Asphalt pavement maintenance decision-making method based on multi-objective function

Abstract

The invention discloses an asphalt pavement maintenance decision-making method based on a multi-objective function. The method comprises the following steps: S1, constructing a highway asphalt pavement maintenance measure library; s2, calculating the total carbon emission amount of each maintenance measure in S1; s3, the economic cost of each maintenance measure in the S1 is calculated; s4, calculating an evaluation index of the asphalt pavement maintained by each maintenance measure in the S1; s5, dividing the asphalt pavement into a plurality of road section units, and establishing a 0-1 linear programming model; s6, solving the model established in the step S5 based on an NSGA-II algorithm to obtain a group of non-dominated solutions; and S7, selecting an optimal solution from the non-dominated solutions obtained in the step S6 by adopting an ideal point method to obtain an optimal maintenance measure of each road section unit. According to the method, the problems that factors such as economic benefits, pavement performance and traffic conditions are pursued unilaterally in the project-level asphalt pavement maintenance decision-making process, the influence of a maintenance scheme on the environment is neglected, and decision-making is carried out only by relying on subjective experience of engineers are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of road engineering, and more specifically, to an asphalt pavement maintenance decision method based on multi-objective functions. Background Art

[0002] Highway project-level asphalt pavement maintenance decisions are often based on the results of pavement disease detection, combined with the experience of engineers, to select a final maintenance plan from several suitable candidate plans. This method of determining maintenance measures entirely based on the experience of experts has not been scientifically and rationally calculated and decided, and there are mainly the following problems: 1) The maintenance measures database is not sound, and the maintenance plans included are not specific enough, and it is not possible to accurately optimize the maintenance plan selection according to the specific disease type of the maintenance unit; 2) When implementing asphalt pavement maintenance projects, the impact of maintenance carbon emissions on the environment is not considered, and only considering maintenance benefits and maintenance costs lacks scientificity and rationality; 3) There is a lack of research on customized maintenance of special sections in the current highway project-level asphalt pavement maintenance. For example, for maintenance sections specially designated by the owner, reasonable methods should be used and reasonable maintenance decisions should be made based on the actual pavement damage.

[0003] In the decision-making of asphalt pavement maintenance at the highway project level, the most important goals are maintenance benefits, maintenance costs and maintenance carbon emission levels. However, in actual engineering, multiple goals are mutually restricted and contradictory, and it is impossible to achieve the optimal goal at the same time. Therefore, how to use multi-objective optimization theory and algorithms to reasonably make optimization decisions is a problem that needs to be solved. Since there are a large number of maintenance measures in the maintenance unit and maintenance measure library, it is difficult to directly solve the optimization problem. How to reduce the scale of the optimization problem is also a key issue. Summary of the invention

[0004] The purpose of the present invention is to provide an asphalt pavement maintenance decision-making method based on multi-objective functions in order to solve the above problems.

[0005] In order to achieve these purposes and other advantages according to the present invention, a method for asphalt pavement maintenance decision-making based on a multi-objective function is provided, comprising the following steps:

[0006] S1. Construct a highway asphalt pavement maintenance measure library, wherein the measure library includes multiple groups of measure groups, each of which corresponds to a different pavement maintenance thickness, and each of which includes multiple different maintenance measures;

[0007] S2, calculate the total carbon emissions of each maintenance measure in S1;

[0008] S3. Calculate the economic cost of each maintenance measure in S1;

[0009] S4, calculating the evaluation index of the asphalt pavement after each maintenance measure in S1, wherein the evaluation index at least includes the base structure strength index BSSI;

[0010] S5. Divide the asphalt pavement into multiple road section units and establish a 0-1 linear programming model with X ij is the decision variable, the maintenance benefit, maintenance cost and total carbon emission of the road section unit are taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance and the road section unit can only adopt one maintenance measure at most as the constraint conditions, among which, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0;

[0011] S6. Solve the 0-1 linear programming model established in S5 based on the NSGA-Ⅱ algorithm to obtain a set of non-dominated solutions;

[0012] S7. Use the ideal point method to select the optimal solution from the non-dominated solutions obtained in S6 to obtain the optimal maintenance measures for each road section unit.

[0013] Preferably, in the asphalt pavement maintenance decision method based on a multi-objective function, the calculation method of the maintenance benefit in S5 is as follows:

[0014]

[0015] Among them, x is a two-dimensional matrix of decision variables, , n is the number of road section units, m is the number of maintenance measures;

[0016] The pavement performance of section i is determined by q evaluation indicators, which are expressed by vector r i Represents the state of road segment i, that is:

[0017]

[0018] Among them, d i It is an evaluation index of pavement performance;

[0019] By vector It indicates the state of the road section after using the jth maintenance measure, that is:

[0020]

[0021] For the i-th road section, after adopting the j-th maintenance measure, its benefit improvement value is , that is, the vector Sum all elements of :

[0022] .

[0023] Preferably, in the project-level asphalt pavement maintenance decision method considering carbon emissions, the calculation method of the maintenance cost in S5 is as follows:

[0024]

[0025] in, is the width of the i-th road section; is the length of the i-th road segment; is the cost per square meter of the jth maintenance measure.

