CN110390491A - A kind of highway engineering multiple target construction plan determines method - Google Patents

A kind of highway engineering multiple target construction plan determines method Download PDF

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CN110390491A
CN110390491A CN201910689044.2A CN201910689044A CN110390491A CN 110390491 A CN110390491 A CN 110390491A CN 201910689044 A CN201910689044 A CN 201910689044A CN 110390491 A CN110390491 A CN 110390491A
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construction
individual
arrangement
fitness function
group
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CN110390491B (en
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唐源洁
胡志远
刘仍奎
王福田
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Beijing Jiaotong University
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Beijing Jiaotong University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06313—Resource planning in a project environment
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06316—Sequencing of tasks or work
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0633—Workflow analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction

Abstract

The invention discloses a kind of highway engineering multiple target construction plans to determine method.This method comprises: obtaining the construction duration of each optional arrangement and method for construction of construction activities and each arrangement and method for construction, expense, quality coefficient, safety coefficient and daily resource usage amount in Highway Project；Using the sequencing of each construction activities and Highway Project daily retrievable stock number as constraint condition, with the construction time is short, operating expenses is low, quality is high and highly-safe for optimization aim, the method being integrated using genetic algorithm and linear programming, one group of Pareto optimal solution is determined, wherein the information of each solution includes: arrangement and method for construction corresponding to each construction activities, construction time started.The present invention has comprehensively considered time, expense, quality and the safety factor of highway engineering, it joined resource constraint simultaneously, the method for solving that genetic algorithm is integrated with linear programming is devised, has the characteristics that the information for solving high quality, solution efficiency height, solving is comprehensive, practical.

Description

A kind of highway engineering multiple target construction plan determines method
Technical field
The present invention relates to building cost management fields, true more particularly to a kind of highway engineering multiple target construction plan Determine method.
Background technique
Existing highway engineering construction planning and optimization method are generally divided into the establishment of single goal construction plan and optimize, is double Target construction plan establishment optimization and the establishment optimization of three target construction plans.
The establishment optimization of single goal construction plan includes Time Optimization, Cost Optimization and resource optimization etc., and Time Optimization refers to net When the calculating duration of network plan is unsatisfactory for the duration required by contractor, the duration to be worked by compression key, that is, choose More preferably arrangement and method for construction, to meet the process of constructing aims.Time Optimization does not change patrolling between work in every in network planning The relationship of collecting, cannot be compressed into non-key work for key job.In addition, when in network planning there are when a plurality of critical circuits, must The duration of each critical circuits must be compressed identical numerical value.Cost Optimization is also known as Time-cost optimization, refers to constantly in net Network finds out the smallest key job of direct cost rate in the works, shortens its duration, at the same more increased direct cost and The numerical value of the indirect expense of reduction, finally acquire engineering cost it is minimum when Optimal Project Duration or the duration acquires least cost as required Plan arrangement.The resource optimization of network planning is divided into two kinds, i.e., the optimization of " resource is limited, and the duration is most short " and " duration is fixed, The optimization of resources balance ".The former is arranged by adjusting plan, under the conditions of meeting resource constraint, increases the duration least Process.The latter is to arrange by adjusting plan in the case where being kept for the duration constant, make the resource of entire engineering per unit time Demand does not occur excessive peak and low ebb, the process for keeping resource expense as balanced as possible.
Highway construction project construction plan based on Bi-objective works out optimization, generally directed to time and two dimensions of expense into Row optimization, namely the usually described Time-Cost trade-off analysis.It is single with duration or expense etc. is only focused in single object optimization One target is different, and the duration of construction project entirety and expense are carried out integrated decision-making optimization by Time-Cost trade-off analysis, seeks The most cost-benefit engineering construction duration.In order to reach this target, contractor is usually with higher direct Cost is cost, distributes more working sources for construction activities, exchanges shorter construction duration and less construction for Indirect expense.Also or under the premise of meeting construction period, extend the duration, construction direct cost and working sources are reduced with this Consumption.
Highway construction project construction plan based on three targets works out optimization, be extend on the basis of biobjective scheduling and Come, in general, introducing quality dimensions in original Time-Cost trade-off analysis, forms Time-Cost-quality tradeoff point Analysis.In three target construction plans establishment optimization process, what is primarily solved is exactly the quantification treatment of construction quality, and method is usual It is divided into: 1. function of the construction quality as the construction duration；2. construction quality as construction the duration and cost it is non-thread Property function；3. construction quality is as parameter to be estimated in each arrangement and method for construction.After the quantification treatment for completing construction quality, mathematics is constructed Model carries out Time-Cost-quality trade-off analysis.The result of analysis provides for contractor: meeting determining quality requirement Meanwhile the arrangement and method for construction combination of highway construction project is completed within limited duration and cost range.
The method for solving of existing highway engineering multiple target construction plan establishment optimization mainly has two major classes: 1. with target weight Multiple-objection optimization is changed into single object optimization by the methods of method, then according in model selection single object optimization branch-and-bound, The methods of nonlinear optimization seeks optimal solution.2. finding multiple-objection optimization with heuritic approaches such as genetic algorithm, ant group algorithms Under Pareto optimal solution.
Specific method is sorted out as shown in Figure 1.
But the Time-Cost trade-off analysis or Time-Cost-of either single object optimization or multiple target Quality trade-off analysis, all there are following defects:
1) consider that the factor for influencing the establishment of highway construction project construction plan is not comprehensive enough
With the development of the times, the evaluation whether successful important indicator of Highway Construction Project Based has been not limited solely to traditional Time, expense, quality only consider the optimization method of three traditional dimensions, so that analysis result is not comprehensive enough, it is difficult to meet highway Construction project scene practice of construction demand.
2) optimization algorithm existing defects
It according to analysis above, is broadly divided into: being applied to single for the derivation algorithm of highway engineering construction scheduling models The linear programming related algorithm or nonlinear optimization algorithm of objective optimization；Heuritic approach applied to multiple-objection optimization.It inspires Formula algorithm when solving the multi-objective optimization question of three targets or more, having been demonstrated that there are convergence rates, hold back by slow, solving result Dissipate the disadvantages of property is poor.The defect of algorithm will have adverse effect on solving result, so that it is excellent to be as a result unable to reach contractor Change demand.
3) do not consider that there are resource constraints in Practical Project
Each construction activities are not isolated in most of highway construction project, between each other there is resource contention, Resource contention between a variety of connections such as duration conflict, especially concurrent construction activity, exacerbates highway construction project construction plan The difficulty of establishment.Traditional trade-off analysis does not consider the resource contention of concurrent activities only to integral construction scheme Combinatorial Optimization, The presence for ignoring resource constraint cannot be applied effectively in reality in the limited situation of working sources.
4) information solved is not comprehensive enough
Existing highway construction project multiple target construction plan establishment optimization method only chooses arrangement and method for construction conduct mostly and determines Plan variable, thus when output optimal solution, arrangement and method for construction information corresponding to each activity can only be provided, each activity can not be provided Construction time started information.Causing output information incomplete simultaneously, also further resulting in such method can not calculate often Day resource usage amount, it is impossible to be used in meet resource constraint.In reality, contractor will not be satisfied with this offer " semi-finished product " Optimization method.
Summary of the invention
The object of the present invention is to provide it is a kind of consider resource constraint, comprehensive construction engineering time, expense, quality, The multiple target construction of the highway planning optimization method of safety.
