An engineering optimization method based on failure state variant routing and landscape discrimination

Abstract

The application provides an engineering optimization method based on failure state variable routing and landscape discrimination, and relates to the technical field of engineering design optimization.The application comprises the following steps: establishing an engineering design constraint optimization model; constructing a fitness evaluation function; initializing a differential evolution algorithm population and parameters; according to individual historical failure states and population evolution states, self-adaptively selecting and generating a first mutation vector from a plurality of pre-defined mutation strategies; constructing a reference direction based on excellent individuals in the population, discriminating and repairing the first mutation vector for direction consistency, and obtaining a second mutation vector; discriminating the problem form of a current search area according to the correlation between population distribution information and fitness sequences, and adjusting the search behavior accordingly; updating the population through a crossover operation; iterating until a termination condition is met, and outputting optimal engineering design parameters.The application improves the optimization precision and convergence efficiency of complex engineering design problems through failure state driven variable routing and landscape structure discrimination.

Description

Technical Field

[0001] This invention relates to the field of engineering design optimization technology, and more specifically, to an engineering optimization method based on failed state variation routing and landscape discrimination. Background Technology

[0002] Engineering design optimization is a crucial aspect of mechanical structure design, transmission system design, lightweight structural design, and complex equipment design. In practical engineering design, it is typically necessary to optimize structural weight, manufacturing cost, transmission errors, or overall performance indicators while meeting constraints such as strength, stiffness, stability, geometric dimensions, safety factors, and manufacturing costs. Typical engineering design optimization problems include the design of tension and compression springs, pressure vessels, welded beams, reducers, gear transmissions, and three-bar trusses. These problems often exhibit characteristics such as nonlinearity, strong constraints, multivariate coupling, and irregular feasible regions. Traditional mathematical programming methods are easily affected by initial solutions, function differentiability, and constraint handling methods when solving these types of problems.

[0003] Differential evolutionary algorithm (DEA) is an intelligent optimization algorithm based on population search. It boasts advantages such as simple structure, few control parameters, strong global search capability, and ease of implementation, and has been widely applied in engineering design optimization and complex parameter optimization problems. However, traditional DEA still has shortcomings in solving complex constrained engineering design optimization problems. First, the mutation strategy of traditional DEA typically employs a fixed form or simple probability switching, making it difficult to select an appropriate search direction based on the individual's current search state. Second, when an individual fails to generate a better trial vector multiple times consecutively, continuing the search in the original differential direction can easily lead to search direction failure; as the algorithm enters the later stages of iteration, individuals in the population may gradually cluster in local regions, resulting in decreased population diversity and premature convergence. Third, existing DEA algorithms often lack a judgment on the consistency between the differential search direction and potentially superior regions. For constrained engineering design optimization problems, an incorrect differential direction may cause individuals to stray from feasible or potentially superior regions, thereby reducing the algorithm's solution accuracy.

[0004] Furthermore, different engineering design optimization problems exhibit different search landscape characteristics. Some problems show a clear unimodal convergence trend in local regions, while others have multimodal, complex, or uncertain search structures. Most existing differential evolution algorithms only perform selection operations based on fitness values, and rarely utilize the relationship between population spatial distribution and fitness changes to determine the problem form of the current search region.

[0005] In view of the above, this application is hereby submitted. Summary of the Invention

[0006] This invention provides an engineering optimization method based on failed state variation routing and landscape discrimination to improve at least one of the above-mentioned technical problems.

[0007] In a first aspect, the present invention provides an engineering optimization method based on failed state variation routing and landscape discrimination, comprising the following steps:

[0008] S1: Establish a constrained optimization model for the engineering design problem, and determine the design variables and their range of values, objective function, and constraints; Furthermore, the constrained optimization model includes the range of values ​​for the design variables, an objective function, and one or more constraints; the objective function is a performance index that measures the quality of the engineering design problem.

[0009] S2: Construct a fitness evaluation function based on the objective function and constraints, specifically including: The engineering design problem is transformed into a fitness minimization problem using the penalty function method, and a fitness evaluation function is established: fitness value = objective function value + penalty term; The penalty term is the product of the penalty coefficient and the sum of the squares of the degree of constraint violation; When the design variable satisfies all constraints, the penalty term is 0; when the design variable violates the constraints, the penalty term is increased according to the degree of violation.

[0010] S3: Initialize the population, algorithm parameters, and archive structure for recording search states in the differential evolution algorithm; the algorithm parameters include: scaling factor and crossover probability; the archive structure includes external archive, auxiliary archive, failed trial vector pool, and individual failure counter, and the specific steps include: S31: Set the maximum fitness evaluation count, the current fitness evaluation count, the initial population size, and the minimum population size; initialize the scaling factor and crossover probability for each individual; S32: Initialize the population individuals within the upper and lower bounds of the design variables; S33: Generate opposing individuals using the opposing learning method, merge random individuals with opposing individuals to form an initial candidate population, and select individuals that meet the population size requirements as the initial population; S34: Initialize the external archive, auxiliary archive, and failed test vector pool to an empty set, and initialize the individual failure counter for each individual to zero.

