CN105718632B - A kind of uncertainty underground water repairs multiple-objection optimization management method - Google Patents
A kind of uncertainty underground water repairs multiple-objection optimization management method Download PDFInfo
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Abstract
The invention discloses a kind of uncertain underground water to repair multiple-objection optimization management method, object function haphazard evaluation, random Pareto are dominated concept and random microhabitat fitness sharing method are introduced into the operation of EMOTS Evolution of Population by the random tabu search algorithm PEMOTS of multiple target based on elite retention strategy.PEMOTS inherits the advantages of EMOTS global searches, and the elite retention strategy that EMOTS is used introduces Latin Hypercube Sampling LHS and generates neighborhood solution, ensures that the noninferior solution that algorithm acquires can converge on true solution, and uniform along tradeoff curve distribution.Difference lies in the uncertainties using sequence Gauss conditions simulation SGSIM reduction aqueous system parameters for the core of PEMOTS and congenic method, while introducing random multi-target evolution operation, reduce the variability of search Pareto optimal solutions.The technology and Groundwater string routine MODFLOW and solute transfer program MT3DMS are coupled, there is stronger reliability and robustness in solving uncertain underground water pollution control multiple-objective management model.
Description
Technical field
The present invention relates to a kind of uncertain underground water to repair multiple-objection optimization management method, belongs to Hydrology and Water Resources
Field.
Background technology
Past more than 20 years, multi-objective Evolutionary Algorithm (Multi-objective evolutionary algorithm,
MOEA) have become the research hotspot in intelligence computation field, and be widely used in solving groundwater management model.
As MOEA is in the deep application of field of water resources, model needs to consider multivariable, and Complex multi-target and aqueous system are not
The factors such as certainty.In Groundwater optimal management model, uncertain systematic parameter can lead to the flow and solute of model output
The random variation of migration state, and then cause the uncertain variation of management objectives functional value.Certainty multi-objective Evolutionary Algorithm, such as
Based on elite retention strategy the random tabu search algorithm of multiple target (Elitist Multi-Objective Tabu Search,
EMOTS) it is not suitable for solving uncertain Optimal management model.For this purpose, how to consider the uncertain to optimization of simulation model
The influence of model, and the tradeoff solution (Pareto optimal solutions) how sought to meet between uncertain target is underground water optimization pipe
Manage the important content of research field.
Previous uncertain water resource optimization problem only considers constraints or the uncertainty of single target, using flat
Equal method evaluates individual with the realization of one group of stochastic variable, calculates individual goal average value of a function, and carry out Evolution of Population
Operation, the method consider the uncertainty of parameter, but relatively easy to object function Uncertainty Management, optimize the reliable of solution
Property is not strong.
Invention content
Technical problem to be solved by the invention is to provide a kind of uncertain underground water to repair multiple-objection optimization manager
Method is a kind of random tabu search algorithm of the multiple target based on elite retention strategy (Probabilistic Elitist
Multi-Objective Tabu Search, PEMOTS), this method has higher computational efficiency, while ensure that algorithm
Search that variability is small, and reliable and stable Pareto optimal solutions.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The present invention provides a kind of uncertain underground water reparation multiple-objection optimization management method, is as follows：
Step 1, simulation model is established, place underground water head and solute concentration are repaired over time and space for portraying
Distribution；
Step 2, it determines Optimal management model, establishes Optimized model；
Step 3, the realization sample set of infiltration coefficient is generated using sequence Gauss conditions simulation SGSIM, and for different
Condition points carry out uncertainty analysis and risk assessment to lnK and simulation model output, to reduce model uncertainty and choosing
Select the lnK sample sets for Optimized model management design；
Step 4, PEMOTS Optimization Method multiobjective management problems tradeoff solution is selected, the specific steps are：
(1) initial solution and corresponding neighborhood population are generated：
First, an initial solution s is generated using random fashion0, initialization elite table, candidate list and taboo list, with initial
Solution is basic point, and it is N to generate number based on Latin Hypercube Sampling LHSTSNeighborhood population St NS；
(2) object function haphazard evaluation：
