29 results about "Topology optimization problem" patented technology

The present invention relates to the technical field of heat sink structure design, and in particular to a micro-channel heat sink structure design method based on a multi-objective function. The method comprises the following specific steps: S1, constructing a general mathematical description of a topology optimization problem; S2, acquiring input conditions for a specific design scenario, and dividing a topology optimization design domain; S3, establishing a governing equation for a topology optimization model; S4, on the basis of an adjoint method, performing sensitivity analysis of a multi-objective function with respect to design variables; S5, solving the topology optimization model by means of a method of moving asymptotes (MMA); S6, obtaining a two-dimensional flow channel configuration of a heat sink on the basis of contour reconstruction, carrying out finite element analysis of a two-dimensional flow channel structure, and narrowing down the selection range of constraint conditions; and S7, on the basis of a two-dimensional finite element analysis result, constructing a corresponding pseudo-three-dimensional model, carrying out finite element analysis, and determining optimal constraint conditions to obtain a final topology-optimized heat sink configuration. Compared with traditional methods, the present invention can more efficiently solve the problem in respect of heat sink structure optimization under different scenarios.

The invention provides a thermal elastic structure joint topological optimization method based on MATLAB and ABAQUS, and belongs to the technical field of thermal elastic structure optimization design. Firstly, finite element models of mechanical loads and thermal loads are established in ABAQUS, and files are exported; then calling an ABAQUS operation model in MATLAB, extracting core data such as nodes, units and a stiffness matrix, and constructing a parameterized thermodynamic finite element model based on an SIMP method; calculating a function value and sensitivity by taking volume minimization as a target and taking global stress and temperature constraint as conditions; and finally, iteratively optimizing the design variables by adopting a moving asymptote algorithm, and obtaining a final topological configuration through a filtering method. Through deep cooperation of MATLAB and ABAQUS, core finite element data of commercial software is extracted at a time for optimization iteration, repeated data generation and interaction are avoided, the calculation efficiency is greatly improved, and an efficient solution is provided for processing the topological optimization problem of stress and temperature constraints under complex heat-force loads.

This invention relates to the field of radiator structure design technology, and provides a microchannel radiator design method based on embedded irregular materials and the obtained microchannel radiator, including: constructing a general mathematical description of the topology optimization problem; obtaining input conditions and dividing the topology optimization design domain; establishing the control equations of the topology optimization model, constructing a dual objective function, and performing sensitivity analysis of the multi-objective function with respect to design variables; solving the topology optimization model, and using filtering methods and projection techniques to obtain material distribution with clear fluid-structure boundaries; obtaining the two-dimensional flow channel configuration of the radiator, performing finite element analysis to obtain the temperature field and velocity field distribution, comprehensively evaluating the heat transfer performance, and determining the two-dimensional flow channel configuration; based on the two-dimensional flow channel configuration, constructing the corresponding three-dimensional model and performing finite element analysis to obtain the temperature field and velocity field distribution, evaluating the heat transfer performance using the PEC criterion, verifying the effectiveness of the method in three dimensions, and obtaining the final topology-optimized radiator configuration.

The invention discloses a structure topological optimization method and device, equipment and a storage medium, and the method comprises the steps: firstly obtaining topological optimization problem data of a target structural member, and inputting the topological optimization problem data into a decision model to obtain a recommended optimization strategy; and then, starting a CAE solver by taking the strategy as a parameter to carry out iterative calculation. In the calculation process, state information representing the optimization process is fed back to the decision model in real time for evaluation. And if the model judges that the strategy needs to be adjusted, updating solving parameters according to an output instruction and continuing iteration until a final optimization result is obtained. The decision model is based on historical case data and can learn complex mapping and adjustment strategies between optimization parameters and results, so that manual intervention is remarkably reduced, and optimization efficiency and result quality are improved. The method can be widely applied to the technical field of industrial design.

The application relates to a fully decoupled movable piezoelectric drive flexible parallel mechanism topology optimization method, which comprises the following steps: obtaining the density field distribution of a flexible parallel mechanism based on participation parameters and through an independent point density interpolation method; constructing a target function based on the density field distribution and taking the sum of expected output displacements of each branch of the flexible parallel mechanism as maximum; modifying the target function based on preset constraints to obtain an initial topology optimization model, wherein the preset constraint conditions comprise the volume fraction of the flexible parallel mechanism, the non-interference between a piezoelectric driver and a main design domain of the flexible parallel mechanism, and the non-rotation of a moving platform in a plane under the action of a load; and solving a topology optimization problem through a gradient-based moving asymptote optimization algorithm based on the initial topology optimization model. Through the application, the problems of input and output coupling effects of the flexible parallel mechanism, reduced motion accuracy and poor controllability can be improved.

