Multi-target multi-bar truss optimization method based on single-target sequence search assistance

Abstract

The invention discloses a multi-target multi-bar truss optimization method based on single-target sequence search assistance. The method comprises the following steps: preliminarily locking an angular solution region by using an angular solution search mechanism; introducing a crossover operator to communicate with a population history optimal individual to generate an excellent individual; a mutation operator is introduced, so that the population is more diversified; an adaptive strategy is introduced, so that the offspring population is more excellent; external archives are introduced to improve the error-tolerant rate during individual selection; the angular solution quality is improved by adopting an angular solution detection mechanism; using the obtained angular solution to guide a multi-target algorithm to carry out further diversity search; selecting a plurality of non-dominated solutions using a non-dominated sorting method and the congestion distance; and evaluating the result on a plurality of test problem sets. A two-stage search mode is adopted, in the first stage, targets are searched in sequence on the whole, and an angular solution and a non-dominated solution are obtained; in the second stage, the solution obtained in the first stage serves as an initial population, evolution is conducted through a multi-objective optimization algorithm, and therefore better convergence and non-dominated solution diversity are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of truss structures, and in particular relates to a multi-objective multi-rod truss optimization method based on single-objective sequence search assistance. Background Art

[0002] With the development of modern architecture and mechanical engineering, multi-bar truss structures have been widely used in various engineering fields due to their excellent load-bearing capacity and cost-effectiveness. These truss structures play a vital supporting role in buildings, bridges, and mechanical equipment. In practical applications, truss design must not only meet strength and stability requirements but also meet multiple objectives, such as optimizing material usage, reducing costs, and controlling deformation and displacement. Therefore, how to effectively perform multi-objective optimization during the design process has become a major challenge for structural engineers.

[0003] In multi-bar truss design, engineers typically face several key challenges: first, how to minimize material usage while ensuring load-bearing capacity; second, how to optimize the truss geometry to improve structural stiffness and stability; and finally, how to reduce manufacturing costs and construction difficulty. The complexity of these issues means that traditional single-objective optimization methods often struggle to effectively address practical problems, as they fail to simultaneously consider the balance of multiple objectives. To address this, multi-objective optimization algorithms have emerged as a crucial tool for addressing the multidimensional challenges of truss design. These algorithms can help designers find a range of compromise solutions by balancing the conflicts between different objectives.

[0004] The main challenge of multi-objective optimization lies in the diversity and complexity of its problems. Traditional mathematical methods, such as linear programming (LP) and integer programming (IP), can be used to solve certain types of problems, but their scope of applicability is limited, especially when the number of objectives increases, nonlinear factors are introduced, or the constraints become complex. These methods often have difficulty handling complex multi-objective problems, and the computational time increases exponentially with the increase in the scale of the problem. In contrast, evolutionary algorithms, as a heuristic algorithm, are particularly suitable for solving multi-objective optimization problems. By simulating the selection, crossover, mutation and other processes in natural evolution, evolutionary algorithms can explore a larger solution space and gradually generate a Pareto front solution set.

[0005] A number of multi-objective evolutionary algorithms have been designed and widely recognized for their effectiveness in solving multi-objective problems. As problems become increasingly complex, researchers have devised various operations to improve the performance of multi-objective algorithms. However, these operations also significantly increase the operational complexity of the algorithms. Therefore, it is necessary to improve the performance of these algorithms without significantly increasing their complexity, thereby broadening their application.

[0006] To achieve this goal, some researchers began to use single-objective search algorithms to assist in searching the Pareto front. Since the complexity of single-objective search algorithms is lower than that of multi-objective search algorithms, the corresponding algorithms can have better performance and lower complexity. They divided single-objective search and multi-objective search into two different stages. It is expected that the results obtained by using single-objective search will provide an ideal search environment for multi-objective optimization. However, the algorithms proposed by existing methods for single-objective solutions are relatively simple, and it may be difficult to guarantee the quality of the results when dealing with more complex problems. This may undermine the effectiveness of the multi-objective search algorithm in the second stage. In addition, using multiple populations to collaboratively optimize multiple objectives does not take into account the areas between objectives, which may result in the loss of additional computing resources and ignore some high-quality solutions. Summary of the Invention

[0007] In order to solve the above problems, the present invention proposes a new multi-objective algorithm framework, called a multi-objective multi-bar truss optimization method based on single-objective sequential search assistance, to improve the efficiency of existing multi-objective algorithms while reducing the computational cost.

