A multi-objective optimization design method for asphalt mixture based on genetic algorithm

Abstract

The application provides a genetic algorithm-based multi-objective optimization design method for asphalt mixture, constructs a mapping relationship model between different design parameters and volume indexes and performance indexes based on an asphalt mixture design database; determines an optimization direction according to engineering requirements, constructs an optimization objective function based on the mapping relationship model, and constructs a multi-objective optimization model with the design parameters as decision variables according to the optimization direction, the optimization objective function and preset constraint conditions; solves the optimization model by using a genetic algorithm including a non-dominated sorting mechanism and a reference point correlation mechanism to obtain an optimal solution set for the engineering requirement data; calculates the performance scores of each solution in the optimal solution set, and selects a solution with the highest performance score in the optimal solution set as an optimal design scheme for the asphalt mixture for the engineering requirement data according to the performance scores. The optimization efficiency and result reliability of the asphalt mixture design are improved, and coordinated optimization between multiple performance indexes is realized.

Description

Technical Field

[0001] This invention belongs to the field of asphalt mixture technology, specifically relating to a multi-objective optimization design method for asphalt mixtures based on genetic algorithms. Background Technology

[0002] Asphalt mixtures are widely used pavement materials in road engineering, and their design quality directly affects the pavement's rutting resistance, crack resistance, and durability. A reasonable asphalt mixture design requires comprehensive consideration of multiple design parameters, such as the asphalt-aggregate ratio and aggregate composition, while simultaneously satisfying multiple performance indicators. Different performance indicators often have interdependent relationships; therefore, asphalt mixture design is essentially an optimization problem with multiple variables, constraints, and objectives. Current asphalt mixture design typically relies on numerous experiments to adjust design parameters to meet specifications, resulting in heavy experimental workload, low design efficiency, and difficulty in simultaneously achieving coordinated optimization of multiple performance indicators.

[0003] With the development of computing technology, some studies have introduced multi-objective optimization algorithms into the asphalt mixture design problem. Among them, the third-generation non-dominated sorting genetic algorithm (NSGA-III) has good multi-objective optimization capabilities and can obtain a relatively balanced Pareto solution set among multiple objectives. However, in practical applications, when the generated design scheme does not meet constraints such as gradation range, asphalt-aggregate ratio, or volume index requirements, existing methods usually handle this by directly deleting the scheme or setting a penalty value in the objective function to reduce its fitness. These methods tend to reduce the number of effective schemes in the population, thus affecting the algorithm's convergence efficiency. Furthermore, the NSGA-III algorithm mainly achieves population updates and elite individual selection through non-dominated sorting and reference point guidance, lacking staged dynamic adjustment to meet the requirements of algorithm convergence and solution set diversity. This leads to the algorithm easily getting trapped in local optima in the later stages of iteration or causing uneven distribution of the solution set. Furthermore, in the process of selecting reference points, the NSGA-III algorithm only considers the vertical distance between the individual target vector and the reference point, which cannot effectively reflect the consistency between the individual and the reference point in the direction. This can lead to some reference points being crowded and others being idle, ultimately affecting the diversity and balance of the solution set. Summary of the Invention

[0004] To address the shortcomings of existing asphalt mixture design methods, this invention provides a multi-objective optimization design method for asphalt mixtures based on genetic algorithms. This method solves the problem of inadequate constraint handling in existing methods and improves the stability and uniformity of solution set distribution, thereby effectively improving the design efficiency and reliability of asphalt mixtures.

[0005] This application provides a multi-objective optimization design method for asphalt mixtures based on a genetic algorithm, comprising the following steps:

[0006] Based on the asphalt mixture design database, a mapping relationship model between different design parameters and volume index and performance index is constructed. The optimization direction is determined according to the engineering requirements, the optimization objective function is constructed based on the mapping relationship model, and a multi-objective optimization model with design parameters as decision variables is constructed according to the optimization direction, the optimization objective function, and the preset constraints. The optimization model is solved using a genetic algorithm that includes a non-dominated sorting mechanism and a reference point association mechanism to obtain the optimal solution set for the engineering requirements data. Calculate the performance score of each solution in the optimal solution set, and select the solution with the highest performance score in the optimal solution set as the optimal design scheme for asphalt mixture based on the engineering requirements data.