The present invention discloses a method and system for mechanical-thermal coupling simulation and structural optimization of ultra-complex structures. The method comprises: generating parameters and data structures required for subsequent simulation and optimization for a given model and design domain; constructing a background coarse grid, seed points and radii, modeling a porous structure based on a Voronoi structure, and precalculating its stress field; calculating a density field, performing thermodynamic simulation on the generated porous structure based on the density field, the background coarse grid, and a shape function; querying the stress matrix corresponding to each seed point based on the obtained stress field, performing eigendecomposition and extraction on the stress matrix, and obtaining a weight matrix corresponding to the seed point; using a topology optimization method, updating control parameters through a GCMMA method based on sensitivity, thereby updating the porous structure and optimizing material distribution, and continuously optimizing until the change in control parameters is less than a threshold. The method can quickly and effectively solve the topology optimization problem of anisotropic porous structures under multi-physics field conditions.

This invention discloses a topology optimization method for an electrothermal driven compliant mechanism based on minimum size control. It defines the design domain and boundary conditions of the electrothermal driven compliant mechanism, initializes design parameters, and uses a sequential coupling method to solve the multi-physics structural response of the electrothermal-structural fields. The optimization objective is to maximize the output displacement of the mechanism. By introducing a structural indicator function, minimum size constraint functions for real and empty phase material structures are constructed, establishing a topology optimization model for the electrothermal driven compliant mechanism based on minimum size control. The moving asymptotic algorithm is used to solve the topology optimization problem, determining whether the convergence criterion is met, and finally outputting the optimal topology configuration of the electrothermal driven compliant mechanism. This method effectively suppresses the occurrence of small-sized structures, facilitating processing and manufacturing.

The present invention discloses a method and system for dynamic decoupling planning of a large-scale offshore wind farm power system. The method includes constructing a two-stage dynamic decoupling planning model based on wind farm data: in the first stage, all wind turbines are pre-coded to divide the wind turbines in the loop into static and dynamic categories; in the second stage, a two-layer dynamic decoupling model of static and dynamic wind turbines in the loop is established, a multi-cable planning model under different operating conditions is constructed, and the objective function of the bilateral ring network collection system topology optimization problem is constructed with the minimum total investment and operating cost and constraints are added; the bilateral ring network collection system topology optimization problem is converted into an integer linear programming problem and the bilateral ring network collection system topology and total cost are solved. The present invention aims to improve and balance the computational efficiency and cost-effectiveness of planning for large-scale offshore wind farm power systems, and to take into account both the minimization of investment costs and operating losses under high reliability requirements.

The invention discloses a topological optimization design method for an actual product structure, and the method comprises the following steps: 1, analyzing the demands of a customer, and obtaining an image model of a product based on the demands of the customer; 2, constructing a topological optimization model based on material field series expansion, wherein the topological optimization model is used for reducing the number of non-gradient algorithm variables in product structure design; and a third step of solving a topological optimization problem of a non-gradient algorithm in product structure design based on the non-gradient optimization algorithm of the Kriging agent model. The invention not only can meet the emotion demand of a user, but also has a product structure with perfect mechanical property (light weight), and meets the compound demand of the user on the product function reliability and the emotion demand.

The invention relates to a fully-decoupled movable piezoelectric driving compliant parallel mechanism topological optimization method, which comprises the following steps of: obtaining a density field distribution condition of a compliant parallel mechanism based on participation parameters through an independent point density interpolation method; the sum of the expected output displacements corresponding to all the branch chains of the flexible parallel mechanism is maximized to construct a target function; the target function is corrected on the basis of preset constraints, an initial topological optimization model is obtained, and preset constraint conditions include the volume fraction of the compliant parallel mechanism, the piezoelectric actuator and the main design domain of the compliant parallel mechanism do not interfere with each other, and the movable platform does not rotate in a plane under the action of a load; and based on the initial topological optimization model, solving a topological optimization problem through a gradient-based moving asymptote optimization algorithm. According to the flexible parallel mechanism, the problems that the motion precision is reduced and the controllability is poor due to the input and output coupling effect of the flexible parallel mechanism can be solved.

