A truss topology optimization design method based on information acquisition algorithm

Abstract

This invention proposes a truss topology optimization design method based on an information acquisition algorithm, comprising the following steps: S1, constructing an objective function based on truss mass; S2, solving the objective function based on truss mass using an information acquisition algorithm; S2-1, initializing parameters; S2-2, initialization stage: randomly generating an initial population j = 1, ..., Popsize, where P is the population size. iter The process begins with the j-th individual in the algorithm. Then, individuals are randomly initialized (S2-3), and their fitness values ​​are calculated. In S2-4, the current evaluation count (FEs) is set to FEs + Popsize. If the iteration count (iter) is greater than the maximum iteration count (Max_iter), the current optimal individual is output. If the iteration count (iter) is less than the maximum iteration count (Max_iter), the next step is executed. In S2-5, the optimal solution for the individual is updated during the exploration phase. In S2-7, the current iteration count is set to iter = iter + 1. In S2-8, steps S2-4 to S2-7 are repeated until the current evaluation count (FEs) reaches MAX_FEs, at which point the process ends. The optimal individual obtained during this process is the result of the truss topology optimization design. This invention can quickly and accurately obtain the optimal truss topology design scheme.

Description

Technical Field

[0001] This invention relates to the field of truss structure technology, and in particular to a truss topology optimization design method based on information acquisition algorithms. Background Technology

[0002] Truss structures are widely used in engineering fields such as bridges and buildings. They are also frequently used in telescopes and airplane wings due to their advantages, including light weight, material savings, high load-bearing capacity, large span, and ease of installation. However, truss structure optimization problems are often high-dimensional, discontinuous, and non-differentiable nonlinear implicit problems, involving enormous difficulty and computational complexity.

[0003] In truss optimization design, it is often necessary to perform evolutionary optimization of truss dimensions. Truss cross-section optimization typically refers to minimizing the overall mass of the truss structure by optimizing the cross-sectional area of ​​each component, given the truss structure, material, layout topology, and shape. Compared to truss cross-section optimization, truss topology optimization can eliminate many unnecessary components and nodes, thus more effectively addressing the challenges of considering large node costs, and significantly improving search results in highly nonlinear and highly nonconvex search spaces.

[0004] Traditional optimization methods suffer from drawbacks such as local optima, the curse of dimensionality, initial point dependence, and lack of robustness when dealing with these complex problems. In contrast, metaheuristic algorithms, as an effective optimization technique, can efficiently solve multivariate and high-dimensional problems, and are particularly suitable for large-scale and nonlinear problems. Therefore, there is an urgent need for a metaheuristic algorithm method to solve the truss topology optimization design problem. Summary of the Invention

[0005] This invention aims to at least solve the technical problems existing in the prior art, and in particular, it innovatively proposes a truss topology optimization design method based on information acquisition algorithm.

[0006] To achieve the above-mentioned objectives of this invention, the information acquisition algorithm designed in this invention is a novel metaheuristic optimization algorithm that combines information collection, filtering and evaluation, analysis and organization. It exhibits excellent solution performance when dealing with large and complex problems, and has advantages such as escaping local optima, fast convergence speed, and high-quality optimization design. At the same time, it also possesses advantages such as robustness, accuracy, and effectiveness.

[0007] Based on the designed information acquisition algorithm, this invention proposes a truss optimization design method based on an information acquisition optimization algorithm, which includes the following steps:

[0008] S1, Construct an objective function based on truss mass;

[0009]

[0010] S2, an information acquisition algorithm is used to solve the objective function based on truss mass;

[0011] S2-1, Initialize parameters:

[0012] Set the number of member groups D that need to be optimized, the population size Popsize, the maximum number of iterations Max_iter, and the maximum number of evaluations MAX_FEs = Popsize × Max_iter; and the current iteration number iter = 0, the current number of evaluations FEs = 0;

[0013] S2-2, Initialization Phase:

[0014] Randomly generate the initial population For population P iter The j-th individual in the array corresponds to a truss structure scheme, i.e., the number of members and their cross-sectional area for each category. Then, the individuals are randomly initialized.

[0015]

[0016] Where D represents the number of sets of members in the truss structure that need to be optimized in design;

[0017] For population P iter The j-th individual in the array stores the cross-sectional area of ​​the j-th group of rods;

[0018] θ is a random number that follows a uniform distribution between [0, 1].

[0019] Lo j and Up j These are the lower and upper bounds of the range of values ​​for the cross-sectional area of ​​the j-th member, respectively.

[0020] S2-3, Calculate individuals fitness value;

[0021]

[0022] in Let j be the j-th individual in the iter-th iteration (where j is the population P). iter (C - cross-sectional area of ​​the j-th group of members); C j ρ represents the mass of the j-th group of bars; j Let L be the density of the j-th group of bars; jLet be the length of the j-th group of members; the critical value is defined as a small positive number. When the cross-sectional area is less than this value, the corresponding component element is removed; otherwise, the element is retained. λ·M represents the penalty term, where M is a predefined number much larger than the cross-sectional area, and λ is the penalty coefficient. If the cross-sectional area of ​​the D-th group of members in the optimized design satisfies all the constraints, then λ = 0; otherwise, λ = 1.