Using noise genetic algorithm NGA, population S is calculated one by one with the lnK sample sets generated in step 3t NSIn per each and every one
The target function value of body, and count expectation and the variance of the target function value of each individual；According to target function value, using random
Pareto controls sequence and random niche technique calculate the Pareto rankings and the crowded angle value of individual of individual；Using ideal adaptation
Degree functional value archival strategy records the solution searched for the first time, and the solution of repeat search then directly invokes the letter of the solution in functional value library
Breath；
(3) random multi-target evolution：
1. planting the selection of subsolution：Compare neighborhood population St NSWith the elite table S of previous generationE t-1Pareto controllabilitys, will
St NSIn all noninferior solutions be considered as candidate seed disaggregation S1；By S1The candidate list S of previous generation is addedC t-1In, from S1And SC t-1Merging
Select noninferior solution as contemporary candidate seed disaggregation S in solution3；Finally from S3It is middle to select maximum two solutions of crowding distance as under
The kind subsolution S of a generationS t+1；
2. more new strategy：By neighborhood population St NSWith the elite table S of previous generationE t-1Merge, retains the noninferior solution composition present age
Elite table SE t, while by neighborhood population St NSIn the uncontrolled elite table S in previous generationE t-1Solution, be added previous generation candidate lists
SC t-1In, remove two kinds of subsolution S of the controlled solution and present age selection in candidate listS t+1, it is updated to contemporary candidate list SC t；
(4) judge whether to meet stopping criterion
In optimization process, if reached preset maximum iteration, or search certain generation when, would choose seeds
Subsolution collection is sky, while candidate list is also sky, then can not find next kind of subsolution, cannot be introduced into the search in next stage,
Stop and exports Pareto optimal solution sets.
Step 5, optimum results are exported, Monte Carlo MC analyses are carried out to Pareto optimal solutions using lnK sample sets, are examined
The reliability of the Pareto optimal solution sets of PEMOTS outputs.
As a further optimization solution of the present invention, the object function of Optimized model is as follows in step 2：
MAX MR (%)=(massend/mass0)×100
Wherein, RC is to minimize treatment cost, Qi,tFor the flow that draws water of i-th mouthful of well t stress phase, △ ttFor t stress
The duration of phase, zgsFor earth's surface elevation, hi,tIt is the calculated water head of i-th mouthful of well t stress phase, zgs-hi,tFor drawing water for i-th mouthful of well
Lift, NwAnd NtRespectively well number and stress issue, N are administered in pre-selectionSCount for known conditions, α and β be draw water cost coefficient and
The cost coefficient of acquisition condition point K values；MR is to maximize contaminant remaining percentage, massendIt is total to administer all end of term pollutants
Amount, mass0For the total amount of pollutant under original state.
As a further optimization solution of the present invention, the constraints of Optimized model includes administering well sum about in step 2
Beam, head constraint, hydraulic gradient constraint, pollutant concentration constraint, water withdrawal traffic constraints and overall balance constraint.
As a further optimization solution of the present invention, Pareto optimal solutions cover using lnK sample sets in step 5 special
Caro MC analyses examine the reliability of the Pareto optimal solution sets of PEMOTS outputs, specially：Using lnK sample sets to step 4
In obtained Pareto optimal solution sets carry out Monte Carlo MC analyses, count the mean value each solved, confidence level is not 95% not
The upper boundary values and lower border value in certainty section judge by comparing the degree of closeness that Pareto solutions are averagely solved with MC
PEMOTS is used to solve the reliability that uncertain underground water pollution repairs problem.
As a further optimization solution of the present invention, groundwater modeling has by the three-dimensional that US Geological Survey develops
Difference program MODFLOW is limited to solve；Solute transport model utilizes Zheng Chunmiao based on the MODFLOW heads solved and velocity field
The modularization three-dimensional solute transfer program MT3DMS of research and development is solved.
The present invention has the following technical effects using above technical scheme is compared with the prior art：In uncertain underground
In water optimum management problem, computational efficiency and Pareto solution stability be often determine algorithm whether be applicable in it is most important because
Element, PEMOTS use the individual archival strategy based on a small amount of random sample number, greatly reduce the meter of object function haphazard evaluation
Calculation amount, while the guarantee of random multi-target evolution searches that variability is small, highly reliable Pareto optimal solutions.For this purpose, PEMOTS
It has broad application prospects in uncertain underground water pollution repairs multiobjective management problem.