[0007] Optionally, before the step of constructing a mapping model between different design parameters and volumetric and performance indices based on an asphalt mixture design database, the method further includes: Design parameters for different types of asphalt mixtures and corresponding index data are collected to construct a design database for asphalt mixtures. The index data includes at least volumetric and performance indices.

[0008] Optionally, the step of solving the optimization model using a genetic algorithm that includes a non-dominated sorting mechanism and a reference point association mechanism to obtain the optimal solution set for the engineering requirement data includes: The design parameters, which are used as decision variables, are encoded to obtain the initial population; The initial population is subjected to at least one of selection, crossover, and mutation processes to generate a subpopulation of the initial population. Each individual in the offspring population is subjected to constraint checks according to preset constraint rules. Individuals that fail the constraint checks are identified as violating individuals, and the decision variables of the violating individuals are adjusted to obtain adjusted individuals that satisfy the preset constraint rules. The adjusted individuals are used to form a repair population with the individuals that pass the constraint checks. The initial population and the repair population are merged to form a temporary population. Based on the mapping relationship model, the objective function value of each individual in the temporary population is calculated. The population is then subjected to non-dominated sorting according to the objective function value to obtain the non-dominated sorting hierarchy. A preset reference point association mechanism is used to associate each individual in the temporary population with a preset reference point to obtain the reference point association result; Based on the non-dominated sorting hierarchy and the association result of the reference point, a dynamic elite selection strategy is adopted to determine the next generation population from the temporary population. The next generation population is then used as the initial population to perform at least one of the selection, crossover, and mutation processes on the initial population to generate the offspring population of the initial population. This process continues until a preset termination condition is met, resulting in the optimal solution set for the engineering requirement data.

[0009] Optionally, the preset constraint rules include at least gradation constraints, oil-aggregate ratio constraints, and volume index constraints. The step of performing constraint checks on each individual in the offspring population according to the preset constraint rules, identifying individuals that fail the constraint checks as violating individuals, and adjusting the decision variables of the violating individuals to obtain adjusted individuals that satisfy the preset constraint rules, wherein the adjusted individuals are used to form a repair population with the individuals that pass the constraint checks, includes: When an individual material violates the gradation constraint, the aggregate throughput of each sieve aperture size is reordered, and values ​​exceeding the set range are adjusted to the nearest upper or lower limit value. When an individual violates the oil-stone ratio constraint, the oil-stone ratio of the violating individual will be adjusted to the upper or lower limit value that is closest to the oil-stone ratio constraint. When an individual violates the volume index constraint, the gradation parameters and the oil-aggregate ratio are randomly adjusted within the range of gradation constraints and oil-aggregate ratio constraints, and the volume index is recalculated until the volume index meets the constraint conditions or reaches the preset number of adjustments.

[0010] Optionally, the step of associating each individual in the temporary population with a preset reference point using a preset reference point association mechanism to obtain the reference point association result includes: Map each individual in the population to the target space where the preset reference point is located to obtain the normalized target vector of each individual in the population; Calculate the orientation angle and Euclidean distance between each individual in the population and the preset reference point based on the normalized target vector; Find the reference point with the smallest angle and the reference point with the smallest distance, and calculate the crowding degree of the reference point with the smallest angle and the crowding degree of the reference point with the smallest distance. By comparing the crowding of the reference point with the smallest angle with the crowding of the reference point with the smallest distance, a preset reference point associated with the individual is determined.

[0011] Optionally, the step of determining the next generation population from the temporary population using a dynamic elite selection strategy based on the non-dominant ranking hierarchy and the association result of the reference point includes: Individuals within the same non-dominated hierarchy are identified based on the non-dominated ranking hierarchy. A preset evaluation function is used to rank and filter these individuals within the same non-dominated hierarchy, selecting individuals from the current non-dominated hierarchy to serve as the next generation population. The mathematical representation of the preset evaluation function is as follows:

[0012] in, Let Euclidean distance be the distance between the individual and the reference point. The angle between the individual and the reference direction. This is the adjustment function for the evolutionary stage.