[0026] Preferably, in the project-level asphalt pavement maintenance decision method considering carbon emissions, the calculation method of the total carbon emissions from maintenance in S5 is as follows:

[0027]

[0028] in, is the carbon emission per square meter of the jth conservation measure.

[0029] Preferably, in the project-level asphalt pavement maintenance decision-making method considering carbon emissions, S5 specifically includes:

[0030] S51, establish a pre-processing 0-1 linear programming model, with X ij is the decision variable, the maintenance benefit of the road section unit is taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance, and the road section unit can only adopt one maintenance measure at most as the constraint conditions. Among them, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0;

[0031] S52, solving the preprocessing 0-1 linear programming model by Gurobi, and allocating n road section units to each of the maintenance measure groups in an optimal manner;

[0032] S53, establishing the second-stage 0-1 linear programming model for each road section unit in the maintenance measure group.

[0033] Preferably, in the project-level asphalt pavement maintenance decision-making method considering carbon emissions, the first-stage 0-1 linear programming model is as follows:

[0034]

[0035]

[0036] in, is the maximum maintenance cost of the road section unit; is the total carbon emission of road section maintenance; It is the minimum value of BSSI after maintenance of the road section unit; It is the BSSI value of the road section unit maintenance.

[0037] Preferably, in the project-level asphalt pavement maintenance decision-making method considering carbon emissions, the second stage 0-1 linear programming model is as follows:

[0038]

[0039]

[0040] in, It is the minimum improvement coefficient of maintenance efficiency.

[0041] Preferably, in the project-level asphalt pavement maintenance decision-making method considering carbon emissions, solving the 0-1 linear programming model established in S5 based on the NSGA-Ⅱ algorithm specifically includes the following steps:

[0042] S6.1. Generate initial parent population , sort all individuals according to the non-dominated relationship and determine the fitness value;

[0043] S6.2. Use crossover and mutation operations to generate a descendant population Q of size N 0 , and then the new offspring population Q generated by the tth generation t and the parent population P t Combined into a population R of size 2N t , R t Perform non-dominated sorting and construct non-dominated solution sets Z of all different levels i and calculate the degree of crowding;

[0044] S6.3. Sort the non-dominated solution set by crowding distance, find the top N solutions according to fitness, and form the parent population P for the next iteration. i Iterate the above steps and when the number of individuals in the non-dominated solution set generated by sorting is sufficient to fill P t+1 When , the maximum evolutionary generation is reached, the result converges, the iteration is terminated, and a set of non-dominated solutions is obtained.

[0045] Preferably, in the project-level asphalt pavement maintenance decision method considering carbon emissions, selecting the optimal solution from the non-dominated solutions obtained in S6 using the ideal point method specifically includes the following steps:

[0046] S7.1. Solve the three single-objective problems in the second-stage 0-1 linear programming model under the same constraints. The solution results are used as reference points for selecting the optimal solution from the Pareto frontier. The constraints in the second-stage 0-1 linear programming model are abbreviated as , the three single-objective optimization problems are as follows:

[0047] Maximizing maintenance benefits of road section units:

[0048]

[0049]

[0050] Minimized total carbon emissions of road section maintenance:

[0051]

[0052]

[0053] Minimum maintenance cost of road section unit:

[0054]

[0055]

[0056] S7.2, let the optimal solutions of the above three problems be , and , the coordinates of the reference point in the three-dimensional solution space are , then the decision variables corresponding to the optimal solution on the Pareto frontier can be solved as follows:

[0057]

[0058] in, It is a matrix with n rows and m columns, indicating which maintenance measure is selected for a certain road section.

[0059] The beneficial effects of the present invention are:

[0060] The project-level asphalt pavement maintenance decision-making method considering carbon emissions of the present invention solves the problem of one-sided pursuit of economic benefits, road performance and traffic conditions in the decision-making process of highway asphalt pavement maintenance, while ignoring the impact of maintenance plans on the environment, and the problem of relying solely on the subjective experience of engineers to make decisions. The method disclosed in the present invention can take into account environmental impact, maintenance cost and maintenance benefit, and can obtain the optimal solution of multi-objective balance, and adopt the optimal asphalt pavement maintenance plan according to the calculation results.

[0061] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The carbon emission calculation project of the highway project-level asphalt pavement maintenance plan described in the present invention;

[0063] Figure 2 A decision tree model for customizing maintenance sections in highway project-level asphalt pavement maintenance according to the present invention;

[0064] Figure 3 The basic steps of the NSGA-II algorithm for multi-objective optimization described in the present invention;

[0065] Figure 4 is the first set of Pareto frontiers, reference points and optimal reconciliation solutions in an embodiment of the present invention;

[0066] Figure 5 The second group of Pareto frontiers, reference points and optimal reconciliation solutions in an embodiment of the present invention;

[0067] Figure 6 The third group of Pareto frontiers, reference points and optimal reconciliation solutions in the embodiment of the present invention;

[0068] Figure 7 This is the fifth set of Pareto frontiers, reference points, and optimal reconciliation solutions in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The present invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0070] An embodiment of the present invention provides a project-level asphalt pavement maintenance decision-making method considering carbon emissions, comprising the following steps:

[0071] S1. Construct a highway asphalt pavement maintenance measure library, wherein the measure library includes multiple groups of measure groups, each of which corresponds to a different pavement maintenance thickness, and each of which includes multiple different maintenance measures;

[0072] Specifically, the maintenance measures are divided into five intensities according to the maintenance thickness: M1 maintenance thickness is 0-3cm, M2 maintenance thickness is 4-5cm, M3 maintenance thickness is 5-10cm, M4 maintenance thickness is 10-18cm, and M5 maintenance thickness is greater than 18cm. Each type of maintenance intensity includes a variety of specific maintenance measures, as shown in Table 1.