[0011] S4: In each iteration of the differential evolution algorithm, for each individual in the current population, based on the individual's historical failure state and the population's evolutionary state, a current mutation strategy is selected from a variety of predefined mutation strategies, and the first mutation vector is generated using the selected current mutation strategy. Furthermore, the mutation strategy includes: basic mutation branch, historical route mutation branch, and cross-archive mutation branch; The criteria for selecting the current mutation strategy include: Individual consecutive failures, population diversity indicators, archive freshness, ranking normalization indicators, and the proportion of the current evolutionary stage.

[0012] S5: Construct a reference direction based on the superior individuals in the current population, determine the consistency of the direction of each dimension of the first mutation vector with the reference direction in each dimension, and repair the direction of the first mutation vector according to the judgment result to obtain the second mutation vector; Furthermore, the superior individuals in the current population are specifically defined as: the set of elite individuals and the current best individual; Furthermore, the specific operations for directional repair include: Determine the strong response dimension in the reference direction; Detect the conflict between the differential search direction of the first mutation vector and the reference direction in the strong response dimension; Conflicting dimensions are weakened, consistent dimensions are strengthened, and the overall difference search direction is scaled according to the proportion of conflicting dimensions. The scaling degree is negatively correlated with the proportion of the conflict dimension; that is, the higher the proportion of the conflict dimension, the greater the scaling magnitude of the overall difference search direction.

[0013] S6: Based on the correlation between the distribution information of all individuals in the population in the search space and the fitness sequence, determine the problem type of the current search area, and adjust the subsequent search behavior according to the determination result; Furthermore, the specific problem type for determining the current search region includes: Calculate the distance from each individual in the population to the current best individual, and form a distance sequence; Obtain the fitness values ​​of each individual in the population to form a fitness sequence; Calculate the Spearman rank correlation coefficient between the distance sequence and the fitness sequence; Based on the magnitude of the Spearman rank correlation coefficient, the current search region is determined to be in a unimodal convergence trend state, an uncertain state, or a multimodal complex trend state.

[0014] S7: Perform a crossover operation on the second mutation vector to generate a test vector, specifically including the following steps: S71: Perform a crossover operation between the second mutation vector and the current target vector to generate a trial vector, wherein each dimension adopts the value of the second mutation vector with a crossover probability, and at least one dimension is forced to adopt the value of the second mutation vector; S72: When any dimension of the experimental vector exceeds the range of the design variable, perform boundary processing on that dimension.

[0015] S8: Based on the fitness evaluation function, perform a selection operation according to the fitness comparison result between the experimental vector and the target vector, and update the population; Further, specific operations for updating the population include: When the fitness value of the experimental vector is less than or equal to the fitness value of the target vector, the target vector is replaced by the experimental vector, the replaced target vector is added to the external file, and the failure counter of the corresponding individual is cleared. When the fitness value of the experimental vector is greater than the fitness value of the target vector, the target vector is retained, the experimental vector is added to the failed experimental vector pool, and the failure counter of the corresponding individual is incremented by one. When the capacity of the external file, the auxiliary file, or the failed test vector pool exceeds a preset limit, pruning is performed using one of the following methods: random deletion, fitness deletion, or time deletion.

[0016] S9: Iterate through steps S4 to S8 until the termination condition is met, and output the optimal engineering design parameters; Furthermore, the termination condition is: the current fitness evaluation count reaches the preset maximum fitness evaluation count.

[0017] It should be noted that the numbering of steps S4 to S8 above is only used to distinguish the various operations and does not constitute a strict limitation on the execution order. Those skilled in the art, based on the technical concept of this invention, can adjust the order of some steps while achieving the same technical effect. For example, there is no data dependency between step S6 (landscape discrimination) and step S7 (cross-operation), and their execution order can be interchanged without affecting the realization of the core function of this invention.

[0018] By adopting the above technical solution, the present invention can achieve the following technical effects: By using a failure-state-driven multi-branch mutation routing mechanism, mutation branches are selected based on individual consecutive failure states, population collapse states, archive freshness, individual fitness ranking, and current evolutionary stage, which improves the adaptability of differential search direction and avoids the limitations of fixed mutation strategies. By identifying landscape characteristics, the system can recognize single-peak / multi-peak / uncertain states and dynamically adjust search behavior. By initializing using an oppositional learning method, the initial population can more comprehensively cover the search space, thus accelerating convergence. Attached Figure Description

[0019] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. It should be understood that the following drawings only show some specific embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating an engineering optimization method based on failed state variation routing and landscape discrimination.

[0021] Figure 2 This is a schematic diagram of an engineering optimization system based on failure state variation routing and landscape discrimination. Detailed Implementation

[0022] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0023] Example 1 Please see Figure 1 The first embodiment of the present invention provides an engineering optimization method based on failed state variation routing and landscape discrimination, including the following steps: S1: Establish a constrained optimization model for the engineering design problem, determine the design variables and their ranges, the objective function, and the constraints, specifically including: S11: Determine the design variables for the engineering design problem, wherein the design variables are represented as follows: ; In the formula, To design the dimension of variables; S12: Determine the range of values ​​for the design variables, expressed as: ; In the formula, and The first Lower and upper bounds of a design variable; S13: Determine the objective function of the engineering design problem. and constraint functions Establish the constraint engineering design optimization model: ; satisfy ; In the formula, The number of constraint functions; Furthermore, the engineering design problems include one or more of the following: tension / compression spring design, pressure vessel design, welded beam design, reducer design, gear transmission design, and three-bar truss design.

