A multi-objective decision-making method for sustainable maintenance of large-scale road networks

Abstract

The present invention discloses a multi-objective decision-making method for sustainable maintenance of large-scale road networks, which uses binary conversion and decision trees to carry out section unit-level maintenance decisions for regional road networks; determines the sustainable target values at the section unit level according to the section unit-level maintenance decision results and the spatio-temporal distribution characteristics of traffic flow; merges large-scale section units into small-scale maintenance units based on the principle of decision space dimension reduction and calculates the network-level sustainable target values for carrying out network-level maintenance decisions; uses a multi-objective evolutionary algorithm to solve the optimization model of the network-level sustainable target combination and forms a set of strategies with multiple potential feasible solutions at the network level; determines the final feasible solution through an interactive method, and links the network-level decision result to the section unit level according to the decision space conversion principle. The present invention realizes the solution of the sustainable multi-objective decision-making of large-scale road networks while coordinating the decision results at the network level and the section unit level.

Description

Technical Field

[0001] The present invention belongs to the technical field of road engineering, and particularly relates to a multi-objective decision-making method for sustainable maintenance of large-scale road networks. Background Art

[0002] With the continuous increase in the mileage of asphalt pavements on expressways in China, highway maintenance departments are facing huge challenges in scientifically managing pavement assets. The challenges and pressures they face are mainly reflected in the following aspects: In terms of resource allocation, although pavement maintenance can provide pavement performance, it is accompanied by a large amount of capital consumption, environmental pollution caused by the consumption of asphalt, stones, and mechanical equipment required for the implementation of maintenance technologies, and user delays. How highway maintenance departments make decisions that take into account multiple sustainable development strategic goals under limited resources is extremely important; in terms of spatial distribution, highway pavement maintenance management has characteristics such as many nodes, long routes, and wide areas, making management difficult. With the continuous response to the needs of regional maintenance systems, how to achieve regional large-scale road network unit decision-making is an urgent problem to be solved; in terms of the coordination between network level and section level, pavement maintenance implementation has characteristics such as regionalization and gridification. Maintenance technologies need to be accurately positioned in small-scale pavement grid units, and the group-based maintenance funds supply needs to be allocated to regional maintenance management units. How to coordinate network-level fund decision-making and section-level fund decision-making is a difficult problem that needs to be focused on solving currently.

[0003] In the design of pavement maintenance decision-making methods, although some studies have successfully developed decision-making methods, very few maintenance decision-making methods can conduct resource scheduling for regional large-scale road networks and carry out asset management from a sustainable perspective. Constructing a maintenance decision-making method with functions such as alternative sustainable goals and participatory interactive decision-making is one of the key problems that need to be solved urgently.

[0004] Therefore, in view of the key problems in the asphalt pavement maintenance decision-making in China's expressways in terms of resource allocation, spatial distribution, and the coordination between network level and section level, as well as the technical bottlenecks in the current maintenance decision-making methods in coordinating section-level and network-level decisions, it is necessary to develop a multi-objective decision-making method for sustainable maintenance of large-scale road networks, so as to solve the sustainable multi-objective decision-making of large-scale road networks and coordinate the decision-making results between network level and section level. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the purpose of the present invention is to provide a multi-objective decision-making method for sustainable maintenance of large-scale road networks, which realizes multi-objective decision-making for sustainable maintenance of large-scale road networks.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions to achieve:

[0007] A multi-objective decision-making method for sustainable maintenance of large-scale road networks, which uses binary conversion and decision trees to carry out section unit-level maintenance decisions for regional road networks; according to the section unit-level maintenance decision results and the spatio-temporal distribution characteristics of traffic flow, determine four sustainable objective values at the section unit level: user delay cost, maintenance cost, performance, and environmental impact index; based on the principle of decision space dimensionality reduction, merge large-scale section units into small-scale maintenance units, and calculate four sustainable objective values at the network level for subsequent network-level maintenance decision-making; use a multi-objective evolutionary algorithm to solve the optimization model of various sustainable objective combinations at the network level, and provide a set of alternative strategies containing multiple potential feasible solutions at the network level; select the final feasible solution from the alternative strategies through an interactive method, and then link the network-level decision results to the section unit level according to the principle of decision space conversion.

[0008] The present invention further includes the following technical features:

[0009] Specifically, it includes the following steps:

[0010] Step 1, regional section unit-level maintenance decision:

[0011] Construct a combination of maintenance plans with different performance requirements according to the established maintenance technologies, perform binary conversion on the combination of maintenance plans, describe the service performance in the characteristics of the regional road network, establish a decision tree at the section unit level, and use binary arrays to determine the maintenance plans for each section unit.

[0012] Step 2, calculate the sustainable objective values at the section unit level:

[0013] Determine the user delay cost at the section unit level based on the spatio-temporal distribution characteristics of traffic flow, calculate the maintenance cost and environmental impact index at different section unit levels according to the life cycle assessment theory, and calculate the comprehensive performance improvement scores at different section unit levels according to the difference method and normalization.

[0014] Step 3, generate small-scale maintenance units:

[0015] According to the basic information of the regional road network, obtain the key attributes affecting the scheduling of maintenance funds, use the principle of decision space dimensionality reduction to merge large-scale section units into small-scale maintenance units, construct the mapping relationship between the two-level units, and calculate four sustainable objective values at the network level for subsequent network-level maintenance decision-making.