Description of the drawings
Fig. 1 is PEMOTS flow charts.
Fig. 2 be it is non-determined under the conditions of Pareto control ordering chart.
Fig. 3 is that underground water pollution repairs place schematic diagram.
Fig. 4 is the variation tendency of pollutant risk level and the coefficient of variation in the case of different condition points.
Fig. 5 is ideal PAT systems PEMOTS optimum results and Monte Carlo simulation analysis result.
Specific implementation mode
Technical scheme of the present invention is described in further detail below in conjunction with the accompanying drawings：
The present invention constructs the uncertain foggara being made of object function haphazard evaluation and random multi-target evolution
Manage model evaluation method, i.e., the random tabu search algorithm (Probabilistic of multiple target based on elite retention strategy
Elitist Multi-Objective Tabu Search, PEMOTS), and pass through the uncertain two-dimentional underground water of infiltration coefficient
Pollution amelioration application example is verified.This method application order Gauss conditions first simulate (Sequential Gaussian
Simulation, SGSIM) lnK realization sample sets are generated, and lnK and model output are carried out for different condition points
Analysis of uncertainty and risk assessment, to reduce the lnK sample sets of model uncertainty and selection for optimization design.Then,
Random Pareto controls sequence and random niche technique have been introduced, the elite solution of population is selected, intersected and made a variation
Multi-target evolution operates, and optimization obtains Pareto optimal solution sets.The invention is by PEMOTS and Simulation of Groundwater Flow program MODFLOW
It is coupled together with solute transfer simulation program MT3DMS, to design the multiple target of underground water pollution control under condition of uncertainty
Prioritization scheme.
The program design of the random tabu search algorithm of multiple target (PEMOTS) based on elite retention strategy is target letter
Number haphazard evaluation and random multi-target evolution two parts, as shown in Figure 1, specific solution procedure is as follows：
1. object function haphazard evaluation
Object function haphazard evaluation handles the uncertainty of model parameter with the thought of noise genetic algorithm (NGA).
Since most of Actual Water Resource optimization problem is there are uncertain factor, need to portray the not true of mode input with one group of realization
It is qualitative.It is adjoint and to need to solve two problems：The uncertainty of numerical model is portrayed using one group of which type of realizationFrom this
Great sample number is selected to carry out the object function of haphazard evaluation individual in group realizationThe Monte Carlo of SGSIM is respectively adopted in we
Method and individual archival strategy, to solve the problems, such as two above.
1) Monte Carlo method of SGSIM：SGSIM is that sequence simulation thought and Gauss are simulated to the one kind being combined at random
Analogy method.All conditions data are subjected to normal transformation first, as priori conditions probability distribution, according to a stochastic simulation
Path, each unconditional point value of sequence simulation, is a little modeled until needing to be estimated, and repeats above step simulation generation and refers to
Fixed number purpose realizes that constituting stochastic variable realizes sample set.This method can not only make the analogue value etc. of the stochastic variable at condition point
In measured value, the spatial characteristics of variables model value can also be maintained to survey Distribution value consistency with condition point, substantially reduced
The uncertainty of model output.
2) individual archival strategy：In search process, for the individual evaluated for the first time, by the individual (binary coding)
And its object function statistical value (sample number, individual goal mean value functions and the variance of evaluation individual) is stored in individual archives
In, and before calculating each individual, it is first determined whether being stored in individual file store, the individual is evaluated and if so, increasing
Sample number, and information in individual file store of statistics target function value and more new individual again.Go out in certain evolutionary process
Existing optimum individual, is constantly retained in tournament selection, it was demonstrated that its being dominant property of Pareto is strong, for such individual, leads to
It crosses and is continuously increased sample number to ensure the stability and reliability of solution.Based on this, herein by the sample set generated from SGSIM with
Machine chooses a small amount of realization (5) to evaluate and count the target function value of individual.
2. random Multi-target evaluation
For uncertain multi-objective optimization question, the uncertainty of model parameter leads to the uncertainty of object function.