[0024] S2: Construct a fitness evaluation function based on the objective function and constraints, specifically including: The engineering design problem is transformed into a fitness minimization problem using the penalty function method, and a fitness evaluation function is established: ; The penalty coefficient is... The fitness value represents the design variable; the smaller the fitness value, the better the design scheme. When the design variable satisfies all constraints, the penalty term is 0; when the design variable violates the constraints, the penalty term is increased according to the degree of violation.

[0025] S3: Initialize the population, algorithm parameters, and archive structure for recording search states in the differential evolution algorithm; the algorithm parameters include: scaling factor and crossover probability; the archive structure includes external archive, auxiliary archive, failed trial vector pool, and individual failure counter, and the specific steps include: S31: Set the maximum number of fitness evaluations Current fitness evaluation count Initial population size Minimum population size Initialize the scaling factor for each individual. Crossover probability External archives Supporting documents Failed test vector pool and individual failure counter ; S32: Initialize the population individuals within the upper and lower bounds of the design variables to generate random individuals. The individual Each dimension is represented as: ; In the formula, A random number between 0 and 1; S33: Using an oppositional learning method to generate opposing individuals: ; The random individuals are merged with the opposing individuals to form an initial candidate population, and individuals that meet the population size requirements are selected as the initial population. Furthermore, the population size requirement can be: the number of individuals in the final selected initial candidate population is equal to the initial population size preset by the algorithm; for example, if the preset initial population size is 100, the number of generated random individuals and the number of opposing individuals are both 100, then the number of individuals in the merged initial candidate population is 200, and the optimal 100 individuals are selected from them as the initial population.

[0026] S34: Transfer external files Supporting documents Failed test vector pool Initialize to an empty set, and set the individual failure counter for each individual. Initialize to zero.

[0027] S4: In each iteration of the differential evolution algorithm, for each individual in the current population, based on the individual's historical failure state and the population's evolutionary state, a current mutation strategy is selected from multiple predefined mutation strategies, and the first mutation vector is generated using the current mutation strategy. This specifically includes the following steps: S41: Calculate the current evolutionary stage proportion: ; Calculate the number of consecutive failures for an individual: ; In the formula, For the first The generation The number of consecutive times an individual fails to improve. This is the adjustment coefficient for the failure state; Furthermore, the failure state adjustment coefficient can be set to 1.0. It is understood that the value can be adaptively adjusted according to specific engineering design problems.

[0028] Calculate population diversity indicators: ; In the formula, For the sake of current population diversity, For initial population diversity, It is a very small positive number; Calculate the population collapse state index: ; In the formula, The threshold for population collapse; Furthermore, the population collapse threshold The value can be selected within the range of [0.1, 0.3]. It can be understood that the population collapse threshold is... Not limited to this, those skilled in the art can adaptively select other reasonable values ​​based on actual factors such as population size, problem dimension and convergence status.

[0029] S42: Based on external files Supporting documents and failed test vector pool The update time of an individual is used to calculate the freshness of the archive: ; In the formula, For the individual's age in the archives, This is the age decay coefficient; Calculate the ranking normalization index based on individual fitness ranking: ; In the formula, For the first The fitness ranking of each individual in the current population; S43: Based on the current evolutionary stage ratio, the number of consecutive individual failures, the population collapse status index, the archive freshness and the ranking normalization index, select a mutation strategy from a variety of predefined mutation strategies. The mutation strategies include: basic mutation branch, historical route mutation branch, and cross archive mutation branch. For example, the mutation strategy for the current individual can be selected according to the following rules: If the population collapse state index is met >0.6 or file freshness If the value is less than 0.2, it is considered that the population diversity is severely insufficient or the historical information is too outdated. In this case, the cross-archive variation branch is selected. If the above indicators are not met, and the individual experiences consecutive failures... If the individual is considered to be stuck, then the historical route mutation branch is selected. If none of the above indicators are met, then the basic variant branch is selected; In the later stages of evolution, that is, the proportion of the current evolutionary stage And the ranking normalization index Even if the above indicators are not met, a historical route mutation branch can be temporarily selected to accelerate convergence; in the early stages of evolution, i.e., the proportion of the current evolutionary stage. Furthermore, the risk of population collapse is low, indicating a low population collapse status index. When this is the case, prioritize basic mutation branches to maintain global exploration.

[0030] It is understood that the above method is only a specific example, and the implementation of the present invention is not limited thereto.