To achieve the above object, the present invention provides following schemes:
A kind of highway engineering multiple target construction plan determines method, comprising:
Obtain Highway Project in the construction duration of each optional arrangement and method for construction of construction activities and each arrangement and method for construction, Expense, quality coefficient, safety coefficient and daily resource usage amount；
Determine the sequencing of each construction activities；
Determine the Highway Project retrievable stock number daily；
With the sequencing of each construction activities and the Highway Project, retrievable stock number is about daily Beam condition, with the construction time is short, operating expenses is low, quality is high and highly-safe for optimization aim, using genetic algorithm and linearly It plans the method for solving being integrated, one group of Pareto optimal solution is determined, wherein the information of each solution includes: each construction activities institute The fitness function value of corresponding arrangement and method for construction, construction time started, arrangement and method for construction combination includes in being combined according to arrangement and method for construction The fitness function value for the representative duration that the construction duration of each arrangement and method for construction determines, according to arrangement and method for construction combine in each arrangement and method for construction Expense determine representative expense fitness function value, according to arrangement and method for construction combine in each arrangement and method for construction quality coefficient determine Representation quality fitness function value and according to arrangement and method for construction combine in each arrangement and method for construction safety coefficient determine representative The fitness function value of safety.
Optionally, the method for solving is NSGA-III genetic algorithm and the method that linear programming is integrated.
Optionally, according toDetermine the fitness function value f for representing the duration1, whereinFor construction activities i institute The construction duration of the jth kind arrangement and method for construction of selection, M are the total quantity of construction activities on critical circuits.
Optionally, according toDetermine the fitness function value f for the expense that represents2, whereinFor The direct cost of jth kind arrangement and method for construction selected by construction activities i, L are the total quantity of construction activities in Highway Project, B For the daily engineering cost of Highway Project.
Optionally, according toDetermine the fitness function value f for the expense that represents3, whereinConstruction activities i is in the case where selecting jth kind arrangement and method for construction for expression, the numerical value of quality factor k, wti,kIndicate quality factor k Weight, wtiIndicate the weight of construction activities i, K indicates the sum of quality factor k in Highway Project.
Optionally, according toDetermine the fitness function value f for the expense that represents4, whereinIndicate construction Movable i is when using jth kind arrangement and method for construction, the safety coefficient of construction activities i.
Optionally, described retrievable daily with the sequencing of each construction activities and the Highway Project Stock number is constraint condition, with the construction time is short, operating expenses is low, quality is high and highly-safe for optimization aim, using heredity The method that algorithm and linear programming are integrated, determines one group of Pareto optimal solution, wherein the information of each solution includes: each construction Arrangement and method for construction corresponding to activity, construction time started, specifically include:
Determine initial population P0, the individual in the initial population is applying of selecting of each construction activities in Highway Project The combination of work scheme；
According to cv (t)=Rt/R0After individual computing resource constraint violation value in -1 pair of initial population, progress selection operation, Crossover operation and mutation operation, and the individual after operation again after computing resource constraint violation value, is merged with initial population, obtained To new population Kt, whereinRtFor the t days consumed resources, RoFor the daily available resources of Highway Project Amount, ri jDaily consumed resource when selecting jth kind arrangement and method for construction for construction activities i, wi,tWhether carried out at the t days for movable i Construction is 1 if carrying out, is otherwise 0；
The individual that resource constraint violation value is 0 is divided into one group, is denoted as first group；
The individual that resource constraint violation value is not 0 is divided into one group, is denoted as second group；
First group of individual is according to individual fitness function value f1、f2、f3、f4Carry out Pareto sequence, second group of individual root Pareto sequence is carried out according to the resource constraint violation value CV of individual, and by the individual row in described second group in described first group Individual behind；
Elite reservation operations are carried out, the forward individual of selected and sorted generates population PtAfterwards, it jumps to the population In individual carry out selection operation, crossover operation, mutation operation, after generating progeny population, calculate individual money in progeny population Source constraint violation value merges parent and progeny population, carries out Pareto sequence, elite reservation operations, generates follow-on population, When reaching setting the number of iterations, then no longer jump, wherein PtIndicate the population obtained after the t times iteration；
Output reaches the individual in population corresponding when setting the number of iterations.
Optionally, first group of individual is according to individual fitness function value f1、f2、f3、f4Pareto sequence is carried out, Second group of individual carries out Pareto sequence according to the resource constraint violation value CV of individual, specifically includes:
By the fitness function value f of each of described first group individual1、f2、f3、f4With described first group in remaining The fitness function value of body is compared, and after comparison, determines two attributes m and S of the individual, four adaptations of m expression Degree functional value is respectively less than the individual amount of the individual, and S indicates that four fitness function values are all larger than the individual of the individual Set；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as first non-dominant layer F1；
By F1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and The m individual for being 0 is put into second non-dominant layer F2In；
By F2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and The m individual for being 0 is put into the non-dominant layer F of third3In；Until all individuals are divided into non-dominant layer F1,F2,F3…,FnIn；
By the money of individual remaining in each of described second group individual resource constraint violation value CV and described second group Source constraint violation value is compared, and after comparison, determines two attributes m and S of the individual, m expression resource constraint violates Value is respectively less than the individual amount of the individual, and S indicates that resource constraint violation value is all larger than the group of individuals of the individual；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as (n+1)th non-dominant layer Fn+1；
By Fn+1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, And the m individual for being 0 is put into second non-dominant layer Fn+2In；
By Fn+2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, And the m individual for being 0 is put into the non-dominant layer F of thirdn+3In；Until all individuals are divided into non-dominant layer Fn+1,Fn+2, Fn+3…,FmIn.
Optionally, described to choose the forward individual that sorts, generate population Pt, it specifically includes:
From first non-dominant layer F of first group of solution1, start, by each non-dominant layer FiIn individual NiIt is packed into Pt In, when the quantity of individual is greater than or equal to N for the first time, the non-dominant layer where individual is F to note at this timel, take F1,F2,F3…,Fl-1 In individual and from non-dominant layer FlMiddle selectionIndividual.
Optionally, described from non-dominant layer FlMiddle selectionIndividual specifically includes:
To FlThe magnitude of four fitness function values of middle individual carries out unification, obtains the fitness function of magnitude after reunification Value；
Four-dimensional hyperplane, the reference point equal with population scale are constructed according to the fitness function value of four magnitudes after reunification It is evenly distributed on the hyperplane；
The fitness function value of magnitude after reunification is normalized, the fitness function value after normalized is Coordinate of the individual on the hyperplane；
The vertical range of the individual distance reference line is calculated, the reference line is the hyperplane origin and reference point Line；
By the individual reference point association relevant to most short vertical range；
Choose the reference point composition reference set J for possessing minimum microhabitat pointmin={ j:argminjρj, j-th reference point Microhabitat point ρjIt is defined as associated with the reference point and from FlThe quantity of middle individual；
In reference point set JminIn randomly select a reference point:
If the ρ of selected reference pointj=0, then choose with the shortest individual of reference line vertical range where selected reference point, And by the ρ of selected reference pointjAdd one；It jumps in reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping；
If ρj>=1, randomly select one and the associated individual of selected reference point, and by the ρ of selected reference pointjAdd one, jumps It goes in reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping.