[0008] The technical solution adopted in the present invention is:

[0009] The multi-objective multi-link truss optimization method based on single-objective sequential search assistance includes the following steps:

[0010] S1. Determine truss structure parameters and constraints: Establish a multi-bar truss model, clarify the design objectives including structural weight and node displacement, define design variables including component cross-sectional area and node location, and set constraints including stress constraints for each component;

[0011] S2. Establishing a multi-objective function: Based on the design goal of step S1, construct a multi-objective optimization objective function including structural weight, material usage, and node displacement, and establish a mathematical expression for each objective function;

[0012] S3. Initialize design variables: Determine the initial value range of the design variables in the parameter space to provide the parameter boundary of the initial solution for the subsequent optimization algorithm;

[0013] S4, using a multi-objective algorithm assisted by a single-objective sequence search to solve the model. The specific steps are as follows:

[0014] S41, initialize population and external archive;

[0015] S42, determining the computing resources allocated to each search phase;

[0016] S43, performing the first stage search using the corner solution search mechanism;

[0017] S44, obtaining the angle solution corresponding to each target;

[0018] S45, using the corner solution to initialize the population for multi-objective search;

[0019] S46, performing the second stage search using a multi-objective optimization algorithm;

[0020] S47, each search obtains a child population and merges it with its corresponding parent population;

[0021] S48, using an environmental selection method to screen the obtained population and determine the parent population for the next generation search;

[0022] S49, evaluate the results obtained at the end of evolution.

[0023] Furthermore, the specific steps of S43 are:

[0024] S431, divide a multi-objective problem into multiple single-objective problems;

[0025] S432, determining computing resources allocated to each search target, and determining the first target as the current search target;

[0026] S433, performing a single target search on the current search target using a single target search algorithm, and obtaining an angular solution of the current search target within limited search resources;

[0027] S434, reinitialize the population near the corner solution;

[0028] S435, using a single target search algorithm to perform a deeper local search for the corner solution of the current target;

[0029] S436, taking the final high-quality single-objective solution as the corner solution of the current objective;

[0030] S437, merge the corner solution with the initial population, and re-screen the initial population for searching the next target;

[0031] S438, change the search target and repeat S433-S437 operations until all targets are searched.

[0032] Furthermore, the specific steps of S433 are:

[0033] S4331, initialize a new archive F;

[0034] S4332, using the adaptive differential evolution algorithm to perform single-target search and obtain the offspring population;

[0035] S4333, further optimizing the obtained offspring population using a diversity search method to obtain a new offspring population;

[0036] S4334, store the best individual in the current offspring population into F;

[0037] S4335, repeating S4332-S4334 operations until the evaluation resources allocated to the current single target search are exhausted;

[0038] S4336, storing the population obtained from the last single target search as the angle solution of the current target;

[0039] S4337, perform non-dominated sorting on the diagonal solutions and store them in an external archive.

[0040] Furthermore, the specific steps of S4332 are:

[0041] S43321, the parent population is crossed with the global optimal individual to produce 60 individuals;

[0042] S43322, the parent population mutates to produce 60 new individuals;

[0043] S43323, the parent population uses the adaptive differential evolution algorithm to generate 60 individuals.

[0044] Furthermore, the formula of the adaptive differential evolution algorithm is:

[0045] X new =X1+ω*(X2-X3)

[0046] Where, X new is the position of the current individual in the next generation; X1 and X2 use the individuals with the top two fitness values in the current population respectively; X3 is an individual randomly selected from the current population; ω represents the weight of the weighted difference, and the update formula of ω is as follows:

[0047]

[0048] Where i represents the search generation; max_i represents the maximum search generation; ω0 represents the initial weight set to 1, ω i+1 represents the weight of the i+1th generation.

[0049] Furthermore, the specific steps of S4333 are:

[0050] S43331, read the data in archive F and determine whether the best individuals of the two latest offspring are the same;

[0051] S43332, if they are not the same, terminate the current search;

[0052] S43333, if they are the same, then calculating the values of a pair of complementary parameters OD1 and OD2 for determining the degree of congestion;

[0053] S43334, if the corresponding degree is 1, the population is randomly initialized within the range of S1;

[0054] S43335: If the corresponding degree is 2, the population is randomly initialized within the range of S2;

[0055] S43336: Output the obtained population as the new offspring population.