[0073] Table 1 Maintenance measures library

[0074]

[0075] S2, calculate the total carbon emissions of each maintenance measure in S1;

[0076] Specifically, different measures in highway asphalt pavement maintenance correspond to different carbon emissions. The carbon emission calculation of each maintenance measure takes into account the equivalent carbon emissions of five items: road milling machinery fuel consumption, waste transportation vehicle fuel consumption, air pollutant emissions during raw material production, raw material transportation vehicle fuel consumption, and construction machinery fuel consumption. Equivalent carbon emissions refer to the greenhouse gases generated by various energy consumption during highway maintenance, which are equivalent to CO 2 Emissions, in kgCO 2 e. The carbon emission items of each maintenance measure calculated in this project are as follows Figure 1 shown.

[0077] In this embodiment, the carbon emission calculation content is the carbon emission index of each measure in the maintenance database, that is, 2 The total amount of carbon emissions generated by implementing each maintenance measure on the road surface. It should be noted that since the treatment depths corresponding to each maintenance measure are different, the calculation of physical quantities involving volume should take different treatment depths according to actual conditions.

[0078] This embodiment uses the carbon emission factor method to calculate the carbon emissions of the highway maintenance and treatment process, and calculates the carbon emission index of the maintenance measures through the activity intensity and the corresponding carbon emission factor. The carbon emission factors used include fossil energy carbon emission factors and electric energy carbon emission factors, as shown in Table 2.

[0079] Table 2 Energy types and their equivalent carbon emissions

[0080]

[0081] (1) Carbon emissions from raw material production

[0082] The carbon emission model of the raw material production stage is the sum of carbon emissions generated by the raw materials used for pavement construction during the production stage. In a certain maintenance measure, the carbon emissions of raw material production The calculation is as follows:

[0083]

[0084] In the formula, n is the number of raw material types required in a certain maintenance and repair measure; For the Amount of raw materials used (kg); To produce each kilogram Carbon emissions of raw materials (kgCO 2e / kg). Raw materials include asphalt, aggregate, cement and mineral powder, etc. The equivalent carbon emissions are shown in Table 3.

[0085] Table 3 Raw materials and their equivalent carbon emissions

[0086]

[0087] (2) Carbon emissions during the construction phase

[0088] ① Mixing of mixed materials

[0089] Asphalt pavement mixture mixing is mainly divided into asphalt mixture mixing and stabilized soil mixture mixing. The carbon emissions in the mixing process include the energy consumption emissions of the loader in the mixing station and the energy consumption emissions of the mixing equipment.

[0090] a. Carbon emissions from material transfer machinery in mixing plants

[0091] Assume that a certain maintenance measure requires the use of m types of mixed materials. The carbon emissions of the material transfer machinery used in the mixing station are:

[0092]

[0093] In the formula, To use this measure, Volume of the mixture (m 3 ); For loading 1 m 3 No. The demand for material transfer machinery for this type of mixture (machine shift / m 3 ); Carbon emission factor for fuel used in material handling machinery (kgCO 2 e / kg); For the Fuel consumption of material transfer machinery configured in this type of mixture mixing station (kg / shift).

[0094] b. Carbon emissions from mixing equipment

[0095] Assume that a certain maintenance measure requires the use of m types of mixtures. The carbon emissions generated by the mixing equipment in the mixing station are:

[0096]

[0097] In the formula, To use this measure, Volume of the mixture (m 3 ); Mixing equipment for 1 m 3 No. The number of loaders required for each mixture (unit / m3 ); is the carbon emission factor of the fuel used in the mixing equipment (kgCO 2 e / kg); For the Fuel consumption of each type of mixed material mixing equipment (kg / shift); is the average carbon emission factor of the power grid (kgCO 2 e / kWh); For the Power consumption of various mixture mixing equipment (kWh / shift).

[0098] In summary, the total carbon emissions generated by a certain maintenance measure during the mixture mixing stage is:

[0099]

[0100] ②Mixed material transportation

[0101] The calculation of carbon emissions during the transportation of mixed materials starts from the time when the mixed materials are unloaded from the mixing station storage hopper to the delivery truck after the mixing is completed, and ends when the mixed materials are transported to the construction site. The carbon emission source of this process is the carbon emissions generated by the fuel consumption in the transportation vehicle, and the emissions of the materials themselves during the transportation stage are not considered. Assume that a single transportation is fully loaded, and consider the fuel consumption of the return trip without load. Assume that a certain maintenance measure requires the use of m types of mixed materials. The carbon emissions generated by this maintenance measure during transportation are:

[0102]

[0103] In the formula, To use this measure, The mass of the mixture (kg); For transport Full load of the transport truck for the mixture (kg); For transport Carbon emission factor of a truck transporting a mixture (kgCO 2 e / kg); For the Transportation distance of the mixed materials (km); is the fuel consumption of the transport vehicle when fully loaded (kg / km); It is the fuel consumption of the transport vehicle without load (kg / km).