[0013] Optionally, the preset constraints include gradation conditions, oil-aggregate ratio conditions, or volume index conditions, wherein the gradation condition is expressed as:

[0014] in, Indicates the size of the sieve opening. The aggregate throughput rate and These represent the lower and upper limits of the sieve aperture throughput, respectively. The oil-stone ratio condition is expressed as:

[0015] in, This indicates the asphalt-aggregate ratio in asphalt mixtures. and These represent the lower and upper limits of the oil-stone ratio, respectively. The volume index conditions are expressed as follows:

[0016] in, Represents the first obtained through the mapping relationship model A volume index value, and These represent the lower and upper limits of the volume index value, respectively.

[0017] The beneficial effects of this application's embodiments compared to existing technologies are as follows: By constructing a mapping relationship model between mixture design parameters and volume and performance indicators, rapid prediction of mixture indicators under different parameter combinations is achieved, and a multi-objective optimization model is established based on this. Simultaneously, the third-generation non-dominated sorting genetic algorithm is improved by optimizing constraint processing methods, improving reference point selection strategies, and introducing a dynamic elite selection strategy. Furthermore, the improved algorithm is used to solve the multi-objective optimization model to obtain an asphalt mixture design scheme that meets the preset performance indicator requirements. This invention significantly improves the optimization efficiency and reliability of asphalt mixture design, achieves coordinated optimization among multiple performance indicators, reduces the number of experiments, and improves the intelligence and stability of the design process, demonstrating promising engineering application prospects. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of a multi-objective optimization design method for asphalt mixtures based on a genetic algorithm, provided in an embodiment of this application. Figure 2 This is a flowchart of another multi-objective optimization design method for asphalt mixture based on genetic algorithm provided in the embodiments of this application; Figure 3 This is a flowchart of the genetic algorithm in a multi-objective optimization design method for asphalt mixtures based on a genetic algorithm provided in an embodiment of this application. Detailed Implementation

[0020] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0021] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0022] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0023] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [the described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [the described condition or event] is detected," or "in response to detection of [the described condition or event]."

[0024] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0026] like Figures 1-2 As shown in the figure, this application provides a multi-objective optimization design method for asphalt mixtures based on genetic algorithms, including the following steps: S101. Based on the asphalt mixture design database, construct a mapping relationship model between different design parameters and volume index and performance index; For example, an extreme gradient boosting algorithm is used to construct a mapping model between asphalt mixture design parameters and volumetric indices (void ratio, aggregate void ratio, and asphalt saturation) and performance indices (Marshall stability, dynamic stability, low-temperature flexural strain, and residual stability). Five-fold cross-validation is used to train and test the model, enabling the prediction of asphalt mixture indices under different parameter combinations.

[0027] For example, the mapping relationship model includes, but is not limited to, statistical regression models or machine learning models. Statistical regression models include, but are not limited to, multiple linear regression models or multinomial regression models. Machine learning models include, but are not limited to, kernel method models, tree models, ensemble learning models or neural network models.

[0028] S102. Determine the optimization direction according to the engineering requirements, construct the optimization objective function based on the mapping relationship model, and construct a multi-objective optimization model with design parameters as decision variables according to the optimization direction, the optimization objective function, and preset constraints. For example, based on engineering requirements, the multi-objective optimization direction of asphalt mixtures is determined, an optimization model is constructed, and optimization objective functions and constraints are set. The design parameters of the asphalt mixture are encoded as decision variables. The optimization objective direction is to maximize Marshall stability, dynamic stability, low-temperature flexural strain, and residual stability to ensure performance stability and durability during long-term use. The optimization objective function is determined based on a mapping relationship model. The constraints include gradation constraints, asphalt-aggregate ratio constraints, or volume index constraints to ensure that the design parameters meet the requirements of the "Technical Specifications for Construction of Highway Asphalt Pavement" and engineering practice.

