CN-121119304-B - Multi-objective robust optimization method for bay nutrient salt pollution treatment

CN121119304BCN 121119304 BCN121119304 BCN 121119304BCN-121119304-B

Abstract

The invention discloses a multi-objective robust optimization method for the treatment of the pollution of a gulf nutrient salt, which comprises the following steps of S1, carrying out global sensitivity analysis by utilizing a Sobol variance analysis method, setting a threshold value, screening out high-sensitivity parameters, S2, generating a plurality of disturbance scene parameter combinations for the high-sensitivity parameters by adopting a Latin hypercube sampling method, constructing a unified disturbance sample space, S3, constructing a multi-objective optimization model for the treatment of the pollution of the nutrient salt, determining water quality optimization and treatment cost minimization targets, S4, calling an NSGA-II algorithm, respectively solving the multi-objective optimization problem, obtaining Pareto solution sets under different disturbance scenes, S5, calculating expected values, standard deviations and gradient change rates under decision disturbance of each solution under representative disturbance samples, S6, evaluating the robustness of each candidate solution to obtain a representative solution set, S7, checking the response performance of objective functions of each representative solution in a non-original disturbance scene, and outputting an optimal solution for the pollution treatment of the gulf nutrient salt in a river basin.

Inventors

LI SHAOBIN
LI WEIYE
CHEN NENGWANG
Huang Zhehan
SUN WEIWEI

Assignees

厦门大学

Dates

Publication Date: 20260508
Application Date: 20251112

Claims (9)