[0031] S44: Generate the first mutation vector according to the selected current mutation strategy; The differential search direction of the basic mutation branch is represented as follows: ; In the formula, The first individual randomly selected from the current population. This refers to the second individual randomly selected from the current population. The differential search direction of the historical route mutation branch is represented as: ; In the formula, The first adjustment coefficient, For individuals selected from supplementary files, Individuals randomly selected from the current population; The differential search directions for the cross-file mutation branches are represented as follows: ; In the formula, Individuals selected from external archives. This is the second adjustment coefficient; Generate the first mutation vector based on the selected differential search direction:

[0032] in, These are the guiding individuals selected from the set of outstanding individuals. The first generation in the G generation population Each individual entity, i.e., the target vector; For example, all individuals in the current population are sorted by fitness value from smallest to largest, and the top-ranked individuals are selected. The individuals constitute the set of excellent individuals, and an individual is randomly selected from the set of excellent individuals to be the guiding individual. .

[0033] S5: Correct the direction of the first mutated vector to obtain the second mutated vector, including the following steps: S51: Construct a reference direction based on the superior individuals in the current population; Furthermore, the superior individuals in the current population are specifically defined as: the set of elite individuals and the current best individual; Based on the current population's fitness ranking, i.e., fitness value Smaller individuals build elite individual sets And calculate the elite center : ; In the formula, The number of elite individuals; Combined with the aforementioned elite center Current optimal individual and current individuals Construction reference direction: ; In the formula, This refers to the weighting coefficient for elite centers; Furthermore, the value range of the Elite Center weight coefficient is (0,1]; The reference direction integrates the guidance information of the elite center and the current best individual, and is used to determine whether the differential search direction of the first mutation vector is oriented towards the superior region.

[0034] S52: Based on the reference direction, determine the consistency of the direction of each dimension of the first mutation vector with the direction of the reference direction in each dimension, and perform direction repair on the first mutation vector based on the determination result; Determine the strong response dimension in the reference direction. : ； In the formula, This indicates that the median of the absolute values ​​of each dimension with respect to the reference direction is taken. Indicates the number of generations in the G-th population. The reference direction of each individual is in the 1st Components in the dimension; The strong reference dimension is defined by calculating the absolute value of each dimension component and comparing it with the median of the absolute values ​​of all dimensions.

[0035] Compare the difference search directions of the first mutation vector The conflict with the reference direction in the strong response dimension; if the signs are opposite, it is determined to be a conflict dimension, and a set of conflict dimensions is obtained. : ; Based on the assessment results, conflicting dimensions are weakened, while consistent dimensions are strengthened: ; In the formula, To reduce the coefficient of conflict dimension, For consistency dimension enhancement coefficient; For example, the conflict dimension weakening coefficient The value range of is [0,1]. In a preferred embodiment, The value is 0.5. In another implementation, The value is set to 0.3. This is to avoid completely losing the ability to search along the conflict dimension. It is usually set to a positive number that is greater than 0 and less than 1; For example, the consistency dimension enhancement coefficient The range of values ​​for is [1, +∞]. The overall differential search direction is scaled according to the proportion of the conflict dimension, wherein the degree of scaling is negatively correlated with the proportion of the conflict dimension, i.e., the conflict dimension proportion... The higher the value, the greater the scaling of the overall difference search direction: ; According to the aforementioned conflict dimension ratio Determine the overall scaling factor : ; In the formula , is the minimum scaling factor. To adjust the strength coefficient; The minimum scaling factor This is used to limit the lower limit of the overall scaling factor, preventing the scaling factor from becoming too small or even negative due to excessively high conflict ratios; for example, The value range of is [0,1], but it is usually set to a positive number greater than 0 and less than 1; in a preferred embodiment, =0.2; In another implementation, =0.5; those skilled in the art can choose an appropriate value between 0.2 and 0.5 depending on the degree of conflict sensitivity of the specific problem.

[0036] It should be noted that, if If the value is too small (e.g., close to 0), the algorithm may almost stop searching in that dimension when there is severe conflict, which is not conducive to the optimization of complex problems; if If the value is too large (e.g., close to 1), the effect of the conflict ratio adjustment mechanism is weakened, which is not conducive to suppressing erroneous search directions; therefore, the minimum scaling factor... The preferred value is between 0.2 and 0.5.

[0037] Based on the overall scaling factor The differential search direction is scaled as a whole to obtain the scaled differential search direction. : ; S53: After correcting the direction of the first mutation vector, a second mutation vector is obtained. : .

