to detect Whether the physical validity-based indicators are met includes: When subproblems Chebyshev function value At that time, determine Those belonging to the high-quality experience group are stored in the experience buffer pool; When subproblems Chebyshev function value At that time, determine This constitutes construction noise and should be discarded. It is the quality threshold and is determined based on the optimal value of the Chebyshev function for all subproblems.
[0010] Its further technical solution is to extract sub-problems. Multidimensional feature vectors include: Subproblems Chebyshev function value Chebyshev function value The smaller the value, the better the welded beam design scheme. The closer it is to the Pareto optimal front and the more mechanical constraints are satisfied; And, sub-problems Corresponding weight vector Boundary features; And, the ratio of the number of iterations in the current iteration round to the maximum number of iterations; And all sub-problems The mean and standard deviation of the decision variables in each corresponding welded beam design scheme.
[0011] Its further technical solution is, sub-problem Chebyshev function value The calculation formula is:
[0012] in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under action, It is the manufacturing cost of the ideal point in the current iteration round. It is the beam end deflection at the ideal point in the current iteration round; It is a sufficiently large penalty factor. This indicates that the welded beam design scheme is adopted. The sum of the violations of physical constraints.
[0013] A further technical solution is that the evolutionary operators included in the operator pool are at least two of the following: differential evolution operator (DE), simulated binary crossover operator (SBX), polynomial mutation operator (PM), and particle swarm optimization operator (PSO).
[0014] Further technical solutions include the following: The multi-objective welded beam design method also includes: Based on the weld thickness of the welded beam Length of the clamp strip Cross-sectional length and cross-sectional width As decision variables, determine the design scheme for each welded beam. The multi-objective function is constructed as follows:
[0015] in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under action, Indicates intermediate parameters. , , They are coefficients, respectively. The physical constraints for the welded beam are determined as follows:
[0016] in, It is a welded beam in the design scheme Welding stress at that time, It is the maximum value of welding stress; It is a welded beam in the design scheme Bending stress at that time, It is the maximum bending stress; It is a welded beam in the design scheme The buckling capacity in the vertical direction is calculated using the following formula:
[0017] in,
[0018] In the above formula, Indicates the length of the welded beam. This indicates the elastic modulus of the welded beam material. This indicates the shear modulus of the welded beam material.
[0019] The beneficial technical effects of this application are: This application discloses a multi-objective welded beam design method based on an adaptive evolutionary algorithm. This method comprehensively considers two objectives: the manufacturing cost of the welded beam and the beam end deflection under load. Through multi-objective optimization, it can effectively reduce manufacturing costs while ensuring the structural safety and stability of the welded beam (deflection within a reasonable range), achieving a good balance between performance and cost. To address the complex coupled constraints such as shear stress, bending stress, and buckling capacity in the welded beam design, this application employs a state splitting tree as... The function approximator perceives the constraint environment of the current design scheme (e.g., whether it is on the verge of buckling failure) by extracting multi-dimensional feature vectors reflecting the degree of approximation to the physical constraint boundary, including convergence, diversity, temporal characteristics, and solution structural characteristics. Based on this, it dynamically selects the most suitable evolutionary operator (e.g., a fine-tuning operator at the constraint boundary), effectively avoiding local optima and infinite loops. Furthermore, through a unique experience filtering mechanism based on physical validity, this application only stores high-quality design experiences that meet mechanical and performance indicators in a buffer pool, avoiding interference from a large number of "useless solutions" that violate physical common sense in the early stages of evolution. The resulting Pareto optimal solution set is not only sufficiently convergent and uniformly distributed, but each solution also corresponds to a structurally reliable and technologically sound welded beam design scheme, significantly improving the engineering practical value of the design scheme and promoting the application effect and economic benefits of welded beams in actual engineering projects. Attached Figure Description
[0020] Figure 1 This is a flowchart of a multi-objective welded beam design method according to an embodiment of this application.
[0021] Figure 2 This is a structural schematic diagram of a welded beam.
[0022] Figure 3 This is a schematic diagram of an embodiment where a state split tree determines the evolutionary operator that achieves the optimal action. Figure 4 This is an example of using the method of this application with existing methods. algorithm, algorithm, Comparison of Pareto front plots of the solution sets obtained by the algorithm. Detailed Implementation
[0023] The specific embodiments of this application will be further described below with reference to the accompanying drawings.