In purpose-function space, the corresponding solution not instead of fixed point of each decision vector, a uncertain rectangle region
Domain；The forward positions the Pareto not instead of determining curve that nondominated solution is constituted is made of not true Pareto up-and-down boundaries
Qualitative region, as shown in Figure 2.For this purpose, uncertain multi-target evolution is by random Pareto controls sequence and random microhabitat skill
Art is introduced into EMOTS, is carried out the uncertainty of processing target function and is sought Pareto optimal solutions.
1) random Pareto controls sequence：For uncertain problem, individual d is judged1Whether individual u is controlled by1, need
Parameter Estimation and hypothesis testing are carried out to the difference of the mean value of individual goal functional value.Assuming thatMeet t- distributions：
Wherein, TiFor t- distribution functions,WithRespectively individual d1And u1I-th of target letter
Several sample averages and standard deviation,For the d of individual1And u1Expectation, n and m are evaluation individual d1And u1Sample
Number namely the degree of freedom of this distribution are min (n-1, m-1).For given confidence level а, can table look-up point position accordingly
Point b (degree of freedom n+m-2), obtainsConfidence level be а confidence interval be
Assuming that Hi：If the up-and-down boundary value of confidence interval is positive value or negative value, it assumes that it is invalid,OrIf the lower boundary of confidence interval is less than or equal to zero, coboundary is more than or equal to zero, in conspicuousness water
Assume to set up under the conditions of flat а.Parameter Estimation and the significance test that object function mean value is carried out to each target, if individual
u1Pareto is dominant d1, thenAnd at least make in the presence of a target jBy the individual two in population
Two carry out random Pareto sequences, and individual Pareto rankings are equal to the quantity for the individual that it can be controlled in population, Pareto
Optimal solution is not controlled by any individual, ranking 0.
2) random niche technique：Niche technique is by judging Descartes's distance between individual and microhabitat radius
Between relationship, to solve individual crowding, in the case that Pareto sort it is identical, the solution for selecting crowding small as
Advantage individual, to ensure the diversity of solution.With individual u1And d1For, first to the target function value of individual scaling transformation
DifferenceParameter Estimation and hypothesis testing are carried out,For individual d1And u1Object function
Value.If assuming to set up,Equally parameter is carried out to the object function mean value that each is changed proportionally to estimate
Meter and significance test solve Descartes's distance between individual according to formula (3)：
Wherein,For individual u1And d1Between Descartes's distance, k be object function number.
Individual crowding is solved by formula (4) and is obtained, and is other individual on its surrounding space in the individual and population
A microhabitat radius rnicheIt inside solves, rnicheFor in population two-by-two individual between Descartes's distance average value.
Wherein, ncdFor the individual crowding of d-th of individual, NPFor the individual sum in population, EduBetween individual d and u
Descartes's distance.
The present invention is used for uncertain underground water and repairs multiobjective management problem, is as follows：
Step 1 establishes simulation model, and place underground water head and solute concentration are repaired over time and space for portraying
Distribution.Groundwater modeling can be solved by the Three dimensional finite difference program MODFLOW that US Geological Survey develops,
And the head and velocity field that solute transport model is then solved based on MODFLOW, the modularization three-dimensional solute researched and developed using Zheng Chun seedlings
Program MT3DMS migrate to solve.Primary condition and boundary condition described in pattern of water flow and solute transport model will be with realities
The place situation on border is consistent, and the simulation model finally established is exactly pattern of water flow that is corrected and examining and solute transfer mould
Type.
Step 2 determines Optimal management model, establishes Optimized model.Established in Groundwater optimal management model object function and
It is to establish the core of Optimal management model that constraints, which is arranged,.This Study of The Underground water is repaired in multiobjective management problem, is most attached most importance to
The object function wanted is the minimum warp that recovery well optimization design is realized on the basis of meeting ground water regime various constraintss
It helps cost, refers to formula (5), recovery well optimization design includes that well location sets optimization with well yield.In addition to this underground water pollution
The quality of contaminant remaining has become an important indicator for differentiating optimization design success or not after reparation, refers to formula (6) formula.