[0023] Then save the population P. iter The individual with the lowest fitness value For the optimal individual

[0024] S2-4, the current number of evaluations FEs = FEs + Popsize. If the number of iterations iter is greater than the maximum number of iterations Max_iter, then output the current best individual. If the iteration count iter is less than the maximum iteration count Max_iter, then proceed to the next step;

[0025] S2-5, during the exploration phase, continue to update the optimal solution for each individual:

[0026] Calculate the individual in the (iter+1)th iteration of the exploration phase.

[0027]

[0028] Where D represents the number of sets of members in the truss structure that need to be optimized in design;

[0029] Represents an individual The individual after another iteration;

[0030] rand is a random number that follows a uniform distribution between [0, 1].

[0031] Population P iter A random individual within;

[0032] Δ represents the error factor;

[0033] Individuals in the computational exploration phase fitness value:

[0034]

[0035] Current number of evaluations FEs = FEs + Popsize, comparison and The size, if Less than Then preserve population P iter The individual with the lowest fitness value For the optimal individual Otherwise, the optimal individual in the population remains unchanged;

[0036] S2-7, the current iteration number is iter = iter + 1;

[0037] S2-8, Repeat steps S2-4 to S2-7. The process ends when the current number of evaluations (FEs) reaches MAX_FEs. The optimal individual obtained during the process is then considered. This is the result of truss topology optimization design.

[0038] Furthermore, the value of M is:

[0039]

[0040] in,

[0041] W(A) represents the mass of member A;

[0042] ε represents the equilibrium constant, which takes the value 2;

[0043] p j Indicates the degree of violation of constraints;

[0044] Indicates the maximum extent to which the constraint is violated;

[0045] αc represents the activity constraint.

[0046] Furthermore, it also includes S2-6, which continues to update the optimal solution for individuals during the development phase:

[0047] The individual in the (iter+1)th iteration of the computational development phase

[0048]

[0049] In the formula, express The individual is the result of another iteration;

[0050] This represents the best individual saved in the previous iteration;

[0051] This represents the average value of the best individuals generated during the previous iterations;

[0052] ε, ζ, κ and ω are four real numbers randomly generated between [-1, 1].

[0053] Λ represents the control factor;

[0054] Calculate the population P during the development phase using the following formula. iterFitness value of each individual:

[0055]

[0056] Current number of evaluations FEs = FEs + 1, comparison and The size, if Less than Then update population P iter The individual with the lowest fitness value For the optimal individual Otherwise, the optimal individual in the population remains unchanged.

[0057] Furthermore, after each fitness value calculation, the cross-sectional area of ​​the members is determined based on the fitness value to determine whether the constraint conditions are met, and nodal trusses that do not meet the constraint conditions are eliminated.

[0058] The constraints include any combination of stress constraints, displacement constraints, Euler buckling constraints, natural frequency constraints, and upper and lower section limit constraints; the expressions for the constraints are as follows:

[0059]

[0060] Where, σ j Indicates stress;

[0061] These represent the maximum and minimum stresses, respectively.

[0062] C j Indicate the mass of the j-th group of bars;

[0063] δ j Let be the displacement of the j-th group of members;

[0064] These represent the maximum and minimum displacements, respectively.

[0065] A j Let be the cross-sectional area of ​​the j-th group of members;

[0066] L j This represents the length of the j-th group of members.

[0067] k j The Euler buckling coefficient is based on the member cross section.

[0068] E represents stress intensity;

[0069] f j Indicates the natural frequency of the truss structure;

[0070] and These represent the range of values ​​for the upper and lower cross-sectional areas, respectively.

[0071] Furthermore, the formula for calculating the error factor Δ is as follows:

[0072]

[0073] Where Ξ represents the subjective influencing factor during information filtering and evaluation;

[0074] Γ represents the reliability factor of information acquisition.

[0075] Furthermore, the formula for calculating the subjective influence factor Ξ during information filtering and evaluation is as follows:

[0076] Ξ=2×(mod(3.468×υ×(1-β)×cos(arccos(γ×10 4 ))),1);

[0077] The mod() function is used to calculate the remainder when two numbers are divided.

[0078] υ, β, γ and δ are four real numbers randomly generated between [-1, 1].

[0079] Furthermore, the formula for calculating the control factor is as follows:

[0080]

[0081] Where Γ represents the reliability factor of information acquisition.

[0082] Furthermore, the formula for calculating the reliability factor Γ of the information acquisition is as follows:

[0083]

[0084] Where Φ represents the quality factor of information acquisition. δ is a real number randomly generated between [-1, 1].

[0085] Max_iter represents the maximum number of iterations;

[0086] iter represents the current iteration number.

[0087] In summary, by employing the above-mentioned technical solutions, this invention can quickly and accurately obtain the optimal truss topology design scheme. Specifically, it selects member dimensions as optimization variables for parameter design, removes some inefficient members for structural design, incorporates constraints as penalties into the fitness function calculation formula, and uses an information acquisition optimization algorithm for iterative optimization. This enables the design of optimal design parameters for each member that satisfy the working conditions, and it exhibits strong search capabilities, high computational efficiency, and is less prone to getting trapped in local optima. The information acquisition optimization algorithm uses collected information for population updates, eliminating the need to set parameter values ​​and reducing the impact of parameter selection on the optimization results.