The invention discloses a two-stage efficient solution method for topological optimization of structural dynamic reliability under random excitation. According to the method, firstly, deterministic topological optimization with the most unfavorable condition performance function as the constraint is carried out, and then reliability topological optimization with the reliability as the constraint is solved. A time domain explicit method and a direct probability integral method are combined, and the structural dynamic reliability is calculated efficiently and accurately. Under a sensitivity solving framework of a direct probability integral method, a time domain explicit method is further combined, an adjoint method is adopted to deduce a sensitivity formula of failure probability about design variables in a dynamic problem, and an efficient sensitivity calculation framework suitable for power reliability topological optimization is established by utilizing an importance representative point screening strategy. A sequence approximation integer programming method is used for efficiently solving the structural dynamic reliability topological optimization problem under the action of random excitation, design meeting the reliability requirement is obtained, and theoretical support is provided for design of an actual engineering structure.

The invention discloses a swarm intelligence optimization method based on time sequence topology, and relates to the field of artificial intelligence. A time sequence network model composed of static network fragments is provided to describe the process that the network structure changes along with the time determinacy period; the long-term average frequency of a certain strategy in a strategy evolution game is used as a quantitative index for measuring the emergence degree of specific cluster behaviors (swarm intelligence), and the long-term average frequency is used as a target function to optimize time sequence topology. According to the method, a complex swarm intelligence emerging problem is converted into a clearly defined time sequence topological optimization problem; the performance index is directly reflected as the lifting amplitude or the reached absolute level of the target strategy frequency; according to the time sequence topology obtained through the method, key group intelligent indexes such as the cooperation level and the consensus achievement speed can be remarkably improved under the given condition, and the optimization effect can be quantified and reproduced.

The invention discloses a full-scale functional gradient porous hierarchical structure transient dynamics topological optimization method and system, and belongs to the field of topological optimization design of functional gradient structures. The problem to be solved is how to construct a transient isogeometric analysis method compatible with a traditional finite element method and integrate the transient isogeometric analysis method into a full-scale functional gradient porous hierarchical structure topological optimization problem, and the engineering expandability of an optimization algorithm is improved. According to the method, a self-adaptive growth strategy of projection parameters is constructed, and continuous regulation and control of structure topology in the optimization process are realized. According to the technical key points, a structure isogeometric transient dynamics finite element model is constructed; constructing a functional gradient porous hierarchical constraint and a material interpolation model based on a sharpness parameter adaptive increase strategy, and proposing a transient dynamic topological optimization model of a full-scale functional gradient porous hierarchical structure; constructing a time domain adjoint equation of the topological optimization model; and the optimal anti-vibration design of the functional gradient porous hierarchical structure is obtained. The designed porous structure has good structural performance and functional characteristics, and can meet the requirements of complex engineering environments in the fields of aerospace, deep sea and the like.

The application discloses a flexible tooling design method based on topology optimization, which comprises the following steps: S1, taking a test piece in an overall model state as a research object to perform finite element analysis, and extracting displacement of a displacement constraint point of the test piece and a support reaction force; S2, adopting a local stiffness constraint method to constrain local displacement of the model; S3, establishing a topology optimization problem; S4, dividing a design domain of the flexible tooling, and constructing an equivalent configuration of the flexible tooling; S5, topologically optimizing the equivalent configuration of the flexible tooling to obtain an optimized configuration of the flexible tooling; and S6, comparing simulation data of the test piece in a tooling clamping state with simulation data of the test piece in the overall model, and if a difference between the two is greater than a threshold value, returning to step S5; otherwise, ending. The application applies the topology optimization technology to the flexible tooling design, and the design process is simple; through local stiffness control of the tooling, real boundary conditions of the test piece are accurately simulated, and the test is improved in authenticity.