[0024] This application discloses a multi-objective welded beam design method based on an adaptive evolutionary algorithm. Please refer to [reference needed]. Figure 1 The flowchart shown illustrates that the method includes the following steps: Step S1: Using multiple geometric design parameters of the welded beam as decision variables, construct a system based on these decision variables that minimizes the manufacturing cost of the welded beam and the load... A multi-objective function is used to minimize the beam end deflection under load, and the physical constraints of the welded beam are determined.
[0025] In one embodiment, four geometric design parameters of the welded beam are selected as decision variables, namely: weld thickness of the welded beam. Length of the clamp strip Cross-sectional length and cross-sectional width Please refer to Figure 2 Each decision variable has its own range of values. Therefore, the design scheme for each group of welded beams can be expressed as follows: The constructed multi-objective function is as follows:
[0026] in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under load. It is a pre-determined custom value. Indicates intermediate parameters. , , These are the coefficients. In one example, , , , , .
[0027] In one embodiment, the physical constraints constructed based on the above four decision variables are as follows:
[0028] in, It is a welding stress constraint condition. It is a welded beam in the design scheme Welding stress at that time, It is the preset maximum welding stress. It is a bending stress constraint condition. It is a welded beam in the design scheme Bending stress at that time, It is the preset maximum bending stress. These are the geometric constraints of the weld. It is a buckling capacity constraint condition. It is a welded beam in the design scheme The buckling capacity in the vertical direction.
[0029] Welded beams are used in the design scheme. Welding stress at time Bending stress Buckling bearing capacity The calculation formula is:
[0030] The calculation formulas for each intermediate parameter are as follows:
[0031] in, Indicates the length of the welded beam. This indicates the elastic modulus of the welded beam material. This indicates the shear modulus of the welded beam material.
[0032] Step S2, generate A uniformly distributed weight vector is initialized randomly. A design scheme for a welded beam was constructed. The subproblems, from which any number of subproblems are constructed, yield the first subproblem. Size problem Corresponding welded beam design scheme and weight vector Integer parameters .
[0033] Each weight vector is generated through uniform design. Each weight vector characterizes the different trade-offs between manufacturing cost and beam end deflection in the multi-objective welded beam design. For example, Represents the weight vector China's preference for trade-offs in manufacturing costs Represents the weight vector The trade-off preference regarding beam end deflection. The larger the value, the more emphasis is placed on reducing manufacturing costs. A larger value indicates a greater emphasis on reducing beam end deflection.
[0034] In generation After having a weight vector, for each weight vector It can also calculate all Among the weight vectors, the weight vector is... The set of the nearest weight vectors is called the weight vector. The neighborhood of each weight vector can be customized, and the number of other weight vectors contained in the neighborhood of each weight vector can be customized.
[0035] Then for each weight vector Randomly initialize the corresponding welded beam design scheme To construct subproblems Each welded beam design scheme includes design values for various decision variables. In one embodiment, the welded beam design schemes are randomly initialized. At that time, according to Random initialization yields the design scheme for the welded beam. Decision variables Design value , Decision variables The minimum value in the range of values, Decision variables The maximum value in the range of values, It represents a random number that is uniformly distributed from 0 to 1.
[0036] Step S3: Initialize the operator pool containing multiple evolution operators, the state split tree, and an empty experience buffer pool. The state split tree is a binary tree-form intelligent decision maker used as a Q-function approximator. Initialize the state split tree as an empty tree.
[0037] Different evolutionary operators have different search strategies and characteristics. Considering the complex constraints of the terrain under the welded beam, a single fixed evolutionary operator often cannot balance search efficiency and feasibility. Therefore, in order to obtain a high-quality welded beam design scheme with good convergence and uniform distribution, this application uses an operator pool to maintain multiple selectable evolutionary operators, so that the corresponding evolutionary operator can be selected from the operator pool in the future, thereby achieving the effect of dynamically adjusting the search strategy.