[0056] Furthermore, the specific calculation method of S43333 is:

[0057] Calculate the Euclidean distance between individuals in the current population and get the sum of the Euclidean distances between each individual and all other individuals; then calculate the average value of the Euclidean distances of these individuals Euclidean distances mean And the maximum value of Euclidean distance Euc max Finally, the values of OD1 and OD2 are calculated using the following formulas to determine the degree of congestion:

[0058]

[0059] Where, Euc mean Represents the average value of the Euclidean distance between individuals; Euc max Indicates the maximum value of the Euclidean distance between individuals;

[0060] If there are 60*OD2 individuals whose Euclidean distance is less than OD1×(X max -X min ), the congestion level is determined to be case 1, otherwise it is case 2.

[0061] Furthermore, the specific calculation method of S43334 is:

[0062] When it is judged as case 1, it means that the individuals in the current population are too concentrated and easily fall into the local optimum. Therefore, it is necessary to make the population jump out of the current area and search in a larger range. Therefore, the calculation method of the search range S1 is:

[0063] S1=OD2×(X max -X min );

[0064] Where, X max and X min They correspond to the upper and lower limits of the search space respectively.

[0065] Furthermore, the specific calculation method of S4335 is: when it is determined to be case 2, it means that the individuals in the current population are too loose and it is difficult to search for the optimal solution. Therefore, it is necessary to perform a local search near the global optimal solution. Therefore, the calculation method of the search range S2 is:

[0066] S2=OD1×(X max -X min ).

[0067] Furthermore, the specific steps of S46 are:

[0068] S461, select individuals in the population one by one, and randomly select their corresponding individuals for crossover to obtain a progeny population;

[0069] S462, perform mutation operation on all individuals in the population to obtain another offspring population;

[0070] S463, merge the two offspring populations as the offspring population obtained by searching this generation.

[0071] Furthermore, the specific steps of S48 are:

[0072] S481, perform non-dominated sorting on all individuals in the population;

[0073] S482, according to the ranking level, prioritize the individuals with the highest non-dominant level;

[0074] S483, for individuals of the same level, calculate their crowding distances respectively, and prioritize individuals with larger crowding distances;

[0075] S484, repeat S482-S483 operations until 60 individuals are retained as the parent population for the next generation search.

[0076] The beneficial effects produced by the present invention are:

[0077] 1. A multi-objective optimization algorithm framework is proposed, which can simultaneously consider multiple objectives in truss design, such as load-bearing capacity, material usage, and cost control, to achieve more comprehensive optimization;

[0078] 2. Improve optimization efficiency through optimization methods: By adopting a two-stage search mode, the optimization efficiency of truss design is significantly improved, reducing calculation time and resource consumption;

[0079] 3. Provides engineers with a series of compromise reference solutions: enabling them to make reasonable trade-offs between multiple design goals to meet different engineering needs;

[0080] 4. Wide application: This algorithm framework is not only applicable to the design optimization of two-bar trusses and four-bar trusses, but can also be extended to other multi-objective optimization problems in structural engineering and industrial applications, with good versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is a flow chart of the method of the present invention;

[0082] Figure 2 This is a mathematical example diagram of a double-bar truss;

[0083] Figure 3 This is a mathematical example diagram of a four-bar truss. DETAILED DESCRIPTION

[0084] The present invention will be further described below with reference to the accompanying drawings.