[0016] Step 4, multi-objective optimization calculation:

[0017] Using the maintenance units formed in Step 3 as decision variables, a multi-objective evolutionary algorithm is employed to solve the optimization models formed by different objective combinations. Based on the non-dominated sorting principle, the optimal Pareto-Front surface or curve is determined, and a set of strategies with multiple potential feasible solutions is formed at the network level;

[0018] Step 5, Interactive Decision-Making and Decision Unit Conversion:

[0019] According to the set of multiple potential feasible solution strategies formed in Step 4, the final solution is selected from the set of strategies through an interactive method. Combining the two-level unit mapping relationship constructed in Step 3, the decision-making results at the network level are mapped to the section unit level, and statistical methods are used to describe the distribution of various sustainable target values among section units and maintenance plans.

[0020] Specifically, Step 1 includes:

[0021] Step 1.1, Binary Conversion of Maintenance Plan Combinations:

[0022] Based on the current road network conditions, determine the number of maintenance technology types m, and based on the implementation of maintenance activities, determine the number of maintenance plan combinations n. Let the text format of the plan combination be A, and each plan is composed of a vector a i1 =(a i1 ,…,a ij ,…,a im ), where i = 1~n, j = 1~m, and each element in the vector represents the serial number of the maintenance technology. Then, the construction method of the plan array B n×m is as follows:

[0023]

[0024]

[0025] Step 1.2, When constructing a decision tree at the section unit level for the performance of regional road network characteristics, construct a decision tree based on performance and determine the maintenance plan for each section unit based on this decision tree:

[0026] Let the performance array of the road network be P s×g , where s represents the number of section units in the road network, g represents the number of performance indicators used in the decision tree, and the performance of each section is composed of a vector p s1 =(p s1 ,…,p sg ). Define f s to represent the plan number of section s, and any f s can be found in the plan array B n×mFind a row vector in it that corresponds to it; then the maintenance plan description array F obtained after quantization s is constructed as follows:

[0027]

[0028] where f i = b j1 , …, b jm ), i = 1, …, s; j = 1, …, n. According to the mapping relationship, it can be considered that f i,1 = b j1 , ……, f i,m = b jm .

[0029] Specifically, step 2 includes:

[0030] Step 2.1, before calculating the user delay cost of each section according to the classification of different sustainable goals, the traffic volume Q of each time period of the section unit should be calculated first t,s . Assuming that the traffic volume of section s is AADT s , and the traffic volume flat period time point, the first peak period time point, the first peak period dissipation point, the second peak period time point, and the second traffic volume dissipation point within 0 to 24 hours are t1, t2, t3, t4, t5 respectively, then the traffic volume Q of each time period t,s is calculated as follows:

[0031]

[0032] where c1 to c 10 are constants;

[0033] Step 2.2, before calculating the user delay cost of each section according to the classification of different sustainable goals, based on obtaining the traffic volume Q of each time period of the section unit t,s , combined with the traffic capacity calculation method, the traffic capacity of the closed section during the implementation of the maintenance technology for section s can be obtained as C s,zone , the traffic capacity of the normal section C s,d , define the running speed as V l , and the running speed of the normal section as V c , the length of the section to be maintained is L s , the total length of acceleration and deceleration is L a , the transition section length of the closed section is L p , the start time of implementing the corresponding maintenance technology for each section is t ss , t se , the proportion of the v-th vehicle type in section s is r s,v , and the unit delay cost is cost s,v, then the user delay cost RUC caused by the implementation of maintenance technologies in each road section unit s The calculation method is as follows:

[0034]

[0035]

[0036] Step 2.3, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance plan array F determined for the road network in Step 1.2 s , determine the maintenance cost per unit area UAC of different maintenance technologies according to the life cycle assessment theory m , assuming that the length of the road section s to be maintained is L s , and the width is W s , the maintenance cost LCAC generated after the implementation of the corresponding maintenance technology for road section s can be obtained s The calculation method is as follows:

[0037]

[0038] Step 2.4, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance plan array F determined for the road network in Step 1.2 s , determine the environmental impact index UEI per unit area of different maintenance technologies according to the life cycle assessment theory m , the environmental impact index LCEI generated after the implementation of the corresponding maintenance technology for road section s can be obtained s The calculation method is as follows:

[0039]

[0040] Step 2.5, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m , assume that the number of target performance indicators is P, and define the target performance array OP formed after the implementation of the maintenance plan n×P , then the target performance array TP formed after the implementation of the maintenance plan for each road section can be obtained s×P , the original performance array of each road section is OP s×P , according to the relative value of the target performance and the current performance value, define the weight value α of different performance index types P , the comprehensive performance improvement score RP after the implementation of the corresponding maintenance technology for road section s can be obtained s The calculation method is as follows:

[0041]

[0042] Specifically, step 3 includes:

[0043] Step 3.1: Using the sustainable target values calculated for each road section in steps 2.2 to 2.5 above, in multi-objective optimization, assuming the selected number of objective dimensions is o, the array composed of objective function values is O s×o , select r attributes from the pavement network characteristic attributes to divide s road section units into m maintenance units, so assume the attribute array is I s×r , combine it with O s×o to form an augmented array (I, O), and the construction method of the mapped augmented array (I′, O) is as follows:

[0044]

[0045] Step 3.2: Using the mapped augmented array (I′, O), according to the principle of merging the same elements in the left column array, recalculate the four sustainable target values at the network level, and convert (I′, O) into (I″, O′). The row dimension of (I″, O′) after conversion is k, where the left column array is composed of k numbers (k << s), then the construction method is as follows:

[0046]

[0047] Specifically, step 4 includes:

[0048] Step 4.1: Using the augmented array constructed in step 3.2 above, use the k×o array on the right to construct a mathematical model for multi-objective optimization. Assume the binary decision variable for implementing the maintenance technology for each maintenance unit is X k×1 = [x1, x2, …, x k T , assume the constraint function is H i (X) ≤ 0, then the construction method of the mathematical model is:

[0049] Min.Y = (O″ k×o ) T X k×1

[0050] s.t. H i (X) ≤ 0, (i = 1, 2, …)

[0051] Step 4.2: Based on the non-dominated solution rank sorting principle, use a multi-objective evolutionary algorithm to solve the mathematical model constructed in step 4.1. The obtained Pareto-Front front solution set, assume the number of feasible solutions in the solution set is l, then the feasible solution array PF X in the decision variable space formed by the feasible solutions and the decision objective space array PF O ​Are respectively described as:

[0052]

[0053]

[0054] Specifically, step 5 includes:

[0055] Step 5.1, using the feasible solution array PF of the decision variable space obtained in step 4.2 X and the decision objective space array PF O , a final solution can be selected from the set of strategies based on an interactive method. The interactive method includes the following three categories:

[0056] The first category is to directly select the number of the feasible solution. That is, assuming that the determined feasible solution number is i, the decision variable corresponding to the feasible solution is X i =[x i,1 ,x i,2 ,…,x i,k T , and the objective space is O i =[o i,1 ,o i,2 ,…,o i,r T ;

[0057] The second category is to use the ideal point method to determine the number of the final feasible solution. Assuming that in the i-th PF solution, the maximum value of each objective value is max.o i,r , then the shortest distance d min,i from the i-th feasible solution to the ideal point is constructed as follows:

[0058]

[0059] And according to the smallest feasible solution number i is determined;

[0060] The third category is to use the weighting method to determine the number of the final feasible solution. Assuming that in the i-th PF solution, the maximum and minimum values of each objective value are Max.o i,r , Min.o i,r respectively, and the weight of the r-th objective is α r , then the comprehensive value F i of the i-th feasible solution is constructed as follows:

[0061]

[0062] And according to the smallest feasible solution number i is determined;

[0063] ​​Step 5.2, using the feasible solution number i obtained by any type of interactive method in step 5.1, combined with the mapping relationship constructed in step 3.2, the decision result at the network level can be mapped to the segment unit level. According to the decision variable space and decision target space defined in step 4.2, the conversion method of linking the decision result at the network level to the decision result at the segment unit level is as follows:

[0064]

[0065]

[0066] Based on the converted results, the distribution of various sustainable development goals formed by the implementation of corresponding maintenance plans for each road section unit can be obtained.

[0067] Compared with the prior art, the present invention has the following technical effects:

[0068] The present invention can solve the problem of maintenance decision-making of regional large-scale pavement network group units, determine the type and quantity of maintenance technology according to the maintenance needs of decision makers, and use binary conversion and decision trees to carry out maintenance decisions at the section unit level in the regional pavement network. According to pavement characteristic information data, the user delay cost at the section unit level is determined by using the spatiotemporal distribution characteristics of traffic flow, and the corresponding sustainable target values ​​such as maintenance cost, performance and environmental impact index are calculated. The division attributes of the section unit are determined according to the needs of decision makers, and the large-scale section units are merged into small-scale maintenance units by using the decision space dimensionality reduction principle, so as to establish a mapping relationship between the section unit and the maintenance unit. The multi-objective evolutionary algorithm is used to calculate the optimization model of multiple sustainable target combinations, so as to generate a set of alternative strategies containing multiple potential feasible solutions, and the final feasible solution is selected from the alternative strategies according to an interactive method, and then the network-level decision results are linked to the section unit level according to the mapping relationship between the two-level units.

[0069] Because the road section units contained in the regional large-scale road network may cause an exponential explosion during the optimization solution, for example, under the condition of provincial-level maintenance units, there are usually 7,000 to 10,000 road section units to be decided, and for multi-objective optimization, the number of variable scales exceeds 100, which is a large-scale decision-making problem; most traditional methods merge multiple road sections through cluster analysis to reduce the variable scale, but this method cannot determine the best maintenance plan for each road section after the merger; in addition, most traditional decision-making methods specify the maintenance fund allocation plan based on a certain indicator as the target, and do not consider the current demand for sustainable development. Therefore, the present invention can scientifically solve the problem of super-large variable scale in the regional large-scale road network, so as to achieve a sustainable decision-making plan by weighing multiple goals such as economic cost, user cost, environmental protection, and performance improvement, and at the same time link the decision results at the network level to the road section unit level. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is the implementation framework diagram of the present invention;

[0071] Figure 2 This is the distribution diagram of the maintenance cost and environmental impact index in the route during the case experiment;

[0072] Figure 3 This is the distribution diagram of the maintenance cost and environmental impact index in the maintenance and management unit during the case experiment;

[0073] Figure 4 This is the distribution diagram of the comprehensive performance improvement score in the route during the case experiment;

[0074] Figure 5 This is the distribution diagram of the comprehensive performance improvement score in the maintenance and management unit during the case experiment. Specific implementation manner