The specific embodiment provided according to the present invention, the invention discloses following technical effects: highway provided by the invention Engineering multiple target construction plan determine method obtain in Highway Project first each optional arrangement and method for construction of construction activities and Construction duration, expense, quality coefficient, safety coefficient and the daily resource usage amount of each arrangement and method for construction；Then, with each construction work Retrievable stock number is constraint condition to dynamic sequencing and Highway Project daily, with the construction time is short, construction cost High and highly-safe for optimization aim with low, quality, the method being integrated using genetic algorithm and linear programming determines one group of pa Tired support optimal solution, wherein the information of each solution includes: arrangement and method for construction corresponding to each construction activities, construction time started are applied The fitness function value of work scheme combination includes the representative that the construction duration of each arrangement and method for construction in being combined according to arrangement and method for construction determines The fitness function value of duration, according to arrangement and method for construction combine in each arrangement and method for construction expense determine representative expense fitness letter Numerical value, according to arrangement and method for construction combine in each arrangement and method for construction quality coefficient determine representation quality fitness function value and root According to arrangement and method for construction combine in each arrangement and method for construction safety coefficient determine representative safety fitness function value.When having comprehensively considered Between, expense, quality and safety factor, while joined resource constraint, and devise unique genetic algorithm and linear programming phase The method for solving of integration, so that the construction plan obtained according to the present invention has the characteristics that quality is high, high-efficient, practical.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention Example, for those of ordinary skill in the art, without creative efforts, can also obtain according to these attached drawings Obtain other attached drawings.
Fig. 1 is the classification figure that highway construction project construction plan works out optimization method in the prior art；
Fig. 2 is that highway engineering of embodiment of the present invention multiple target construction plan determines method flow diagram；
Fig. 3 is chromosome of embodiment of the present invention building mode figure；
Fig. 4 is that the highway engineering multiple target construction plan of further embodiment of this invention determines method flow diagram；
Fig. 5 is chiasma of embodiment of the present invention figure；
Fig. 6 is chromosomal variation of embodiment of the present invention figure；
Fig. 7 is the construction activities figure that the embodiment of the present invention is applied；
Fig. 8 is the exemplary construction network scheme of the present invention；
Fig. 9 is the chromosome knob composition in example of the present invention；
Figure 10 is that daily stock number of the example of the present invention under selected arrangement and method for construction combination consumes figure；
Figure 11 is the daily resource consumption figure of a certain Pareto optimal solution of example of the present invention；
Figure 12 is the exemplary execution scheme drawing of the present invention；
Figure 13 is the exemplary Time-Cost of the present invention-quality three-dimensional trade-off analysis visualization figure；
Figure 14 is the exemplary Time-Cost two dimension trade-off analysis visualization figure of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide it is a kind of consider resource constraint, comprehensive construction engineering time, expense, quality, The multiple target construction of the highway planning optimization method of safety.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real Applying mode, the present invention is described in further detail.
Embodiment one
As shown in Fig. 2, highway engineering multiple target construction plan provided by the invention determine method the following steps are included:
Step 201: obtaining the construction of each construction activities optional arrangement and method for construction and each arrangement and method for construction in Highway Project Duration, expense, quality coefficient, safety coefficient and daily resource usage amount；
Step 202: determining the sequencing of each construction activities；
Step 203: determining Highway Project retrievable stock number daily；
Step 204: with the sequencing of each construction activities and Highway Project, retrievable stock number is about daily Beam condition, with the construction time is short, operating expenses is low, quality is high and highly-safe for optimization aim, using genetic algorithm and linearly It plans the method being integrated, one group of Pareto optimal solution is determined, wherein the information of each solution includes: corresponding to each construction activities Arrangement and method for construction, construction the time started.
Wherein, the fitness function value of arrangement and method for construction combination includes the construction of each arrangement and method for construction in being combined according to arrangement and method for construction Duration determine the representative duration fitness function value, according to arrangement and method for construction combine in each arrangement and method for construction expense determine representative The fitness function value of expense, according to arrangement and method for construction combine in each arrangement and method for construction quality coefficient determine representation quality adaptation Degree functional value and according to arrangement and method for construction combine in each arrangement and method for construction safety coefficient determine representative safety fitness function Value；The structure of chromosome (individual) in genetic algorithm is as shown in figure 3, the quantity L of construction activities determines chromosome in project Length, the jth kind arrangement and method for construction that i-th of construction activities is selectedConstitute the gene in chromosome；
Method of determination at the beginning of construction activities are as follows: ST at the beginning of by introducing construction activitiesi, establish target letter Number is
Constraint condition are as follows: ETj< STi
ETj=STj+dj i≠j
System of linear equations, at the beginning of solving each construction activities with linear programming method.
In one embodiment, above-mentioned method for solving is NSGA-III genetic algorithm and the method that linear programming is integrated.
In step 204, the calculation method of each fitness function value is as follows:
According toDetermine the fitness function value f for representing the duration1, whereinIt is selected by construction activities i The construction duration of j kind arrangement and method for construction, M are the total quantity of construction activities on critical circuits.Wherein, critical circuits refer to network planning figure In total construction duration longest route, i.e. duration longest route, the non-key line construction duration be centainly less than Critical circuits.
According toDetermine the fitness function value f for the expense that represents2, whereinFor construction activities The direct cost of jth kind arrangement and method for construction selected by i, L are the total quantity of construction activities in Highway Project, and B is highway work The daily engineering cost of journey project, wherein direct cost refers to the general expenses of the composition engineering entity consumed in work progress, packet Include labour cost, fee of material, construction machinery usage charges etc..
According toDetermine the fitness function value f for the expense that represents3, whereinIt indicates Construction activities i is in the case where selecting jth kind arrangement and method for construction, the numerical value of quality factor k, wti,kIndicate the weight of quality factor k, wtiIndicate the weight of construction activities i, K indicates the sum of quality factor k in Highway Project.
According toDetermine the fitness function value f for the expense that represents4, whereinIndicate that construction activities i exists When using jth kind arrangement and method for construction, the safety coefficient of construction activities i.
Step 204 determines that the process of optimal construction plan combination is as follows:
According to population scale N, N number of engineering construction scheme combination is generated at random, constitutes initial population P0, initial population In individual be Highway Project arrangement and method for construction combination；
According to cv (t)=Rt/R0After individual computing resource constraint violation value in -1 pair of initial population, progress selection operation, Crossover operation and mutation operation, and the individual after operation again after computing resource constraint violation value, is merged with initial population, obtained To new population Kt, whereinRtFor the t days consumed resources, RoFor the daily available resources of Highway Project Amount, ri jDaily consumed resource when selecting jth kind arrangement and method for construction for construction activities i, wi,tWhether carried out at the t days for movable i Construction is 1 if carrying out, is otherwise 0；
The individual that resource constraint violation value is 0 is divided into one group, is denoted as first group；
The individual that resource constraint violation value is not 0 is divided into one group, is denoted as second group；
First group of individual is according to individual fitness function value f1、f2、f3、f4Carry out Pareto sequence, second group of individual root According to individual resource constraint violation value CV carry out Pareto sequence, and by second group individual row in first group individual Below；
Elite reservation operations are carried out, the forward individual of selected and sorted generates population PtAfterwards, it jumps to the population In individual carry out selection operation, crossover operation, mutation operation, after generating progeny population, calculate individual money in progeny population Source constraint violation value merges parent and progeny population, carries out Pareto sequence, elite reservation operations, generates follow-on population, When reaching setting the number of iterations, then no longer jump, wherein PtIndicate the population obtained after the t times iteration；
Output reaches the individual in population corresponding when setting the number of iterations.