[0104] ③Mixture paving

[0105] The carbon emission source of the mixture paving process is mainly the carbon emission generated by the fuel consumption of the paver during the paving process. The paver consists of two parts: the main machine and the ironing device. The main machine provides the power required for paving, and the flat plate has the functions of self-heating, self-leveling, and road crown adjustment. If a certain maintenance measure requires paving a u-layer structure, then the total carbon emission during the paving process using this maintenance measure is:

[0106]

[0107] In the formula, is the carbon emission factor of the fuel used by the paving machinery (kgCO 2 e / kg); The number of times of layer paving; is the paving area of ​​the vth layer in a certain maintenance measure (take 1m 2 ); is the demand for paving machinery (shift / m 2 ); Fuel consumption of paving equipment (kg / shift).

[0108] ④Mixture rolling

[0109] Mixture rolling is the process of compressing a certain volume of hot mix asphalt concrete into a smaller volume through various types of rolling machinery and certain rolling processes. The carbon emission source of the road rolling process is mainly caused by the fuel consumption of the roller:

[0110]

[0111] In the formula, is the carbon emission factor of fuel used in rolling machinery (kgCO 2 e / kg); is the number of layer rolling; is the rolling area of ​​the vth layer in a certain maintenance measure (take 1m 2 ); is the demand for rolling machinery (shift / m 2 ); It is the fuel consumption of rolling equipment (kg / shift).

[0112] (3) Carbon emissions from original road surface treatment

[0113] During the maintenance process, the original road surface disposal work mainly includes the milling of the asphalt pavement structure layer and the transportation and recycling of waste materials.

[0114] ①Milling

[0115] Some measures in the maintenance measures database require milling of the original diseased road surface before implementation. For such measures, the calculation method of carbon emissions caused by milling is as follows:

[0116]

[0117] In the formula, is the carbon emission factor of fuel used in milling machinery (kgCO 2 e / kg); The required milling area for a certain maintenance measure (take 1m 2 ); is the demand for milling machinery (shift / m 2 ); Fuel consumption of milling equipment (kg / shift).

[0118] ② Waste transportation

[0119] The waste generated by the original road surface disposal needs to be transported for recycling and disposal. The calculation method of carbon emissions generated during the waste transportation process is as follows:

[0120]

[0121] In the formula, Carbon emission factor for fuel used in waste transport machinery (kgCO 2 e / kg); For some 1m 2 Volume of waste generated by milling before maintenance measures are implemented (m 3 ), ,in is the milling depth; is the amount of waste transport machinery used (shift / m 3 ); It is the fuel consumption of transport machinery (kg / shift).

[0122] In summary, the calculation method for the carbon emission index of implementing any maintenance measure in the maintenance measures database is:

[0123]

[0124] Wherein, set M is a set consisting of carbon emissions from raw material production, carbon emissions from the construction phase, and several sub-processes in the original pavement disposal process.

[0125] S3. Calculate the economic cost of each maintenance measure in S1;

[0126] Specifically, the economic cost model includes pavement pretreatment costs, raw material costs, construction machinery costs and labor costs. The economic costs of each specific maintenance measure are determined based on the "Highway Engineering Cost Management Measures" and "Highway Engineering Machinery Unit Cost Quota" issued by the Ministry of Transport of the People's Republic of China.

[0127] S4, calculating the evaluation index of the asphalt pavement after each maintenance measure in S1, wherein the evaluation index at least includes the base structure strength index BSSI;

[0128] Specifically, considering the highway project with hidden diseases of asphalt pavement, the five pavement performance evaluation indicators are the pavement skid resistance index SRI, the pavement rutting depth index RDI, the pavement ride quality index RQI, the pavement damage condition index PDCI and the base structure strength index BSSI. This embodiment uses the improvement values ​​of these five key indicators to judge the effectiveness of maintenance measures.

[0129] The economic costs, carbon emissions and benefit improvement levels corresponding to each maintenance measure are summarized in Table 4.

[0130] Table 4 Benefits, unit prices and carbon emission coefficients of maintenance measures

[0131]

[0132] In highway maintenance projects, for maintenance sections specially designated by the owner, a decision tree model is used to select maintenance measures. The decision tree model matches the road surface in a specific state with various maintenance measures, and can make reasonable maintenance decisions based on the actual damage of a certain road section. According to 5 evaluation indicators, the road surface state is divided into 18 types, and each road surface state corresponds to a maintenance intensity, and the decision tree model of maintenance measures is obtained (M0 represents daily maintenance), such as Figure 2 shown.

[0133] S5. Divide the asphalt pavement into multiple road section units and establish a 0-1 linear programming model with X ij is the decision variable, the maintenance benefit, maintenance cost and total carbon emission of the road section unit are taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance and the road section unit can only adopt one maintenance measure at most as the constraint conditions, among which, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0;

[0134] Specifically, the decision variable X of the 0-1 linear programming model is ij , indicating whether the jth measure in the maintenance database is adopted for the i-th section of road. If so, X ij =1, if not adopted then X ij =0.