[0075] The present invention provides a multi-objective decision-making method for sustainable maintenance of large-scale road surface networks. The basic framework for implementing this method is as Figure 1 shown. This method uses binary conversion and decision trees to carry out maintenance decisions at the section unit level of regional road surface networks; according to the maintenance decision results at the section unit level and the spatio-temporal distribution characteristics of traffic flow, four sustainable target values at the section unit level are determined: user delay cost, maintenance cost, performance, and environmental impact index; based on the principle of decision space dimensionality reduction, large-scale section units are merged into small-scale maintenance units, and four sustainable target values at the network level are calculated for subsequent network-level maintenance decisions; a multi-objective evolutionary algorithm is used to solve the optimization model of each sustainable target combination at the network level, and a set of alternative strategies containing multiple potential feasible solutions is provided at the network level; the final feasible solution is selected from the alternative strategies through an interactive method, and then the network-level decision result is linked to the section unit level according to the decision space conversion principle.

[0076] Specifically, it includes the following steps:

[0077] Step 1, maintenance decision at the regional section unit level:

[0078] According to the established maintenance technologies, a combination of maintenance plans with different performance requirements is constructed, and binary conversion is performed on the combination. The service performance in the characteristics of the regional road surface network is described, and a decision tree at the section unit level is established, and the maintenance plan for each section unit is determined using binary arrays;

[0079] Step 2, calculate the sustainable target values at the section unit level:

[0080] Determine the user delay cost at the section unit level based on the spatio-temporal distribution characteristics of traffic flow, calculate the maintenance cost and environmental impact index at different section unit levels according to the life cycle assessment theory, and calculate the comprehensive performance improvement score at different section unit levels according to the difference method and normalization;

[0081] Step 3, generate small-scale maintenance units:

[0082] According to the basic information of the regional road network, obtain the key attributes affecting the maintenance fund scheduling, use the principle of decision space dimensionality reduction to merge large-scale section units into small-scale maintenance units, construct the mapping relationship between the two-level units, and calculate four sustainable target values at the network level for subsequent network-level maintenance decision-making;

[0083] Step 4, multi-objective optimization calculation:

[0084] Use the maintenance units formed in Step 3 as decision variables, solve the optimization models formed by different objective combinations using the multi-objective evolutionary algorithm, determine the optimal Pareto-Front surface or curve based on the non-dominated solution rank sorting principle, and form a set of strategies with multiple potential feasible solutions at the network level;

[0085] Step 5, interactive decision-making and decision unit conversion:

[0086] According to the set of multiple potential feasible solution strategies formed in Step 4, select the final solution from the set of strategies through an interactive method, combine the mapping relationship between the two-level units constructed in Step 3, map the network-level decision result to the section unit level, and use statistical methods to describe the distribution of various sustainable target values among section units and maintenance plans.

[0087] Among them, Step 1 includes:

[0088] Step 1.1, binary conversion of maintenance plan combinations includes:

[0089] Determine the number of maintenance technology types m according to the current road network conditions, determine the number of maintenance plan combinations n according to the implementation of maintenance activities, set the text format of the plan combination as A, and each plan is composed of a vector a i1 =(a i1 ,…,a ij ,…,a im ), where i = 1~n, j = 1~m, and each element in the vector represents the serial number of the maintenance technology. Then the construction method of the plan array B n×m is:

[0090]

[0091]

[0092] Step 1.2, when constructing a decision tree at the section unit level for the service performance of the regional road network features, construct a decision tree based on performance and determine the maintenance plan for each section unit based on this decision tree:

[0093] Let the service performance array of the road network be P s×g , where s represents the number of section units in the road network, g represents the number of service performance indicators used in the decision tree, and the service performance of each section is represented by the vector p s1 =(p s1 ,…,p sg ). Define f s to represent the plan number of section s, and any f s can find a row vector corresponding to it in the plan array B n×m ; then the construction method of the maintenance plan description array F s is as follows:

[0094]

[0095] Among them, f i =(b j1 ,…,b jm ), i = 1,…, s; j = 1,…, n. According to the mapping relationship, it can be considered that f i,1 = b j1 ,……, f i,m = b jm .

[0096] Step 2 includes:

[0097] Step 2.1, before calculating the user delay cost of each section according to the classification of different sustainable goals, the traffic volume Q of each time period of the section unit should be calculated first t,s , assuming that the traffic volume of section s is AADT s , and the traffic volume flat period time point, the first peak period time point, the first peak period dissipation point, the second peak period time point, and the second traffic volume dissipation point within 0 to 24 hours are t1, t2, t3, t4, t5 respectively. Then the traffic volume Q of each time period t,s is calculated as follows:

[0098]

[0099] Among them, c1~c 10 are constants;

[0100] Step 2.2, before calculating the user delay cost of each section according to the classification of different sustainable goals, after obtaining the traffic volume Q of each time period of the section unit t,sBased on this, combined with the traffic capacity calculation method, the traffic capacity of the closed section of road section s during the implementation of the maintenance technology can be obtained as C s,zone , the traffic capacity of the normal road section C s,d , define the operating speed as V l , and the operating speed of the normal road section is V c , the length of the road section to be maintained is L s , the total length of acceleration and deceleration is L a , the transition section length of the closed section is L p , the start times of implementing the corresponding maintenance technology for each road section are t ss 、t se , the proportion of the vth vehicle type in road section s is r s,v , the unit delay cost is cost s,v , then the user delay cost RUC caused by the implementation of the maintenance technology in each road section unit s The calculation method is as follows:

[0101]

[0102]

[0103] Step 2.3, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance scheme array F determined for the road network in Step 1.2 s , determine the unit area maintenance cost UAC of different maintenance technologies according to the life cycle assessment theory m , assuming the length of the road section s to be maintained is L s , the width is W s , the maintenance cost LCAC generated after implementing the corresponding maintenance technology for road section s can be obtained s The calculation method is as follows:

[0104]

[0105] Step 2.4, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance scheme array F determined for the road network in Step 1.2 s , determine the unit area environmental impact index UEI of different maintenance technologies according to the life cycle assessment theory m , the environmental impact index LCEI generated after implementing the corresponding maintenance technology for road section s can be obtained s The calculation method is as follows:

[0106]

[0107] Step 2.5, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m , let the number of target performance indicators be P, and define the target performance array OP formed after implementing the maintenance plan n×P , then the target performance array TP formed after implementing the maintenance plan for each road section can be obtained s×P , the original performance array of each road section is OP s×P , according to the relative value of the target performance and the current performance value, define the weight value α of different performance indicator types P , the comprehensive performance improvement score RP of road section s after implementing the corresponding maintenance technology can be obtained s The calculation method is as follows:

[0108]

[0109] Step 3 includes:

[0110] Step 3.1, using the sustainable goal values calculated for each road section in the above Steps 2.2 - 2.5, in multi-objective optimization, assume that the selected number of target dimensions is o, then the array composed of the objective function values is O s×o , select r attributes from the pavement network characteristic attributes to divide s road section units into m maintenance units, so assume the attribute array is I s×r , combine it with O s×o to form an augmented array (I, O), and the construction method of the mapped augmented array (I′, O) is:

[0111]

[0112] In this implementation plan, when constructing a decision tree at the road section unit level for the service performance of regional pavement network characteristics, the pavement network characteristic attributes include the service performance data of each road section unit (structural strength, rutting index, evenness index, skid resistance performance index, damage index and its sub-item data), traffic volume and composition data (annual average daily traffic volume AADT, vehicle type distribution ratio, spatio-temporal distribution characteristics of traffic volume), road characteristic information (number of each road section unit, pile numbers of upstream and downstream units, pavement width, number of lanes, secondary maintenance unit to which it belongs, self-defined road section attribute value);

[0113] Step 3.2, using the mapped augmented array (I′, O), according to the principle of merging the same elements in the left column array, recalculate the four sustainable goal values at the network level, and convert (I′, O) into (I″, O′). The row dimension of (I″, O′) after conversion is k, where the left column array is composed of k numbers (k << s), then the construction method is as follows:

[0114]

[0115] Step 4 includes:

[0116] In step 4.1, using the augmented array constructed in step 3.2 above, the k×o array on the right is used to construct a mathematical model for multi-objective optimization. Assume that the binary decision variable for implementing the maintenance technology for each maintenance unit is X k×1 =[x1,x2,…,x k T , and assume that the constraint function is H i (X) ≤ 0. Then the method for constructing the mathematical model is:

[0117] Min.Y=(O″ k×o ) T X k×1

[0118] s.t.H i (X) ≤ 0, (i=1,2,…)

[0119] In step 4.2, based on the principle of non-dominated solution ranking, a multi-objective evolutionary algorithm is used to solve the mathematical model constructed in step 4.1. The Pareto-Front set of the obtained solutions is set. Assume that the number of feasible solutions in the solution set is l. Then the feasible solution array PF in the decision variable space and the decision objective space array PF formed among the feasible solutions X and the decision objective space array PF O are respectively described as:

[0120]

[0121]

[0122] Step 5 includes:

[0123] In step 5.1, using the feasible solution array PF in the decision variable space and the decision objective space array PF X and the decision objective space array PF O obtained in step 4.2, the final solution can be selected from the policy set based on an interactive method. The interactive method includes the following three categories:

[0124] The first category is to directly select the number of the feasible solution. That is, assume that the determined feasible solution number is i. Then the decision variable corresponding to the feasible solution is X i =[x i,1 ,x i,2 ,…,x i,k T , and the objective space is O i =[o i,1 ,o i,2 ,…,o i,r T ; ​​​

[0125] The second type is to determine the number of the final feasible solution by using the ideal point method. Assume that in the i-th PF solution, the maximum value of each objective value is max.o i,r , then the shortest distance d from the i-th feasible solution to the ideal point min,i The construction method is as follows:

[0126]

[0127] And according to Determine the number i of the smallest feasible solution;

[0128] The third type is to determine the number of the final feasible solution by using the weighting method. Assume that in the i-th PF solution, the maximum and minimum values of each objective value are Max.o i,r , Min.o i,r , and the weight of the r-th objective is α r , then the comprehensive value F of the i-th feasible solution i The construction method is as follows:

[0129]

[0130] And according to Determine the number i of the smallest feasible solution;

[0131] Step 5.2. Using the number i of the feasible solution obtained by any one of the interactive methods in Step 5.1 and combining with the mapping relationship constructed in Step 3.2, the decision result at the network level can be mapped to the section unit level. According to the decision variable space and decision objective space defined in Step 4.2, the method for converting the decision result at the network level linked to the decision result at the section unit level is as follows:

[0132]

[0133] According to the converted result, the distribution of various sustainable objectives formed by each section unit due to the implementation of the corresponding maintenance plan can be obtained.