[0085] like Figure 1 As shown, the present invention is a multi-objective multi-rod truss optimization method based on single-objective sequence search assistance, comprising the following steps:

[0086] A multi-bar truss model was established, with clear design objectives including structural weight and node displacements. Design variables were defined, including component cross-sectional area and node location, and constraints were set, including stress constraints for each component. In the double-bar truss problem, structural symmetry was ensured while considering the overall stability of the truss under load. The weight of the structure and the displacement of connection point 3 needed to be minimized while satisfying the component stress constraints:

[0087]

[0088] ρ=0.283lb / in 3 ,h=100in,P=10 4 lb, E = 3.0E07 lb / in 2 ,

[0089] σ0=2.0E04lb / in 2 ,A min =1.0in 2

[0090] Where g1(x) and g2(x) are constraint functions representing the stress constraints of the first and second members in the truss; x1 is the horizontal coordinate of the truss; x2 is the cross-sectional area of the truss member; P is the external concentrated load applied to the truss node; σ0 is the allowable stress of the material; ρ is the density of the material used to make the truss member; h is a characteristic height dimension of the truss; E is the elastic modulus of the material used to make the truss member; A min is the minimum allowable cross-sectional area of the member.

[0091] S2, establish the objective function: Based on the design goal of step S1, define the objective function of multi-objective optimization, and construct a multi-objective optimization objective function that includes structural weight, material usage, and node displacement. At this time, clarify the mathematical expression of each objective function in the model to provide a basis for subsequent solution:

[0092]

[0093] S3, Initialize design variables: According to the problem requirements, determine the initial value range of the design variables in the parameter space, and provide the parameter boundary of the initial solution for the subsequent multi-objective algorithm based on single-objective sequence search assistance:

[0094] 0.10≤x1≤2.25,0.50≤x2≤2.50

[0095] S4, a multi-objective algorithm based on single-objective sequence search assistance is used to solve the model, such as Figure 2 As shown, the specific steps are:

[0096] S41, initialize population and external archive;

[0097] S42, determining the computing resources allocated to each search phase;

[0098] S43, performing the first stage search using the corner solution search mechanism;

[0099] S44, obtaining the angle solution corresponding to each target;

[0100] S45, using the corner solution to initialize the population for multi-objective search;

[0101] S46, performing the second stage search using a multi-objective optimization algorithm;

[0102] S47, each search obtains a child population and merges it with its corresponding parent population;

[0103] S48, using an environmental selection method to screen the obtained population and determine the parent population for the next generation search;

[0104] S49, evaluate the results obtained at the end of evolution.

[0105] The specific steps for performing the first stage search using the angle solution search mechanism in step S43 are:

[0106] S431, divide the double-rod truss problem into two single-objective problems, corresponding to f1 and f2;

[0107] S432, determining the computing resources allocated to each search target, and determining f1 as the current search target;

[0108] S433, performing a single target search on the current search target using a single target search algorithm, and obtaining an angular solution of the current search target within limited search resources;

[0109] S434, reinitialize the population near the corner solution;

[0110] S435, using a single target search algorithm to perform a deeper local search for the corner solution of the current target;

[0111] S436, taking the final high-quality single-objective solution as the corner solution of the current objective;

[0112] S437, merge the corner solution with the initial population, and re-screen the initial population for searching the next target;

[0113] S438, change the search target to f2, and repeat the operations S433-S437 until all targets are searched.

[0114] The specific steps for performing a single target search on the current search target using the single target search algorithm in step S433 and obtaining the angle solution of the current search target within the limited search resources are as follows:

[0115] S4331, initialize a new archive F;

[0116] S4332, using the adaptive differential evolution algorithm to perform single-target search and obtain the offspring population;

[0117] S4333, further optimizing the obtained offspring population using a diversity search method to obtain a new offspring population;

[0118] S4334, store the best individual in the current offspring population into F;

[0119] S4335, repeating S4332-S4334 operations until the evaluation resources allocated to the current single target search are exhausted;

[0120] S4336, storing the population obtained from the last single target search as the angle solution of the current target;

[0121] S4337, perform non-dominated sorting on the diagonal solutions and store them in an external archive.

[0122] The specific steps for using the adaptive differential evolution algorithm to perform single-target search and obtain the offspring population in step S4332 are as follows:

[0123] S43321, the parent population is crossed with the global optimal individual to produce 60 individuals;

[0124] S43322, the parent population mutates to produce 60 new individuals;

[0125] S43323, the parent population uses the adaptive differential evolution algorithm to generate 60 individuals.