[0135] The objective function of the 0-1 linear programming model is:

[0136] 1. Maintenance benefits of road section units

[0137] The pavement maintenance benefit is determined by the difference between the evaluation index score of the pavement maintenance measures (as shown in Table 4 above) and the status of the road section to be maintained.

[0138] Since the road performance of a road section is determined by q evaluation indicators, the available vector Represents the state of road segment i, that is:

[0139]

[0140] Similarly, the available vector It indicates the state of the road section after using the jth maintenance measure, that is:

[0141]

[0142] Therefore, for the i-th road section, after adopting the j-th maintenance measure, the benefit improvement value of the road section is The calculation method is: transform the vector The sum of all elements of is:

[0143]

[0144] In summary, taking the overall benefit improvement value of the maintenance project as the objective function, the expression is constructed as follows:

[0145]

[0146] In the formula, —two-dimensional matrix of decision variables, .

[0147] 2. Maintenance cost of road section unit

[0148] The total cost of highway maintenance project is calculated based on the cost per square meter of the jth maintenance measure. Sure:

[0149]

[0150] In the formula, —The width of the i-th road section unit; —The length of the i-th section unit; —two-dimensional matrix of decision variables, .

[0151] 3. Total carbon emissions from road section maintenance

[0152] In the highway maintenance project, the total carbon emissions of maintenance are calculated based on the carbon emission index per square meter of the jth maintenance measure. Sure:

[0153]

[0154] In the formula, —The width of the i-th road section unit; —The length of the i-th section unit; —two-dimensional matrix of decision variables, .

[0155] Constraint function of the 0-1 linear programming model:

[0156] When using optimization models to make decisions for highway maintenance projects, the actual situation should be fully considered, mainly including the project's funding limitations, the degree of improvement in maintenance benefits, and some necessary constraints to ensure the rationality of the mathematical optimization model.

[0157] 1. Funding restrictions

[0158] In the actual maintenance process, it is necessary to ensure that the sum of the costs of all maintenance measures taken is within the funding limit. Assuming that the project funding is, then the constraints should satisfy:

[0159]

[0160] 2. Maintenance benefit constraints

[0161] After the highway is maintained, if its benefits need to be increased by a certain percentage, the following constraints should be added:

[0162]

[0163] This constraint represents the minimum improvement in the benefits of the highway after maintenance, where: It is the minimum benefit improvement coefficient, which indicates the minimum multiple of the benefit improvement after expressway maintenance compared with before maintenance.

[0164] In order to make The value of meets the model requirements. The lower bound is 0 and the upper bound is ,in The following optimization model is obtained:

[0165]

[0166]

[0167] therefore, The value range of is: .

[0168] 3. Ensure that the base indicators of each road section unit after maintenance meet the minimum requirements

[0169] According to the guidance of "strong base layer, weak surface layer", when selecting road section units for maintenance, the sections with more serious damage to the base layer should be considered first. Therefore, it is stipulated in the constraints that the base layer indicators of all sections after maintenance must meet the minimum requirements, that is, BSSI is greater than the threshold . Let the i-th road section unit after maintenance be , calculated as follows:

[0170]

[0171] In the formula, — the status of road segment i, ; —The state of the road section after the jth type of maintenance, .

[0172] It can be seen from this that is also a q-dimensional vector, and The number of evaluation indicators in S4 is 5, then q=5, and represents the BSSI of the i-th road segment unit, then the constraint can be expressed as:

[0173]

[0174] 4. Each road section unit can only adopt one maintenance measure at most

[0175] Each road section unit can only use one maintenance measure at most, which is a necessary constraint to ensure the rationality of the mathematical model. This constraint on the model can avoid the unreasonable situation that a road section is maintained with both measure A and measure B. That is, a road section unit either uses one measure in the database or does not maintain it temporarily. The constraint is expressed as follows:

[0176]

[0177] S5 specifically includes:

[0178] First-stage optimization: When there are too many solutions in the maintenance database, the scale of the optimization problem will increase dramatically, and the solution of the integer programming problem will become quite difficult. Therefore, a two-stage optimization is considered. First, the solutions in the maintenance database are divided into l categories according to the treatment depth. The representative maintenance measures of each category are the measures with the best maintenance benefits in that category. In the first stage, the single-objective optimization method is used to select the appropriate maintenance category for each maintenance unit. In the second stage, multi-objective optimization is used in each maintenance category to subdivide the maintenance measures for each maintenance unit.

[0179] S51, establish a pre-processing 0-1 linear programming model, with X ijis the decision variable, the maintenance benefit of the road section unit is taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance, and the road section unit can only adopt one maintenance measure at most as the constraint conditions. Among them, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0;

[0180] The first stage 0-1 linear programming model is as follows:

[0181]

[0182]

[0183] in, is the maximum maintenance cost of the road section unit; is the total carbon emission of road section maintenance; It is the minimum value of BSSI after maintenance of the road section unit; It is the BSSI value of the road section unit maintenance.

