CN107958304B - Pavement maintenance and renovation scheduling method considering performance improvement and budget utility - Google Patents

Pavement maintenance and renovation scheduling method considering performance improvement and budget utility Download PDF

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CN107958304B
CN107958304B CN201711156308.5A CN201711156308A CN107958304B CN 107958304 B CN107958304 B CN 107958304B CN 201711156308 A CN201711156308 A CN 201711156308A CN 107958304 B CN107958304 B CN 107958304B
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谢驰
李明宇
刘海洋
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Abstract

The invention discloses a pavement maintenance and renovation scheduling method considering performance improvement and budget effectiveness, wherein the device of the method comprises a storage module for registering map data information and a data processing module, results are obtained according to two steps of road network establishment and scheduling, the efficient and comprehensive solution method can greatly save time, improve the working efficiency of a manager, provide powerful guarantee for further development of subsequent decision-making work and provide basis for scientific, reasonable and optimal maintenance and renovation plan selection.

Description

Pavement maintenance and renovation scheduling method considering performance improvement and budget utility
Technical Field
The invention relates to the field of traffic, in particular to a pavement maintenance and renovation scheduling method.
Background
Road pavement maintenance and renovation are among the most expensive activities in the management of transportation infrastructure. The construction of transportation infrastructure has a powerful propulsion effect on the development of economy in China, and is a powerful guarantee for the smooth performance of economic activities. However, as the amount of road construction increases, a large amount of already constructed road surfaces inevitably lose, and the problems of maintenance and renovation of the road surfaces are faced. The road section and the time of maintenance, how to plan the maintenance plan and the selected maintenance measures, etc. are all the problems that need to be considered by the manager.
The traffic students often construct and solve two types of models based on different mastered information and different targets, the roads are divided into different grades according to the road conditions, and maintenance plans of each grade of road surface every year are formulated. The first type is the budget planning problem. When the budget information is unknown, the road condition on the road network level or an independent road area level is ensured to meet the requirement, and the maintenance and renovation cost in the planning period is minimized. The calculation results can be used for decision makers to determine the actual budget level. The second category, the budget allocation problem, minimizes the cost of use or maximizes the utility of maintenance and refurbishment without exceeding the budget after the budget information is known.
The existing dual-target pavement maintenance and renovation method is poor in solution scheme capable of simultaneously ensuring solving efficiency and comprehensiveness. Currently, there are two representative types of solutions to this problem. The integer programming model can efficiently solve an accurate solution when the problem scale is not large, and the solving time is exponentially increased along with the expansion of the problem scale; the genetic algorithm widely used cannot ensure to obtain the optimal solution within a limited time due to the nature of the genetic algorithm, and the weighting method serving as another special genetic algorithm cannot ensure to obtain the complete pareto optimal solution. The scale of the problem of timing schedule maintenance and renovation of the dual-target pavement is often large, and the completeness of the solution has a large influence on the decision, so that a model and an algorithm which take efficiency and the accuracy of the solution into consideration should be designed.
Disclosure of Invention
The invention aims to overcome the problems and provides a pavement maintenance and renovation scheduling method which has performance improvement and budget effectiveness, and when a road maintenance and renovation plan is prepared, the method has the double goals of lowest cost and maximized performance, and can provide richer information for a manager to make a more reasonable decision.
The invention provides a pavement maintenance and renovation scheduling method considering performance improvement and budget utility, the device of the method comprises a storage module for registering map data information and a data processing module, and the method is characterized by comprising the following steps:
firstly, building a road network, marking functions and road surface conditions of all roads in an area through a data processing module, dividing the functions into S types according to the functions, and then obtaining an in-area road set S ═ {1,2 …, S } and a road surface condition set I ═ 1,2 …, I };
secondly, the total length L of each road is counted by a data processing module in time sequence arrangementSThe planning period T, the most efficient but expensive maintenance and renovation measures M e M {1,2 …, M }, the cost C incurred in the year T for taking the measure M for a road of class s per unit lengthsmtAnd when the measure m is applied to the s-th road, the conversion rate P of the road surface condition from i to j is obtainedsijmAnd a proportion X of s-class roads with a road surface condition i of which the road surface condition of the measure m is accepted at the time of t yearsimtThe proportion z of the road in the optimal condition during planning1And annual average maintenance and refurbishment costs z2Satisfy the relationship of
Figure GDA0003076074820000031
The initial constraint condition of the road surface condition is satisfied
Figure GDA0003076074820000032