[0038] S6: Based on the correlation between the distribution information of all individuals in the population in the search space and the fitness sequence, determine the problem type of the current search area, and adjust the subsequent search behavior according to the determination result; Furthermore, the specific problem type for determining the current search region includes: Calculate the first Each target vector in the population To the current optimal individual Euclidean distance : ; In the formula, Represents the Euclidean distance (norm 2); Forming distance sequences : ; In the formula, This represents the current population size; Obtain the fitness value of each individual in the population. Forming a fitness sequence : ; Calculate the distance sequence With fitness sequence Spearman rank correlation coefficient between : ; Furthermore, the Spearman rank correlation coefficient can be... After smoothing, the smoothed Spearman rank correlation coefficient is obtained. To avoid drastic changes in the discrimination results due to random fluctuations in a single generation of the population: ; In the formula, For smoothing coefficients, The Spearman rank correlation coefficient is the smoothed version of the previous generation. Furthermore, the smoothing coefficient The value range is (0,1], preferably, ; Furthermore, the previous generation smoothed Spearman rank correlation coefficient initial value It can be set to 0; The problem type of the current search region is determined based on the magnitude of the smoothed Spearman rank correlation coefficient. : ; In the formula, This indicates the question type used to determine the current search area. The upper threshold; This indicates the question type used to determine the current search area. The lower threshold; According to the problem form The current search area is classified as either a single-peak convergent trend, an uncertain trend, or a multi-peak complex trend. This indicates a unimodal convergence trend. Indicates an uncertain state. It indicates a complex trend with multiple peaks.

[0039] Adjust subsequent search behavior based on the results of the current search area; Furthermore, when a unimodal convergence trend is identified, one or more of the following methods, or other equivalent methods, can be used to adjust subsequent search behavior: reducing the range of values ​​for the scaling factor F; performing a finer search near the optimal solution to enhance local search capabilities; and increasing the number of guiding individuals. The weights are included to make the population converge to the current optimal region more quickly; Furthermore, when the state is determined to be uncertain, one or more of the following methods, or other equivalent methods, can be used to adjust the subsequent search behavior: maintain the current mutation routing strategy and direction repair parameters, do not make special interventions, continue to collect population evolution data, and wait for the determination results of the next generation; Furthermore, when a multi-peak complex trend is identified, one or more of the following methods, or other equivalent methods, can be used to adjust subsequent search behavior: [The text abruptly ends here, likely due to an incomplete sentence or a missing section.] Historical failure information is selected to generate new mutation directions, activating the failed experiment vector backtracking mechanism; the range of scaling factor F is expanded to appropriately increase the mutation branch. The trigger probability is used to enhance population diversity restoration strategies; when the population diversity index When the population falls below a certain threshold, some individuals are reinitialized or individuals generated through adversarial learning are introduced to activate the population collapse recovery mechanism.

[0040] S7: Perform a crossover operation on the second mutation vector to generate a test vector, specifically including the following steps: S71: Perform a crossover operation between the second mutation vector and the current target vector to generate a trial vector, wherein each dimension adopts the value of the second mutation vector with a crossover probability, and at least one dimension is forced to adopt the value of the second mutation vector: ; In the formula, For the test vector, The experimental vector is the first dimensional components, For the first The crossover probability of each individual, The dimension index is randomly selected; Furthermore, The value range is [0,1]; S72: When any dimension of the experimental vector exceeds the range of the design variable, boundary processing is performed on the dimension; For example, boundary processing can be performed on the dimension according to one or a combination of the following methods: If the experimental vector of the first Dimensional components Then the first experimental vector will be... Dimensional components Set as If the experimental vector of the first... Dimensional components Then the first experimental vector will be... Dimensional components Set as ; If the experimental vector of the first Dimensional components If it exceeds the range, then in The value of the dimension is then randomly regenerated.

[0041] It is understood that the above method is only a specific example, and the implementation of the present invention is not limited thereto.

[0042] S8: Based on the fitness evaluation function, perform a selection operation according to the fitness comparison result between the experimental vector and the target vector, and update the population; Further, specific operations for updating the population include: When satisfied When the test vector is used to replace the target vector, the replaced target vector is added to the external file, and the failure counter of the corresponding individual is cleared. When the satisfaction When the target vector is retained, the experimental vector is added to the failed experimental vector pool, and the failure counter of the corresponding individual is incremented by one; When the capacity of the external file, the auxiliary file, or the failed test vector pool exceeds a preset limit, pruning is performed using one of the following methods: random deletion, fitness deletion, or time deletion. Furthermore, the random deletion refers to randomly removing a certain number of individuals from the file structure that exceeds the preset upper limit; Furthermore, the fitness deletion refers to removing individuals with poor fitness values ​​(i.e., high fitness values) from the file structure that exceeds a preset upper limit; Furthermore, the time deletion refers to removing the individual with the longest storage time (i.e., the lowest freshness value) from the archive structure that exceeds the preset upper limit, while retaining the fresh individuals.

[0043] S9: Iterate through steps S4 to S8 until the termination condition is met, and output the optimal engineering design parameters. : ; Furthermore, the termination condition is: the current fitness evaluation count reaches the preset maximum fitness evaluation count; Furthermore, the preset maximum fitness evaluation count is set according to the complexity of the engineering design problem; for example, it can be set to 50,000 times.