[0126] The adaptive differential evolution algorithm is an improvement and optimization based on the standard differential evolution algorithm. It can adaptively adjust parameter values, improve search efficiency, and balance global and local search capabilities. The standard differential evolution algorithm is a heuristic optimization algorithm used to find the optimal solution or near-optimal solution for complex problems. The core idea of the algorithm is to continuously update the positions of individuals to guide them to the vicinity of the global optimal solution. The typical update formula is as follows:

[0127] X new =X1+ω*(X2-X3)

[0128] Where, X new is the position of the current individual in the next generation; X1, X2 and X3 are individuals randomly selected from the current population, and ω represents the weight of the weighted difference, which is usually a random number between [-1, 1] and is used to balance global search and local search;

[0129] The adaptive differential evolution algorithm, based on the standard differential evolution algorithm, first changes the selection method of X1 and X2. Instead of random selection, the two variables are replaced by the individuals with the top two fitness values in the current population. X3 is still generated by random selection to maintain the diversity of the population. In addition, the update method of ω is updated. At the beginning, a larger ω encourages particles to have greater randomness and explore more to find new areas in the potential solution space. This helps to overcome the trap of local optimal solutions. As the search generation i increases, gradually reducing ω can slow down the span of individual updates, making it focus more on the known more promising solutions, which helps to accelerate the convergence of the global optimal solution until i equals the maximum search generation max_i. The update formula of ω is as follows:

[0130]

[0131] Where i represents the search generation; max_i represents the maximum search generation; ω0 represents the initial weight set to 1, ω i+1 represents the weight of the i+1th generation.

[0132] Adopting this adaptive strategy, using a larger ω value in the early stage and then gradually reducing the ω value can help the differential evolution algorithm find a good trade-off between global search and local search, and improve the performance of the algorithm.

[0133] The specific steps for further optimizing the obtained offspring population using the diversity search method in step S4333 to obtain a new offspring population are as follows:

[0134] S43331, read the data in archive F and determine whether the best individuals of the two latest offspring are the same;

[0135] S43332, if they are not the same, terminate the current search;

[0136] S43333, if they are the same, then calculating the values of a pair of complementary parameters OD1 and OD2 for determining the degree of congestion;

[0137] S43334, if the corresponding degree is 1, the population is randomly initialized within the range of S1;

[0138] S43335: If the corresponding degree is 2, the population is randomly initialized within the range of S2;

[0139] S43336: Output the obtained population as the new offspring population.

[0140] The specific calculation method for calculating the values of a pair of complementary parameters OD1 and OD2 in step S43333 for judging the degree of congestion is:

[0141] Calculate the Euclidean distance between individuals in the current population and get the sum of the Euclidean distances between each individual and all other individuals; then calculate the average value of the Euclidean distances of these individuals Euclidean distances mean And the maximum value of Euclidean distance Euc max Finally, the values of OD1 and OD2 are calculated using the following formulas to determine the degree of congestion:

[0142]

[0143]

[0144] Where, Euc mean Represents the average value of the Euclidean distance between individuals; Euc max It represents the maximum Euclidean distance between individuals.

[0145] If there are 60*OD2 individuals whose Euclidean distance is less than OD1×(X max -X min ), the congestion level is determined to be case 1, otherwise it is case 2.

[0146] The specific calculation method for step S43334 is:

[0147] When it is judged as case 1, it means that the individuals in the current population are too concentrated and easily fall into the local optimum. Therefore, it is necessary to make the population jump out of the current area and search in a larger range. Therefore, the calculation method of the search range S1 is:

[0148] S1=OD2×(X max -X min );

[0149] Where, X max and X min They correspond to the upper and lower limits of the search space respectively.

[0150] The specific calculation method for step S43335 is:

[0151] When it is judged as case 2, it means that the individuals in the current population are too loose and it is difficult to search for the optimal solution. Therefore, it is necessary to perform a local search near the global optimal solution. The calculation method of the search range S4 is:

[0152] S2=OD1×(X max -X min ).

[0153] The specific steps for performing the second stage search using the multi-objective optimization algorithm in step S46 are:

[0154] S461, select individuals in the population one by one, and randomly select their corresponding individuals for crossover to obtain a progeny population;

[0155] S462, perform mutation operation on all individuals in the population to obtain another offspring population;

[0156] S463, merge the two offspring populations as the offspring population obtained by searching this generation.