[0088] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0089] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0090] Figure 1 This is a diagram illustrating the principle of information acquisition.

[0091] Figure 2 The convergence behavior graph of the information acquisition optimization algorithm.

[0092] Figure 3 A population diversity analysis diagram for information acquisition optimization algorithms.

[0093] Figure 4 Analysis diagram for exploring and developing optimization algorithms for information acquisition.

[0094] Figure 5 The convergence curves of the information acquisition optimization algorithm and its comparison algorithm are shown.

[0095] Figure 6 A comparison chart showing the running time of the information acquisition optimization algorithm and its comparative algorithms.

[0096] Figure 7 This is a diagram of the truss structure to be optimized in the embodiment.

[0097] Figure 8 This is a diagram of the optimized truss structure in the embodiment. Detailed Implementation

[0098] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0099] This invention proposes a truss optimization design method based on an information acquisition optimization algorithm, which includes the following steps:

[0100] Step 1: To rationally allocate nodes and optimize the overall structure's mass, stiffness, strength, and other performance indicators, a mathematical model minimizing the optimization objective needs to be established for the truss structure designed according to requirements. This is achieved by sequentially solving for the cross-sectional area A = [A1, A2, ..., A...] of each group (node) of members. D To minimize the total mass of the truss structure, the objective function expression for truss mass design is as follows:

[0101]

[0102] Where D represents the number of sets of members in the truss structure that need to be optimized; A j ρ is the cross-sectional area of ​​the j-th group of members; j Let L be the density of the j-th group of bars; j C is the length of the j-th group of members; j This represents the mass of the j-th group of members. A critical value is defined as a small positive number. When the cross-sectional area is less than this value, the corresponding component element is removed; otherwise, the element is retained. The cross-sectional area is used to determine whether a member is inefficient, and some inefficient members are removed for structural optimization design.

[0103] Then, determine whether the results (cross-sectional areas of each group of members) meet the various constraints according to the following formula, which are expressed as follows: stress constraint, displacement constraint, Euler buckling constraint, natural frequency constraint, and upper and lower section limit constraints.

[0104]

[0105] Where, σ j C represents stress. j δ represents the mass of the j-th group of bars; j Let A be the displacement of the j-th group of members; j Let L be the cross-sectional area of ​​the j-th group of members. j k represents the length of the rod. j Here, E represents the Euler buckling coefficient based on the member's cross-section, and f represents the stress intensity. j This represents the natural frequency of the truss structure. Additionally, and These represent the range of values ​​for the upper and lower cross-sectional areas, respectively.

[0106] Furthermore, λ·M represents a penalty term, the purpose of which is to ensure that the constraints are met. λ is the penalty coefficient; if the target member in group D of the optimized design satisfies all the constraints, then λ = 0; otherwise, λ = 1. M is a predefined number much larger than the cross-section, as shown in the following formula:

[0107]

[0108] In the formula, Where, p j Indicates the degree of violation of constraints, subject to Constraints, αc represents activity constraints. ε is assigned a value of 2 to ensure a balance between the exploration and development phases during the execution of the information acquisition algorithm.

[0109] Step 2, user initialization parameters, including the number of truss structure members to be optimized (D), population size (Popsize), maximum number of iterations (Max_iter), and maximum number of evaluations (MAX_FEs = Popsize × Max_iter);

[0110] Step 3, current iteration number iter = 0, current evaluation number FEs = 0;

[0111] Step 4: Randomly generate the initial population Let j be the j-th individual in the Piter population, representing the cross-sectional area of ​​the rods for each category. Then, randomly initialize the individuals.

[0112]

[0113] Where D represents the number of sets of members in the truss structure that need to be optimized in design;

[0114] For population P iter The j-th individual in the array stores the cross-sectional area of ​​the j-th group of rods;

[0115] θ is a random number that follows a uniform distribution between [0, 1].

[0116] Lo j and Up j These are the lower and upper bounds of the range of values ​​for the cross-sectional area of ​​the j-th member, respectively.

[0117] Step 5, calculate population P using the following formula. iter The fitness value of each individual in the group;

[0118]

[0119] in For population Piter The cross-sectional area of ​​the j-th group of members; ρ j Let L be the density of the j-th group of bars; j C is the length of the j-th group of members; j This represents the mass of the j-th group of members; the critical value is defined as a small positive number. When the cross-sectional area is less than this value, the corresponding component element is removed; otherwise, the element is retained.

[0120] λ·M represents the penalty term, where M is a predefined number much larger than the cross-section, and λ is the penalty coefficient. If the cross-sectional area of ​​the D group of members in the optimized design satisfies all the constraints, then λ = 0; otherwise, λ = 1.

[0121] Step 6, save the population P iter The individual with the lowest fitness value For the optimal individual Current number of evaluations FEs = FEs + Popsize.