[0134] The following gives specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments, and any equivalent transformation made on the basis of the technical solution of this application falls within the protection scope of the present invention.

[0135] Embodiment 1:

[0136] This embodiment conducts pavement maintenance decision analysis with three objectives of optimizing maintenance cost, environmental impact index, and comprehensive performance, including the following contents:

[0137] (1) Regional section unit-level maintenance decision:

[0138] 1) Binary conversion of the maintenance plan combination:

[0139] Five maintenance techniques were selected (m = 5), and the unit maintenance cost and unit environmental impact index of the five maintenance techniques were defined. The five maintenance techniques were used to form nine maintenance plan combinations (n = 9). The basic parameters of the five maintenance techniques are shown in Table 1:

[0140] Table 1 Basic parameters of five maintenance techniques

[0141]

[0142] The basic parameters of the nine maintenance plan combinations are shown in Table 2. The results after binary conversion are shown in the last column of Table 2. The number of target performances is 4 (P = 4). The target performance array OP formed after each maintenance plan is implemented is 9×4 as follows:

[0143] Table 2 Basic parameters of nine maintenance plan combinations

[0144]

[0145]

[0146] Note: N indicates no improvement. When calculating the improvement value of the performance score, it is processed according to the original pavement performance.

[0147]

[0148] Preparation of pavement network characteristic information dataset:

[0149] A highway asphalt pavement network formed by 1100 km was selected. The basic characteristic information of the pavement includes ① performance data: direct indicators such as structural strength, damage index, rutting index, evenness index, skid resistance performance index, etc. and percentile indicators calculated according to the highway maintenance technology evaluation standard, ② traffic volume and composition data: AADT, vehicle type distribution ratio, spatio-temporal distribution characteristics of traffic volume; ③ road characteristic information: section unit number, up and down directions, pavement width, number of lanes, secondary maintenance unit to which it belongs;

[0150] The characteristic information data of 1100 section units are shown in Table 3:

[0151] Table 3 Characteristic information data of 1100 section units

[0152]

[0153]

[0154] Among them, all the data in the first 4 columns of the direct performance in Table 3 constitute the performance array P 1100×4 .

[0155] 2) Determination of maintenance decision tree and maintenance plan for road section units:

[0156] According to the highway asphalt pavement maintenance design specification and its related specifications, determine the upper and lower limits of performance when different maintenance plans are implemented, classify the performance combinations of each road section according to the range of performance, and finally obtain the plan array F for each road section. 1100 , taking only road section 1 and road section 1100 as examples, the plan array is obtained as follows:

[0157]

[0158] Among them, f1=(0,0,1,0,0,0), according to the mapping relationship, it can be considered that f 1,1 =0, f 1,2 =0, f 1,3 =1, f 1,4 =0, f 1,5 =0, f 1,6 =0.

[0159] (2) Calculate the sustainable target value at the road section unit level:

[0160] Since the selected optimization objectives are the maintenance cost LCAC, the environmental impact index LCEI, and the comprehensive performance score value RP respectively, according to the given calculation formula, the sustainable target values of all road section units can be obtained, and the results are shown in Table 4:

[0161] Table 4 Sustainable target values of all road section units

[0162]

[0163] (3) Generate maintenance units in a small-scale space:

[0164] According to the implementation steps, the selected target dimension o = 3, and the route number, up and down directions, and maintenance unit are selected as attribute values, that is, r = 3 attribute values, which are used to divide s = 1100 road section units into k = 30 maintenance units. Then, the elements of the sustainable target array at the maintenance unit level after division are shown in Table 5:

[0165] Table 5 Elements of the sustainable target array at the maintenance unit level

[0166]

[0167]

[0168] At the same time, it is divided into I1,…I 30 types by 3 attribute values. Then, the mapping relationship between the road section unit level and the maintenance unit level is:

[0169]

[0170] (4) Multi-objective optimization calculation:

[0171] Using the array elements in Table 5 as the coefficient array for the multi-objective linear programming problem, two constraint conditions are selected (the upper and lower limits of the maintenance ratio are 8% and 100% respectively, and the upper and lower limits of the maintenance budget are 10 million and 100 million); the NSGA-II evolutionary algorithm is selected as the model solving method, and 200 Pareto-front solution sets are obtained through calculation.

[0172] (5) Interactive decision-making and decision unit conversion:

[0173] Adopting the best ideal point method in interactive decision-making, the solution with PF number 185 (i = 185) is determined as the final solution. The characteristics of this solution are: the decision variable space array X i = [0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,1,1,0] T , and the objective space array O i = [3457.292,24513.221,1883.202] T ; Therefore, through the mapping relationship between the road section unit level and the maintenance unit level, the decision variables and decision objective space arrays at the road section unit level, as well as the plan number and the corresponding maintenance unit, can be obtained as shown in Table 6. Based on this, the distributions of different maintenance costs, environmental indices, and comprehensive performance improvement scores in the spatial dimension can be further obtained. As shown in the figure, this case also verifies the effectiveness of the model for sustainable maintenance decision-making of large-scale road networks, such as Figures 2 to 5 shown, Figure 2 is the distribution diagram of maintenance cost and environmental impact index in the route in the case experiment (the abscissa is the route name, and the ordinate is the maintenance cost LCAC and environmental impact index LCEI); Figure 3 is the distribution diagram of maintenance cost and environmental impact index in the maintenance and management unit in the case experiment (the abscissa is the maintenance and management unit, and the ordinate is the maintenance cost LCAC and environmental impact index LCEI); Figure 4 is the distribution diagram of comprehensive performance improvement score in the route in the case experiment (the abscissa is the route name, and the ordinate is the performance improvement score PI); Figure 5 is the distribution diagram of comprehensive performance improvement score in the maintenance and management unit in the case experiment (the abscissa is the maintenance and management unit, and the ordinate is the performance improvement score PI).