[0157] The specific steps for using the environmental selection method to screen the obtained population in step S48 and determine the parent population for the next generation search are as follows:

[0158] S481, perform non-dominated sorting on all individuals in the population;

[0159] S482, according to the ranking level, prioritize the individuals with the highest non-dominant level;

[0160] S483, for individuals of the same level, calculate their crowding distances respectively, and prioritize individuals with larger crowding distances;

[0161] S484, repeat S482-S483 operations until 60 individuals are retained as the parent population for the next generation search.

[0162] To further illustrate the superiority of the present invention in solving multi-objective optimization problems, Table 1 shows the results obtained by the method of the present invention and some typical multi-objective optimization algorithms Multi-objective Evolutionary Algorithm based on Decomposition (MOEA / D), Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ) and Non-dominated Sorting Genetic Algorithm-Ⅲ (NSGA-Ⅲ) in processing multi-objective two-bar truss and four-bar truss test examples.

[0163] The experimental results on a multi-objective problem test set are given in the examples. Figure 2 A two-bar truss problem model is presented, where the weight of the structure and the displacement of the connection point 3 need to be minimized while satisfying the stress constraints of the member. The cross-sectional area A of the member and the half distance x between the connection points 1 and 2 need to be varied while maintaining the symmetry of the truss geometry. Similarly, Figure 3 This paper presents a four-bar truss problem model in which the structural volume (f1) and the displacement of connection point 2 (f2) need to be minimized while satisfying the stress constraints of the members. The cross-sectional areas of members 1, 2, 3, and 4 are the design variables, denoted as x1, x2, x3, and x4, respectively.

[0164] The number of evaluations in the experiment was set to 10,000 times, and the population size was set to 100. Each algorithm was run 10 times on each test problem, and the number of times the optimal result was obtained in the 10 times was recorded. The indicator of the evaluation results uses the inverse generation distance (IGD). Table 1 shows the number of times each algorithm achieved the optimal result on each test problem. By comparison, it can be seen that the method proposed in the present invention demonstrates superior optimization performance in solving multi-objective optimization problems. Specifically, no matter which optimization problem is tested, the number of optimal results obtained is much greater than that of other optimization algorithms. These results also show that the proposed method has excellent performance than other methods in multi-objective optimization problems.

[0165] In summary, the multi-objective multi-link truss optimization method based on single-objective sequence search assistance proposed in the present invention can effectively handle multi-objective optimization problems and provide decision makers with a series of ideal compromise solutions.

[0166] Table 1 Comparison of experimental results on datasets

[0167]

[0168] Multi-objective optimization algorithms play a crucial role in solving practical problems related to multi-bar trusses. By simultaneously considering multiple optimization objectives, such as structural weight, load-bearing capacity, material usage, and deformation control, these algorithms help engineers find optimal solutions within complex design spaces. With the continuous advancement of engineering technology, the use of advanced multi-objective optimization algorithms can effectively promote innovation and progress in the field of structural engineering, providing strong support for the realization of safer, more economical, and sustainable truss structures.

[0169] The present invention introduces crossover factors, mutation factors, and adaptive factors to generate some combinations of good characteristics and excellent solutions that can inherit from parent individuals, thereby generating some elite solutions. The use of a corner solution search mechanism improves the quality of corner solutions in the first-stage search, providing a good initial environment for the multi-objective search in the second stage. In addition, a diversity search method is introduced into the single-objective search to evaluate the degree of crowding of the population, perform an enhanced search in a local area, and prevent it from falling into a local optimum. In general, in the solution to the multi-objective multi-bar truss problem, the present invention provides a multi-objective multi-bar truss optimization method based on a single-objective sequence search auxiliary. Compared with other methods, this method not only improves the efficiency of truss design, but also enhances the quality of the design scheme, so that it can meet different engineering needs.