The constraint condition of the road surface condition conversion relation satisfies
Figure GDA0003076074820000033
The budget constraint condition is satisfied
Figure GDA0003076074820000034
Wherein, BtIs the upper budget available in the t year;
the constraint condition of the optimal pavement proportion requirement meets
Figure GDA0003076074820000035
Figure GDA0003076074820000036
Wherein, X*The road surface is the requirement of the lowest proportion of the road surfaces under the conditions of 1 and the like in a road network;
the constraint condition of the feasible interval of the decision variable is satisfied
Figure GDA0003076074820000037
Data processing modules respectively using z1、z2And obtaining a time sequence arrangement result for the objective function.
Further, in the scheduling step, a parameter method is used to obtain the scheduling result according to the following steps:
the first step, initialization, the data processing module converts the objective function into
Figure GDA0003076074820000041
Wherein, w1、w2The weights of performance and cost in this utility function, respectively; k is a radical ofmaxIs the upper limit of the iteration times; w is a1＝1-ε、w2ε or w1＝ε，w21-epsilon is an initial weight coefficient assignment, and epsilon is a small enough number which satisfies that epsilon is more than or equal to 0 and less than or equal to 1; in the case of k being 1, the data processing module introduces a parameter w (w)1,w2) Obtaining the result (x)1，x2)；
Second, parameter generation, new weight parameter w ═ w (w)1,w2) Satisfy the requirement of
Figure GDA0003076074820000042
Wherein
Figure GDA0003076074820000043
The data processing module then compares the result (x)1，x2) Deleting from the first-in first-out form;
thirdly, checking results, and substituting the new weight w into the initialization step by the data processing module to calculate to obtain a new optimal solution x;
the fourth step, if x ═ x1Or x ═ x2Terminating the step; otherwise, the neighboring solution (x)1，x)(x，x2) Deposit formStoring the adjacent pareto optimal solution in the form to be used for subsequent interval segmentation work, and updating k to k +1 until k>kmaxOr terminates when the form is empty.
Further, since the function has been transformed into the classical linear programming problem, the result (x) obtained by the following steps is obtained by the simplex method as follows1，x2)：
In a first step, the data processing module takes an initial feasible basis B ═ p1,p2,…pm) Calculating the initial base feasible solution
Figure GDA0003076074820000044
Current value of objective function
Figure GDA0003076074820000045
And all check numbers σj,j＝ 1,2,…,n,
Figure GDA0003076074820000046
Second, the data processing module checks all the check numbers σjJ is 1,2, …, n, if all the check numbers σjIf the current base is more than or equal to 0, the current base is the optimal solution, and the iteration is stopped;
if it is
Figure GDA0003076074820000047
Let σ bek＝max{σj|σj>0} when B is equal to-1pkWhen the solution is less than or equal to 0, no optimal solution exists, and iteration is stopped; when B is present-1pk>0 season
Figure GDA0003076074820000051
By xkIn place of xrObtaining a new base, obtaining a feasible solution and a judgment number of the new initial base, and re-executing the step;
data processing module reinitialize w1＝ε，w21-epsilon to obtain
Figure GDA0003076074820000052
ExecuteSteps i, ii;
the data processing module will obtain the result (x)1，x2) Storing the first-in first-out list in the memory module and repeating the steps.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 shows a road condition transformation matrix according to various measures of the invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the technical scheme is further explained below by combining the figures.
As shown in the figure, a road maintenance and renovation scheduling method for improving performance and budgeting effectiveness, the road category S includes only one category. The road condition I is divided into two levels of 1 and 2, wherein the level 1 is better than the level 2, and the proportion of the level 1 is 70 percent and the proportion of the level 2 is 30 percent respectively. Planning year is 1 year, budget B190, the minimum requirement X of the proportion of the road surface in the road network under the condition of 1 and the like*90%. The maintenance measures are divided into 1 renovation and 2 maintenance. The road condition conversion matrix under different measures is shown in figure 2.
Figure GDA0003076074820000053
X11+X12＝0.7 (10)
X21+X22＝0.3 (11)
100X11+100X12≤90 (12)
1X11+0.8X12+0.9X21≥0.9 (13)
0≤X11≤1 (14)
0≤X12≤1 (15)
0≤X21≤1 (16)
0≤X22≤1 (17)
The first iteration:
step 1: an initial solution. Setting an upper limit k of iteration timesmax5. When w is1＝1，w 20, has z1(0.95, 90). When w is1＝0，w 21, has z2(0.90, 65). Will (z)1,z2) The neighboring solution form is stored.
Step 2: and generating new parameters. a is1＝65-90＝-25，a20.95-0.90-0.05. New w1＝1.002，w2＝-0.002。
And step 3: and (5) generating and checking a solution. Will be new w1＝1.002，w2Substitution of-0.002 into the model gave z3＝z1(0.95,90), there are no other pareto optimal solutions in the interval, and (z) will be1,z2) The adjacent solution form is removed.
And 4, step 4: criteria for termination of the calculation: the neighboring solution form is empty, all pareto optimal solutions have been found, and the computation terminates.
After 1 iteration, z is obtained1＝(0.95,90)，z2That is, in this case, the pareto optimal solution existing in the interval is the value of two extreme cases.
The method can be used for rapidly determining the pareto optimal solution in the interval, obtaining a comprehensive solution set, ensuring the solving speed and providing comprehensive and rapid reference information for a manager so as to make a decision.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are given by way of illustration of the principles of the present invention, and that various changes and modifications may be made without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (3)