[0029] S103. Solve the optimization model using a genetic algorithm that includes a non-dominated sorting mechanism and a reference point association mechanism to obtain the optimal solution set for the engineering requirement data; S104. Calculate the performance score of each solution in the optimal solution set, and select the solution with the highest performance score in the optimal solution set as the optimal design scheme for asphalt mixture based on the engineering requirements data.

[0030] In one possible implementation, before the step of constructing a mapping model between different design parameters and different index data using a preset algorithm based on a preset design database for asphalt mixtures, the method further includes: Design parameters for different types of asphalt mixtures and corresponding index data are collected to construct a pre-designed database for asphalt mixtures. The index data includes at least volumetric and performance indices.

[0031] For example, design parameters include, but are not limited to, basic asphalt properties, asphalt-aggregate ratio, and aggregate gradation parameters; volumetric indices of asphalt mixtures are selected from one or more of porosity, aggregate void ratio, density, and asphalt saturation; performance indices of asphalt mixtures are selected from one or more of strength, high-temperature stability, low-temperature crack resistance, water stability, or other performance indices commonly used in the field; specifically, design parameters and corresponding volumetric and performance indices of different AC-13 modified asphalt mixtures are collected to construct an asphalt mixture design database. The asphalt mixture design parameters include asphalt penetration, softening point, ductility, asphalt-aggregate ratio, and aggregate gradation. The sieve sizes are sequentially 0.075 mm, 0.15 mm, 0.3 mm, 0.6 mm, 1.18 mm, 2.36 mm, 4.75 mm, 9.5 mm, 13.2 mm, and 16 mm. The volumetric indices include porosity, aggregate void ratio, and asphalt saturation. The performance indicators include Marshall stability, splitting tensile strength, and dynamic stability, designed to evaluate the compressive strength, crack resistance, and stability of asphalt mixtures under dynamic loads. Relevant data were obtained through indoor Marshall tests, rutting tests, low-temperature beam bending tests, and immersion Marshall tests, with a total of 350 samples collected. In one possible implementation, the step of solving the optimization model using a genetic algorithm that includes a non-dominated sorting mechanism and a reference point association mechanism to obtain the optimal solution set for the engineering requirement data includes: The design parameters, which are used as decision variables, are encoded to obtain the initial population; The initial population is subjected to at least one of selection, crossover, and mutation processes to generate a subpopulation of the initial population. Each individual in the offspring population is subjected to constraint checks according to preset constraint rules. Individuals that fail the constraint checks are identified as violating individuals, and the decision variables of the violating individuals are adjusted to obtain adjusted individuals that satisfy the preset constraint rules. The adjusted individuals are used to form a repair population with the individuals that pass the constraint checks. The initial population and the repair population are merged to form a temporary population. Based on the mapping relationship model, the objective function value of each individual in the temporary population is calculated. The population is then subjected to non-dominated sorting according to the objective function value to obtain the non-dominated sorting hierarchy. A preset reference point association mechanism is used to associate each individual in the temporary population with a preset reference point to obtain the reference point association result; Based on the non-dominated sorting hierarchy and the association result of the reference point, a dynamic elite selection strategy is adopted to determine the next generation population from the temporary population. The next generation population is then used as the initial population to perform at least one of the selection, crossover, and mutation processes on the initial population to generate the offspring population of the initial population. This process continues until a preset termination condition is met, resulting in the optimal solution set for the engineering requirement data.

[0032] In one possible implementation, the preset constraint rules include at least gradation constraints, oil-aggregate ratio constraints, and volume index constraints. The step of performing constraint checks on each individual in the offspring population according to the preset constraint rules, identifying individuals that fail the constraint checks as violating individuals, and adjusting the decision variables of the violating individuals to obtain adjusted individuals that satisfy the preset constraint rules, wherein the adjusted individuals are used to form a repair population with the individuals that pass the constraint checks, includes: When an individual material violates the gradation constraint, the aggregate throughput of each sieve aperture size is reordered, and values ​​exceeding the set range are adjusted to the nearest upper or lower limit value. When an individual violates the oil-stone ratio constraint, the oil-stone ratio of the violating individual will be adjusted to the upper or lower limit value that is closest to the oil-stone ratio constraint. When an individual violates the volume index constraint, the gradation parameters and the oil-aggregate ratio are randomly adjusted within the range of gradation constraints and oil-aggregate ratio constraints, and the volume index is recalculated until the volume index meets the constraint conditions or reaches the preset number of adjustments.