[0038] In one embodiment, the evolutionary operators included in the operator pool are at least two of the following: differential evolution operator (DE), simulated binary crossover operator (SBX), polynomial mutation operator (PM), and particle swarm optimization operator (PSO). These evolutionary operators each have their own characteristics; some excel at global search, while others excel at local search. For example, differential evolution operator (DE) excels at global search, but it is prone to generating a large number of infeasible solutions that violate mechanical constraints when approaching shear stress boundaries. While the simulated binary crossover operator (SBX) is beneficial for local fine-tuning, it is prone to stagnation in complex buckling constraint traps, causing the algorithm to get stuck in local optima.
[0039] Additionally, the ideal point needs to be initialized. And an empty external file EP.
[0040] Step S4: Begin iteration. In each iteration round, traverse all subproblems and for any given subproblem... Size problem Perform the following steps (1) to (5): (1) Extracting subproblems Multidimensional feature vectors .
[0041] In order for the state split tree to be able to perceive the current welded beam design scheme To determine the location and optimization potential within the constrained space, multidimensional feature vectors are first extracted. This multidimensional feature vector Used to characterize welded beam design schemes The degree of approximation to the physical constraint boundary and the optimization potential. In one embodiment, multidimensional feature vectors... It should include at least the following features that reflect the physical scene: (a) Convergence characteristics: subproblems Chebyshev function value .
[0042] This value is based on a subproblem determined using the Chebyshev method. The target value. In welded beam design, due to strict physical constraints such as shear stress, bending stress, and buckling capacity constraints, in another embodiment, the constraint violation value is also incorporated to define the Chebyshev function value. The calculation formula is:
[0043] in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under load. It is the manufacturing cost of the ideal point in the current iteration round. It is the beam end deflection at the ideal point in the current iteration round. It is a sufficiently large penalty factor. This indicates that the welded beam design scheme is adopted. The sum of the violations of physical constraints.
[0044] The Chebyshev function value obtained from this This not only represents the current design scheme for welded beams The combined performance in terms of manufacturing cost and beam end deflection more directly reflects the current welded beam design scheme. The degree of approximation to the "feasible physical boundary". Chebyshev function value. The smaller the value, the better the welded beam design scheme. The closer it is to the Pareto optimal frontier and the more mechanical constraints are satisfied.
[0045] (b) Diversity characteristics: sub-problems Corresponding weight vector Boundary features.
[0046] This feature is used to represent the current subproblem. Whether the goal is to achieve extreme optimization for a single objective (such as the boundary region with extremely low cost) or to achieve a balance of comprehensive performance (the central region), the requirements for the search strategy differ depending on the region of the welded beam design. In practical applications, this can be achieved by selecting... As a weight vector Boundary features.
[0047] (c) Time stage characteristics: the number of iterations in the current iteration round With maximum number of iterations ratio This feature indicates the time stage of the iteration, such as the early exploration stage or the later convergence stage.
[0048] (d) Solution structure characteristics: all subproblems The mean and standard deviation of the decision variables in each corresponding welded beam design scheme. This feature reflects the distribution of the current population in the geometric parameter space, and can help the state split tree determine whether to expand the search range to find new configurations that meet buckling constraints, or to narrow the range to fine-tune the dimensions and reduce costs.
[0049] (2) Using the state split tree as a Q-function approximator for multidimensional feature vectors Select the best-matching evolution operator from the operator pool. .
[0050] The state split tree serves as an intelligent decision-maker, based on the multidimensional feature vector extracted in step (1) above. It can predict the impact of different evolutionary operators on welded beam design schemes under the current environment. The potential for improvement is significant. At the beginning of the iteration, since the initial state split tree is empty, the evolutionary operator that achieves the optimal action can be randomly selected from the operator pool. Subsequently, the state split tree is used to select the evolution operator. The specific process is as follows, please refer to... Figure 3 : (a) State mapping: mapping multidimensional feature vectors Starting from the input state, split the tree from the root node and traverse the internal nodes according to the splitting rules based on the feature values until a leaf node is reached.
[0051] (b) Obtain the Q value: Extract the vector stored in the leaf node, which approximates the expected engineering value improvement that can be brought about by executing each evolution operator in this physical state region.