[0122] Step 7: If the iteration count iter is greater than the maximum iteration count Max_iter, then output the current best individual. The results of the truss topology optimization design are obtained; if the number of iterations iter is less than the maximum number of iterations Max_iter, the filtering and evaluation information strategy (exploration phase) in the information acquisition algorithm is used to continue updating the optimal solution of the individual;

[0123] Step 7.1: Randomly generate four real numbers υ, β, γ and δ between [-1, 1];

[0124] Step 7.2, calculate the subjective influence factor Ξ during information filtering and evaluation:

[0125] Ξ=2×(mod(3.468×υ×(1-β)×cos(arccos(γ×10 4 ))),1);

[0126] The mod() function is used to calculate the remainder when two numbers are divided.

[0127] Step 7.3, calculate the reliability factor Γ of information acquisition:

[0128]

[0129] Where Φ represents the quality factor of information acquisition. Max_iter represents the maximum number of iterations; iter represents the current number of iterations.

[0130] Step 7.4, calculate the error factor Δ during information filtering and evaluation:

[0131]

[0132] Step 7.6, calculate the individual x in the (iter+1)th iteration of the exploration phase. j iter+1 :

[0133]

[0134] Where D represents the number of sets of members in the truss structure that need to be optimized in design; express The individual after one more iteration stores the cross-sectional area of ​​the j-th group of bars; rand is a random number that follows a uniform distribution between [0, 1]. Population P iter A random individual within;

[0135] Step 8: Calculate the population P during the exploration phase using the following formula. iter Fitness value of each individual:

[0136]

[0137] Step 9, current number of evaluations FEs = FEs + Popsize, compare. and The size, if Less than Then preserve population P iter The individual with the lowest fitness value For the optimal individual Otherwise, maintain population P iter The individual with the best fitness value constant;

[0138] Step 10: Further optimize the truss structure by utilizing the information organization and analysis strategies (development phase) in the information acquisition algorithm, and continue to update the optimal solution for each individual.

[0139] Step 10.1: Randomly generate four real numbers ε, ζ, κ and ω between [-1, 1];

[0140] Step 10.2, Control Factors When Organizing and Analyzing Information

[0141] Step 10.3, calculate the individual in the (iter+1)th iteration of the development phase.

[0142]

[0143] In the formula, express The individual after one more iteration stores the cross-sectional area of ​​the j-th group of members; This represents the best individual saved in the previous iteration; This represents the average value of the best individuals generated during the previous iterations;

[0144] Step 11, calculate the population P during the development phase using the following formula. iter Fitness value of each individual:

[0145]

[0146] Step 12, current evaluation count FEs = FEs + 1, compare and The size, if Less than Then update population P iter The individual with the lowest fitness value For the optimal individual Otherwise, the optimal individual in the population remains unchanged;

[0147] Step 13, save population P iter The individual with the lowest fitness value is the optimal individual. The current iteration number is iter = iter + 1;

[0148] Step 15: Repeat steps 7 to 13 until the current number of evaluations (FEs) reaches MAX_FEs, then the process ends. The optimal individual obtained during this process is then selected. This is the result of truss topology optimization design.

[0149] This invention utilizes the uncertainty and determinism inherent in information acquisition behavior, combining stable and changing factors. A mechanism integrating randomness and stability tendencies is employed to generate new individuals within the search space, maintaining population diversity and reducing the probability of getting trapped in local optima. Simultaneously, the method uses the optimal solutions obtained during the search process to guide evolutionary operations, and incorporates filtering and evaluation strategies to accelerate the algorithm's convergence speed. Furthermore, based on the current iteration, individual behavior is adjusted through organizing and analyzing information strategies, enhancing the algorithm's robustness. Compared to similar methods, this invention reduces the probability of getting trapped in local optima, accelerates convergence, and improves the performance of truss topology optimization design. To verify the effectiveness of this invention, numerical simulation experiments were conducted on the proposed information acquisition algorithm.

[0150] First, to demonstrate the effectiveness of the proposed algorithm, the performance of the proposed Information Acquisition (IAO) algorithm was evaluated on the CEC2014, CEC2017, CEC2020, and CEC2022 test suites. These suites included four types of functions: unimodal, multimodal, hybrid, and combined functions. The unimodal function had only one optimal solution, used to evaluate the algorithm's convergence speed and exploration capability. The other three algorithms had multiple optimal solutions, used to test the algorithm's local optimum avoidance and exploration capabilities. The experiments were conducted using Matlab2021a software on a computer running Windows 10 with 16GB of memory and a 2.3GHz processor. The IAO algorithm was compared with 11 other popular algorithms: Particle Swarm Optimization (PSO), Artificial Bee Swarm Optimization (ABC), Sine & Cosine Algorithm (SCA), Snake Optimizer (SO), Chameleon Swarm Optimizer (CSA), Raccoon Optimizer (COA), Gravity Search Algorithm (GSA), Whale Optimizer (WOA), African Vulture Optimizer (AVOA), Artificial Gorilla Force Optimizer (GTO), and Dung Beetle Optimizer (DBO). The parameters used in these metaheuristic algorithms were summarized. The maximum number of iterations was set to 1000, and the overall size for all algorithms was 50 and 30 independent runs. The mean (Ave) and standard deviation (Std) were recorded, and the best results among the 12 algorithms were highlighted in bold.