[0033] In one possible implementation, the step of associating each individual in the temporary population with a preset reference point using a preset reference point association mechanism to obtain the reference point association result includes: Map each individual in the population to the target space where the preset reference point is located to obtain the normalized target vector of each individual in the population; Calculate the orientation angle and Euclidean distance between each individual in the population and the preset reference point based on the normalized target vector; Find the reference point with the smallest angle and the reference point with the smallest distance, and calculate the crowding degree of the reference point with the smallest angle and the crowding degree of the reference point with the smallest distance. By comparing the crowding of the reference point with the smallest angle with the crowding of the reference point with the smallest distance, a preset reference point associated with the individual is determined.

[0034] In one possible implementation, the step of determining the next generation population from the temporary population using a dynamic elite selection strategy based on the non-dominated ranking hierarchy and the association result of the reference point includes: Individuals within the same non-dominated hierarchy are identified based on the non-dominated ranking hierarchy. A preset evaluation function is used to rank and filter these individuals within the same non-dominated hierarchy, selecting individuals from the current non-dominated hierarchy to serve as the next generation population. The mathematical representation of the preset evaluation function is as follows:

[0035] in, Let Euclidean distance be the distance between the individual and the reference point. The angle between the individual and the reference direction. This is the adjustment function for the evolutionary stage.

[0036] Optionally, the preset constraints include gradation conditions, oil-aggregate ratio conditions, or volume index conditions, wherein the gradation condition is expressed as:

[0037] in, Indicates the size of the sieve opening. The aggregate throughput rate and These represent the lower and upper limits of the sieve aperture throughput, respectively. The oil-stone ratio condition is expressed as:

[0038] in, This indicates the asphalt-aggregate ratio in asphalt mixtures. and These represent the lower and upper limits of the oil-stone ratio, respectively. The volume index conditions are expressed as follows:

[0039] in, Represents the first obtained through the mapping relationship model A volume index value, and These represent the lower and upper limits of the volume index value, respectively.

[0040] For example, such as Figure 3 As shown, a multi-objective optimization design method for asphalt mixtures based on genetic algorithms includes: The standard third-generation non-dominated sorting genetic algorithm is used to perform selection, crossover, and mutation operations to generate offspring populations from parent populations. Constraint checks are performed on individuals in the offspring population. When an individual is detected to have violated the constraints, a constraint repair mechanism is activated to automatically adjust its decision variables so that they meet the preset conditions before participating in subsequent iterations.

[0041] The adjustment process includes: when an individual violates the gradation constraint, the aggregate passing rate of each sieve aperture size is reordered, and values ​​exceeding the set range are adjusted to the closest upper or lower limit; when an individual violates the asphalt-aggregate ratio constraint, its asphalt-aggregate ratio is adjusted to the closest upper or lower limit; when an individual violates the volume index constraint, the gradation parameters and asphalt-aggregate ratio are randomly adjusted within the gradation constraint and asphalt-aggregate ratio constraint range, and the volume index is recalculated until the volume index meets the constraint conditions or reaches the preset number of adjustments.

[0042] The parent population is merged with the constrained and repaired offspring population to form a temporary population. Then, based on the aforementioned mapping model, the objective function value of each individual in the temporary population is calculated. A non-dominated sort is performed on the population, and an improved reference point association mechanism is used to associate individuals with preset reference points to maintain population diversity in the target space. The improved reference point association mechanism introduces a comprehensive association criterion that considers both directional consistency and local crowding of reference points. After an individual is mapped to the target space, its Euclidean distance to the reference direction must be taken into account. Additionally, the angle between the individual target vector and the reference direction must be considered. (i.e., direction angle) serves as a measure of directional consistency.