[0044] Compared with the prior art, the present invention has the following beneficial effects: By using a failure-state-driven multi-branch mutation routing mechanism, mutation strategies are selected based on individual consecutive failure states, population collapse state indicators, archive freshness, individual fitness ranking, and current evolutionary stage, thereby improving the adaptability of differential search direction. By using historical route mutation branches and cross-archive mutation branches, the algorithm can utilize historical search information to enhance its ability to escape local optima when individuals stagnate or population diversity declines. By using direction consistency gating and conflict ratio adjustment mechanisms, the dimensions that conflict with the reference direction are weakened, and the differential search direction is scaled as a whole according to the conflict ratio, thereby reducing the adverse effects of erroneous search directions on the population evolution process. By using a landscape discrimination mechanism based on distance-fitness correlation, the algorithm identifies the single-peak convergence trend state, uncertain state, or multi-peak complex trend state of the current search area, thereby improving the algorithm's adaptability to different engineering design optimization problems. It can be applied to constrained engineering design problems such as tension and compression spring design, pressure vessel design, welded beam design, reducer design, gear transmission design, and three-bar truss design, improving the optimization accuracy, search stability, and anti-premature convergence ability of engineering design variables.

[0045] Example 2 Referring to Embodiment 1, Embodiment 2 will provide a detailed explanation of the present invention using different engineering design problems as examples, in order to facilitate understanding of the present invention.

[0046] In one specific embodiment, the present invention can be applied to the design problems of compression springs (F1), pressure vessels (F2), welded beams (F3), reducers (F4), gear transmissions (F5), and three-bar trusses (F6). For different engineering design problems, only the corresponding design variables, variable upper and lower bounds, objective functions, and constraints need to be replaced to use the present invention for optimization and solution.

[0047] In this embodiment, the compression spring design problem F1 is used to minimize the spring structure weight or material consumption, and the design variables for the tension / compression spring design problem are determined as follows: ; In the formula, The diameter of the spring wire. The average coil diameter of the spring. This represents the effective number of coils of the spring. The range of values ​​for the design variables in the compression spring design problem F1 is determined as follows: ; Determine the objective function for the design problem of the tension / compression spring. for: ; The constraints of the compression spring design problem F1 include shear stress constraints, deformation constraints, frequency constraints, and geometric constraints.

[0048] In this embodiment, the pressure vessel design problem F2 is used to minimize the manufacturing cost of the pressure vessel, and the design variables for the pressure vessel design problem are determined as follows: ; In the formula, For shell thickness, For the thickness of the end cap, Let the inner radius of the container be . The length of the cylindrical portion of the container; The range of values ​​for the design variables in the pressure vessel design problem F2 is determined as follows: ; Determine the objective function of the pressure vessel design problem F2. for: ; The constraints of the pressure vessel design problem F2 include shell thickness constraints, head thickness constraints, volume constraints, and length constraints.

[0049] In this embodiment, the welded beam design problem F3 is used to minimize the structural cost of the welded beam, and the design variables for the welded beam design problem F3 are determined as follows: ; In the formula, For weld thickness, For weld length, For Liang Gao, For Liang Hou; The range of values ​​for the design variables in the welding beam design problem F3 is determined as follows: ; Determine the objective function of the welded beam design problem F3. for: ; The constraints of the welded beam design problem F3 include shear stress constraints, bending stress constraints, geometric constraints, cost constraints, end deflection constraints, and buckling load constraints.

[0050] In this embodiment, the reducer design problem F4 is used to minimize the structural weight of the reducer, and the design variables for the reducer design problem F4 are determined as follows: ; In the formula, For tooth width, For gear module, This refers to the number of teeth on the pinion. The length of the first shaft (between the bearings). The length of the second shaft (between the bearings). The diameter of the first shaft. The diameter of the second shaft; The range of values ​​for the design variables in the aforementioned reducer design problem F4 is determined as follows: ; ; Determine the objective function of the reducer design problem F4. for: ; The constraints of the reducer design problem F4 include gear bending strength constraints, surface stress constraints, shaft stress constraints, shaft deflection constraints, tooth width constraints, and geometric dimension constraints.

[0051] In this embodiment, the gear transmission design problem F5 is used to minimize the gear ratio error, and the design variables for the gear transmission design problem F5 are determined as follows: ; In the formula, Design variables for the gear tooth count class; The range of values ​​for the design variables in the gear transmission design problem F5 is determined as follows: ; Determine the objective function of the gear transmission design problem F5. for: ; The constraints of the gear transmission design problem F5 include strength constraints, geometric and kinematic constraints, performance constraints, and interference constraints. Furthermore, the gear tooth count design variable undergoes integer mapping processing on the corresponding dimension before fitness evaluation.

[0052] In this embodiment, the three-bar truss design problem F6 is used to minimize the weight of the truss structure, and the design variables for the three-bar truss design problem F6 are determined as follows: ; In the formula, and These represent the cross-sectional area parameters in the three-bar truss structure; The range of values ​​for the design variables in the three-bar truss design problem F6 is determined as follows: ; Determine the objective function of the three-bar truss design problem F6. for: ; The constraints of the three-bar truss design problem F6 include member stress constraints and structural bearing constraints.

[0053] For any of the above-mentioned engineering design optimization problems, this embodiment uses the engineering design as the design variable in the differential evolution algorithm, and uses the fitness evaluation function composed of the objective function and the constraint penalty term as the optimization basis. The optimization search process is completed collaboratively through the failure state-driven multi-branch mutation routing mechanism, the direction consistency gating and conflict ratio adjustment mechanism, and the landscape discrimination mechanism based on distance-fitness correlation.