The invention provides a specified flexibility compliant mechanism topological optimization method based on adaptive volume constraint, and the method comprises the steps: defining design conditions of a compliant mechanism, and setting material attribute indexes of the compliant mechanism; obtaining the structure displacement response of the compliant mechanism under the action of the input load and the virtual unit load; adaptively changing the volume constraint value of the mechanism according to the difference between the total flexibility and the specified total flexibility; establishing a specified flexibility compliant mechanism topological optimization mathematical model based on adaptive volume constraint; calculating and optimizing an objective function and constrained sensitivity information; correcting the sensitivity of the optimization target and the constraint; and solving a topological optimization problem by adopting a moving asymptote algorithm, judging whether a convergence condition is met or not, and if yes, outputting an optimal compliant mechanism topological configuration. According to the method, the topological optimization design of the compliant mechanism based on the adaptive volume constraint is realized, and the obtained compliant mechanism has specified flexibility performance.

This invention relates to the field of intelligent agent construction and application technology, specifically disclosing a two-layer optimization method for constructing multi-agent systems. The method models the multi-agent system based on a large language model as a learnable graph, abstracts agents as nodes, and abstracts the interaction and communication between agents as edges. It introduces unbiased policy gradient estimation to transform the topology optimization problem into a continuous optimization problem, calculating gradients and updating connection probabilities. Based on Shapley values ​​from cooperative game theory, it quantifies the marginal contribution of each edge to system performance, optimizing the directed acyclic graph. Based on a black-box tuning mechanism, it introduces an optimization degree evaluator to ensure that prompts are iteratively updated towards the optimal fit, collaboratively optimizing the system's topology and prompts. This invention promotes the improvement of information interaction quality and overall decision-making ability among agents, providing support for the construction of multi-agent systems based on large language models and the optimization of their topology and prompts.

The application discloses a topology optimization design method for integrated emission antenna heat dissipation flow channels, and specifically relates to the following steps: establishing a simplified two-dimensional plane heat source model; initializing and applying boundary conditions at the inlet; distributing compact support radial basis functions with an expansion coefficient on the obtained finite element grid nodes divided in a design domain, then linearly superimposing the radial basis functions to obtain a parameterized level set function; obtaining the distribution of solid and fluid in the design domain according to the level set function value; solving the heat exchange performance of the heat dissipation flow channel configuration represented by the parameterized level set function; establishing a mathematical model of the topology optimization problem, calculating the sensitivity of the objective function and the constraint condition with respect to the design variable expansion coefficient; and obtaining a complete heat dissipation flow channel design. The method can meet the demand of maximizing the heat exchange capacity at a high heat flow density heat source while simplifying the calculation, and improve the heat dissipation performance.

The invention discloses an unmanned aerial vehicle bearing joint structure design optimization method based on topological optimization, and the method comprises the steps: (1) employing a variable density method continuum topological optimization method, based on an SIMP interpolation model, taking the unit relative density ai as a design variable, and building a topological optimization mathematical model; (2) post-processing the optimized structure; (3) setting structural design optimization operation parameters of the unmanned aerial vehicle bearing joint; and (4) solving an optimization model of the topological optimization problem, and drawing a structural topological optimization result. By combining the variable density method, the symmetry constraint and the multi-scale grid strategy, high-rigidity and low-weight joint structure design is achieved.

The present application relates to a kind of structural topology optimization complexity control method based on morphological feedback, comprising the following steps: modeling reaction diffusion equation level set structural topology optimization problem, and volume fraction constraint is executed;Solving structural topology optimization problem, and sensitivity analysis is carried out, and assembly physical drive item under defined target and constraint;Judge whether control is activated, if control is activated, then measure structural morphological complexity, determine corresponding control mode, regulate structural morphological complexity, obtain revised drive item, replace original physical drive item in reaction diffusion equation with revised drive item, and update reaction diffusion equation;Otherwise, keep original physical drive item and update reaction diffusion equation;Only when the convergence of target and constraint of structural topology optimization problem and the number of structure hole equal target value, iteration terminates, output structure based on the solving result of structural topology optimization problem and end process, otherwise, carry out next iteration.Compared with prior art, the present application has the advantages of no initial layout dependence and accurate control of structural complexity.