1. A pavement maintenance and renovation scheduling method with performance improvement and budget utility, the device of the method comprises a storage module for storing map data information and a data processing module, and the method is characterized by comprising the following steps:
1) establishing a road network, marking functions and road surface conditions of all roads in an area through a data processing module, dividing the functions into S types according to the functions, and then obtaining an in-area road set S ═ {1,2 …, S } and a road surface condition set I {1,2 …, I };
2) time sequence arrangement, data processing module counts total length L of each type of roadSThe planning period T, the most efficient but expensive maintenance and renovation measures M e M {1,2 …, M }, the cost C incurred in the year T for taking the measure M for a road of class s per unit lengthsmtAnd when the measure m is applied to the s-th road, the conversion rate P of the road surface condition from i to j is obtainedsijmAnd a proportion X of s-class roads with a road surface condition i of which the road surface condition of the measure m is accepted at the time of t yearsimtThe proportion z of the road in the optimal condition during planning1And annual average maintenance and refurbishment costs z2Satisfy the relationship of
Figure FDA0003076074810000011
The initial constraint condition of the road surface condition is satisfied
Figure FDA0003076074810000012
The constraint condition of the road surface condition conversion relation satisfies
Figure FDA0003076074810000013
The budget constraint condition is satisfied
Figure FDA0003076074810000014
Wherein, BtIs the upper budget available in the t year;
the constraint condition of the optimal pavement proportion requirement meets
Figure FDA0003076074810000021
Figure FDA0003076074810000022
Wherein, X*The road surface is the requirement of the lowest proportion of the road surfaces under the conditions of 1 and the like in a road network;
the constraint condition of the feasible interval of the decision variable is satisfied
Figure FDA0003076074810000023
Data processing modules respectively using z1、z2And obtaining a time sequence arrangement result for the objective function.
2. The method of claim 1, wherein the scheduling step comprises the step of obtaining the scheduling result, and comprises:
a) initialization, the data processing module converts the objective function into
Figure FDA0003076074810000024
Wherein, w1、w2Performance and cost weights, respectively; k is a radical ofmaxIs the upper limit of the iteration times; w is a1＝1-ε、w2ε or w1＝ε，w21-epsilon is primaryAssigning a weight coefficient, wherein epsilon is a small enough number and satisfies that epsilon is more than or equal to 0 and less than or equal to 1; in the case of k being 1, the data processing module introduces a parameter w (w)1,w2) Obtaining the result (x)1，x2)；
b) Generating parameters, new weight parameter w ═ w (w)1,w2) Satisfy the requirement of
Figure FDA0003076074810000025
Wherein
Figure FDA0003076074810000026
The data processing module then compares the result (x)1，x2) Deleting from the first-in first-out form;
c) checking the result, and substituting the new weight w into the initialization step by the data processing module for calculation to obtain a new optimal solution x;
d) if x ═ x1Or x ═ x2Terminating the step; otherwise, the neighboring solution (x)1，x)(x，x2) Storing the form, and updating k to k +1 until k>kmaxOr terminates when the form is empty.
3. A method of scheduling maintenance and renovation of a roadway with improved performance and budgetary utility according to claim 2, wherein the data processing module obtains the result (x) by the following steps1，x2)：
i) The data processing module obtains an initial feasible base B ═ p1,p2,…pm) Calculating the initial base feasible solution
Figure FDA0003076074810000031
Current value of objective function
Figure FDA0003076074810000032
And all check numbers σj,j＝1,2,…,n,
Figure FDA0003076074810000033
Figure FDA0003076074810000034
ii) the data processing module checks all the check numbers σjJ is 1,2, …, n, if all the check numbers σjIf the current base is more than or equal to 0, the current base is the optimal solution, and the iteration is stopped;
if it is
Figure FDA0003076074810000037
Let σ bek＝max{σj|σj>0} when B is equal to-1pkWhen the solution is less than or equal to 0, no optimal solution exists, and iteration is stopped; when B is present-1pk>0 season
Figure FDA0003076074810000035
By xkIn place of xrObtaining a new base, obtaining a feasible solution and a judgment number of the new initial base, and re-executing the step;
data processing module reinitialize w1＝ε，w21-epsilon to obtain
Figure FDA0003076074810000036
Performing steps i and ii;
the data processing module will obtain the result (x)1，x2) Storing the first-in first-out list in the memory module and repeating the steps.
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