[0054] In actual implementation, parameters such as the maximum fitness evaluation times, population size, scaling factor, crossover probability, upper limit of file structure capacity, various thresholds, and various adjustment coefficients can be adaptively set according to the characteristics of specific engineering design problems.

[0055] To verify the effectiveness of the engineering optimization method based on failed state mutation routing and landscape discrimination proposed in this invention for engineering design problems, the method of this invention (FSMR-LCDE) was compared with several existing differential evolution algorithms (including L-SHADE, jSO, PaDE, DA2MODE, SFG-DE, and ASMRDE) on six typical engineering design problems. This embodiment uses Matlab R2024a simulation software, with the maximum fitness evaluation count (nfes_max) uniformly set to 50,000. Each algorithm was run independently 30 times to obtain statistical results.

[0056] Refer to Table 1, which records the optimization results of each algorithm for the above six problems. The data in the table are presented in the form of "mean / standard deviation". The mean reflects the average optimization accuracy of the algorithm, and the standard deviation reflects the stability of the algorithm. Table markers: > indicates that the comparison algorithm is better than the method of the present invention; < indicates that the comparison algorithm is worse than the method of the present invention; ≈ indicates that the optimization results of the comparison algorithm and the method of the present invention are basically the same. The algorithm results represent the FSMR-LCDE method of this invention. All six engineering design optimization problems mentioned above are minimization problems; that is, the smaller the objective function value, the better the optimization effect of the design scheme. Therefore, when comparing the optimization performance of different algorithms, the one with the smaller objective function value is considered to have a better optimization result.

[0057] Table 1. Comparison of optimization results of different algorithms on different engineering design problems

[0058] Experimental results show that the FSMR-LCDE method of this invention can achieve better objective function values ​​than the comparative algorithms in engineering design problems with complex constraints, such as pressure vessel design F2 and reducer design F4. In problems such as tension and compression spring design F1, welded beam design F3, gear transmission design F5, and three-bar truss design F6, it can achieve optimization results comparable to or even better than existing excellent algorithms. This fully verifies the good adaptability of the method of this invention to various types of engineering design problems, as well as its excellent engineering applicability and optimization stability.

[0059] The win / tie / loss statistics further corroborate this: compared to L-SHADE (3 wins, 3 draws, 0 losses), compared to jSO (4 wins, 2 draws, 0 losses), compared to PaDE (2 wins, 3 draws, 1 loss), compared to DA2MODE (2 wins, 4 draws, 0 losses), compared to SFG-DE (3 wins, 3 draws, 0 losses), and compared to ASMRDE (3 wins, 3 draws, 0 losses), the overall win rate is outstanding, the number of losing samples is scarce, and the comprehensive optimization performance has significant advantages.

[0060] The above results demonstrate that the present invention, through a failure-state-driven multi-branch mutation routing mechanism, a direction consistency gating and conflict ratio adjustment mechanism, and a landscape discrimination mechanism based on distance-fitness correlation, can effectively improve the search accuracy and stability of the differential evolution algorithm on several typical engineering design optimization problems, and has clear practical value.

[0061] Example 3 See Figure 2 The third embodiment of the present invention provides an engineering optimization system based on failed state variation routing and landscape discrimination, comprising: Model building module: Used to build constrained optimization models for engineering design problems; Fitness evaluation module: used to construct fitness evaluation functions; Population initialization module: Used to initialize the population, algorithm parameters, and file structure for recording the search state of the differential evolution algorithm; Failure State Mutation Routing Module: This module is used to select a current mutation strategy from a variety of predefined mutation strategies based on the historical failure states of an individual and the evolutionary state of the population, and to generate a first mutation vector using the current mutation strategy. Directional Consistency Repair Module: Used to construct a reference direction determined based on superior individuals in the current population, determine the directional consistency between each dimension of the first mutation vector and the reference direction in each dimension, and repair the direction of the first mutation vector according to the determination result to obtain the second mutation vector; Landscape discrimination module: It is used to determine the problem type of the current search area based on the correlation between the distribution information of all individuals in the population in the search space and the fitness sequence, and to adjust the subsequent search behavior according to the discrimination results; Crossover selection module: used to perform crossover operation on the second mutation vector to generate experimental vectors; File update module: Based on the fitness evaluation function, perform a selection operation according to the fitness comparison results between the trial vector and the target vector, and update the population; Results output module: Used to output the optimal engineering design parameters after the maximum number of fitness evaluations has been reached.

[0062] Example 4 The fourth embodiment of the present invention provides an engineering optimization device based on failed state variation routing and landscape discrimination, comprising: a processor, a memory, and a computer program stored in the memory; the computer program can be executed by the processor to implement an engineering optimization method based on failed state variation routing and landscape discrimination as described in the first embodiment.

[0063] Example 5 The fifth embodiment of the present invention provides a computer-readable storage medium, the computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform an engineering optimization device based on failure state variation routing and landscape discrimination as described in Embodiment 1.

