CN101799846A - Multi-objective groundwater remediation optimization method - Google Patents
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- 238000005457 optimization Methods 0.000 title claims abstract description 41
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- 239000003673 groundwater Substances 0.000 title abstract description 10
- 238000005067 remediation Methods 0.000 title abstract description 3
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- 238000005516 engineering process Methods 0.000 abstract description 4
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- 230000002068 genetic effect Effects 0.000 description 9
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- 231100000719 pollutant Toxicity 0.000 description 4
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Abstract
The invention discloses a multi-objective groundwater remediation optimization method. The individual fitness function value archiving strategy, the Pareto dominance concept and a niche fitness sharing method are combined with tabu search (TS) to systematically form a new multi-objective optimization method. The method integrates the advantages of various optimization technology and is high in computing efficiency and strong in global search capability. Compared with the similar methods, the method of the invention mainly avoids repeated search in the optimization process and improves the diversity and the global property of seed solutions. The technology is coupled with the groundwater flow program (MODFLOW) and the solute transport program (MT3DMS) and has strong applicability to solving the multi-objective management model for groundwater pollution control.
Description
Technical field
The present invention relates to the Hydrology and Water Resources field, specifically is that underground water is repaired Multipurpose Optimal Method.
Background technology
Groundwater contamination is repaired in the optimum management system, often relate to a plurality of conflicting management objectives, have some characteristics between these targets, the linear module that comprises each target can not commensurability, conflicting between each objective function, this makes separating of multi-objective optimization question not be unique, and the task of multiobjective management is the pros and cons of each target of balance, seeks to satisfy the compromise of each target interests and separates.
Simulative optimization model (simulation-optimization model) is to find the solution the groundwater contamination repair system to manage effective method, also is that purposes is found the solution instrument the most widely.Analogy model is used for bringing in constant renewal in state variable, comprises groundwater flow motion model and solute transfer model; Optimization Model is used for selecting the optimizing decision variable, finds the solution the balance of multi-objective problem and separates, the foundation of making a strategic decision as the supvr.Repair in the multiobjective management problem at underground water, often relate to a plurality of conflicting objective functions, wherein of paramount importance is the minimum economic cost of realizing the recovery well optimal design on the basis of various constraint conditions of sewerage contentedly, and the recovery well optimal design comprises that well location puts the optimization with well yield.In addition the quality of residual contamination thing has become an important indicator differentiating the optimal design success or not after the groundwater contamination reparation.
In recent years based on population and in finding the solution multi-objective optimization question, obtained using widely based on the Multiobjective Intelligent algorithm of Pareto, in underground water remediation management model, also obtained development rapidly.For example, compared Pareto genetic algorithm (Pareto GA), vector is estimated genetic algorithm (Vector Evaluated GA, VEGA), microhabitat multi-objective genetic algorithm (Niched Pareto Genetic Alogrithm, NPGA), improved non-domination ordering genetic algorithm (Improved Non-dominated Sorting Genetic Algorithm, ε-NSGAII), at random multi-objective genetic algorithm (Probabilistic multi-objective genetic algorithm, PMOGA).More than finding the solution underground water multiobjective management model all is the Multiobjective Intelligent algorithm of utilization based on GA.Yet the Multiobjective Intelligent algorithm based on tabu search does not use as yet in finding the solution underground water multiobjective management problem.
Summary of the invention
The invention provides a kind of underground water and repair the new method of multi-objective optimization question, this method has higher counting yield, has guaranteed the ability of searching optimum of algorithm simultaneously.
Underground water of the present invention is repaired Multipurpose Optimal Method, and it may further comprise the steps:
Step 3 coupled simulation model and Optimization Model;
The result is optimized in step 5 output, analyzes the of overall importance and counting yield that balance is separated, and adjusts parameters optimization.