[0052] (c) Action selection: using The strategy selects the evolutionary operator with the optimal action from the operator pool. : by Probability (utilized): Selection The evolutionary operator with the largest value. For example, when solving problems that severely violate buckling capacity constraints, state split trees tend to select evolutionary operators with strong global search capabilities (such as...). This allows for escaping the infeasible region. When the solution already satisfies the constraints and is near the stress boundary, a fine-tuning operator (such as...) is preferred. To minimize costs.
[0053] by The probability of exploration: Randomly select an operator to maintain the diversity of search strategies.
[0054] Each node of the state split tree corresponds to a pair of multidimensional feature vectors. The judgment condition is that when the multidimensional feature vector Upon reaching a node in the state split tree, the system determines whether to proceed to the left or right child node of the split node based on the judgment conditions set for that node. Figure 3 For example, the judgment condition for the current node is " "If multidimensional feature vectors" In If the condition is met, proceed to the right child node; otherwise, proceed to the left child node. This process is repeated for each node until the multidimensional feature vector is reached. Upon reaching a leaf node, each leaf node stores a Q-value. The system will then select the evolutionary operator that achieves the optimal action from the operator pool based on this Q-value. .
[0055] (3) Call the evolution operator determined in step (2) above from the operator pool. Design scheme for welded beams and sub-problems Modify the existing welded beam design schemes within the adjacent area to generate a new welded beam design scheme. This process simulates tentative modifications to the geometry of the welded beam (e.g., attempting to reduce the weld thickness). To reduce costs, or to increase the cross-sectional height (To improve bending resistance), the aim is to explore better geometric configurations in the design space.
[0056] Among them, sub-problems The design scheme for welded beams within the neighborhood is a weighted vector. The design scheme of the welded beam corresponding to the subproblems to which several weight vectors in the neighborhood belong.
[0057] In another embodiment, when executing the optimal evolution operator At the same time, it can also be combined with the individual historical optimal solution ( ) and from external archives ( The globally optimal solution selected from ) This guides the search towards known high-quality design areas.
[0058] (4) Utilizing the new welded beam design scheme Update the design scheme for welded beams and sub-problems Design welding beam schemes within the neighborhood and calculate immediate rewards. .
[0059] For the design scheme of welded beams and sub-problems Any welded beam design scheme within the adjacent area First, examine the new welded beam design. Is it better than existing welded beam design schemes? Furthermore, in one embodiment, the evaluation is performed using Chebyshev function values: when At that time, it indicates a new welded beam design scheme. Under the premise of satisfying mechanical constraints, for the subproblem The weighted objective (the trade-off between manufacturing cost and beam end deflection) is superior to the original welded beam design. Then, a new welded beam design scheme will be used. Replacement welded beam design scheme Otherwise, retain the welded beam design. Unchanged. Additionally, the ideal point for the current iteration round needs to be updated. .
[0060] in, Subproblems Chebyshev function value, It utilizes a welded beam design scheme. Subtotal problem Design scheme for welded beams in China The Chebyshev function value after that.
[0061] To guide the state split tree learning to generate high-value designs that align with engineering realities, immediate rewards are provided. Defined as executing evolution operator This leads to improved engineering performance of welded beams. Specifically, it is based on a new welded beam design scheme. Pair problem The fitness improvement rate of the parent's welded beam design schemes within the neighborhood is used for calculation: For each successful replacement (i.e., utilizing a new welded beam design scheme) Replacement welded beam design scheme ) Calculation using the new welded beam design scheme Replacement welded beam design scheme Improvement rate:
[0062] Calculate all new welded beam design schemes Replacement welded beam design scheme The sum of the improvement rates generated serves as an immediate reward. .
[0063] When the calculated instant reward When, it represents the evolution operator. A new welded beam design was successfully generated that satisfies both strength and stability requirements, and also has lower manufacturing costs or smaller beam end deflection compared to the parent welded beam design. The state split tree should reinforce the selection bias of this action.
[0064] When the calculated instant reward At that time, it indicates a new welded beam design scheme. The inability to replace any parent welded beam design is usually due to the new welded beam design. Violation of hard constraints such as buckling capacity constraints or excessive manufacturing costs. This "zero-reward" mechanism forces the state split tree to avoid evolutionary operators that would lead to physical failure of the design.