Object function one
Two MAX MR (%) of object function=(massend/mass0)×100 (6)
Wherein, RC is to minimize treatment cost, Qi,tFor the flow (m that draws water of i-th mouthful of well t stress phase3/d-1), △ ttFor
The duration (d) of t stress phases, zgsFor earth's surface elevation (m), hi,tIt is the calculated water head (m) of i-th mouthful of well t stress phase, zgs-hi,t
For the pumping head (m) of i-th mouthful of well, NwAnd NtRespectively well number and stress issue, N are administered in pre-selectionSFor known conditions count, α and
β be draw water cost coefficient and obtain condition point K values cost coefficient；MR is to maximize contaminant remaining percentage, massendFor
Administer all end of term total amount of pollutant (Kg), mass0For the total amount of pollutant (Kg) under original state.
Constraints includes administering the constraint of well sum, head constraint, hydraulic gradient constraint, pollutant concentration constraint, individual well
Traffic constraints of drawing water and overall balance constraint.The object function and constraints changed at random constitutes uncertain underground water and repaiies
The mathematical model of multiple optimum management problem.
The analysis of uncertainty of step 3 simulation system
This research generates the realization sample set of infiltration coefficient using SGSIM condition simulations.It is generated using SGSIM methods in text
LnK distributions in the case of different condition points, generate the sample set for realizing that number is 1000 respectively.Based on lnK sample sets, illiteracy is utilized
Special Caro method simulates the pollution concentration distribution of different infiltration coefficients off field, is missed using actual value and the root mean square of condition simulation value
Poor RMS carries out infiltration coefficient analysis of uncertainty, and using pollution risk level and pollutant risk variation coefficient come quantitative point
Analyse pollution risk.In conjunction with the optimization treatment cost of pollution risk level and PAT systems, optimal condition is selected to count, and will
It is used in the multi-objective optimization design of power of uncertain PAT systems.
Step 4 selects PEMOTS optimisation techniques to solve multiobjective management problem tradeoff solution.Optimization Solution technology is exactly certainly
In the Feasible Solution Region of plan variable, by judging that target function value and constraints select uncontrolled decision variable to combine, as
The compromise solution of multi-objective optimization question, the pros and cons that policymaker weighs between each target make administrative decision.
Step 5 exports optimum results, to the Pareto optimal solutions that PEMOTS optimizes cover using lnK sample sets special
Caro is analyzed, and counts the mean value each solved, the upper boundary values and lower border value in the uncertain section that confidence level is 95%,
In to obtain average solution by Monte Carlo simulation be most reliable and stable.
Technical scheme of the present invention is further elaborated below by specific embodiment：
A uncertain groundwater remediation multiobjective management problem is designed below, is solved and is met using PEMOTS optimisation techniques
The tradeoff solution of management objectives and constraints.
2.1 Problem Overview
One stochastic variable of this research and design is the uncertain underground water repair system of infiltration coefficient (K).Study area
The pollution situation of hydrogeologic condition and nitrate (in terms of nitrogen) is as shown in Figure 3."●" is 4 mouthfuls of pretreatment wells in figure, grey
Rectangular area is concentration restriction range, i.e., is no more than defined upper limit value by PAT optimization designs come the concentration of control area.Contain
The infiltration coefficient of water layer is that meet mean value be 2.5m/d, and fields lnK for the random distribution that variance is 0.2, infiltration coefficient is not known,
Result in the random variation of model delivery head and pollutant concentration.
The analysis of uncertainty of 2.2 simulation systems
This research generates the realization sample set of infiltration coefficient using SGSIM condition simulations.6 kinds of situations, item are provided in text
Part points are respectively NS=10,20,30,40,50,60, lnK points in the case of different condition points are generated using SGSIM methods
Cloth generates the sample set for realizing that number is 1000 respectively.Based on lnK sample sets, system is permeated using Monte-carlo Simulation difference
It is not true to carry out infiltration coefficient using the root-mean-square error (RMS) of actual value and condition simulation value for the pollution concentration distribution of number off field
Qualitative analysis, and using pollution risk level and pollutant risk variation coefficient come quantitative analysis pollution risk, as shown in Figure 4.