Wherein, step 4 comprises following detailed process:
1) producing initial solution and corresponding neighborhood separates
At first, from initial solution, adopt random fashion to produce an initial solution to the search in feasible solution territory, it then is to be basic point with the initial solution that neighborhood is separated, and carries out neighborhood according to the neighborhood move function and moves the back and produce, and the neighborhood move function is defined as follows:
s
i＝(2×random()-1)×stepsize，i＝1，2，…，i
max????????????????????????(1)
S wherein
i(i=1 ..., i
Max) represent that neighborhood moves rule function, i
MaxBe the number of times that neighborhood moves, random () is the random function that produces real number between the 0-1, and stepsize is the neighborhood moving step length.Initial solution and neighborhood are separated to produce and are had randomness in this research;
2) calculate target function value, Pareto rank and the individual crowding that neighborhood is separated
After the generation neighborhood is separated, calculate the target function value that all neighborhoods are separated,, calculate Pareto rank and individual crowding value that each neighborhood is separated according to target function value; The Pareto rank number of separating equal neighborhood separate in all Pareto control the skill that this separates, the Pareto rank is 0 separates and be nondominated solution;
3) select kind of a subsolution
Kind of subsolution is the initial solution of searching in per generation, and the selection of planting subsolution is derived from the previous generation neighborhood and separates, and promptly finds to separate separating as candidate seed that Pareto is dominant with respect to other neighborhood and separate from neighborhood is separated, and must satisfy the uncontrolled property of Pareto;
4) upgrade Pareto table, candidate list and taboo table
Pareto table and candidate list are respectively applied for the kind subsolution of depositing each generation and do not have selected other candidate solution for kind of subsolution; To no longer have separating from Pareto table and candidate list of Pareto optimality in per generation search and remove, the individuality that is chosen as kind of subsolution in the candidate list will be removed from table; Upgrade the taboo table with kind of subsolution as the taboo object, selected kind subsolution is avoided in the taboo algebraically of regulation, and seed is lifted a ban the new taboo kind subsolution in back replacement is deposited in the taboo table;
5) judge whether to satisfy stopping criterion
In the optimizing process, if reached predefined maximum iteration time, seed selection subsolution collection also is empty for empty candidate list simultaneously when perhaps searching certain generation, then can't find the next subsolution of planting, algorithm can't enter the search in next stage, and algorithm stops, output Pareto optimal solution set.
Said process 2) adopt in ideal adaptation degree functional value archival strategy note first search to separate the information of separating in the direct call function value storehouse of separating then of repeat search.
The selection of planting subsolution said process 3) has following several situation: if a) only exist a candidate seed to separate, then this is separated as follow-on kind of subsolution; B) if existence is separated more than one candidate seed, contrast the individual crowding that candidate seed is separated, the individuality of choosing crowding value minimum is as follow-on kind of subsolution; C) if there is no candidate seed is separated, and then selects to enter separating as new kind subsolution in the table the earliest from candidate list, and this is separated from candidate list delete.
Optimization method of the present invention can be coupled with groundwater simulation model (MODFLOW+MT3DMS), is applied to optimal design underground water and repairs the multiple-objection optimization problem of management.The notion that the present invention is dominant according to Pareto is found the solution the balance of multi-objective optimization question and is separated, and has only the nondominated solution of neighborhood in separating just might win in competition in each iteration of search optimization solution.The mode of NPTS search is based on the neighborhood search of certain initial solution, and progressively to the process of global search, nondominated solution and be positioned at the neighborhood in loose zone and separate and be chosen as follow-on initial solution in each neighborhood search has strengthened the ability of algorithm global search greatly.
This method has been inherited tabu search search capability efficiently, guarantees the diversity of understanding simultaneously by taboo strategy and microhabitat fitness technology of sharing, has strengthened the ability of searching optimum of algorithm.NPTS repairs in the multiobjective management problem at underground water and has broad application prospects.
Description of drawings
Fig. 1 is the NPTS process flow diagram;
Fig. 2 is the Pareto ordering chart, and the Pareto diagram of sorting: the rank number equals to separate other number of separating that comprises in the square frame of lower left;
Fig. 3 is individual crowding comparison diagram, " △ " expression separate in the microhabitat radius is the round territory of radius population density greater than
Represented separates;
Fig. 4 administers place hydrogeological characteristics planimetric map;
Fig. 5 is that the Pareto that NPTS optimization obtains separates along the distribution plan of balance curve, and wherein horizontal ordinate is first objective function a---treatment cost, and ordinate is second objective function---residual contamination amount ratio." zero " is for satisfying the Pareto optimum solution of optimal design;
Fig. 6 is to use the step figure of ideal adaptation degree when strategy filing calculating target function number of times, the relation when ideal adaptation degree filing strategy is not used in straight line "-" expression that the figure top is parallel to transverse axis between objective function calculation times and the iterations.