Wherein, first group of individual is according to individual fitness function value f1、f2、f3、f4Progress Pareto sequence, second group Individual carries out Pareto sequence according to the resource constraint violation value CV of individual, specifically includes:
By the fitness function value f of each of first group individual1、f2、f3、f4With first group in remaining individual adaptation Degree functional value is compared, and after comparison, determines two attributes m and S of individual, four fitness function values of m expression are small In the individual amount of individual, S indicates that four fitness function values are all larger than the group of individuals of individual；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as first non-dominant layer F1；
By F1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and The m individual for being 0 is put into second non-dominant layer F2In；
By F2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and The m individual for being 0 is put into the non-dominant layer F of third3In；Until all individuals are divided into non-dominant layer F1,F2,F3…,Fl-1 In；
By the resource constraint violation value CV of each of second group individual with second group in remaining individual resource constraint disobey Converse value is compared, and after comparison, determines two attributes m and S of individual, m expression resource constraint violation value is less than individual Individual amount, S indicate that resource constraint violation value is greater than the group of individuals of individual；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as (n+1)th non-dominant layer Fn+1；
By Fn+1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, And the m individual for being 0 is put into second non-dominant layer Fn+2In；
By Fn+2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, And the m individual for being 0 is put into the non-dominant layer F of thirdn+3In；Until all individuals are divided into non-dominant layer Fn+1,Fn+2, Fn+3…,FmIn.
Wherein, the forward individual that sorts is chosen, population P is generatedt, it specifically includes:
From first non-dominant layer F of first group of solution1, start, by each non-dominant layer FiIn individual NiIt is packed into Pt In, when the quantity of individual is greater than or equal to N for the first time, the non-dominant layer where individual is F to note at this timel, choose F1,F2,F3…, Fl-1In individual and from non-dominant layer FlMiddle selectionIndividual.
From non-dominant layer FlMiddle selectionThe specific method is as follows for individual:
To FlThe magnitude of four fitness function values of middle individual carries out unification, obtains the fitness function of magnitude after reunification Value；
Four-dimensional hyperplane, the reference point equal with population scale are constructed according to the fitness function value of four magnitudes after reunification It is evenly distributed on hyperplane；
The fitness function value of magnitude after reunification is normalized, the fitness function value after normalized is Coordinate of the individual on hyperplane；
The vertical range of individual distance reference line is calculated, reference line is the line of hyperplane origin and reference point；
Individual reference point relevant to most short vertical range is associated with；
Choose the reference point composition reference set J for possessing minimum microhabitat pointmin={ j:argminjρj, j-th reference point Microhabitat point ρjIt is defined as associated with reference point and from FlThe quantity of middle individual；
In reference point set JminIn randomly select a reference point:
If the ρ of selected reference pointj=0, then choose with the shortest individual of reference line vertical range where selected reference point, And by the ρ of selected reference pointjAdd one；It jumps in reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping；
If ρj>=1, randomly select one and the associated individual of selected reference point, and by the ρ of selected reference pointjAdd one, jumps It goes in reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping.
Embodiment two
Highway engineering multiple target construction plan provided by the invention determines that method is compiled by: basic data settlement, construction plan The execution of optimization algorithm processed, construction plan based on solving result such as draw at three steps compositions.
Step 1: basic data settlement
(1) construction activities data
Construction activities data include: the quantity of construction activities, the optional arrangement and method for construction of each construction activities, each arrangement and method for construction institute it is right The construction activities duration answered/expense/quality coefficient (%)/safety coefficient (%)/daily resource usage amount.
(2) logical relation data between activity
Sequencing constraint of the logical relation data between each construction activities between activity.
(3) resource availability data
Resource availability data are the daily resource constraint amount of entire project.
(4) supplemental characteristic needed for NSGA-III algorithm
Parameter needed for NSGA-III algorithm includes: algebra, the crossover probability, mutation probability of population scale, algorithm traversal.
Step 2: the execution of construction plan establishment optimization algorithm
Highway construction project multiple target construction plan based on NSGA-III method frame works out Optimization Solution algorithm, to public affairs Road engineering construction plan carry out: it is under resource constraint and consider simultaneously the time, expense, quality, safety four optimization The Optimization Solution of target.
The logical relation of this step can be expressed as, and propose algorithm frame, the data input frame that will be put in order using this patent In frame, operation solution is then carried out, solving result is finally exported.Detailed logic sequence is as follows:
(1) content inputted: the basic data that 1. first step is arranged includes: the movable quantity L of engineering construction, each Construction activities corresponding arrangement and method for construction quantity n, construction activities weight wti, the construction time of construction activities under each arrangement and method for construction ExpenseQuality factorAnd its corresponding weight wti,k, safety coefficientAnd daily consumed resource ri j；2. each construction Sequencing between activity；3. the entire daily resource constraint amount R of project0；4. parameter needed for NSGA-III algorithm, comprising: Algebra Gen, the crossover probability P of population scale N, algorithm traversalc, mutation probability Pm。
(2) the content operation of input is solved: carries out operation and solution using the optimization algorithm that this patent is proposed, and obtains To one group of Pareto optimal solution.
(3) content exported: obtained Pareto optimality disaggregation is exported.Pareto optimality disaggregation includes one group of pa Tired support optimal solution.Each Pareto optimal solution contains following information: at the beginning of each construction activities, each construction live The dynamic arrangement and method for construction used.
It is determined using genetic algorithm with the method for solving that linear programming is integrated and is opened containing each movable arrangement and method for construction and activity The step of Pareto optimality disaggregation of beginning temporal information, is as shown in Figure 4:
(1) chromosome is constructed
The building mode of chromosome are as follows: the quantity L of construction activities determines the length of chromosome in project, and i-th of construction is lived The dynamic jth kind arrangement and method for construction selectedThe gene in chromosome is constituted, the structure of chromosome is as shown in figure 3, a chromosome generation A kind of arrangement and method for construction combination that each construction activities use in table construction project.
(2) initial population is generated
According to population scale N, N number of engineering construction scheme combination is generated at random, constitutes initial population.
(3) fitness function value is calculated
Fitness function value is used to evaluate the superiority and inferiority of chromosome, and every kind of arrangement and method for construction is combined, the finger of its superiority and inferiority is evaluated It is designated as: duration, expense, quality, safety, therefore chromosome fitness function value respectively represents this four indexs, the first two index It pursues and minimizes, latter two index, which is pursued, to be maximized.It is calculated to facilitate Pareto sequence, quality is needed to locate with safety index Reason.The calculation method of chromosome fitness value is as follows:
1. representing the fitness function value f of duration1
f1That is construction project duration, calculation are that the construction duration of all construction activities on critical circuits is cumulative. Calculation formula are as follows:
When indicating using jth kind arrangement and method for construction, the construction duration of activity i on critical circuits；
M: activity sum on critical circuits.
2. representing the fitness function value f of expense2
f2I.e. construction project expense, expense are made of direct cost and indirect expense, and direct cost in project according to respectively applying The arrangement and method for construction that work activity uses determines that indirect expense is obtained according to day's work expense (definite value) multiplied by calculating time claimed.Specifically Calculation formula are as follows:
Tc: the construction project duration；B: day's work expense in construction project is indicated；It indicates to use n arrangement and method for construction When, the direct cost of activity i in construction project；L: activity sum in project.
3. the fitness function value f of representation quality3
First quantification treatment is carried out for construction quality, quality maximization target is then become into quality adaptation degree functional value It minimizes, concrete operations are as follows:
In formula,In the case where indicating that construction activities i utilizes arrangement and method for construction j, the numerical value of quality factor k；
wti,k: it indicates compared to other quality factors in construction activities i, the weight of quality factor k；
wti: it indicates compared to other construction activities in project, the weight of construction activities i；
K: the sum of quality factor k in construction project is indicated.