[0184] S52, solving the preprocessing 0-1 linear programming model by Gurobi, and allocating n road section units to each of the maintenance measure groups in an optimal manner;

[0185] S53, establishing the second-stage 0-1 linear programming model for each road section unit in the maintenance measure group.

[0186] Second-stage optimization: Based on the optimization in the first stage, for each maintenance unit and the specific maintenance measures in the class, considering the three objective functions and necessary constraints, the second-stage 0-1 linear programming model is established for the unit set N of the conventional road section to be maintained as follows:

[0187]

[0188]

[0189] in, is the minimum improvement coefficient of maintenance benefit. Note that the above three objective functions are all decision variables function, since the target The maximum value can be converted into The minimum value of , so the three objective functions are written as the target vector , and find its minimum value. Objective function After taking the opposite number, it can be restored to the maximum value, while the decision variable space remains unchanged.

[0190] S6. Solve the 0-1 linear programming model established in S5 based on the NSGA-Ⅱ algorithm to obtain a set of non-dominated solutions;

[0191] Combination Figure 3 As shown in the figure, the basic operation steps of the NSGA-II algorithm in the optimization of highway asphalt pavement maintenance decision are as follows:

[0192] S6.1. Generate initial parent population , sort all individuals according to the non-dominated relationship and determine the fitness value;

[0193] S6.2. Use crossover and mutation operations to generate a descendant population Q of size N 0 , and then the new offspring population Q generated by the tth generation t and the parent population P t Combined into a population R of size 2N t , R t Perform non-dominated sorting and construct non-dominated solution sets Z of all different levels i and calculate the degree of crowding;

[0194] S6.3. Sort the non-dominated solution set by crowding distance, find the top N solutions according to fitness, and form the parent population P for the next iteration. i Iterate the above steps and when the number of individuals in the non-dominated solution set generated by sorting is sufficient to fill P t+1 When , the maximum evolutionary generation is reached, the result converges, the iteration is terminated, and a set of non-dominated solutions is obtained.

[0195] A set of non-dominated solutions, namely the Pareto frontier, is obtained by solving the NSGA-Ⅱ algorithm. The distribution in the three-dimensional solution space is a series of points, set as set V. These points are approximately located on a space curve. , and Represents three objective functions, and the points on the curve are represented by R, then .

[0196] S7. Use the ideal point method to select the optimal solution from the non-dominated solutions obtained in S6 to obtain the optimal maintenance measures for each road section unit.

[0197] Specifically, they include:

[0198] S7.1. Solve the three single-objective problems in the second-stage 0-1 linear programming model under the same constraints. The solution results are used as reference points for selecting the optimal solution from the Pareto frontier. The constraints in the second-stage 0-1 linear programming model are abbreviated as , the three single-objective optimization problems are as follows:

[0199] Question 1: Maximize the maintenance benefits, that is, solve model M-1:

[0200]

[0201] (M-1)

[0202] Problem 2: Minimize the total carbon emissions from maintenance, that is, solve model M-2:

[0203]

[0204] (M-2)

[0205] Let the optimal solutions of the above three problems be , and , then the coordinates of the reference point in the three-dimensional solution space are . Then the decision variables corresponding to the optimal solution on the Pareto frontier can be solved as follows:

[0206] (M-4)

[0207] in, It is a matrix with n rows and m columns, indicating which maintenance measure is selected for a certain road section.

[0208] In order to verify the above embodiment, a certain highway maintenance project is taken as an example in the embodiment of the present invention to further illustrate the maintenance multi-objective decision-making method in the embodiment of the present invention.

[0209] A certain expressway underwent a major overhaul of the entire line in 2010. The maintenance section selected in this embodiment is located in the upward main lane, with the starting and ending pile numbers being K2091+000~K2097+400. The inspection data of this section in 2022 is shown in Table 5.

[0210] Table 5 Overview of maintenance section units

[0211]

[0212] (1) Phase 1

[0213] Since there are many maintenance plans and sections to be maintained, it is difficult to directly use a multi-objective evolutionary algorithm to solve the problem. Therefore, in the first stage, a single-objective optimization was used. First, the 31 maintenance measures were divided into 5 groups according to the treatment depth in the maintenance plan library, and then a single-objective maintenance model was established. The integer programming problem was solved by Gurobi to allocate the 65 maintenance units to each group in the best way.

[0214] Specifically, taking M-5 as the mathematical model, the total maintenance budget of this project is 6 million yuan, and the carbon emission control amount is 400tCO 2 e. According to the "strong base" constraint, the BSSI index value of each maintenance unit must be above 85 points. The solution results of the single-objective model are shown in Table 6.

[0215] Table 6 Optimization results of the first stage

[0216]

[0217] The maximum maintenance benefit of the first stage decision is 5825.7 points; the maintenance cost is 4.98075 million yuan, which is less than the given funding constraint of 6 million yuan; the total maintenance carbon emission is 399.97 tons, which is less than the carbon emission limit of 400 tons. The number of units to be maintained using the first group of maintenance measures is 4, the number of units to be maintained using the second group of maintenance measures is 12, the number of units to be maintained using the third group of maintenance measures is 39, no unit uses the fourth group of maintenance measures, the number of units to be maintained using the fifth group of maintenance measures is 8, and units 46 and 65 do not need maintenance because they are in good condition.