Embodiment
1, the present invention is used for finding the solution underground water to repair the concrete steps of multiobjective management problem as follows:
Minimize
Minimize J
2=MR=(mass
End/ mass
0) * 100% (3)
J wherein
1Expression treatment cost (RC), N
wFor administering the number of well, y
iBinary number (y during employing whether expression well i adopts
i=1, y when not adopting
i=0), Q
i tBe taking out in the t management phase/water injection rate (negative value is represented to draw water, on the occasion of the expression water filling) of well i, N
tBe total management issue, Δ t
tBe the duration of t stress phase, M
i tBe the quality of in the t management phase, removing pollutant of well i, α
i(i=1,2,3) expression well is installed, is taken out/water filling, the cost coefficient of pollutant control.J
2End of term residual contamination amount number percent (MR), mass are administered in expression
0And mass
EndExpression is administered under the original state and the pollutant quality in the improvement end of term respectively.
Constraint condition comprises administers the constraint of well sum, head constraint, hydraulic gradient constraint, pollutant levels constraint, individual well draw water traffic constraints and overall balance constraint.Objective function and constraint condition have constituted the mathematical model of underground water reparation optimum management problem.
Step 3 coupled simulation model and Optimization Model.The target of optimum management is the function (formula (2)) of decision variable (well yield) and state variable (head and solute concentration), need bring in constant renewal in state variable by analogy model, calculating target function value and judge whether to satisfy constraint condition; By Optimization Model trade-off decision variable, turn back to update mode variable in the analogy model simultaneously.Decision variable and state variable satisfy analogy model and state model simultaneously in the optimum management model, and upgrade synchronously.
Its Chinese style (4) and (5) expression system be t state variable h at a time
tAnd C
tBe this period decision variable Q
tAn and last period t-1 state variable h
T-1And C
T-1Function, state transition function trans
hAnd trans
CExpression.
The concrete steps of optimization method are (see figure 1):
1) producing initial solution and corresponding neighborhood separates
NPTS from initial solution, adopts random fashion to produce an initial solution to the search in feasible solution territory.It then is to be basic point with the initial solution that neighborhood is separated, and carries out neighborhood according to the neighborhood move function and moves that the back produces, and the neighborhood move function is defined as follows:
s
i＝(2×random()-1)×stepsize，i＝1，2，…，i
max????????????????????????(1)
S wherein
i(i=1 ..., i
Max) represent that neighborhood moves rule function, i
MaxBe the number of times that neighborhood moves, random () is the random function that produces real number between the 0-1, and stepsize is the neighborhood moving step length.Initial solution and neighborhood are separated to produce and are had randomness in this research.
2) calculate target function value, Pareto rank and the individual crowding that neighborhood is separated
After producing neighborhood and separating, calculate the target function value that all neighborhoods are separated, this method introduce ideal adaptation degree functional value archival strategy note first search to separate the information of separating in the direct call function value storehouse of separating then of repeat search; According to target function value, calculate Pareto rank and individual crowding value that each neighborhood is separated.The Pareto rank number of separating equal neighborhood separate in all Pareto control the skill that this separates, the Pareto rank is 0 separates and be nondominated solution (seeing Fig. 2,3).
3) select kind of a subsolution
Planting subsolution is the initial solution of searching in per generation, and the selection of planting subsolution is derived from the previous generation neighborhood and separates, and must satisfy the uncontrolled property of Pareto.Before determining kind of subsolution, need from neighborhood is separated, find and separate separating that Pareto is dominant with respect to other neighborhood and separate as candidate seed, the selection of planting subsolution can be summarized as following several situation: if a) only exist a candidate seed to separate, then this is separated as follow-on kind of subsolution; B) if existence is separated more than one candidate seed, contrast the individual crowding that candidate seed is separated, the individuality of choosing crowding value minimum is as follow-on kind of subsolution; C) if there is no candidate seed is separated, and then selects to enter separating as new kind subsolution in the table the earliest from candidate list, and this is separated from candidate list delete.
4) upgrade Pareto table, candidate list and taboo table
Pareto table and candidate list are respectively applied for the kind subsolution of depositing each generation and do not have selected other candidate solution for kind of subsolution.To no longer have separating from Pareto table and candidate list of Pareto optimality in per generation search and remove, the individuality that is chosen as kind of subsolution in the candidate list will be removed from table.Upgrade the taboo table with kind of subsolution as the taboo object, for fear of being absorbed in cyclic search, selected kind subsolution is avoided in the taboo algebraically of regulation, and seed is lifted a ban the new taboo kind subsolution in back replacement is deposited in the taboo table.
5) judge whether to satisfy stopping criterion
If reached predefined maximum iteration time in the optimizing process, seed selection subsolution collection then can't find the next subsolution of planting for empty candidate list simultaneously also is empty when perhaps searching certain generation, and algorithm can't enter the search in next stage, algorithm stops, output Pareto optimal solution set.