4. representing safe fitness function value f4
Linear relevant research achievement between this patent incorporation engineering quality and safety, using the safety index coefficient of hypothesis For being directed to safety coefficient quantification treatment, maximizing safety target is then become into safe fitness function value and is minimized, specifically Expression are as follows:
In formula:When indicating using jth kind arrangement and method for construction, the safety coefficient of activity i in construction project.
(4) computing resource constraint violation value
The calculating step of resource constraint violation value are as follows:
1. determining that the construction of each construction activities starts and the end time
Introduce variable STi, deputy activity i's starts the time started of constructing.In the arrangement and method for construction that each activity known uses In the case of, by the end time ET of construction activitiesiIt indicates are as follows:
ETi=STi+di
In formula, di--- the construction duration of movable i, i.e. fitness function value f1In di。
The meaning of the expression formula is to continue equal to the construction activities time started plus activity construction the construction activities end time Time.
There are sequence of construction logical relations between different construction activities, i.e., some construction activities must be applied at another After work activity end, just it can be carried out.This logical relation expression are as follows:
ETi< STj
The meaning of the expression formula are as follows: at the beginning of less than j-th construction activities of the end time of i-th of construction activities.
During calculating fitness function value, it is known that each construction activities time started on critical circuits, i.e. part STiIt is worth, each construction activities time started calculation is to solve following linear programming problems on remaining non-key route:
By the solution of linear programming problem, each activity construction time started under arrangement and method for construction combination can be obtained.
2. determining the daily consumed resource of engineering
The daily consumed resource of engineering is expressed as completing the stock number needed for same day construction activities, for each construction For activity, construction and two kinds of situations of not constructing are only existed within t days the, can introduce Boolean variable here is illustrated, finally Calculating for consumed resource daily under the program, using following formula:
In formula:
Rt--- the t days consumed resources；
Ro--- the daily available volume of resources of construction project；
ri j--- when utilizing jth kind arrangement and method for construction, the daily consumed resource of movable i；
wi,t--- whether movable i constructs for t days the, is 1 if construction, is otherwise 0；
STi--- the construction time started of movable i；
ETi--- the construction end time of movable i；
Tc--- the duration of construction project.
3. determining resource constraint violation value
As the t days consumed resource RtGreater than resource provision amount RoWhen, then the resource constraint violation value cv (t) of this day are as follows:
Cv (t)=Rt/R0-1
The resource constraint violation value of arrangement and method for construction combination is that daily resource constraint violation value is cumulative in the duration, expression formula Are as follows:
(5) selection operation
The constraint violation value of all arrangement and method for construction combinations known at this time, i.e., individual constraint violation value in population, selection behaviour Make by the way of tournament selection, two individuals (two kinds of arrangement and method for construction combinations) is randomly selected in initial population.
1. only choosing arrangement and method for construction combination of the resource constraint violation value CV equal to 0 in two kinds of arrangement and method for construction combinations is used as father Generation；
2. the smaller individual of selected value is used as father if the resource constraint violation value CV of two kinds of arrangement and method for construction combination is not 0 Generation；
3. randomly selecting any one individual conduct if the resource constraint violation value CV of two kinds of arrangement and method for construction combination is 0 Parent.
(6) crossover operation
According to crossover probability pc, choose individual to be intersected and enter mating pond, in mating pond, randomly select two individuals aiWith aj, carry out crossover operation.Crossover process is to select a crosspoint b at randomc, two individuals intercourse from crosspoint bc Start to the genetic fragment after chromosome length L, forms two new chromosome ai' and aj', detailed process is as shown in Figure 5.
(7) mutation operation
According to mutation probability pm, select individual ak, carry out mutation operation.Mutation process is to select a variation at random Point bm, which represents length as b in the chromosome of LmA construction activities, by the arrangement and method for construction of the construction activitiesReplacement For another arrangement and method for construction random in the activity arrangement and method for construction alternative collectionForm new individual ak', as shown in Figure 6.
(8) new population is synthesized
Will experience selection, intersect, generated after variation N number of new arrangement and method for construction combination calculate after constraint violation value with it is N number of just The combination of beginning arrangement and method for construction merges, and generation includes the new population K of 2N arrangement and method for construction combinationt。
(9) to new population KtCarry out Pareto sequence
For KtIn all individuals, be divided into two groups and be ranked up.
First group: resource constraint violation value CV is 0 all individuals, i.e., all feasible arrangement and method for construction combinations.According to suitable Response functional value carries out Pareto sequence, and sequencer procedure is as follows: by each individual aiFitness function value f1、f2、f3、f4With it is remaining Under the fitness function values of all individuals be compared, after comparison, give this individual two attribute, be respectively as follows:
①mi: refer to that four fitness function values are respectively less than all individual amounts of this individual；
②Si: refer to that four fitness function values are all larger than all individual collections of this individual.
By all miArrangement and method for construction combination equal to 0, is put into non-dominant layer, which is that number is 1, refers to first A non-dominant layer, is denoted as F1.For F1Each individual in the middle investigates set Si, by set SiEach of individual miIt subtracts 1, m is found againiFor 0 individual, it is put into the non-dominant layer F that number is 22In.For F2In each individual, investigate set Si, In the same way by SiIn individual be layered, that is, be put into non-dominant layer F3In ... it in this approach, can be by all individuals It is divided into non-dominant layer F1,F2,F3…,FnIn.
Second group: the individual that resource constraint violation value CV is not 0 being divided into one group of solution, is violated according to the resource constraint of individual Value CV is ranked up with above-mentioned non-dominated ranking principle.
Assuming that the quantity of first group of feasible arrangement and method for construction combination is N at this timefIf Nf> N then carries out step (10) elite guarantor When staying operation, feasible solution need to be only considered.If Nf< N, the individual amount N-N of remaining vacancyf, examined since the individual in second group Consider, until supplementing full next-generation parent population Pt+1。
(10) elite retains, and generates next-generation parent population Pt+1。
Construct a new population St, from first non-dominant layer (F1) start, gradually by the arrangement and method for construction of each non-dominant layer It is added in combination StIn, until StIndividual amount be equal to N, or for the first time be greater than N.Assuming that finally by StThe construction party accommodated Non-dominant layer where case combination is Fl, then from Fl+1All individuals that layer starts to the end will be all rejected.In FlLayer Preceding arrangement and method for construction combination has been selected as next-generation parent population Pt+1, Pt+1In remaining individual (N-St\Fl) need from FlMiddle selection.Selection process is as follows:
1. creating hyperplane and normalized
For the magnitude of unified fitness function value, handled using following formula:
In formula: fi(x): referring to i-th of fitness function value in individual x；
The minimum value of fitness function value in all this generation individuals, i.e.,
I-th of fitness function value of worst individual estimated by previous generation individual.
It for treated population, needs to find out limit point in each target axis direction, to constitute the super of a M dimension Plane, wherein target axis is determined that fitness function value of the present invention has four classes, thus M is 4 by fitness function.In each target Limit point on axis, which is defined as finding a solution, can make following formula ASF (x, wj) minimize.
In formula, wj={ wj,1,wj,2,…,wj,M}TIt is target axis fjAxis direction, and if when meeting i=j, wj,i=1； Otherwise wj,i=0, if wj,iWhen=0, the numerical value (generally 10 of a very little is taken-6) replace.The final form of expression of limit point For the object vector of individual.