[0174] Table 6 Decision variables and decision objective space arrays at the road section unit level, as well as the plan number and the corresponding maintenance unit

[0175]

Claims

1. A multi-objective decision-making method for sustainable maintenance of large-scale road networks, characterized in that, This method uses binary conversion and decision trees to carry out regional pavement network section unit-level maintenance decisions; according to the section unit-level maintenance decision results and the spatio-temporal distribution characteristics of traffic flow, four sustainable target values at the section unit level are determined: user delay cost, maintenance cost, performance, and environmental impact index; Based on the principle of decision space dimensionality reduction, large-scale section units are merged into small-scale maintenance units, and four sustainable target values at the network level are calculated for subsequent network-level maintenance decisions; a multi-objective evolutionary algorithm is used to solve the optimization model of each sustainable target combination at the network level, and a set of alternative strategies containing multiple potential feasible solutions is provided at the network level; the final feasible solution is selected from the alternative strategies through an interactive method, and then the network-level decision result is linked to the section unit level according to the decision space conversion principle; It includes the following steps: Step 1, regional section unit-level maintenance decision: According to the established maintenance technologies, a combination of maintenance plans with different performance requirements is constructed, and binary conversion is performed on the combination of maintenance plans. The service performance in the characteristics of the regional pavement network is described, a decision tree at the section unit level is established, and the maintenance plan for each section unit is determined using a binary array; Step 2, calculate the sustainable target values at the section unit level: Based on the spatio-temporal distribution characteristics of traffic flow, the user delay cost at the section unit level is determined. According to the life cycle assessment theory, the maintenance costs and environmental impact indices of different section units are calculated, and the comprehensive performance improvement scores of different section units are calculated using the difference method and normalization; Step 3, generate small-scale maintenance units: According to the basic information of the regional pavement network, the key attributes affecting the scheduling of maintenance funds are obtained. The decision space dimensionality reduction principle is used to merge large-scale section units into small-scale maintenance units, and the mapping relationship between the two-level units is constructed. Four sustainable target values at the network level are calculated for subsequent network-level maintenance decisions; Step 4, multi-objective optimization calculation: Using the maintenance units formed in Step 3 as decision variables, a multi-objective evolutionary algorithm is used to solve the optimization model formed by different target combinations. Based on the non-dominated solution ranking principle, the optimal Pareto-Front surface or curve is determined, and a set of strategies with multiple potential feasible solutions is formed at the network level; Step 5, interactive decision-making and decision unit conversion: According to the set of multiple potential feasible solution strategies formed in Step 4, the final solution is selected from the set of strategies through an interactive method. Combining with the mapping relationship between the two-level units constructed in Step 3, the network-level decision result is mapped to the section unit level, and the distribution of various sustainable target values among section units and maintenance plans is described using statistical methods.

2. The multi-objective decision-making method for sustainable maintenance of large-scale road networks according to claim 1, characterized in that The said Step 1 includes: Step 1.1, perform binary conversion on the combination of maintenance plans: Determine the number of maintenance technology types \(m\) according to the current road network conditions, and determine the number of maintenance plan combinations \(n\) according to the implementation of maintenance activities. Let the text format of the plan combination be \(A\), and each plan consists of a vector \(\mathbf{a}\) i1 =(a i1 ,…,a ij ,…,a im ), where \(i = 1\sim n\) and \(j = 1\sim m\). Each element in the vector represents the serial number of the maintenance technology. Then the construction method of the plan array \(B\) n×m is as follows: When constructing a decision tree at the section unit level for the service performance of the regional pavement network characteristics, a decision tree is constructed based on performance, and the maintenance plan for each section unit is determined based on this decision tree: Let the performance array of the road surface network be P s×g , where s represents the number of section units in the road surface network, g represents the number of performance indicators used in the decision tree, and the performance of each section is represented by the vector p s1 = (p s1 , …, p sg ). Define f s to represent the scheme number of section s, and any f s can find a row vector corresponding to it in the scheme array B n×m ; then the construction method of the maintenance scheme description array F s after quantization is as follows: where, f i =(b j1 , …, b jm ), i = 1, …, s; j = 1, …, n. According to the mapping relationship, it can be considered that f i,1 = b j1 , ……, f i,m = b jm .