The result is optimized in step 5 output, analyzes the of overall importance and counting yield that balance is separated, and adjusts parameters optimization, makes optimization method can reach optimum optimization effect in different problems.
2, underground water of following design is repaired the multiobjective management problem, utilizes the present invention to find the solution to satisfy the balance of management objectives and constraint condition to separate.
2.1 problem overview
Study area is average, isotropic two dimension confined aquifer, has existed nitrate (in nitrogen) to pollute, and pollutes the distribution of plumage and sees Fig. 4.The long 3300m in water-bearing zone, wide 2400m, the square net that with the length of side is 150m is the finite difference grid of 17 row, 23 row with the survey region subdivision.The current boundary condition is: east and western part are respectively 25m and 35m for to decide head boundary, and northern and south is the water proof border.The solute transfer boundary condition is: western, northern and south is solute zero flux border, and the east is the given flux of solute convection border.Other relevant hydrogeological parameter, current and solute transfer parameter are seen Fig. 4.4 mouthfuls of preliminary elections are administered well and are distributed as shown in Figure 4.4 decision variables are set in the Optimization Model, are the flow that draws water of 4 mouthfuls of wells, and limit the traffic constraints (0≤Q that draws water of every mouthful of well
i≤ 10000m
3/ d, i=1,2 ..., 4).The management objectives of Optimization Model satisfy concentration constraint condition simultaneously for minimizing treatment cost (formula (2)) and minimizing the residual contamination amount than (formula (3)), and the concentration that promptly satisfies concentration constraint (shadow region among Fig. 4) internal contamination thing is less than 3ppb.The optimization improvement cycle is assumed to be 5 years.
2.2 application the present invention
Being provided with of correlation parameter of the present invention is as follows: calculating algebraically is 400; The number of times that neighborhood moves is i
Max=2; Neighborhood moving step length stepzize=3; The discretize interval number of each parameter is 32; The microhabitat radius is 0.05; The length of taboo table is 10.Often adopt penalty function that the administrative model of constraint is converted to the unconfinement administrative model when using intelligent algorithm to be optimized design, promptly to not satisfying separating of constraint condition, the form of employing penalty function is added in the corresponding objective function, optimizes to the results are shown in Figure 5.
2.3 optimize result's comparative analysis
The calculating of objective function needs to call analogy model in a large number repeatedly, has occupied more than 90% of total computation optimization time its computing time, and for the simulative optimization problem of actual large scale, the ratio that the time occupies is infinitely near 100%.So the calculation times of objective function, promptly the call number of analogy model is a reflection algorithm computation efficient important indicator.Fig. 6 has compared NPTS and has used and do not using each generation under the ideal adaptation degree functional value archival strategy to call the number of times of analogy model.Under the situation of not using ideal adaptation degree functional value archival strategy, each generation the number of times that calls analogy model equal number of times product (n * i that decision variable number and neighborhood move
Max).As can be seen from Figure 6 along with the increase of iterations, the individuality of a large amount of double countings occurred, table 1 has been added up the number of times of the actual analogy model that calls of convergence algebraic sum, calculates the double counting rate of separating.The number of individuals of double counting reaches 831, and repetition rate reaches 38.0%, and this has proved absolutely that also ideal adaptation degree functional value archival strategy has improved algorithm computation efficient widely.
Table 1. uses and does not use the Pareto optimum solution statistical form of ideal adaptation degree functional value archival strategy
| The number of times that neighborhood is separated in per generation | Optimize iterations when reaching convergence | Objective function calculation times when not using ideal adaptation degree functional value archival strategy | Objective function calculation times when using ideal adaptation degree functional value archival strategy | Objective function does not calculate repetition rate (%) when not using ideal adaptation degree functional value file plan |
| ??8 | ??273 | ??2184 | ??1353 | ??38.0 |
With the present invention with based on the multi-target evolution algorithm of genetic algorithm, comprise NPGA and VEGA, it is as follows that NPGA and VEGA are provided with identical parameter: population size, 100; Crossing-over rate P
c, 0.95; Aberration rate P
m, 0.05, all the other settings are identical with NPTS.The Pareto optimum solution that pairs of three kinds multiple goal algorithm optimizations of table 2 obtain is added up, NPTS optimizes that to obtain number and NPGA that Pareto separates suitable with the VEGA number, but the calculation times of objective function then is 1/9 and 1/10 of NPGA and VEGA, the result shows NPTS under the situation that guarantees global search, has improved the counting yield of optimizing greatly.