[0151] Table 1 Algorithm Parameter Description

[0152]

[0153] The qualitative analysis of the IAO algorithm is as follows:

[0154] 1) Convergence behavior analysis

[0155] To examine the convergence behavior of IAO, we tested the benchmark function suites of CEC2014, CEC2017, CEC2020, and CEC2022. From each test suite, we randomly selected two test results, for a total of eight test results for analysis. A four-column graph was generated for each function. (See figure below.) Figure 2 As shown, the first column displays the two-dimensional shape of the benchmark function, which helps us understand the complexity of the problem. The second column illustrates the variation in the average fitness value among the search agents. As can be seen from the graph, the fitness value starts high and then drops rapidly. This indicates the potential of the search agent to find the optimal solution. The third column shows the trajectory of the search agent, transitioning from fluctuation to stability. This marks a shift from global exploration to local exploitation, which is beneficial for obtaining the global optimum. The last column is the convergence curve of the IAO. Figure 2As shown, this curve converges continuously, indicating that the algorithm can find the optimal solution while effectively avoiding local optima and achieving a global optimum. By analyzing these graphs, we can evaluate the performance and convergence behavior of the IAO algorithm, thereby verifying its performance in different test functions.

[0156] 2) Population diversity analysis

[0157] To verify the population diversity of the proposed IAO algorithm, we use formula (1) to calculate the population diversity, where I C Represents the moment of inertia, x id (t) represents the d-th dimension value of the i-th search agent at iteration t, c d (t) represents the dispersion of the population and its mass center c in each iteration, as shown in formula (2).

[0158]

[0159]

[0160] Figure 3 The results show the population diversity of the IAO algorithm on four different test function suites. These randomly selected experimental results vividly demonstrate that IAO significantly enhances population diversity in the initial stages of iteration. As the number of iterations increases, the curve gradually converges and stabilizes at a high level, indicating that IAO successfully avoids premature convergence and local optimum stagnation. This further highlights the great potential of the IAO algorithm in finding the optimal solution.

[0161] 3) Exploration and Development Analysis

[0162] According to the introduction, the robustness of metaheuristic algorithms depends on the balance between exploration and exploitation during the search process. To evaluate the robustness of the IAO algorithm, this paper uses equations (3) and (4) to calculate the exploration-exploitation ratio in the IAO algorithm, and introduces the dimensionality diversity metric parameter Div(t), calculated by equation (5). Wherein, Div... max This represents the maximum diversity observed throughout the entire iteration process.

[0163]

[0164]

[0165]

[0166] Figure 4Experimental results show that, across various test functions, the exploration rate of the IAO algorithm consistently remains below 10%, while the exploitation rate consistently exceeds 90%. For most functions, the optimal balance for a good algorithm is an exploitation rate exceeding 90% and an exploration rate below 10%. This indicates that the IAO algorithm can effectively balance the exploration and exploitation processes within the search domain and obtain the optimal solution. Specifically, for unimodal functions, the exploitation curve of IAO improves rapidly with increasing iterations and tends to stabilize at a higher level, indicating that the IAO algorithm has a fast convergence speed. For multimodal functions, the exploration and exploitation percentages of IAO fluctuate in the initial stage but stabilize within the optimal balance range after iterations. This shows that IAO can effectively reduce the risk of getting trapped in local optima. Overall, the IAO algorithm can effectively balance the exploration and exploitation requirements of different benchmark functions.

[0167] The quantitative analysis of the IAO algorithm is as follows:

[0168] 1) CEC 2014 Test Function Suite

[0169] This invention evaluated 12 comparative algorithms on the CEC 2014 test function suite. Based on the mean (Ave) and standard deviation (Std) of the algorithm results provided in Table 2, the last three rows present a statistical analysis of all competitors. The first row shows three symbols (W|T|L), representing the number of functions with the best performance (win), indistinguishable (tie), and worst performance (loss), respectively. The second row represents the Friedman average ranking, and the third row reports the final ranking values ​​of all competitors. The results show that IAO performed best, achieving the best results in 23 out of 30 problems. IAO ranked first with a Friedman average ranking of 2.917. Furthermore, from... Figure 5 The convergence curve clearly shows that the IAO search agent extensively explores promising regions in the design space and develops optimal solutions. In the initial stage of optimization, the search agent undergoes abrupt changes and gradually converges. This guarantees the convergence of the algorithm within the search space. Therefore, the algorithm possesses excellent global exploration and local development capabilities, demonstrating its effectiveness and superiority.