3. The multi-objective decision-making method for sustainable maintenance of large-scale road networks according to claim 2, characterized in that, The said Step 2 includes: Step 2.1, before calculating the user delay cost of each section according to the classification of different sustainable goals, the traffic volume Q of each time period of the section unit should be calculated first t,s , assuming that the traffic volume of section s is AADT s , and the traffic volume stable period time point, the first peak period time point, the first peak period dissipation point, the second peak period time point, and the second traffic volume dissipation point within 0 to 24 hours are t1, t2, t3, t4, and t5 respectively. Then the traffic volume Q of each time period t,s The calculation method is as follows: Among them, c1 to c 10 are constants; Step 2.2, before calculating the user delay cost of each section according to the classification of different sustainable goals, after obtaining the traffic volume Q of each time period of the section unit t,s Based on this, combined with the traffic capacity calculation method, the traffic capacity of the closed section of section s during the implementation of the maintenance technology can be obtained as C s,zone , the traffic capacity of the normal section C s,d , define the running speed as V l , and the running speed of the normal section is V c , the length of the section to be maintained is L s , the total length of acceleration and deceleration is L a , the length of the transition section of the closed interval is L p , the start times of implementing the corresponding maintenance technology for each section are t ss , t se , the proportion of the v-th vehicle type in section s is r s,v , the unit delay cost is cost s,v , then the user delay cost RUC caused by the implementation of the maintenance technology in each section unit s The calculation method is as follows: Step 2.3, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance scheme array F determined for the pavement network in Step 1.2 s , determine the unit area maintenance cost UAC of different maintenance technologies according to the life cycle assessment theory m , assuming that the length of the section s to be maintained is L s , and the width is W s , the maintenance cost LCAC generated after implementing the corresponding maintenance technology for section s can be obtained s The calculation method is as follows: Step 2.4, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m and the maintenance scheme array F determined for the pavement network in Step 1.2 s , according to the life cycle assessment theory, determine the environmental impact index UEI per unit area of different maintenance technologies m , and the environmental impact index LCEI generated by implementing the corresponding maintenance technology for section s can be obtained s The calculation method is as follows: Step 2.5, according to the classification of different sustainable goals, through the binary scheme array B determined in Step 1.1 n×m , let the number of target performance indicators be P, and define the target performance array OP formed after implementing the maintenance plan n×P , then the target performance array TP formed after implementing the maintenance plan for each section can be obtained s×P , the original performance array of each section is OP s×P , according to the relative value of the target performance and the current performance value, define the weight value α of different performance indicator types P , the comprehensive performance improvement score RP of section s after implementing the corresponding maintenance technology can be obtained s The calculation method is as follows:

4. The multi-objective decision-making method for sustainable maintenance of large-scale road networks according to claim 3, characterized in that, The said Step 3 includes: Step 3.1: Using each sustainable objective value calculated for each road section in the above Steps 2.2 to 2.5, in multi-objective optimization, assuming the selected number of objective dimensions is o, the array composed of objective function values is O s×o , select r attributes from the road network characteristic attributes to divide s road section units into m maintenance units, so assume the attribute array is I s×r , combine it with O s×o to form an augmented array (I, O). The construction method of the mapped augmented array (I′, O) is as follows: Step 3.2: Using the augmented array (I′, O) after mapping, according to the principle of merging the same elements in the left column array, recalculate the four sustainable target values at the network level, and convert (I′, O) into (I″, O′). After conversion, the row dimension of (I″, O′) is k, where the left column array consists of k numbers (k << s). The construction method is as follows:

5. The multi-objective decision-making method for sustainable maintenance of large-scale road networks according to claim 4, characterized in that The said step 4 includes: Step 4.1, using the augmented array constructed in the above Step 3.2, the right k×o array is used to construct a mathematical model for multi-objective optimization. Assume that the binary decision variable for each maintenance unit to implement the maintenance technology is X k×1 =[x1,x2,…,x k T , assume that the constraint function is H i (X) ≤ 0, then the method for constructing the mathematical model is:​ Min.Y=(O″ k×o ) T X k×1 s.t.H i (X) ≤ 0, (i = 1, 2, …) Step 4.2: Based on the non-dominated ranking principle, use a multi-objective evolutionary algorithm to solve the mathematical model constructed in Step 4.

1. The obtained Pareto-Front front solution set is set. Let the number of feasible solutions in the solution set be l, then the feasible solution array PF in the decision variable space formed by the feasible solutions X and the decision objective space array PF O are respectively described as:

6. The multi-objective decision-making method for sustainable maintenance of large-scale road networks according to claim 5, wherein The said step 5 includes: Step 5.1, using the feasible solution array PF of the decision variable space obtained in Step 4.2 X and the decision objective space array PF O , a final solution can be selected from the policy set based on an interactive method, and the interactive method includes the following three categories: The first type is to directly select the number of the feasible solution. That is, assuming that the number of the feasible solution is determined to be i, the decision variables corresponding to the feasible solution are X i =[x i,1 ,x i,2 ,…,x i,k T , and the objective space is O i =[o i,1 ,o i,2 ,…,o i,r T ;​​ The second category is to use the ideal point method to determine the number of the final feasible solution. Assume that in the $i$-th PF solution, the maximum value of each objective value is $\max.o$ i,r , then the shortest distance $d$ from the $i$-th feasible solution to the ideal point min,i The construction method is as follows: and based on determine the smallest feasible solution number i; The third category is to determine the number of the final feasible solution by the weight method. Assume that in the $i$-th PF solution, the maximum and minimum values of each objective value are Max.o i,r , Min.o i,r , and the weight of the $r$-th objective is $\alpha$ r . Then the construction method of the comprehensive value $F$ i of the $i$-th feasible solution is as follows: and based on determine the smallest feasible solution number i; Step 5.2: Using the feasible solution number i obtained by any one of the interactive methods in step 5.1, combined with the mapping relationship constructed in step 3.2, the decision result at the network level can be mapped to the link unit level. According to the decision variable space and decision target space defined in step 4.2, the conversion method for linking the decision result at the network level to the decision result at the link unit level is as follows: According to the converted result, the distribution of multiple sustainable targets formed by each link unit due to the implementation of the corresponding maintenance plan can be obtained.

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