[0065] (5) As a data tuple, and by introducing an empirical filtering mechanism based on physical validity, when a physical validity is detected... When the physical validity-based indicators are met, it is considered a high-quality experience group. Data is stored in the experience buffer pool; otherwise, it is discarded as noise. The purpose of this is to eliminate noise from invalid designs and ensure that the data stored in the experience buffer pool reflects real and feasible engineering optimization principles. In one embodiment, the welded beam design scheme is based on the parent design. To judge Does it meet the criteria based on physical validity? When subproblems Chebyshev function value At that time, it indicated the design scheme of the welded beam of the parent generation. This is a physically reasonable and competitive welded beam design. The experience gained from this state transition is valuable for learning "how to further optimize near the feasible region boundary." As a high-quality experience group Store in the experience buffer pool.
[0066] Sure Those belonging to the high-quality experience group are stored in the experience buffer pool. When a subproblem... Chebyshev function value This indicates that the parent generation's welded beam design may have seriously violated mechanical constraints (such as excessive shear stress) or was in an extremely poor performance range, resulting in empirical evidence. These are considered engineering noise and discarded. This mechanism can significantly improve the accuracy of state splitting trees in learning under complex constraints.
[0067] in, It is a quality threshold and is determined based on the optimal value of the Chebyshev function of all subproblems. For example, it can be a certain proportion of the optimal value of the Chebyshev function of all subproblems in the current population.
[0068] When the number of high-quality experience groups in the experience buffer pool reaches the buffer pool threshold, the high-quality experience groups in the experience buffer pool are updated using a first-in-first-out strategy. The buffer pool threshold can be set customarily, for example, to 500.
[0069] Step S5, after completing the current iteration round... After processing the sub-problems, the state split tree is reconstructed through supervised learning using high-quality experience groups from the experience buffer pool.
[0070] This step aims to leverage the high-quality welded beam design experience accumulated in the experience buffer pool to reconstruct the state split tree through supervised learning, thereby updating the algorithm's understanding of "which operator is most effective under specific physical constraints," including: All high-quality experience sets are retrieved from the experience pool. These high-quality experience sets reflect the actual engineering feedback obtained from executing specific evolutionary operators under different welded beam design states (such as stress critical state or cost redundancy state). For any given set in the experience pool... A high-quality experience group Design scheme for welded beams Extraction status This state The generated welded beam design scheme It is derived from physical features. Then, the current state is used to split the tree. Calculate multidimensional feature vectors Maximum Q value And obtain the Bellman objective value. .
[0071] in, It is a discount factor. Indicates splitting the tree using the current state. Multidimensional feature vectors Evolution operators selected from the operator pool The Q value at that time. The physical meaning of this formula is: when evaluating the value of current adjustments to the welded beam parameters, not only the immediate performance improvement should be considered. (For example, an immediate reduction in manufacturing costs), it is also considered whether this action guides the welded beam design to a more promising physical area. (For example, the feasible boundary region that approximates the buckling constraint, and the region that facilitates further optimization).
[0072] Then with As input features, with Bellman objective values To output labels, a new binary regression tree is trained using the fitted Q-iteration algorithm based on all high-quality experience groups in the experience buffer pool as the updated state split tree. To accurately capture nonlinear characteristics in the welded beam design space (such as abrupt changes in operator effectiveness near constraint boundaries), the construction of the new tree strictly follows the following splitting criteria and objectives: (1) Splitting stopping criterion (to prevent overfitting and physical noise) To ensure that the state split tree learns universally applicable design principles rather than noise specific to a particular sample, the following stopping condition is set: The number of observations (data points) within a node, i.e., the number of high-quality experience groups, must be at least [number missing]. When the number of high-quality experience groups within a node is less than When this happens, stop splitting the current node. This represents the minimum number of samples allowed by the terminal node and is a pre-defined parameter.
[0073] Check the mean squared error (MSE) of the Bellman objective values of all high-performing experience groups within a node. When the MSE of the Bellman objective values of all high-performing experience groups within a node is below a threshold... When the state of the welded beams within the node is "sufficiently homogeneous" in the operator response (i.e., having similar physical properties and optimization potential), the splitting of the current node should be stopped. It is a pre-set parameter that represents the tolerance level.