As can be seen from Figure 4 with the increase that condition is counted, pollution risk reduces and the value that tends towards stability, and considers the optimization of PAT systems
Treatment cost selects 40 condition points to generate the sample set that 1000 lnK are realized, and uses it for uncertain PAT systems herein
In the multi-objective optimization design of power of system, seek random Pareto optimal solutions.
2.3 apply PEMOTS optimisation techniques
The setting of PEMOTS relevant parameters of the present invention is as follows：Computer algebra is 100；Population Size is 100；Pareto disaggregation
Filter size is 100；The discretization interval number of each parameter (pump-out) is 32；Uniform crossover probability is 0.95；Single-point becomes
Different probability is 0.05；M ü hlenbein mutation probabilities are 0.25；The subsample number of evaluation goal functional value is 5, for having searched
The individual that rope is crossed, the subsample number for often re-searching for once evaluating the individual increase by 5 (maximum subsample number is 30).It is using
Pair the administrative model of constraint is often converted to by unconstrained administrative model using penalty function when intelligent algorithm optimizes, i.e.,
It is unsatisfactory for the solution of constraints, is added in the form of penalty function in corresponding object function.Such as using PEMOTS optimum results
Shown in Fig. 5.
The comparative analysis of 2.4 optimum results
It is based on 40 equally distributed condition points herein, the sample that 1000 lnK are realized is generated using SGSIM condition simulations
Collection, and randomly select 5 from this sample set and realize the target function value for evaluating individual as subsample, it is more by PEMOTS
Target, which is evolved, finds uncertainty Pareto optimal solutions, ("+" solution) as shown in Figure 5.For the reliability of test result, use
The sample set of 1000 realizations solves each Pareto and carries out Monte Carlo simulation analysis, counts the mean value ("+" solution) each solved,
And confidence level be 95% uncertain section upper boundary values ("○" solution) and lower border value (" △ " solution), wherein passing through illiteracy
It is most reliable and stable that special Monte Carlo Simulation of Ions Inside, which obtains average solution, and the Pareto optimal solutions that PEMOTS optimizes are distributed in uncertainty
In region, uncertain Pareto optimal solutions superiority-inferiority can be judged in terms of following two, (1) single Pareto solutions
Uncertain interval width it is smaller, show that the variability of the solution is small, in practical problem, the variability of solution is small, then corresponding
It is highly reliable；(2) closer to average solution, the reliability of solution is stronger for Pareto angle distribution.The Pareto optimal solutions that PEMOTS is acquired
Close to average solution, show that random Pareto controls sequence and random niche technique are handling uncertain multiobjective selection
Validity, obtained Pareto optimal solution variability is small, highly reliable.
The above, the only specific implementation mode in the present invention, but scope of protection of the present invention is not limited thereto, appoints
What is familiar with the people of the technology within the technical scope disclosed by the invention, it will be appreciated that expects transforms or replaces, and should all cover
Within the scope of the present invention, therefore, the scope of protection of the invention shall be subject to the scope of protection specified in the patent claim.