[0170] Table 2. Experimental results of 12 algorithms at CEC 2014

[0171]

[0172]

[0173]

[0174] 2) CEC 2017 Test Function Suite

[0175] A detailed analysis of the IAO algorithm's performance in the CEC 2017 test suite yielded a series of meaningful statistical results, further validating its superiority. According to the data in Table 3 regarding the mean and standard deviation of the compared algorithms, IAO achieved the highest win rate across 30 problems. Furthermore, the Friedman average ranking score was used to evaluate IAO's performance in the competition. Data shows that IAO's Friedman average ranking score was 1.650, ranking first among all compared algorithms. This result further emphasizes the outstanding capabilities of the IAO algorithm in both global exploration and local exploitation. Further observation of the convergence curve (e.g.) Figure 5 As shown in the diagram, the IAO algorithm continuously converges until it reaches the optimal solution. This demonstrates that the algorithm can effectively find the best solution to a problem. Therefore, based on these analytical results, it is proven that the developed IAO algorithm provides a powerful and reliable method for solving complex problems, and its excellent performance has made it highly valued and respected in the current field.

[0176] Table 3. Experimental results of 12 algorithms at CEC 2017

[0177]

[0178]

[0179]

[0180] 3) CEC 2020 Test Function Suite

[0181] Twelve algorithms were comprehensively evaluated using the CEC 2020 benchmark suite. Table 4 shows that the IAO algorithm performed best among all algorithms, demonstrating significant research value. Statistical analysis revealed that the IAO algorithm outperformed other well-known algorithms in terms of Friedman average ranking. This indicates that the IAO algorithm is the most reliable choice when handling complex test functions. Furthermore, from... Figure 5 It can also be seen that the IAO algorithm reaches the optimal solution in fewer iterations. This means it has a faster convergence speed and the ability to find the global optimum. This is crucial for solving real-world problems, especially in scenarios where the best solution needs to be found quickly. In conclusion, based on our evaluation results and statistical analysis, the IAO algorithm performed outstandingly at CEC2020, highlighting its excellent performance in optimization problems.

[0182] Table 4. Experimental results of 12 algorithms at CEC 2020

[0183]

[0184] 4) CEC 2022 Test Function Suite

[0185] Furthermore, this invention also used the latest CEC 2022 test suite to evaluate the performance of the IAO and comparison algorithms. The experimental results are summarized in Table 5. The data in the table shows that the IAO had the highest average ranking, at 2.450. This finding, combined with… Figure 5 The analysis clearly demonstrates that IAO successfully solves stagnant local optima problems, effectively avoiding premature convergence. These results further confirm the superiority and robustness of the IAO algorithm. Compared with other algorithms, IAO has a significant advantage in its exploration and exploitation capabilities. It can maintain extensive exploration of the search space and find better solutions. Furthermore, IAO has strong resistance to local optima, making it perform exceptionally well in various complex problem scenarios.

[0186] Table 5. Experimental results of 12 algorithms at CEC 2022

[0187]

[0188] In summary, based on the results of this study, it can be concluded that IAO possesses excellent performance. This algorithm demonstrates outstanding ability in solving optimization problems, effectively discovering the optimal solution. Therefore, the application prospects of IAO are exciting and worthy of further in-depth research and exploration.

[0189] Statistical significance analysis of the IAO algorithm:

[0190] Based on the above data, this invention uses the nonparametric Wilcoxon rank-sum test to compare the algorithms. The significance level of the test is set at 0.05. The symbols "+ / = / -" are used to indicate whether the performance of IAO is better than, similar to, or worse than its competitors. The statistical results are shown in Table 6. Clearly, in most cases, there are significant differences between IAO and other competing algorithms. The statistical results are as follows: 216 / 93 / 21, 301 / 16 / 13, 91 / 18 / 1, 115 / 7 / 10. Therefore, based on the preceding analysis, the IAO method proposed in this paper stands out among other competing algorithms, exhibiting the most outstanding overall performance.

[0191] Table 6. Statistical results of the Wilcoxon rank-sum test

[0192]

[0193] Cost analysis of the IAO algorithm:

[0194] Based on the above results, it is clear that IAO has a significant advantage compared to other excellent y-ary heuristic algorithms. Next, we aim to directly demonstrate the differences in computational cost among the compared algorithms by analyzing their computational costs. The population size, maximum number of iterations, and number of independent runs for the compared algorithms are set to 50, 1000, and 30, respectively. Figure 6 The report presents the total time (in seconds) taken by the comparison algorithm to run all functions independently 30 times in different test suites. The figure clearly shows that the IAO algorithm's computation time is significantly lower than other comparative algorithms across all test function suites. Through careful algorithm design and optimization, the IAO algorithm achieves fast computational performance. It employs an efficient search strategy, enabling it to quickly find the optimal solution on large-scale datasets. In contrast, other optimizers require more iterations and longer computation time to achieve the same level of accuracy. The results demonstrate that the IAO algorithm not only has an advantage in execution time but also exhibits excellent performance in accuracy.

[0195] Through evaluation experiments using different test function suites, this invention verifies that the IAO algorithm can provide excellent solution results for various complex optimization problems. This means that the IAO algorithm can provide high-quality solutions to real-world nonlinear optimization problems.