After M all target axis is considered, M limit point can be found.This M limit point is used to composition M The hyperplane of dimension.Intercept d of the hyperplane on each target axis can thus be calculatedi.Later, with following formula to mesh Scalar functions are normalized.
When if there is degenerate solution, either intercept is negative, then diIt is set as StMiddle non-domination solution is in targetOn most Big value.
2. operation associated
After having created hyperplane, the reference point equal with population scale is evenly distributed on entire hyperplane.According to original Point and the reference point on hyperplane, can draw a starting point is origin, and across the line of reference point, this line is defined as referring to Line.After the normalized of previous step, every group of arrangement and method for construction combination can be considered the point for belonging to the same space with hyperplane, The coordinate of this point is the fitness function value after arrangement and method for construction combination normalizationCalculate population StIn each individual aiTo the vertical range d (a of every reference linei), choose shortest vertical range d (ai), it will be individual related to most short vertical range Reference point (reference point is determined according to reference line) association.
3. microhabitat keeps policy
After operation associated, a reference point might have one or more individual and be associated, and may also not have certainly There is individual association.Microhabitat point, the microhabitat point ρ of j-th of reference point are introduced hereinjIt is defined as associated with the reference point And from Pt+1=St/FlThe quantity of middle individual；Selection possesses minimum microhabitat point ρjReference point, composition refer to point set, note Make Jmin={ j:argminjρj}.In reference point set JminIn randomly select a reference point:
If ρj=0, it is meant that in population St/FlIn without individual be associated with the reference point, for FlPareto forward position, It is possible that two kinds of situations.The first situation, in Pareto forward position FlIn, it might have one or more individuals and selection Reference point association.In this case, possess and be selected supplement with the individual of the most short vertical range of reference line where the reference point To Pt+1In.Then, the microhabitat point ρ of the reference pointjValue add one.Second situation, in Pareto forward position FlIn, without individual It is associated with reference point, at this point, not considering reference point this generation population Pt+1Influence.
If ρj>=1, it is meant that in population St/FlIt is middle to be associated in the presence of individual with the reference point, in Pareto forward position FlIn, One is selected at random adds to P with the associated individual of the reference pointt+1In.Then, the microhabitat point ρ of the reference pointjValue add One.
In microhabitat point ρjAfter above-mentioned update, this process is repeated K times, until by population Pt+1The individual of middle vacancy Number supplement is full, makes its population scale N.
Generating new parent Pt+1Afterwards, feasible solution and infeasible solutions are distinguished again, with the selection of genetic algorithm, intersection, Mutation operation generates new filial generation Qt+1, parent is merged with filial generation, repeats elite retention strategy, such interative computation, until meeting Until the number of iterations Gen needed for algorithm.
Finally, algorithm exports one group of Pareto optimal solution, the information that each solution includes includes: that (1) each construction activities use Arrangement and method for construction, (2) each construction activities time started.
Step 3: the construction plan based on solving result is drawn
This step ties up on the basis of solution obtained by second step, draws the corresponding execution scheme drawing of each solution.Each solution The drafting of execution scheme drawing, is made of following steps:
(1) coordinate system is drawn
The horizontal axis of coordinate system is the time, and unit is day, using 10 as scale；The longitudinal axis of coordinate system is activity SN, is made with 1 For scale.
(2) construction activities are drawn
Foundation: the arrangement and method for construction that each construction activities are selected, each activity construction time started.
Bar graph: each flagpole pattern occupies lateral section identical with activity SN, the starting point of bar graph and terminal End respectively correspond at the beginning of the construction activities with the end time, entire bar graph represent the constructions of corresponding construction activities into Journey.As shown in fig. 7, there is the bar graph of oblique line in the inside in figure: the number by bar graph: the construction activities on critical circuits are applied The arrangement and method for construction number that work activity is selected.
It is illustrated in an illustrative manner below
Highway construction project project in the case shares 18 construction activities, and Fig. 8 illustrates the highway construction project and applies Work network planning figure, the available arrangement and method for construction of each activity and arrangement and method for construction corresponding time, expense, quality coefficient, safety system Number is as shown in table 1 with daily consumed resource.
Step 1: case basic data settlement
(1) construction activities data
This engineering shares 18 construction activities, when movable under the optional arrangement and method for construction and the arrangement and method for construction of each construction activities Between, expense, quality coefficient, safety coefficient, daily consumed resource it is as shown in the table
1 construction activities data table related of table
(2) logical constraint between activity
As can be seen from FIG. 8, the logical constraint between activity are as follows:
ET1< ST5At the beginning of the end time of activity 1 is less than activity 5；
ET1< ST6At the beginning of the end time of activity 1 is less than activity 6；
ET2< ST10At the beginning of the end time of activity 2 is less than activity 10；
ET3< ST13At the beginning of the end time of activity 3 is less than activity 13；
ET4< ST14At the beginning of the end time of activity 4 is less than activity 14；
ET5< ST7At the beginning of the end time of activity 5 is less than activity 7；
ET5< ST12At the beginning of the end time of activity 5 is less than activity 12；
ET6< ST8At the beginning of the end time of activity 6 is less than activity 8；
ET6< ST9At the beginning of the end time of activity 6 is less than activity 9；
ET6< ST10At the beginning of the end time of activity 6 is less than activity 10；
ET7< ST11At the beginning of the end time of activity 7 is less than activity 11；
ET8< ST11At the beginning of the end time of activity 8 is less than activity 11；
ET9< ST12At the beginning of the end time of activity 9 is less than activity 12；
ET10< ST12At the beginning of the end time of activity 10 is less than activity 12；
ET10< ST14At the beginning of the end time of activity 10 is less than activity 14；
ET11< ST17At the beginning of the end time of activity 11 is less than activity 17；
ET12< ST15At the beginning of the end time of activity 12 is less than activity 15；
ET13< ST16At the beginning of the end time of activity 13 is less than activity 16；
ET14< ST16At the beginning of the end time of activity 14 is less than activity 16；
ET14< ST17At the beginning of the end time of activity 14 is less than activity 17；
ET15< ST17At the beginning of the end time of activity 15 is less than activity 17；
ET16< ST18At the beginning of the end time of activity 16 is less than activity 18；
ET17< ST18At the beginning of the end time of activity 17 is less than activity 18.
(3) resource availability data
Resource availability data are the daily resource constraint amount R of entire projectoIt is 30.
(4) parameter needed for NSGA-III algorithm
Population scale N=200；Traverse algebra Gen=100；Crossover probability Pc=1；Mutation probability Pm=1/18.
Step 2: the execution of construction plan establishment optimization algorithm
The basic data of the basic data of engineering and algorithm is input in algorithm frame, chromosome is generated, due to algorithm Population scale be 200 (i.e. 200 initial solutions), therefore only randomly select one and be illustrated.
(1) it according to the quantity of construction activities and the available construction activities of each construction activities, produces as shown in Figure 9 Chromosome.
(2) each movable construction duration, expense, quality can be determined according to the arrangement and method for construction that each construction activities use Coefficient, safety coefficient, as shown in the table.