[0064] The terms "first" and "second" used in the embodiments are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0065] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An engineering optimization method based on failed state variation routing and landscape discrimination, characterized in that, Includes the following steps: S1: Establish a constrained optimization model for the engineering design problem, and determine the design variables and their range of values, objective function, and constraints; S2: Construct a fitness evaluation function based on the objective function and constraints; S3: Initialize the population, algorithm parameters, and file structure for recording the search state of the differential evolution algorithm; S4: In each iteration of the differential evolution algorithm, for each individual in the current population, based on the individual's historical failure state and the population's evolutionary state, a current mutation strategy is selected from a variety of predefined mutation strategies, and the first mutation vector is generated using the current mutation strategy. S5: Construct a reference direction based on the superior individuals in the current population, determine the consistency of the direction of each dimension of the first mutation vector with the reference direction in each dimension, and repair the direction of the first mutation vector according to the judgment result to obtain the second mutation vector; S6: Based on the correlation between the distribution information of all individuals in the population in the search space and the fitness sequence, determine the problem type of the current search area, and adjust the subsequent search behavior according to the determination result; S7: Perform a crossover operation on the second mutation vector to generate a test vector; S8: Based on the fitness evaluation function, perform a selection operation according to the fitness comparison result between the experimental vector and the target vector, and update the population; S9: Iterate through steps S4 to S8 until the termination condition is met, and output the optimal engineering design parameters.

2. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, The constrained optimization model in step S1 includes the range of values ​​for the design variables, the objective function, and one or more constraints; the objective function is a performance index that measures the quality of the engineering design problem. The termination condition in step S9 is: the current fitness evaluation count reaches the preset maximum fitness evaluation count.

3. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, Step S2 specifically involves: The engineering design problem is transformed into a fitness minimization problem using the penalty function method, and a fitness evaluation function is established: fitness value = objective function value + penalty term; The penalty term is the product of the penalty coefficient and the sum of the squares of the degree of constraint violation; When the design variable satisfies all constraints, the penalty term is 0; when the design variable violates the constraints, the penalty term is increased according to the degree of violation.

4. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, The algorithm parameters in step S3 include: scaling factor and crossover probability; The archive structure includes external archives, auxiliary archives, a failed trial vector pool, and individual failure counters.

5. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 4, characterized in that, Step S3 includes: S31: Set the maximum fitness evaluation count, the current fitness evaluation count, the initial population size, and the minimum population size; initialize the scaling factor and crossover probability for each individual; S32: Initialize the population individuals within the upper and lower bounds of the design variables; S33: Generate opposing individuals using the opposing learning method, merge random individuals with opposing individuals to form an initial candidate population, and select individuals that meet the population size requirements as the initial population; S34: Initialize the external archive, auxiliary archive, and failed test vector pool to an empty set, and initialize the individual failure counter for each individual to zero.

6. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, The mutation strategies in step S4 include: basic mutation branch, historical route mutation branch, and cross-archive mutation branch; The selection criteria for the current mutation strategy include: Individual consecutive failures, population diversity indicators, archive freshness, ranking normalization indicators, and the proportion of the current evolutionary stage.

7. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, The specific operations for directional repair in step S5 include: Determine the strong response dimension in the reference direction; Detect the conflict between the differential search direction of the first mutation vector and the reference direction in the strong response dimension; Conflicting dimensions are weakened, consistent dimensions are strengthened, and the overall difference search direction is scaled according to the proportion of conflicting dimensions. The scaling degree is negatively correlated with the proportion of the conflict dimension; that is, the higher the proportion of the conflict dimension, the greater the scaling magnitude of the overall difference search direction.

8. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, The specific problem type of the current search region in step S6 includes: Calculate the distance from each individual in the population to the current best individual, and form a distance sequence; Obtain the fitness values ​​of each individual in the population to form a fitness sequence; Calculate the Spearman rank correlation coefficient between the distance sequence and the fitness sequence; Based on the magnitude of the Spearman rank correlation coefficient, the current search region is determined to be in a unimodal convergence trend state, an uncertain state, or a multimodal complex trend state.

9. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 1, characterized in that, Step S7 includes: S71: Perform a crossover operation between the second mutation vector and the current target vector to generate a trial vector, wherein each dimension adopts the value of the second mutation vector with a crossover probability, and at least one dimension is forced to adopt the value of the second mutation vector; S72: When any dimension of the experimental vector exceeds the range of the design variable, perform boundary processing on that dimension.

10. The engineering optimization method based on failed state variation routing and landscape discrimination according to claim 4, characterized in that, The specific operations for updating the population in step S8 include: When the fitness value of the experimental vector is less than or equal to the fitness value of the target vector, the target vector is replaced by the experimental vector, the replaced target vector is added to the external file, and the failure counter of the corresponding individual is cleared. When the fitness value of the experimental vector is greater than the fitness value of the target vector, the target vector is retained, the experimental vector is added to the failed experimental vector pool, and the failure counter of the corresponding individual is incremented by one. When the capacity of the external file, the auxiliary file, or the failed test vector pool exceeds a preset limit, pruning is performed using one of the following methods: random deletion, fitness deletion, or time deletion.

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