[0170] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. A multi-objective multi-link truss optimization method based on single-objective sequence search assistance, characterized in that: The following steps are involved: S1. Determine truss structure parameters and constraints: Establish a multi-bar truss model, clarify the design objectives including structural weight and node displacement, define design variables including component cross-sectional area and node location, and set constraints including stress constraints for each component; S2. Establishing a multi-objective function: Based on the design goal of step S1, construct a multi-objective optimization objective function including structural weight, material usage, and node displacement, and establish a mathematical expression for each objective function; S3. Initialize design variables: Determine the initial value range of the design variables in the parameter space to provide the parameter boundary of the initial solution for the subsequent optimization algorithm; S4, using a multi-objective algorithm assisted by a single-objective sequence search to solve the model, including the following steps: S41, initialize population and external archive; S42, determining the computing resources allocated to each search phase; S43, performing the first stage search using the corner solution search mechanism; S44, obtaining the angle solution corresponding to each target; S45, using the corner solution to initialize the population for multi-objective search; S46, performing the second stage search using a multi-objective optimization algorithm; S47, each generation searches for a child and merges it with its corresponding parent generation; S48, using environmental selection methods to screen the population for the next generation search; S49, evaluate the results obtained at the end of evolution.

2. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 1 is characterized in that: The specific steps of S43 are: S431, divide a multi-objective problem into multiple single-objective problems; S432, determining computing resources allocated to each search target, and determining the first target as the current search target; S433, performing a single target search on the current search target using a single target search algorithm, and obtaining an angular solution of the current search target within limited search resources; S434, reinitialize the population near the corner solution; S435, using a single target search algorithm to perform a deeper local search for the corner solution of the current target; S436, taking the final high-quality single-objective solution as the corner solution of the current objective; S437, merge the corner solution with the initial population, and re-screen the initial population for searching the next target S438, change the search target and repeat S43-S47 operations until all targets are searched.

3. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 1 is characterized in that: The specific steps of S46 are: S461, select individuals in the population one by one, and randomly select their corresponding individuals for crossover to obtain a progeny population; S462, perform mutation operation on all individuals in the population to obtain another offspring population; S463, merge the two offspring populations as the offspring population obtained by searching this generation.

4. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 1 is characterized in that: The specific steps of S48 are: S481, perform non-dominated sorting on all individuals in the population; S482, according to the ranking level, prioritize the individuals with the highest non-dominant level; S483, for individuals of the same level, calculate their crowding distances respectively, and prioritize individuals with larger crowding distances; S484, repeat S482-S483 operations until 60 individuals are retained as the parent population for the next generation search.

5. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 2 is characterized in that: The specific steps of S433 are: S4331, initialize a new archive F; S4332, using the adaptive differential evolution algorithm to perform single-target search and obtain the offspring population; S4333, further optimizing the obtained offspring population using a single-objective search method to obtain a new offspring population; S4334, store the best individual in the current offspring population into F; S4335, repeating S4332-S4334 operations until the evaluation resources allocated to the current single target search are exhausted; S4336, storing the population obtained from the last single target search as the angle solution of the current target; S4337, perform non-dominated sorting on the diagonal solutions and store them in an external archive.

6. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 5, characterized in that: The specific steps of S4332 are: S43321, the parent population is crossed with the global optimal individual to produce 60 individuals; S43322, the parent population mutates to produce 60 new individuals; S43323, the parent population uses the adaptive differential evolution algorithm to generate 60 individuals.

7. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 6, characterized in that: The formula of the adaptive differential evolution algorithm is: X new =X1+ω*(X2-X3) Where, X new is the position of the current individual in the next generation; X1 and X2 use the individuals with the top two fitness values in the current population respectively; X3 is an individual randomly selected from the current population; ω represents the weight of the weighted difference, and the update formula of ω is as follows: In the formula, i represents the search generation; max_i represents the maximum search generation; ω0 represents the initial weight, which is set to 1, ω i+1 Represents the weight of the i+1th generation.

8. The multi-objective multi-link truss optimization method based on single-objective sequence search assistance according to claim 5, characterized in that: The specific steps of S4333 are: S43331, read the data in archive F and determine whether the best individuals of the two latest offspring are the same; S43332, if they are not the same, terminate the current search; If they are the same, then calculate the values of a pair of complementary parameters OD1 and OD2 to determine the degree of congestion: Where, Euc mean Represents the average value of the Euclidean distance between individuals; Euc max Indicates the maximum value of the Euclidean distance between individuals; S43334, if the corresponding degree is 1, the population is randomly initialized within the range of S1; S1=OD2×(X max -X min ); Where, X max and X min Corresponding to the upper and lower limits of the search space respectively; S43335: If the corresponding degree is 2, the population is randomly initialized within the range of S2; S2=OD1×(X max -X min ); S43336: Output the obtained population as the new offspring population.

Images