[0074] Check the variance of the high-quality experience group within the node. When the variance of the input feature of the high-quality experience group within a node is 0 within the potential split range, it means that all values of the physical variable of the node are the same, and stop splitting the current node.
[0075] (2) Core splitting objective (precisely dividing the physical design scenario) In order to find the split point that can best distinguish different optimization scenarios (e.g., distinguish between "scenarios that need to solve buckling constraints" and "scenarios that need to optimize costs"), the algorithm searches for possible candidate split points by sorting each dimension, removing duplicates, and calculating the median.
[0076] Then, the optimal split point among the candidate split points is located. At the optimal split point, the aim is to minimize the squared error and SSE. Since directly calculating the squared error and SSE of each candidate split point is too costly, in one embodiment, it is transformed into maximizing "error reduction", that is, by maximizing The index identifies the optimal split point from the candidate split points and performs the split. Defined as the node before splitting With the left and right child nodes after splitting The difference between the sums:
[0077] in, It is the sum of squared errors of the Bellman objective values of all high-quality empirical groups within the node before the split. It is the sum of the squared errors of the Bellman objective values of all high-quality experience groups within the left and right child nodes after the split. It is the first node within the node before the split. Bellman's target value for high-quality experience groups It refers to all nodes within the node before the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the left child node after the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the right child node after the split. The average of the Bellman target values of the high-quality experience groups.
[0078] maximize Essentially, it is about finding a state feature threshold (such as...) or This allows for the separation of mixed welded beam design states with vastly different operator efficiencies. In this way, the state split tree can automatically identify which physical states require aggressive searching (corresponding to regions of high variance and high expected return) and which require conservative fine-tuning, thus providing a basis for new state split trees. A decision-making logic that is highly consistent with the physical properties of the welded beam is constructed.
[0079] Step S6: Based on the updated state split tree and subproblems, proceed to the next iteration round until the maximum number of iterations is reached, then retrieve from the external archive. The process outputs a Pareto optimal solution set, yielding multiple welded beam design schemes under different trade-off preferences. This final solution set includes a series of rigorously constrained welded beam design schemes, covering a variety of trade-offs from "low cost - general stiffness" to "high cost - high stiffness". Engineers can directly select the most suitable welded beam geometry scheme from this solution set for production based on the specific budget and performance requirements of the actual engineering project.
[0080] To verify the effectiveness of the method provided in this application, the method was tested in an experiment. ) and constrained non-dominated sorting genetic algorithm ( ), push-pull search method for solving constrained multi-objective optimization problems ( Two-stage evolutionary algorithms for solving constrained multi-objective optimization problems To ensure fairness, the population size of the four algorithms was uniformly set to 150, the number of evaluations was uniformly set to 30,000, and each algorithm was run independently 30 times on the multi-objective welded beam design problem.
[0081] The evaluation metric for the final solution set is the hypervolume ( , ). The extent of the target space covered by the solution set is measured by calculating the volume between the final solution set and the reference point. A larger value indicates not only better convergence of the solution set, but also a wider coverage and more uniform distribution of the solution set within the target space. When setting the reference point, it is essential to ensure that all solutions in the final solution set Q dominate the reference point, and that the reference point for all test algorithms is consistent to guarantee fairness.
[0082] Figure 4 The Pareto fronts of the final solution sets obtained by four algorithms for the multi-objective welded beam design problem are shown in the figure. The diversity of the final solution sets obtained by the four algorithms is clearly visible. This diversity mainly examines the coverage and uniformity of the solutions. Regarding the coverage of the solutions… and The distribution range of the obtained Pareto optimal solution set on the deflection target is approximately (0, 0.009). Slightly better, it achieved (0, 0.013), while the present application's It reached (0, 0.015). Clearly, this application's... The method yields a Pareto optimal solution set with a wider coverage.
[0083] In terms of the uniformity of the solutions, The solutions are mainly concentrated in the middle region, and become sparser towards both ends. and There are instances of uneven distribution in certain localized areas. Only this application... The final solution set is the most uniformly distributed.