The invention discloses a stiffened plate structure time domain dynamics topological optimization method and system based on a model reduction method, and relates to the field of topological optimization design of stiffened plate structures. According to the method, efficient solving of the time domain dynamics topological optimization problem of the stiffened plate structure is achieved, and therefore the large-scale lightweight dynamics design requirement of high-performance thin-wall engineering equipment is met. According to the technical key points, a base structure introducing rib unit local geometric control constraints is constructed, the initial connectivity of rib units is ensured, and the problem of local cross interference in the rib unit optimization process is inhibited; based on an equal geometric stiffness diffusion method, a time domain dynamics full-order topological optimization model of the stiffened plate structure is established. Then, on the basis of an intrinsic orthogonal decomposition method and an incremental singular value decomposition method, a time domain dynamics reduction model of the stiffened plate structure is constructed; and meanwhile, a sensitivity analysis adjoint equation of the time domain dynamics optimization problem is cooperatively reduced, so that the time domain dynamics topological optimization problem of the stiffened plate structure is efficiently solved. And finally, on the basis of a modified penalty function method, constructing an updating iteration format of design variables, and seeking an optimal rib layout design of the stiffened plate structure. The method is used for time domain dynamics layout optimization of the stiffened plate structure.

The application provides an efficient fatigue topology optimization method for isogeometric analysis, and belongs to the technical field of geometric analysis, and mainly comprises the following steps: constructing a fatigue problem model, dividing multiple layers of grid methods according to the design domain requirement, and generating the lowest level isogeometric node vector by using h insertion; assembling each level interpolation operator and continuation operator of the multi-grid method according to the isogeometric node vector; decomposing and storing independent load components in a load spectrum, and solving the combination weight of each independent load component; assembling the overall stress spectrum according to the weight; evaluating the fatigue constraint of the unit fatigue damage; expressing the fatigue constraint topology optimization problem by using the augmented Lagrange method; performing the update iteration of the isogeometric analysis design variable until the fatigue constraint topology optimization problem converges according to the design variable change amount. The scheme improves the simplified calculation and counting problem of the multi-cycle general fatigue load spectrum, and reduces the solving cost.

The application provides a turbine disc structure optimization method based on thermal coupling, a topology optimization model is established by taking the relative density of each unit in a finite element analysis model of the turbine disc as a design variable; the elastic modulus of the material of the unit in the topology optimization model at different temperatures is extracted and linearly fitted as a first-order function to construct a mapping relationship between the elastic modulus of any unit in an optimization domain and the design variable, and a topology optimization problem of the structure is converted into an optimal distribution problem of the material; the sensitivity of all units in the optimization domain is calculated, the sensitivity is normalized and filtered, the processed sensitivity is sorted to obtain an array, and the array is updated; an iteration termination judgment condition is set, when the structure volume meets the design requirement and reaches a convergence standard, the optimized structure is output, and the turbine disc structure optimization design is completed. The optimization method provided by the application meets the lightweight design of the turbine disc structure and improves the overall stiffness performance of the disc structure.

The invention discloses a topological optimization method embedded into a physical neural network. The method comprises the following steps: based on target minimization compliance of energy, a dynamic sampling strategy, strain energy of Gaussian integral calculation elements, and displacement analysis of a minimum potential energy principle; the displacement network adopts a sine representation network (SIREN) to activate a function so as to improve the accuracy of calculating a high-order derivative, and the density network uses Fourier feature mapping to define a design variable so as to process complex design configuration; by minimizing potential energy equivalent to compliance minimization or structural stiffness maximization, to update the density distribution while complying with volume constraints; the method is suitable for the topological optimization problem of high resolution, multiple loads and displacement constraints, and the influence of external force on the system balance state can be determined by calculating the second-order variation of external force acting. By means of the topological optimization method, the problem of minimizing the total potential energy can be expressed again, and therefore automation and optimization of structural design are achieved.

This invention proposes a method and system for constructing a high-voltage distribution network operation topology optimization model and its distributed reinforcement learning framework, comprising: Step S1: Constructing a high-voltage distribution network operation topology optimization model for the target high-voltage distribution network; including constructing the high-voltage distribution network operation topology optimization model and proposing its optimization objective and constraints; Step S2: Building and training the distributed reinforcement learning framework; including building a centralized training and distributed execution reinforcement learning computation framework for the high-voltage distribution network operation topology optimization problem of the target high-voltage distribution network, then determining the agents and the state space and action space of each agent, clarifying the reward function and training algorithm, and carrying out model training; Step S3: Formulating auxiliary decision-making for high-voltage distribution network topology optimization during the maintenance period of the target high-voltage distribution network, and finally obtaining the optimal operation topology of the high-voltage distribution network as a whole, and outputting performance evaluation results.