[0196] The specific implementation of the present invention is as follows:

[0197] Truss structures to be optimized, such as Figure 7 As shown, firstly, assume A = [A1, A2, ..., A...] D Then, the objective function for topology optimization is:

[0198]

[0199] Where D represents the number of sets of members in the truss structure that need to be optimized in design;

[0200] A j Let be the cross-sectional area of ​​the j-th group of members;

[0201] ρ j Let be the density of the j-th group of bars;

[0202] L j Let J be the length of the j-th group of members;

[0203] C jLet represent the mass of the j-th group of members. The critical value is defined as a small positive number. When the cross-sectional area is less than this value, the corresponding component element is removed; otherwise, the element is retained. Then, determine whether the obtained result satisfies each constraint condition according to the following formula, specifically expressed as shown in the following formula, where represents the stress constraint, displacement constraint, Euler buckling constraint, natural frequency constraint, and upper and lower section limit constraints, respectively.

[0204]

[0205] Where, σ j C represents stress. j δ represents the mass of the j-th group of bars; j Let A be the displacement of the j-th group of members; j Let L be the cross-sectional area of ​​the j-th group of members. j k represents the length of the rod. j Here, E represents the Euler buckling coefficient based on the member's cross-section, and f represents the stress intensity. j This represents the natural frequency of the truss structure. Additionally, and These represent the ranges of the upper and lower cross-sectional areas, respectively. Furthermore, λ·M represents a penalty term, intended to ensure that the constraints are met. λ is the penalty coefficient; if the target member in group D of the optimized design satisfies all constraints, then λ = 0; otherwise, λ = 1. M is a predefined number much larger than the cross-sectional area, as shown in the following formula:

[0206]

[0207] In the formula, in, p represents the maximum degree of constraint violation. j Indicates the degree of violation of constraints, subject to Constraints, αc represents activity constraints. ε is assigned a value of 2 to ensure a balance between the exploration and development phases during the information acquisition algorithm execution. The invented algorithm is used to optimize the above structure. The initial truss parameters and loads are input into the information acquisition algorithm model to determine the set values ​​of the model parameters, including the number of members to be optimized in the truss structure. D =20, Population size Popsize=50, Maximum number of iterations Max_iter=1000, Maximum number of evaluations MAX_Fes=50000; and the cross-sectional area of ​​the truss members is used as the design variable of the model; in addition, the settings of the other parameters in the above formula are shown in the table below:

[0208] Table 7 Optimization constraint parameter values ​​for the 20-bar truss structure

[0209]

[0210] The fitness function calculation formula with a penalty term is obtained based on constraints and the penalty function method. The objective function of the information acquisition algorithm model and the fitness function values ​​of the population are then calculated based on the fitness function calculation formula and model parameters. If the objective function satisfies the constraints or the number of iterations exceeds the set maximum number of iterations, solutions that do not meet the constraints are discarded to obtain the optimal feasible solution and output the design parameters of the truss members. Specifically, this invention provides an optimization method based on an information acquisition algorithm and the penalty function method for lightweight optimization design of truss structures, aiming to obtain trusses that use less material, are lighter, and are suitable for different scenarios. This invention uses an information acquisition algorithm to iteratively optimize the truss dimensional parameters.

[0211] Furthermore, the information acquisition algorithm can solve all optimization problems solved by other comparative algorithms, with more stable solution quality and efficiency. The penalty function method is widely used and theoretically mature in solving constrained optimization problems. During the solution process, a barrier function is added to the original objective function to obtain an augmented objective function. Because early methods required solving a series of unconstrained penalty function minimization problems, it is usually called a sequential unconstrained minimization method. The function of introducing the penalty function is to assign a maximum value to infeasible points or points attempting to cross the boundary and escape the feasible region, thereby transforming the constrained optimization problem into an unconstrained optimization problem and simplifying computation. Using the penalty function method, the constraint function of the truss topology optimization design problem is added as a penalty term to the objective function to obtain the fitness function of the information acquisition algorithm.

[0212] As one feasible approach, topology optimization is performed on a truss with 20 nodes. During the optimization process, inefficient member elements can be removed, resulting in the following planar truss topology optimization result: Figure 8 Table 8 compares the results of each algorithm in optimizing the truss, where R represents the nodes that were removed during the optimization process.

[0213] Table 8. Truss topology optimization results for each algorithm

[0214]

[0215] As can be seen from the table, the information acquisition algorithm achieved the best results in the experiment. Its weight value was far superior to that of other comparative algorithms. At this point, it only occupied 7 nodes, reduced 13 structures, and obtained the best optimization value of 157.1498. This shows that the algorithm effectively reduced the mass of 20 node trusses while maintaining high-efficiency optimization, and can effectively improve the performance of truss optimization design.