[0218] (2) Second stage

[0219] After grouping, a multi-objective optimization method is used within each group to make decisions on the maintenance plan. The algorithm is a fast non-dominated sorting genetic algorithm NSGA-Ⅱ with an elite strategy.

[0220] ①The first set of multi-objective optimization results

[0221] The first group (M1) has 4 units to be maintained, including 8 maintenance measures, a capital constraint of 105,000 yuan, and an efficiency increase of at least 5% on the original basis. The number of individuals in the NSGA-Ⅱ algorithm population is set to 100, the maximum evolutionary generation is 5000, the mutation probability is 0.2, the crossover probability is 0.85, and real number coding is used. Solve the M-1, M-2 and M-3 models respectively to obtain the ideal point, and the spatial coordinates of the ideal point after normalization Solving the M-4 model yields the optimal harmonic solution , the corresponding decision variable matrix is:

[0222]

[0223] That is, the four maintenance units all adopt the third scheme in the maintenance database for maintenance.

[0224] The multi-objective optimization results are as follows: Figure 4 As shown in the figure, the red dots in the three-dimensional space represent the Pareto frontier, the green dots represent the ideal solution, and the blue diamond dots represent the optimal harmonic solution to the optimization problem.

[0225] ②The second set of multi-objective optimization results

[0226] The second group (M2) has 12 units to be maintained, including 6 maintenance measures, a funding constraint of 540,000 yuan, and an increase of at least 5% in benefits. The number of individuals in the NSGA-Ⅱ algorithm population is set to 100, the maximum evolutionary generation is 5000, the mutation probability is 0.2, the crossover probability is 0.85, and real number coding is used. The above objective function is normalized in the same way, and the data is converted to the interval [0, 1]. Solve the M-1, M-2 and M-3 models respectively to obtain the ideal point, and the spatial coordinates of the ideal point after normalization are Solving the M-4 model yields the optimal harmonic solution , the corresponding decision variable matrix is:

[0227] ,

[0228] That is, among the 12 maintenance units, the 35th, 37th, 48th, 51st, 52nd, 53rd and 54th units adopt the 11th maintenance measure, the 59th unit adopts the 10th maintenance measure, and the remaining units are not maintained. Similarly, the multi-objective optimization results are as follows: Figure 5 shown.

[0229] ③The third group of multi-objective optimization results

[0230] The third group (M3) has 39 units to be maintained, including 5 maintenance measures, with a funding constraint of 2.89575 million yuan, and the benefits are at least 5% higher than the original basis. The number of individuals in the NSGA-Ⅱ algorithm population is set to 100, the maximum evolutionary generation is 5000, the mutation probability is 0.2, the crossover probability is 0.85, and real number coding is used. The above objective function is normalized in the same way, and the data is converted to the interval [0, 1]. Solve the M-1, M-2 and M-3 models respectively to obtain the ideal point, and the spatial coordinates of the ideal point after normalization are Solving the M-4 model yields the optimal harmonic solution , the corresponding decision variable matrix is:

[0231]

[0232] The implementation of maintenance measures is consistent with the above. Similarly, the multi-objective optimization results are as follows Figure 6 shown.

[0233] ④The fourth group of multi-objective optimization results

[0234] As a result of the first stage decision, no unit adopted the fourth group (M4) maintenance measures.

[0235] ⑤The fifth group of multi-objective optimization results

[0236] There are 8 maintenance units in the fifth group (M5), including 6 maintenance measures, with a funding constraint of 1.44 million yuan, and the benefits are at least 5% higher than the original basis. Set the number of individuals in the NSGA-Ⅱ algorithm population to 100, the maximum evolutionary generation to 5000, the mutation probability to 0.2, the crossover probability to 0.85, and real number coding. Normalize the above objective function in the same way and convert the data to the [0, 1] interval. Solve the M-1, M-2 and M-3 models respectively to obtain the ideal point, and the spatial coordinates of the ideal point after normalization Solving the M-4 model yields the optimal harmonic solution , the corresponding decision variable matrix is:

[0237] ,

[0238] The implementation of maintenance measures is consistent with the above. Similarly, the multi-objective optimization results are as follows Figure 7 shown.

[0239] In summary, by comprehensively considering the three important indicators of maintenance benefits, maintenance costs and maintenance carbon emissions, the two-stage optimization method arranged reasonable maintenance measures for 65 maintenance units from the maintenance database. While ensuring benefits, it achieved low-cost and clean maintenance of asphalt pavement, bringing good economic and environmental benefits.

[0240] The two-stage optimization decision results are shown in Table 7:

[0241] Table 7 Two-stage optimization decision results

[0242]

[0243] Among them, the specific optimization results of the second stage are shown in Table 8:

[0244] Table 8 Specific optimization results of the second stage

[0245]

[0246] In summary, after multi-objective optimization, the performance of the maintenance unit was improved by 12.27%, the maintenance cost was only 42.06% of the prescribed limit, and the carbon emissions were 76.23% of the prescribed emission limit.

[0247] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the embodiments shown and described herein.