[0043] Let individuals The normalized target vector is , For the first j One reference point, then The Euclidean distance to the reference point is expressed as:

[0044] The direction angle is defined as:

[0045] Among them, the smaller the orientation angle, the more consistent the orientation of the individual with that of the reference point in the target space.

[0046] Statistics of current reference points The congestion level is:

[0047] in, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise.

[0048] In each iteration, the algorithm performs a process on each... Calculate its Euclidean distance to all reference points. With direction angle Then find the reference point with the smallest angle. The reference point with the smallest distance And determine their corresponding current congestion levels: if The crowding level is less than Given higher congestion levels, priority will be given to options with better directional consistency. Otherwise, choose those with smaller distances and more concentrated distribution. The final reference point association mechanism for an individual is as follows:

[0049] Based on the non-dominated ranking hierarchy and the association results of reference points, a dynamic elite selection strategy is adopted to determine the next generation parent population from the merged temporary population. The dynamic elite selection strategy involves, after establishing a correlation between the population and a reference point, employing a dynamic evaluation function that prioritizes convergence followed by diversity to rank and filter individuals within the same non-dominated layer, thereby selecting individuals from the current non-dominated layer to serve as the next generation of the population. The evaluation function is as follows:

[0050] in, Let Euclidean distance be the distance between the individual and the reference point. The angle between the individual and the reference direction.

[0051] This is the regulation function for the evolutionary stage, and its definition is as follows.

[0052]

[0053] in, , The maximum number of iterations for the population. , In this embodiment, the maximum number of iterations is set to 200.

[0054] Repeat the above steps until the preset maximum number of iterations is reached. The final output is a Pareto optimal solution set containing 36 sets of non-dominated solutions. From this set, the asphalt mixture design scheme that meets the preset performance requirements and has the best overall performance is selected. Its design parameters and expected volume and performance indicators are shown in Table 1. Table 1

[0055] To verify the reliability of the optimized design scheme, specimens were prepared for indoor tests according to the optimal design parameters obtained above, and their volumetric and mechanical properties were tested. The test results show that the relative errors between the measured values ​​and the model predictions are all controlled within ±4%, and all volumetric and performance indicators meet the preset constraints. This indicates that the proposed multi-objective optimization design method for asphalt mixtures based on the improved third-generation non-dominated sorting genetic algorithm can effectively obtain optimized design schemes that meet engineering requirements, and has good reliability and practicality. Specifically, the genetic algorithm including the non-dominated sorting mechanism and the reference point association mechanism is used as the improved third-generation non-dominated sorting genetic algorithm.

[0056] For example, taking SMA-13 ​​modified asphalt mixture as the research object, which requires the addition of 0.3% fiber, its design parameters are optimized through multi-objective methods, including the following steps: Design parameters and corresponding volumetric and performance indices of different SMA-13 ​​modified asphalt mixtures were collected to construct an asphalt mixture design database. The asphalt mixture design parameters included asphalt penetration, softening point, ductility, asphalt-aggregate ratio, and aggregate gradation. The sieve sizes were 0.075 mm, 0.15 mm, 0.3 mm, 0.6 mm, 1.18 mm, 2.36 mm, 4.75 mm, 9.5 mm, 13.2 mm, and 16 mm, respectively. The volumetric indices included porosity and aggregate void ratio. The performance indices included dynamic stability, low-temperature flexural strain, water immersion residual stability, and dispersion loss rate.

[0057] The relevant data were obtained through rutting tests, low-temperature bending tests, immersion Marshall tests, and Kentburgh scattering tests, with a total of 210 samples collected.

[0058] Based on the asphalt mixture design database, a random forest algorithm was used to construct a mapping model between asphalt mixture design parameters and volumetric and performance indices, enabling the prediction of mixture indices under different parameter combinations. Five-fold cross-validation was used for model training and testing, and the model performance evaluation results are shown in the table below. The results indicate that the constructed mapping model has good predictive ability and can be used for calculating the objective function in the optimization process.