2 arrangement and method for construction corresponding data table of table
The fitness function value of the chromosome is carried out according to fitness function value calculation formula:
f1: it is determined according to the key job construction duration in network planning figure on critical circuits, critical circuits are as follows: 1- 6-10-12-15-17-18, therefore the duration of construction project are as follows:
f1=T=15+24+33+28+16+18+18=152
f2: due to not providing the relevant information of indirect expense in present case, period of construction cost herein only considers The sum of the operating expenses of each construction activities of direct cost, i.e. construction project.
f2=C=2150+3000+3200+35000+20000+18000+24000+220+150+320+450+1500+ 3200+3000+3500+1500+3200+2200=124590
f3: the sum of the quality coefficient for subtracting each construction activities of construction project with 100.
f3=100-Q=100- (2.685+4.83+4.948+8.0575+9.92+6.82+7.13+0.95+0.73+ 0.654+1.914+2.151+5.096+5.958+6.958+2.193+4.398+3.2675)=100-78.66=21.34
f4: the sum of the safety coefficient for subtracting each construction activities of construction project with 100.
f4=100-S=100- (2.52+4.45+4.55+7.35+9.03+6.24+6.52+0.96+0.76+0.69+ 1.82+2.04+4.69+5.46+6.36+2.07+4.06+3.04)=100-72.59=27.41
For the chromosome, fitness function value 152,124590,21.34,27.41.
(3) constraint violation value is calculated, if the route is unsatisfactory for critical circuits constraint, its constraint violation value is set as 100000, if meeting critical circuits constraint, need to judge whether to meet resource constraint.
1. solving linear programming
Objective function is
Wherein, the beginning of construction activities is determined with the end time on critical circuits, here with the scale in reference axis Deputy activity starts and the end time.That is ST1=0, ET1=15, ST6=15, ET6=39, ST10=39, ET10=72, ST12= 72, ET12=100, ST15=100, ET15=116, ST17=116, ET17=134, ST18=134, ET18=152.
Constraint condition: sequence of construction is constrained in arrange and has been set out at data, now lists equality constraint:
ET1=ST1+15；ET2=ST2+15；ET3=ST3+33；ET4=ST4+16；ET5=ST5+22；ET6=ST6+24； ET7=ST7+15；ET8=ST8+14；ET9=ST9+23；ET10=ST10+33；ET11=ST11+12；ET12=ST12+28；ET13= ST13+18；ET14=ST14+9；ET15=ST15+16；ET16=ST16+28；ET17=ST17+18；ET18=ST18+18。
Pass through and solves linear programming, it can be deduced that one group of solution for meeting above-mentioned constraint, i.e., each movable construction time started, In the case where the arrangement and method for construction used in each activity known, the movable construction end time is learnt.
3 construction activities of table start and end time table
2. calculating daily consumed resource
Daily consumed resource starts according to each activity construction and the end time, and movable daily consumed resource is with money Source consumption calculation formula is calculated, and is showed in the form of resource consumption figure here, as shown in Figure 10
3. computing resource constraint violation value
Due to daily resource provision amount R0It is 30, is below by the daily consumed resource shown in figure in engineering total construction period 30, therefore the constraint violation value of the assembled scheme is 0.
It (4) is to carry out Pareto sequence to quantity after merging after selecting, intersect, making a variation, merging.Now in addition to institute before Case is lifted, in addition there are three the arrangement and method for construction combination that resource constraint violation value is all 0, the fitness function values of this four schemes For shown in following table:
4 arrangement and method for construction fitness function value of table
By comparing, it is known that each fitness function value of scheme 2 is respectively less than remaining each scheme, in remaining scheme 1,3,4, The fitness function value of scheme is respectively less than other two schemes. none of.It to sum up discusses, the m of each schemeiWith Si, pa is tired Support sequence are as follows:
The m of each scheme of table 5iWith Si
(5) it is determining into next-generation new population Pt+1In individual when (individual amount N), first construct a population St, According to the sequence that Pareto sorts, successively selection is filled into S since the combination of feasible arrangement and method for constructiontIn, it determines for the first time more than N Pareto layer Fl, therefrom remaining N-S is filtered out with elite retention strategyt/FlIndividual.
(6) new population P is being determinedt+1Later, it repeats the above process, the genetic algebra Gen until meeting algorithm requirement is Only.
It by the execution of algorithm, there are out 200 Pareto optimal solutions, randomly select a solution and have to solving result Body display.
The a certain final result of table 6 is shown
Duration under arrangement and method for construction combination is 123, expense 114320, quality coefficient 82.716, and safety coefficient is 76.27。
Corresponding resource consumption is as shown in figure 11.
It can be seen that the consumed resource under the assembled scheme is respectively less than and is equal to 30, meet resource constraint.
According to arrangement and method for construction and construction activities time started, construction plan Figure 12 is drawn out, there is oblique line in the inside in figure Bar graph represents each construction activities on critical circuits.
The present invention is accomplished that the four-dimensional trade-off analysis of Time-Cost-quality-safety can still be chosen on this basis Any three in four targets or any two target, to four trade-off analysis results into three-dimensional or bidimensional visualization exhibition It is existing.Here distinguish access time-expense-quality three-dimensional trade-off analysis visualization and Time-Cost two dimension trade-off analysis is visual Change, present case optimum results are subjected to example displaying.
Figure 13 is Time-Cost-quality three-dimensional trade-off analysis visualization, and Figure 14 is Time-Cost two dimension trade-off analysis Visualization.It is found that solving result has not focused on three-dimensional space from Time-Cost-quality three-dimensional trade-off analysis visualization figure Between in a certain region in, embody solving result to hold back scattered property preferable.From Time-Cost trade-off analysis, also it can be seen that algorithm It is preferable that solving result holds back scattered property.
Resource constraint proposed by the present invention gets down the highway construction project multiple target construction plan establishment optimization method with following Advantage.
(1) security dimension is introduced in traditional Time-Cost-quality trade-off analysis, realizes Time-Cost- The four-dimensional trade-off analysis of quality-safety, can provide under different Resource Allocation Formulas, more comprehensively arrangement and method for construction for contractor Combination decision has higher practicability.
(2) consider that the highway construction project multiple target construction plan under resource constraint works out optimization, not only for building If the combination of engineering integral construction scheme optimizes, also it is contemplated that the whole daily consumed resource of construction project, so that compiling Construction plan must be bonded actual requirement of engineering.
(3) two class details corresponding to each optimal solution, i.e., each construction included in each solution can be exported At the beginning of activity and selected arrangement and method for construction.Based on this two category information, it can completely draw out highway construction project and apply Work planning chart also can calculate daily consumed resource by this.
(4) the multiple target derivation algorithm being integrated based on NSGA-III and linear programming that this patent is proposed, Neng Goushi Now to the solution of the multi-objective optimization question of three targets or more, and has better solution ability.Opposite processing highway construction For other algorithms of engineering multiple target construction plan establishment optimization, which, can be with while having higher solution efficiency Higher-quality optimum results are provided.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other The difference of embodiment, the same or similar parts in each embodiment may refer to each other.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not It is interpreted as limitation of the present invention.

Claims (10)

1. a kind of highway engineering multiple target construction plan determines method characterized by comprising
It obtains the construction duration of each optional arrangement and method for construction of construction activities and each arrangement and method for construction in Highway Project, take With, quality coefficient, safety coefficient and daily resource usage amount；
Determine the sequencing of each construction activities；
Determine the Highway Project retrievable stock number daily；
With the sequencing of each construction activities and the Highway Project, retrievable stock number is constraint item daily Part, with the construction time is short, operating expenses is low, quality is high and highly-safe for optimization aim, using genetic algorithm and linear programming The method for solving being integrated determines one group of Pareto optimal solution, wherein the information of each solution includes: corresponding to each construction activities Arrangement and method for construction, construction the time started, arrangement and method for construction combination fitness function value include respectively being applied in being combined according to arrangement and method for construction The fitness function value for the representative duration that the construction duration of work scheme determines, according to arrangement and method for construction combine in each arrangement and method for construction expense With the fitness function value of determining representative expense, according to arrangement and method for construction combine in each arrangement and method for construction quality coefficient determine generation The fitness function value of table quality and according to arrangement and method for construction combine in each arrangement and method for construction safety coefficient determine representative safety Fitness function value.