[0084] The table below shows the four algorithms for the multi-objective welded beam design problem. The average and standard deviation of the indicators. It is easy to see from the table that the present application... The method runs 30 times The average value is the highest among the four algorithms, indicating that this application's... The Pareto optimal solution set obtained by this method outperforms other algorithms in both convergence and diversity. Furthermore, this application's... Method The standard deviation is also the lowest among the four algorithms, which demonstrates the effectiveness of this application. The method has strong stability.
[0085]
[0086] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.
Claims
1. A multi-objective welded beam design method based on an adaptive evolutionary algorithm, characterized in that, The multi-objective welded beam design method includes: Using multiple geometric design parameters of the welded beam as decision variables, a method is constructed based on these decision variables to minimize the manufacturing cost of the welded beam and to optimize its performance under load. A multi-objective function is used to minimize the deflection at the beam end under action, and the physical constraints of the welded beam are determined. generate A uniformly distributed weight vector is initialized randomly. A design scheme for a welded beam was constructed. Sub-problems, any number of sub-problems Individual problem Corresponding welded beam design scheme and weight vector Each welded beam design scheme includes design values for each decision variable. Represents the weight vector China's preference for trade-offs in manufacturing costs Represents the weight vector The trade-off preference regarding beam end deflection; Initialize the operator pool containing multiple evolution operators, the state split tree, and an empty experience buffer pool; In each iteration round, for any i... Individual problem Perform the following steps (1) to (4): (1) Extracting subproblems Multidimensional feature vectors Multidimensional feature vectors Used to characterize welded beam design schemes The degree of approximation to the boundary of physical constraints and the optimization potential; (2) Using the state split tree as a Q-function approximator for multidimensional feature vectors Select the best-matching evolution operator from the operator pool. Using evolution operators Design scheme for welded beams and sub-problems Modify the existing welded beam design schemes within the adjacent area to generate a new welded beam design scheme. ; (3) Utilizing the new welded beam design scheme Update the design scheme for welded beams and sub-problems Design schemes for welded beams within the neighborhood range, and calculate and execute evolutionary operators. The resulting improvement in the engineering performance of welded beams will serve as an immediate reward. ; (4) When detected When the physical validity-based indicators are met, it is considered a high-quality experience group. Store in the experience buffer pool; After completing the current iteration round After processing each subproblem, the state split tree is reconstructed through supervised learning using all high-quality experience groups in the experience buffer pool. Based on the updated state split tree and subproblems, the next iteration round is entered until the maximum number of iterations is reached. Then, the Pareto optimal solution set is output to obtain multiple sets of welded beam design schemes under different trade-off preferences.
2. The multi-objective welded beam design method according to claim 1, characterized in that, Reconstructing the state split tree using high-quality experience groups from the experience pool through supervised learning includes: For any _th_ in the experience buffer pool A high-quality experience group Design scheme for welded beams Extracting multidimensional feature vectors Split the tree using the current state Calculate multidimensional feature vectors Maximum Q value And obtain the Bellman objective value. , It is a discount factor. Indicates splitting the tree using the current state. Multidimensional feature vectors Evolution operators selected from the operator pool Q value at that time; by As input features, with Bellman objective values To output the labels, a new binary regression tree is trained using all the high-quality experience groups in the experience buffer pool as the updated state split tree based on the fitting Q-iteration algorithm.
3. The multi-objective welded beam design method according to claim 2, characterized in that, Reconstructing the state split tree through supervised learning using high-quality experience groups from the experience buffer pool also includes: In the process of training a new binary regression tree using the fitting Q-iteration algorithm based on various high-quality experience groups: When the number of high-quality experience groups within a node is less than When, or when the mean squared error of the Bellman objective values of all high-quality experience groups within a node is below a threshold. When, or when the variance of the input features of a high-quality experience group within a node is 0 within the potential split range, continue splitting the current node; where, This indicates the minimum number of samples allowed by the terminal node; Candidate split points are found by sorting, deduplicating, and calculating the median across all dimensions, and then maximized. The optimal split point is located from the candidate split points and splitting is performed; where... It is the sum of squared errors of the Bellman objective values of all high-quality empirical groups within the node before the split. It is the sum of the squared errors of the Bellman objective values of all high-quality experience groups within the left and right child nodes after the split; It is the first node within the node before the split. Bellman's target value for high-quality experience groups It refers to all nodes within the node before the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the left child node after the split. The average of the Bellman target values of the high-performing experience groups It refers to all nodes within the right child node after the split. The average of the Bellman target values of the high-quality experience groups.