[0059] Based on engineering requirements, the multi-objective optimization direction of asphalt mixtures is determined. An optimization model is constructed, and the optimization objective function and constraints are set. The asphalt mixture design parameters are encoded as decision variables, and the population is initialized. The optimization objective direction is to maximize dynamic stability, low-temperature flexural failure strain, and water-immersed Marshall residual stability, while minimizing the dispersion loss rate, to ensure its performance stability and durability during long-term use. The optimization objective function is determined based on the mapping relationship model between the mixture design parameters and the above-mentioned indicators established in step S2. The constraints include gradation constraints, asphalt-aggregate ratio constraints, or volume index constraints.

[0060] An improved third-generation non-dominated sorting genetic algorithm is used to iteratively solve the optimization model. In each iteration, the following operations are performed: The standard third-generation non-dominated sorting genetic algorithm is used to perform selection, crossover, and mutation operations to generate offspring populations from parent populations.

[0061] Constraint checks are performed on individuals in the offspring population. When an individual is detected to have violated the constraints, a constraint repair mechanism is activated to automatically adjust its decision variables so that it meets the preset conditions before participating in subsequent iterations. The parent population is merged with the constrained and repaired offspring population to form a temporary population. Then, based on the aforementioned mapping model, the objective function value of each individual in the temporary population is calculated. A non-dominated sort is performed on the population, and an improved reference point association mechanism is used to associate individuals with preset reference points to maintain population diversity in the target space. Based on the non-dominated ranking hierarchy and the association results of reference points, a dynamic elite selection strategy is adopted to determine the next generation parent population from the merged temporary population. Repeat the above steps until the preset maximum number of iterations is reached. The final output is a Pareto optimal solution set containing 21 sets of non-dominated solutions. From this set, the asphalt mixture design scheme that meets the preset performance requirements and has the best overall performance is selected. Its design parameters and expected volume and performance indicators are shown in Table 2. Table 2

[0062] To verify the reliability of the optimized design scheme, specimens were prepared for indoor testing according to the optimal design parameters obtained above, and their volumetric properties and mechanical properties were tested. The test results show that the relative errors between the measured values ​​and the model predictions are all controlled within ±5%, and all volumetric and performance indicators meet the preset constraints. This indicates that the proposed mixture design method can effectively obtain a design scheme that meets engineering requirements, and has good reliability and practicality.

[0063] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0064] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0065] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0066] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0067] In the embodiments provided in this application, it should be understood that the disclosed apparatus / network devices and methods can be implemented in other ways. For example, the apparatus / network device embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0068] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0069] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-objective optimization design method for asphalt mixtures based on genetic algorithms, characterized in that, Includes the following steps: Based on the asphalt mixture design database, a mapping relationship model between different design parameters and volume index and performance index is constructed. The optimization direction is determined according to the engineering requirements, the optimization objective function is constructed based on the mapping relationship model, and a multi-objective optimization model with design parameters as decision variables is constructed according to the optimization direction, the optimization objective function, and the preset constraints. A genetic algorithm, including a non-dominated sorting mechanism and a reference point association mechanism, is used to solve the optimization model to obtain the optimal solution set for the engineering requirement data. Calculate the performance score of each solution in the optimal solution set, and select the solution with the highest performance score in the optimal solution set as the optimal design scheme for asphalt mixture based on the engineering requirements data.

2. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 1, characterized in that, Before the step of constructing a mapping model between different design parameters and volumetric and performance indices based on an asphalt mixture design database, the method further includes: Design parameters for different types of asphalt mixtures and corresponding index data are collected to construct a design database for asphalt mixtures. The index data includes at least volumetric and performance indices.

3. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 1, characterized in that, The step of using a genetic algorithm, including a non-dominated sorting mechanism and a reference point association mechanism, to solve the optimization model and obtain the optimal solution set for the engineering requirement data includes: The design parameters, which are used as decision variables, are encoded to obtain the initial population; The initial population is subjected to at least one of selection, crossover, and mutation processes to generate a subpopulation of the initial population. Each individual in the offspring population is subjected to constraint checks according to preset constraint rules. Individuals that fail the constraint checks are identified as violating individuals, and the decision variables of the violating individuals are adjusted to obtain adjusted individuals that satisfy the preset constraint rules. The adjusted individuals are used to form a repair population with the individuals that pass the constraint checks. The initial population and the repair population are merged to form a temporary population. Based on the mapping relationship model, the objective function value of each individual in the temporary population is calculated. The population is then subjected to non-dominated sorting according to the objective function value to obtain the non-dominated sorting hierarchy. A preset reference point association mechanism is used to associate each individual in the temporary population with a preset reference point to obtain the reference point association result; Based on the non-dominated sorting hierarchy and the association result of the reference point, a dynamic elite selection strategy is adopted to determine the next generation population from the temporary population. The next generation population is then used as the initial population to perform at least one of the selection, crossover, and mutation processes on the initial population to generate the offspring population of the initial population. This process continues until a preset termination condition is met, resulting in the optimal solution set for the engineering requirement data.

4. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 3, characterized in that, The preset constraint rules include at least gradation constraints, oil-aggregate ratio constraints, and volume index constraints. The step of performing constraint checks on each individual in the offspring population according to the preset constraint rules, identifying individuals that fail the constraint check as violating individuals, and adjusting the decision variables of the violating individuals to obtain adjusted individuals that satisfy the preset constraint rules, and using these adjusted individuals to form a repair population with the individuals that pass the constraint check, includes: When an individual material violates the gradation constraint, the aggregate throughput of each sieve aperture size is reordered, and values ​​exceeding the set range are adjusted to the nearest upper or lower limit value. When an individual violates the oil-stone ratio constraint, the oil-stone ratio of the violating individual will be adjusted to the upper or lower limit value that is closest to the oil-stone ratio constraint. When an individual violates the volume index constraint, the gradation parameters and the oil-aggregate ratio are randomly adjusted within the range of gradation constraints and oil-aggregate ratio constraints, and the volume index is recalculated until the volume index meets the constraint conditions or reaches the preset number of adjustments.

5. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 3, characterized in that, The step of associating each individual in the temporary population with a preset reference point using a preset reference point association mechanism to obtain the reference point association result includes: Map each individual in the population to the target space where the preset reference point is located to obtain the normalized target vector of each individual in the population; Calculate the orientation angle and Euclidean distance between each individual in the population and the preset reference point based on the normalized target vector; Find the reference point with the smallest angle and the reference point with the smallest distance, and calculate the crowding degree of the reference point with the smallest angle and the crowding degree of the reference point with the smallest distance. By comparing the crowding of the reference point with the smallest angle with the crowding of the reference point with the smallest distance, a preset reference point associated with the individual is determined.

6. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 3, characterized in that, The step of determining the next generation population from the temporary population using a dynamic elite selection strategy based on the non-dominated ranking hierarchy and the association result of the reference point includes: Individuals within the same non-dominated hierarchy are identified based on the non-dominated ranking hierarchy. A preset evaluation function is used to rank and filter these individuals within the same non-dominated hierarchy, selecting individuals from the current non-dominated hierarchy to serve as the next generation population. The mathematical representation of the preset evaluation function is as follows: in, Let Euclidean distance be the distance between the individual and the reference point. The angle between the individual and the reference direction. This is the adjustment function for the evolutionary stage.

7. The multi-objective optimization design method for asphalt mixtures based on genetic algorithms according to claim 1, characterized in that, The preset constraints include gradation conditions, oil-aggregate ratio conditions, or volume index conditions, wherein the gradation condition is expressed as: in, Indicates the size of the sieve opening. The aggregate throughput rate and These represent the lower and upper limits of the sieve aperture throughput, respectively. The oil-stone ratio condition is expressed as: in, This indicates the asphalt-aggregate ratio in asphalt mixtures. and These represent the lower and upper limits of the oil-stone ratio, respectively. The volume index conditions are expressed as follows: in, Represents the first obtained through the mapping relationship model A volume index value, and These represent the lower and upper limits of the volume index value, respectively.

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