2. highway engineering multiple target construction plan according to claim 1 determines method, which is characterized in that the solution side Method is NSGA-III genetic algorithm and the method that linear programming is integrated.
3. highway engineering multiple target construction plan according to claim 1 determines method, which is characterized in that according toDetermine the fitness function value f for representing the duration1, whereinFor jth kind arrangement and method for construction selected by construction activities i Construction duration, M be critical circuits on construction activities total quantity.
4. highway engineering multiple target construction plan according to claim 3 determines method, which is characterized in that according toDetermine the fitness function value f for the expense that represents2, whereinFor jth selected by construction activities i The direct cost of kind arrangement and method for construction, L are the total quantity of construction activities in Highway Project, and B is that Highway Project is daily Engineering cost.
5. highway engineering multiple target construction plan according to claim 4 determines method, which is characterized in that according toDetermine the fitness function value f for the expense that represents3, whereinIndicate that construction activities i is being selected In the case where jth kind arrangement and method for construction, the numerical value of quality factor k, wti,kIndicate the weight of quality factor k, wtiIndicate that construction is lived The weight of dynamic i, K indicate the sum of quality factor k in Highway Project.
6. highway engineering multiple target construction plan according to claim 5 determines method, which is characterized in that according toDetermine the fitness function value f for the expense that represents4, whereinIndicate that construction activities i is constructed using jth kind When scheme, the safety coefficient of construction activities i.
7. highway engineering multiple target construction plan according to claim 6 determines method, which is characterized in that described with each institute Retrievable stock number is constraint condition to the sequencing and the Highway Project for stating construction activities daily, when constructing Between it is short, operating expenses is low, quality is high and it is highly-safe be optimization aim, the side being integrated using genetic algorithm and linear programming Method determines one group of Pareto optimal solution, wherein the information of each solution includes: arrangement and method for construction corresponding to each construction activities is applied It the work time started, specifically includes:
Determine initial population P0, the individual in the initial population is the construction party that each construction activities are selected in Highway Project The combination of case；
According to cv (t)=Rt/R0After individual computing resource constraint violation value in -1 pair of initial population, carries out selection operation, intersects Operation and mutation operation, and the individual after operation again after computing resource constraint violation value, is merged with initial population, obtained newly Population Kt, whereinRtFor the t days consumed resources, RoFor the daily available volume of resources of Highway Project, ri jDaily consumed resource when selecting jth kind arrangement and method for construction for construction activities i, wi,tWhether applied within t days for movable i Work is 1 if carrying out, is otherwise 0；
The individual that resource constraint violation value is 0 is divided into one group, is denoted as first group；
The individual that resource constraint violation value is not 0 is divided into one group, is denoted as second group；
First group of individual is according to individual fitness function value f1、f2、f3、f4Pareto sequence is carried out, second group of individual is according to a The resource constraint violation value CV of body carries out Pareto sequence, and the individual row in described second group is a in described first group Behind body；
Elite reservation operations are carried out, the forward individual of selected and sorted generates population PtAfterwards, it jumps to in the population Body carries out selection operation, crossover operation, mutation operation, after generating progeny population, calculates resource constraint individual in progeny population Violation value merges parent and progeny population, carries out Pareto sequence, elite reservation operations, generates follow-on population, when reaching When setting the number of iterations, then no longer jump, wherein PtIndicate the population obtained after the t times iteration；
Output reaches the individual in population corresponding when setting the number of iterations.
8. highway engineering multiple target construction plan according to claim 7 determines method, which is characterized in that described first group Individual is according to individual fitness function value f1、f2、f3、f4Carry out Pareto sequence, second group of individual according to individual resource about Beam violation value CV carries out Pareto sequence, specifically includes:
By the fitness function value f of each of described first group individual1、f2、f3、f4With described first group in remaining individual it is suitable Response functional value is compared, and after comparison, determines two attributes m and S of the individual, m four fitness functions of expression Value is respectively less than the individual amount of the individual, and S indicates that four fitness function values are all larger than the group of individuals of the individual；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as first non-dominant layer F1；
By F1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and be by m 0 individual is put into second non-dominant layer F2In；
By F2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and be by m 0 individual is put into the non-dominant layer F of third3In；Until all individuals are divided into non-dominant layer F1,F2,F3…,FnIn；
About by the resource of individual remaining in each of described second group individual resource constraint violation value CV and described second group Beam violation value is compared, and after comparison, determines two attributes m and S of the individual, m expression resource constraint violation value is equal Less than the individual amount of the individual, S indicates that resource constraint violation value is all larger than the group of individuals of the individual；
Attribute m is equal to 0 individual, non-dominant layer is put into, is denoted as (n+1)th non-dominant layer Fn+1；
By Fn+1Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and by m Second non-dominant layer F is put into for 0 individualn+2In；
By Fn+2Each of the m of each of the corresponding set S of individual individual subtract 1, find m again as 0 individual, and by m The non-dominant layer F of third is put into for 0 individualn+3In；Until all individuals are divided into non-dominant layer Fn+1,Fn+2,Fn+3…,Fm In.
9. highway engineering multiple target construction plan according to claim 7 determines method, which is characterized in that the selection row The forward individual of sequence generates population Pt, it specifically includes:
From first non-dominant layer F of first group of solution1, start, by each non-dominant layer FiIn individual NiIt is packed into PtIn, when a When the quantity of body is greater than or equal to N for the first time, the non-dominant layer where individual is F to note at this timel, take F1,F2,F3…,Fl-1In Body and from non-dominant layer FlMiddle selectionIndividual.
10. highway engineering multiple target construction plan according to claim 9 determines method, which is characterized in that described from non- Dominate layer FlMiddle selectionIndividual specifically includes:
To FlThe magnitude of four fitness function values of middle individual carries out unification, obtains the fitness function value of magnitude after reunification；
Four-dimensional hyperplane is constructed according to the fitness function value of four magnitudes after reunification, the reference point equal with population scale is uniform It is distributed on the hyperplane；
The fitness function value of magnitude after reunification is normalized, the fitness function value after normalized is described Coordinate of the individual on the hyperplane；
The vertical range of the individual distance reference line is calculated, the reference line is the company of the hyperplane origin and reference point Line；
By the individual reference point association relevant to most short vertical range；
Choose the reference point composition reference set J for possessing minimum microhabitat pointmin={ j:argminjρj, the your pupil of j-th of reference point Border point ρjIt is defined as associated with the reference point and from FlThe quantity of middle individual；
In reference point set JminIn randomly select a reference point:
If the ρ of selected reference pointj=0, then selection and the shortest individual of reference line vertical range where selected reference point, and general The ρ of selected reference pointjAdd one；It jumps in reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping；
If ρj>=1, randomly select one and the associated individual of selected reference point, and by the ρ of selected reference pointjAdd one, jumps to In reference point set JminIn randomly select a reference point step, until pick outIndividual then stops jumping.
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