4. The multi-objective welded beam design method according to claim 1, characterized in that, Utilizing a new welded beam design Update the design scheme for welded beams and sub-problems The design schemes for welded beams within the vicinity include: For the design scheme of welded beams and sub-problems Any welded beam design scheme within the adjacent area ,when At that time, a new welded beam design scheme was used. Replacement welded beam design scheme Otherwise, retain the welded beam design. Unchanged; among them, Subproblems Chebyshev function value, It utilizes a welded beam design scheme. Subtotal problem Design scheme for welded beams in China The Chebyshev function value after that; Among them, sub-problems The design scheme for welded beams within the neighborhood range is related to the weight vector. The design schemes of welded beams corresponding to the subproblems to which several weight vectors within the neighborhood belong, and the weight vectors. The neighborhood range includes the weight vector The nearest weight vectors.
5. The multi-objective welded beam design method according to claim 4, characterized in that, Computational execution evolution operator The resulting improvement in the engineering performance of welded beams will serve as an immediate reward. include: Calculations utilizing the new welded beam design scheme Replacement welded beam design scheme Improvement rate Calculate all new welded beam design schemes The sum of the improvement rates resulting from the replacement welded beam design will be used as an immediate reward. .
6. The multi-objective welded beam design method according to claim 1, characterized in that, Detection Whether the physical validity-based indicators are met includes: When subproblems Chebyshev function value At that time, determine Those belonging to the high-quality experience group are stored in the experience buffer pool; When subproblems Chebyshev function value At that time, determine This constitutes construction noise and should be discarded. It is the quality threshold and is determined based on the optimal value of the Chebyshev function for all subproblems.
7. The multi-objective welded beam design method according to claim 1, characterized in that, Extracting subproblems Multidimensional feature vectors include: Subproblems Chebyshev function value Chebyshev function value The smaller the value, the better the welded beam design scheme. The closer it is to the Pareto optimal front and the more mechanical constraints are satisfied; And, sub-problems Corresponding weight vector Boundary features; And, the ratio of the number of iterations in the current iteration round to the maximum number of iterations; And all sub-problems The mean and standard deviation of the decision variables in each corresponding welded beam design scheme.
8. The multi-objective welded beam design method according to claim 7, characterized in that, Subproblems Chebyshev function value The calculation formula is: in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under action, It is the manufacturing cost of the ideal point in the current iteration round. It is the beam end deflection at the ideal point in the current iteration round; It is a sufficiently large penalty factor. This indicates that the welded beam design scheme is adopted. The sum of the violations of physical constraints.
9. The multi-objective welded beam design method according to claim 1, characterized in that, The evolutionary operators included in the operator pool are at least two of the following: differential evolution operator (DE), simulated binary crossover operator (SBX), polynomial mutation operator (PM), and particle swarm optimization operator (PSO).
10. The multi-objective welded beam design method according to claim 1, characterized in that, The multi-objective welded beam design method also includes: Based on the weld thickness of the welded beam Length of the clamp strip Cross-sectional length and cross-sectional width As decision variables, determine the design scheme for each welded beam. The multi-objective function is constructed as follows: in, This indicates that the welded beam design scheme is adopted. Manufacturing costs at that time This indicates that the welded beam design scheme is adopted. During the load Beam end deflection under action, Indicates intermediate parameters. , , They are coefficients, respectively. The physical constraints for the welded beam are determined as follows: in, It is a welded beam in the design scheme Welding stress at that time, It is the maximum value of welding stress; It is a welded beam in the design scheme Bending stress at that time, It is the maximum bending stress; It is a welded beam in the design scheme The buckling capacity in the vertical direction is calculated using the following formula: in, In the above formula, Indicates the length of the welded beam. This represents the elastic modulus of the welded beam material. This indicates the shear modulus of the welded beam material.