The invention relates to an efficient additive manufacturing thermal coupling topological optimization method considering suspension constraints. The method comprises the following steps: firstly, constructing a thermal-mechanical coupling topological optimization model considering the suspension constraint based on a suspension angle projection function; secondly, a multi-grid preprocessing conjugate gradient method is introduced to efficiently solve a structure heat conduction and thermal coupling balance equation, and structure temperature field and displacement field information is obtained; and finally, based on an adjoint variable method, deriving the sensitivity of a target function about topological design variables, and updating the topological configuration of the thermal coupling structure by adopting a gradient-based moving asymptote optimization algorithm. According to the method, the topological optimization model considering the suspension constraint is constructed for the topological optimization problem of the thermal coupling structure for additive manufacturing, the efficiency of structural thermal coupling performance analysis is greatly improved through the multi-grid preprocessing strategy, and efficient structural thermal coupling topological optimization design meeting the additive manufacturing requirement is achieved.

This invention provides a topology optimization method for a compliant mechanism with specified compliance based on adaptive volume constraints. The method includes defining design conditions for the compliant mechanism and setting material property indices; obtaining the structural displacement response of the compliant mechanism under input load and virtual unit load; adaptively changing the volume constraint value of the mechanism based on the difference between the total compliance and the specified total compliance; establishing a mathematical model for topology optimization of the compliant mechanism with specified compliance based on adaptive volume constraints; calculating the optimization objective function and the sensitivity information of the constraints; correcting the sensitivity of the optimization objective and constraints; solving the topology optimization problem using the moving asymptote algorithm; and determining whether the convergence condition is met. If so, the optimal topology configuration of the compliant mechanism is output. This invention realizes the topology optimization design of a compliant mechanism based on adaptive volume constraints, and the obtained compliant mechanism has specified compliance performance.

The invention discloses a self-adaptive topological optimization method for a bat algorithm in a meta-heuristic algorithm based on natural heuristic, and the method comprises the following steps: S1, initializing a design space of a topological optimization problem, and defining a design variable-density, an objective function-flexibility and constraint conditions; s2, performing iterative optimization on design variables in the design space by applying a bat algorithm to obtain a preliminary topological optimization solution; s3, dynamically adjusting discretization precision or constraint conditions of a design space according to a current iteration result by setting an adaptive mechanism, and optimizing a topological structure; s4, updating the parameters of the bat algorithm based on an adaptive mechanism; and S5, judging a convergence criterion, and terminating the optimization process. According to the method, the design domain density value is updated by dynamically adjusting the optimization strategy and algorithm parameters, so that the stability of topological optimization is improved, and the problem of'checkerboard 'is solved.

The present invention relates to the technical field of radiator structure design, and relates to a microchannel radiator structure design method based on a multi-objective function, which includes the following specific steps: S1, constructing a general mathematical description of a topology optimization problem; S2, obtaining input conditions under a specific design scenario and dividing the topology optimization design domain; S3, establishing the control equation of a topology optimization model; S4, performing sensitivity analysis of the multi-objective function with respect to design variables based on an adjoint method; S5, solving the topology optimization model by an MMA moving asymptote method; S6, obtaining a two-dimensional flow channel configuration of the radiator based on contour reconstruction, conducting finite element analysis of the two-dimensional flow channel structure, and narrowing the selection range of constraint conditions; S7, constructing a corresponding pseudo-three-dimensional model based on the two-dimensional finite element analysis results and conducting finite element analysis to determine the optimal constraint conditions and obtain the final topology optimized radiator configuration. Compared with traditional methods, the present invention can more efficiently solve radiator structure optimization problems in different scenarios.

The invention discloses a novel meta-heuristic algorithm based on a beaver algorithm, and the method comprises the steps: firstly giving an initial density value of each unit, then setting BA operation parameters, and classifying beavers into three types: quality inspection beavers, development beavers and felling beavers; the optimization problem is solved by simulating the group cooperation in the lumbering process so as to solve the optimization model of the topological optimization problem, and then the density is optimized by using BA and iteration is carried out continuously until the optimal optimization result is obtained. The method is used for solving the topology optimization problem, can overcome the limitation of a traditional numerical method in processing a complex optimization problem, improves the optimization efficiency, in addition, in the topology optimization facing challenging engineering problems, BA solution is rapid, the optimization result is stable, no checkerboard phenomenon exists, and compared with other algorithms, the BA has better performance.