Table 2.NPTS and NPGA and the VEGA Pareto optimum solution contrast table under abundant convergence situation.
Claims (3)
1. a underground water is repaired Multipurpose Optimal Method, and it may further comprise the steps:
Step 1 is set up analogy model, is used to portray reparation place underground water head and the distribution of solute concentration on time and space;
Step 2 is determined management objectives, sets up Optimization Model;
Step 3 coupled simulation model and Optimization Model;
Step 4 is selected for use optimization method to find the solution the balance of multiobjective management problem and is separated;
The result is optimized in step 5 output, analyzes the of overall importance and counting yield that balance is separated, and adjusts parameters optimization;
It is characterized in that step 4 comprises following detailed process:
1) producing initial solution and corresponding neighborhood separates
At first, from initial solution, adopt random fashion to produce an initial solution to the search in feasible solution territory, it then is to be basic point with the initial solution that neighborhood is separated, and carries out neighborhood according to the neighborhood move function and moves the back and produce, and the neighborhood move function is defined as follows:
s
i＝(2×random()-1)×stepsize，i＝1，2，…，i
max????????????????(1)
S wherein
i(i=1 ..., i
Max) represent that neighborhood moves rule function, i
MaxBe the number of times that neighborhood moves, random () is the random function that produces real number between the 0-1, and stepsize is the neighborhood moving step length.Initial solution and neighborhood are separated to produce and are had randomness in this research;
2) calculate target function value, Pareto rank and the individual crowding that neighborhood is separated
After the generation neighborhood is separated, calculate the target function value that all neighborhoods are separated,, calculate Pareto rank and individual crowding value that each neighborhood is separated according to target function value; The Pareto rank number of separating equal neighborhood separate in all Pareto control the skill that this separates, the Pareto rank is 0 separates and be nondominated solution;
3) select kind of a subsolution
Kind of subsolution is the initial solution of searching in per generation, and the selection of planting subsolution is derived from the previous generation neighborhood and separates, and promptly finds to separate separating as candidate seed that Pareto is dominant with respect to other neighborhood and separate from neighborhood is separated, and must satisfy the uncontrolled property of Pareto;
4) upgrade Pareto table, candidate list and taboo table
Pareto table and candidate list are respectively applied for the kind subsolution of depositing each generation and do not have selected other candidate solution for kind of subsolution; To no longer have separating from Pareto table and candidate list of Pareto optimality in per generation search and remove, the individuality that is chosen as kind of subsolution in the candidate list will be removed from table; Upgrade the taboo table with kind of subsolution as the taboo object, selected kind subsolution is avoided in the taboo algebraically of regulation, and seed is lifted a ban the new taboo kind subsolution in back replacement is deposited in the taboo table;
5) judge whether to satisfy stopping criterion
In the optimizing process, if reached predefined maximum iteration time, seed selection subsolution collection also is empty for empty candidate list simultaneously when perhaps searching certain generation, then can't find the next subsolution of planting, algorithm can't enter the search in next stage, and algorithm stops, output Pareto optimal solution set.
2. underground water according to claim 1 is repaired Multipurpose Optimal Method, it is characterized in that process 2) in adopt ideal adaptation degree functional value archival strategy note first search to separate the information of separating in the direct call function value storehouse of separating then of repeat search.
3. underground water according to claim 1 and 2 is repaired Multipurpose Optimal Method, it is characterized in that process 3) in plant subsolution selection following several situation is arranged: if a) only exist a candidate seed to separate, then this is separated as follow-on kind of subsolution; B) if existence is separated more than one candidate seed, contrast the individual crowding that candidate seed is separated, the individuality of choosing crowding value minimum is as follow-on kind of subsolution; C) if there is no candidate seed is separated, and then selects to enter separating as new kind subsolution in the table the earliest from candidate list, and this is separated from candidate list delete.
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| CN109635510A (en) * | 2019-01-15 | 2019-04-16 | 西南交通大学 | The parallel repair line setting method of railway freight-car |
| CN112836459A (en) * | 2021-02-02 | 2021-05-25 | 山东大学 | Circuit analysis model assisted analog circuit automatic optimization method, device and storage medium |
| CN112836459B (en) * | 2021-02-02 | 2022-09-20 | 山东大学 | Circuit analysis model assisted analog circuit automatic optimization method, device and storage medium |
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