Claims (5)
1. a kind of uncertainty underground water repairs multiple-objection optimization management method, which is characterized in that be as follows：
Step 1, simulation model is established, point of place underground water head and solute concentration over time and space is repaired for portraying
Cloth；
Step 2, it determines optimum management target, establishes Optimized model；
Step 3, the realization sample set of infiltration coefficient is generated using sequence Gauss conditions simulation SGSIM, and is directed to different conditions
Points carry out uncertainty analysis and risk assessment to lnK and simulation model output, are used with reducing model uncertainty and selection
In the lnK sample sets of Optimized model management design；
Step 4, PEMOTS Optimization Method multiobjective management problems tradeoff solution is selected, the specific steps are：
(1) initial solution and corresponding neighborhood population are generated：
First, an initial solution s is generated using random fashion0, initialization elite table, candidate list and taboo list, using initial solution as base
Point, it is N to generate number based on Latin Hypercube Sampling LHSTSNeighborhood population St NS；
(2) object function haphazard evaluation：
Using noise genetic algorithm NGA, population S is calculated one by one with the lnK sample sets generated in step 3t NSEach of individual
Target function value, and count expectation and the variance of the target function value of each individual；According to target function value, using random
Pareto controls sequence and random niche technique calculate the Pareto rankings and the crowded angle value of individual of individual；Using ideal adaptation
Degree functional value archival strategy records the solution searched for the first time, and the solution of repeat search then directly invokes the letter of the solution in functional value library
Breath；
(3) random multi-target evolution：
1. planting the selection of subsolution：Compare neighborhood population St NSWith the elite table S of previous generationE t-1Pareto controllabilitys, by St NSMiddle institute
There is noninferior solution to be considered as candidate seed disaggregation S1；By S1The candidate list S of previous generation is addedC t-1In, from S1And SC t-1Merging Xie Zhongxuan
Noninferior solution is selected as contemporary candidate seed disaggregation S3；Finally from S3It is middle to select maximum two solutions of crowding distance as follow-on
Kind subsolution SS t+1；
2. more new strategy：By neighborhood population St NSWith the elite table S of previous generationE t-1Merge, retains the elite in the noninferior solution composition present age
Table SE t, while by neighborhood population St NSIn the uncontrolled elite table S in previous generationE t-1Solution, previous generation candidate lists S is addedC t-1
In, remove two kinds of subsolution S of the controlled solution and present age selection in candidate listS t+1, it is updated to contemporary candidate list SC t；
(4) judge whether to meet stopping criterion
In optimization process, if reached preset maximum iteration, or search certain generation when, would choose seeds subsolution
Collection is sky, while candidate list is also sky, then can not find next kind of subsolution, cannot be introduced into the search in next stage, is stopped
And export Pareto optimal solution sets；
Step 5, optimum results are exported, Monte Carlo MC analyses are carried out to Pareto optimal solutions using lnK sample sets, are examined
The reliability of the Pareto optimal solution sets of PEMOTS outputs.
2. a kind of uncertain underground water according to claim 1 repairs multiple-objection optimization management method, which is characterized in that
The object function of Optimized model is as follows in step 2：
MAX MR (%)=(massend/mass0)×100
Wherein, RC is to minimize treatment cost, Qi,tFor the flow that draws water of i-th mouthful of well t stress phase, △ ttFor the t stress phases
Duration, zgsFor earth's surface elevation, hi,tIt is the calculated water head of i-th mouthful of well t stress phase, zgs-hi,tFor the pumping head of i-th mouthful of well,
NwAnd NtRespectively well number and stress issue, N are administered in pre-selectionSIt counts for known conditions, α and β are draw water cost coefficient and acquisition item
The cost coefficient of part point K values；MR is to maximize contaminant remaining percentage, massendTo administer all end of term total amount of pollutant,
mass0For the total amount of pollutant under original state.
3. a kind of uncertain underground water according to claim 1 repairs multiple-objection optimization management method, which is characterized in that
The constraints of Optimized model includes administering the constraint of well sum in step 2, head constraint, hydraulic gradient constraint, pollutant concentration
Constraint, water withdrawal traffic constraints and overall balance constraint.
4. a kind of uncertain underground water according to claim 1 repairs multiple-objection optimization management method, which is characterized in that
Monte Carlo MC analyses are carried out to Pareto optimal solutions using lnK sample sets in step 5, examine the Pareto of PEMOTS outputs most
The reliability of excellent disaggregation, specially：Monte Carlo is carried out to the Pareto optimal solution sets obtained in step 4 using lnK sample sets
MC is analyzed, and is counted the mean value each solved, the upper boundary values and lower border value in the uncertain section that confidence level is 95%, is passed through
Compare the degree of closeness that Pareto solutions are averagely solved with MC, judges that PEMOTS repairs problem for solving uncertain underground water pollution
Reliability.
5. a kind of uncertain underground water according to claim 1 repairs multiple-objection optimization management method, which is characterized in that
Three dimensional finite difference program MODFLOW that groundwater modeling is developed by US Geological Survey is solved；Solute transfer mould
Type is based on the MODFLOW heads solved and velocity field, the modularization three-dimensional solute transfer program MT3DMS researched and developed using Zheng Chun seedlings
To solve.
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