[0216] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A truss topology optimization design method based on information acquisition algorithm, characterized in that, Includes the following steps: S1, Construct an objective function based on truss mass; S2, an information acquisition algorithm is used to solve the objective function based on truss mass; S2-1, Initialize parameters: Set the number of member groups D that need to be optimized, the population size Popsize, the maximum number of iterations Max_iter, and the maximum number of evaluations MAX_FEs = Popsize × Max_iter; and the current iteration number iter = 0, the current number of evaluations FEs = 0; S2-2, Initialization Phase: Randomly generate the initial population For population P iter The j-th individual in the dataset is selected, and then individuals are randomly initialized. Where D represents the number of sets of members in the truss structure that need to be optimized in design; For population P iter The j-th individual in the array stores the cross-sectional area of ​​the j-th group of rods; θ is a random number that follows a uniform distribution between [0, 1]. Lo j and Up j These are the lower and upper bounds of the range of values ​​for the cross-sectional area of ​​the j-th member, respectively. S2-3, Calculate individuals fitness value; in This represents the j-th individual in the iter-th iteration; C j Indicate the mass of the j-th group of bars; ρ j Let be the density of the j-th group of bars; L j Let J be the length of the j-th group of members; λ·M represents the penalty term, where M is a predefined number much larger than the cross-section, and λ is the penalty coefficient. If the cross-sectional area of ​​the D group of members in the optimized design satisfies all the constraints, then λ = 0; otherwise, λ = 1. Then save the population P. iter The individual with the lowest fitness value For the optimal individual S2-4, the current number of evaluations FEs = FEs + Popsize. If the number of iterations iter is greater than the maximum number of iterations Max_iter, then output the current best individual. If the iteration count iter is less than the maximum iteration count Max_iter, then proceed to the next step; S2-5, during the exploration phase, continue to update the optimal solution for each individual: Calculate the individual in the (iter+1)th iteration of the exploration phase. Where D represents the number of sets of members in the truss structure that need to be optimized in design; Represents an individual The individual after another iteration; rand is a random number that follows a uniform distribution between [0, 1]. Population P iter A random individual within; Δ represents the error factor; Individuals in the computational exploration phase fitness value: Current number of evaluations FEs = FEs + Popsize, comparison and The size, if Less than Then preserve population P iter The individual with the lowest fitness value For the optimal individual Otherwise, the optimal individual in the population remains unchanged; S2-7, the current iteration number is iter = iter + 1; S2-8, Repeat steps S2-4 to S2-7. The process ends when the current number of evaluations (FEs) reaches MAX_FEs. The optimal individual obtained during the process is then considered. This is the result of truss topology optimization design.

2. The truss topology optimization design method based on information acquisition algorithm according to claim 1, characterized in that, The value of M is: in, W(A) represents the mass of member A; ε represents the equilibrium constant, which takes the value 2; p j Indicates the degree of violation of constraints; Indicates the maximum extent to which the constraint is violated; αc represents the activity constraint.

3. The truss topology optimization design method based on information acquisition algorithm according to claim 1, characterized in that, This also includes S2-6, which continues to update the optimal solution for individuals during the development phase: The individual in the (iter+1)th iteration of the computational development phase In the formula, express The individual is the result of another iteration; This represents the best individual saved in the previous iteration; This represents the average value of the best individuals generated during the previous iterations; ε, ζ, κ and ω are four real numbers randomly generated between [-1, 1]. Λ represents the control factor; Calculate the population P during the development phase using the following formula. iter Fitness value of each individual: Current number of evaluations FEs = FEs + 1, comparison and The size, if Less than Then update population P iter The individual with the lowest fitness value For the optimal individual Otherwise, the optimal individual in the population remains unchanged.

4. A truss topology optimization design method based on an information acquisition algorithm according to any one of claims 1 or 3, characterized in that, After each fitness value calculation, the cross-sectional area of ​​the members is determined based on the fitness value to ensure that the constraint conditions are met, and nodal trusses that do not meet the constraint conditions are removed. The constraints include any combination of stress constraints, displacement constraints, Euler buckling constraints, natural frequency constraints, and upper and lower section limit constraints. The expression for the constraint is as follows: Where, σ j Indicates stress; These represent the maximum and minimum stresses, respectively. C j Indicate the mass of the j-th group of bars; δ j Let be the displacement of the j-th group of members; These represent the maximum and minimum displacements, respectively. A j Let be the cross-sectional area of ​​the j-th group of members; L j This represents the length of the j-th group of members. k j The Euler buckling coefficient is based on the member cross section. E represents stress intensity; f j Indicates the natural frequency of the truss structure; and These represent the range of values ​​for the upper and lower cross-sectional areas, respectively.

5. The truss topology optimization design method based on information acquisition algorithm according to claim 1, characterized in that, The formula for calculating the error factor Δ is as follows: Where Ξ represents the subjective influencing factor during information filtering and evaluation; Γ represents the reliability factor of information acquisition.

6. The truss topology optimization design method based on information acquisition algorithm according to claim 5, characterized in that, The formula for calculating the subjective influence factor Ξ during information filtering and evaluation is as follows: Ξ=2×(mod(3.468×υ×(1-β)×cos(arccos(γ×10 4 ))),1); The mod() function is used to calculate the remainder when two numbers are divided. υ, β, γ and δ are four real numbers randomly generated between [-1, 1].

7. The truss topology optimization design method based on information acquisition algorithm according to claim 3, characterized in that, The formula for calculating the control factor is as follows: Where Γ represents the reliability factor of information acquisition.

8. A truss topology optimization design method based on an information acquisition algorithm according to claim 5 or 7, characterized in that, The formula for calculating the reliability factor Γ of the information acquisition is as follows: Where Φ represents the quality factor of information acquisition. δ is a real number randomly generated between [-1, 1]. Max_iter represents the maximum number of iterations; iter represents the current iteration number.

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