Claims

1. A multi-objective function-based asphalt pavement maintenance decision-making method, characterized in that: The following steps are involved: S1. Construct a highway asphalt pavement maintenance measure library, wherein the measure library includes multiple groups of measure groups, each of which corresponds to a different pavement maintenance thickness, and each of which includes multiple different maintenance measures; S2, calculate the total carbon emissions of each maintenance measure in S1; S3. Calculate the economic cost of each maintenance measure in S1; S4, calculating the evaluation index of the asphalt pavement after each maintenance measure in S1, wherein the evaluation index at least includes the base structure strength index BSSI; S5. Divide the asphalt pavement into multiple road section units and establish a 0-1 linear programming model with X ij is the decision variable, the maintenance benefit, maintenance cost and total carbon emission of the road section unit are taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance and the road section unit can only adopt one maintenance measure at most as the constraint conditions, among which, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0; S6. Solve the 0-1 linear programming model established in S5 based on the NSGA-Ⅱ algorithm to obtain a set of non-dominated solutions; S7. Use the ideal point method to select the optimal solution from the non-dominated solutions obtained in S6 to obtain the optimal maintenance measures for each road section unit.

2. The asphalt pavement maintenance decision-making method based on multi-objective function according to claim 1, characterized in that: The calculation method of maintenance benefit in S5 is as follows: ； Among them, x is a two-dimensional matrix of decision variables, , n is the number of road section units, m is the number of maintenance measures; The pavement performance of section i is determined by q evaluation indicators, which are expressed by vector r i Represents the state of road segment i, that is: ； Among them, d i It is an evaluation index of pavement performance; By vector It indicates the state of the road section after using the jth maintenance measure, that is: ； For the i-th road section, after adopting the j-th maintenance measure, its benefit improvement value is , that is, the vector Sum all elements of : 。 3. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 2, characterized in that: The calculation method of maintenance cost in S5 is as follows: ； in, is the width of the i-th road section; is the length of the i-th road segment; is the cost per square meter of the jth maintenance measure.

4. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 3, characterized in that: The calculation method for total carbon emissions from maintenance in S5 is as follows: ； in, is the carbon emission per square meter of the jth conservation measure.

5. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 4, characterized in that: S5 specifically includes: S51, establish a pre-processing 0-1 linear programming model, with X ij is the decision variable, the maintenance benefit of the road section unit is taken as the objective function, the maximum maintenance cost of the road section unit, the minimum improvement of the maintenance benefit after maintenance, the minimum BSSI after maintenance, and the road section unit can only adopt one maintenance measure at most as the constraint conditions. Among them, when the i-th road section unit adopts the j-th measure in the maintenance database, X ij =1, when X is not used ij =0; S52, solving the preprocessing 0-1 linear programming model by Gurobi, and allocating n road section units to each of the maintenance measure groups in an optimal manner; S53, establishing a second-stage 0-1 linear programming model for each road section unit in the maintenance measure group.

6. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 5, characterized in that: The first stage 0-1 linear programming model is as follows: in, is the maximum maintenance cost of the road section unit; is the total carbon emission of road section maintenance; It is the minimum value of BSSI after maintenance of the road section unit; It is the BSSI value of the road section unit maintenance.

7. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 6, characterized in that: The second stage 0-1 linear programming model is as follows: in, It is the minimum improvement coefficient of maintenance efficiency.

8. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 7, characterized in that: The 0-1 linear programming model established in S5 is solved based on the NSGA-Ⅱ algorithm, which specifically includes the following steps: S6.

1. Generate initial parent population , sort all individuals according to the non-dominated relationship and determine the fitness value; S6.2, use crossover and mutation operations to generate a sub-generation population Q0 of size N, and then generate the new sub-generation population Q t and the parent population P t Combined into a population R of size 2N t , R t Perform non-dominated sorting and construct non-dominated solution sets Z of all different levels i and calculate the degree of crowding; S6.

3. Sort the non-dominated solution set by crowding distance, find the top N solutions according to fitness, and form the parent population P for the next iteration. i Iterate the above steps and when the number of individuals in the non-dominated solution set generated by sorting is sufficient to fill P t+1 When , the maximum evolutionary generation is reached, the result converges, the iteration is terminated, and a set of non-dominated solutions is obtained.

9. The asphalt pavement maintenance decision-making method based on multi-objective function as claimed in claim 8, characterized in that: The optimal solution is selected from the non-dominated solutions obtained by S6 using the ideal point method, which specifically includes the following steps: S7.

1. Solve the three single-objective problems in the second-stage 0-1 linear programming model under the same constraints. The solution results are used as reference points for selecting the optimal solution from the Pareto frontier. The constraints in the second-stage 0-1 linear programming model are abbreviated as , the three single-objective optimization problems are as follows: Maximizing maintenance benefits of road section units: ； ； Minimized total carbon emissions of road section maintenance: ； ； Minimum maintenance cost of road section unit: ； ； S7.2, let the optimal solutions of the above three problems be , and , the coordinates of the reference point in the three-dimensional solution space are , then the decision variables corresponding to the optimal solution on the Pareto frontier can be solved as follows: ； in, It is a matrix with n rows and m columns, indicating which maintenance measure is selected for a certain road section.

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