1. The multi-objective robust optimization method for the treatment of the Bay nutrient salt pollution is characterized by comprising the following steps of: S1, identifying an uncertainty parameter set of a bay nutrient salt partition simulation model in a river basin, performing global sensitivity analysis by using a Sobol variance analysis method, and setting a threshold value to screen out high-sensitivity parameters; s2, generating a plurality of disturbance scene parameter combinations for the high-sensitivity parameters by using a Latin hypercube sampling method, and constructing a unified disturbance sample space for multi-scene simulation and optimization solution; s3, constructing a multi-objective optimization model for nutrient salt pollution treatment, defining a water quality optimization and treatment cost minimization objective, taking the implementation proportion of pollution treatment measures as a model decision variable, and setting upper and lower limits of the variable and total constraint conditions; s4, calling an NSGA-II algorithm to respectively solve the multi-objective optimization problem and obtain Pareto solution sets under different disturbance scenes; s5, performing posterior robustness evaluation on the candidate solution set, and calculating an expected value, a standard deviation and a gradient change rate of each solution under decision disturbance under a representative disturbance sample; S6, calculating comprehensive robust scores by using a VIKOR method, and evaluating the robustness of each candidate solution to obtain a representative solution set; S7, verifying response performance of each representative objective function in the non-original disturbance scene, and verifying stability performance of each representative objective function in different disturbance scenes; S8, screening out a feasible solution set based on the constraint of the standard reaching condition, and outputting an optimal solution for the gulf nutrient salt pollution treatment in the watershed.
2. The multi-objective robust optimization method for bay nutrient salt pollution control as claimed in claim 1, wherein the specific process of step S1 is as follows: S11, analyzing and assuming uncertainty distribution of main parameters based on literature collection, field investigation data and reasonable assumption, and sampling by using a Latin hypercube sampling method to generate a plurality of groups of uncertainty parameter groups, wherein the main parameters comprise pollution source nutrient salt emission, biochemical process rate parameters and cost price; s12, inputting an uncertainty parameter set into a nutrient salt partition simulation model and a measure cost reduction function, and analyzing probability distribution of output results of the nutrient salt partition simulation model and the measure cost reduction function; S13, performing sensitivity analysis on key process parameters and reduction measure cost functions of the nutrient salt partition simulation model by using a Sobol variance analysis method, wherein the key process parameters comprise pollution source emission, water exchange flux and culture biological process rate parameters of each partition, and a first-order sensitivity index calculation formula is as follows: , wherein, Is the first Sensitivity index of the individual input parameters; numbering the parameters; is a bay water quality response function; Is the first A plurality of input parameters; To give at the first Input parameters In the case of (a) bay water quality response function Is expected to be the condition of (2); To give at the first Input parameters In the case of (a) bay water quality response function Is a conditional expected variance of (2); the total variance of the water quality response function of the bay; s14, calculating a total sensitivity index of each parameter, and quantifying the influence of the key uncertainty parameter and the represented process on the result, wherein the total sensitivity index comprises the direct influence of the parameter on output and the interaction effect with other parameters, and the calculation formula of the total sensitivity index is as follows: , wherein, A total sensitivity index for the input parameter set; To remove A set of all parameters except for; To remove The conditional expectation variance of the latter other parameters; S15, the first-order sensitivity indexes and the total sensitivity indexes of all input parameters respectively form a first-order sensitivity index set and a total sensitivity index set, the first-order sensitivity index set and the total sensitivity index set are subjected to normalization processing, uniformly scaled to a [0,1] interval, and are arranged in descending order according to the size of the total sensitivity index to obtain the sensitivity ordering of the parameters, a screening threshold value theta is set, and the parameters with the sensitivity index larger than theta are selected as high-sensitivity parameters for subsequent disturbance analysis and optimization design flow.
3. The multi-objective robust optimization method for bay nutrient salt pollution control as claimed in claim 1, wherein the specific process of step S2 is as follows: S21, setting uncertainty distribution types and ranges for a plurality of high-sensitivity parameters related to the nutrient salt partition simulation model; S22, dividing the value range of each high-sensitivity parameter into p equal probability subintervals, and randomly extracting a sample point in each subinterval; S23, carrying out random matching combination on sample points obtained by extracting each parameter dimension to generate p disturbance scene parameter combinations; S24, constructing a unified disturbance sample space through p disturbance scene parameter combinations, wherein the unified disturbance sample space is used as input for multi-scene simulation and optimization solving of a nutrient salt partition simulation model and a measure cost reduction function.
4. The multi-objective robust optimization method for bay nutrient salt pollution control as claimed in claim 1, wherein the specific process of step S3 is as follows: s31, setting an objective function, wherein the objective function comprises an objective function of the nutrient salt concentration of the water body and an objective function of the cost of a nutrient salt pollution reduction scheme, and the calculation formula of the objective function is as follows: , wherein, Is an objective function of the nutrient salt concentration of the water body; an objective function of cost of the nutrient salt pollution abatement protocol; numbering the jurisdictional sea areas; Numbering nutrient salt pollution treatment measures; numbering the water quality section of the bay; Is that The decision variables, i.e. the curtailment scale of different curtailment measures in different jurisdictions, Is the total number of decision variables; Is that The number of uncertainty parameters is a function of the number of uncertainty parameters, Is the total number of uncertainty parameters; is the total number of water quality sections of the bay; Is a water quality section of bay The basic water quality without treatment measures under disturbance situations; Is a measure for controlling the pollution of nutrient salt In jurisdiction of sea area To the water quality section of bay The water quality improvement effect is brought; For jurisdiction of sea areas Medium nutrient salt pollution treatment measure Corresponding treatment cost; S32, constructing a constraint condition of fair distribution, so that each jurisdictional sea area has equal rights on the distribution of the initial pollution reduction target, wherein the constraint condition has a calculation formula as follows: , , , , wherein, For jurisdiction of sea areas The weight coefficient of the production value occupied in the total environment capacity; For jurisdiction of sea areas Yield values achievable under normal conditions; the total number of the jurisdictional sea areas participating in the treatment; The pollution of theoretical nutrient salt can be discharged; Adjusting the coefficient for the total amount; the average discharge amount of nutrient salt pollution for each jurisdiction sea area; the upper limit of the total nutrient salt pollution emission of the bay; the pollution discharge amount of nutrient salt for the jurisdiction sea area; For jurisdiction of sea areas Treatment of internal nutrient salt pollution The pollution reduction amount of the generated nutrient salt; the correction factor is utilized for fairness.
5. The multi-objective robust optimization method for bay nutrient salt pollution control as claimed in claim 1, wherein the specific process of step S4 is as follows: S41, inputting each group of uncertainty parameter groups obtained in the step S1 into a nutrient salt partition simulation model, and taking the uncertainty parameter groups as an environment background for model operation; S42, solving a set multi-objective optimization problem, outputting decision variables as optimization individuals, and initializing to generate a first-generation population, wherein each population individual is a pollution treatment combination scheme to be optimized; S43, invoking an NSGA-II algorithm to perform iterative optimization on the initialized population, calculating the fitness value of each population individual under the disturbance scene based on the objective function of the water body nutrient salt concentration and the treatment cost, and sequentially performing non-dominant sorting, crowding distance calculation, individual selection, intersection and variation operation to iteratively generate a Pareto optimal solution set.
6. The multi-objective robust optimization method for Bay nutrient salt pollution control as claimed in claim 1, wherein the posterior robustness assessment in step S5 is implemented by calculating three robust indexes of expected value, standard deviation and gradient change rate of each candidate solution, comprehensively reflecting stability and reliability of the solution, and specifically comprises selecting representative disturbance scene parameter combinations, assessing expected value and standard deviation of objective function of each candidate solution in different disturbance scene parameter combinations, measuring average performance and response fluctuation of the solution in different disturbance scenes, and comparing the candidate solutions in the context of fixed disturbance scene parameter combinations Disturbance is applied to each dimension of the solution, and the local stability of the solution is reflected through the change of the objective function value, wherein the calculation formula of the expected value and the standard deviation of the objective function is as follows: , , wherein, Is the expected value of the objective function; Is the total number of disturbance samples; Is the first Outputting results of the objective function under the combination of the disturbance scene parameters; Standard deviation as objective function; The gradient rate formula is: , wherein, Is the gradient change rate; Is the first Unit vectors for the direction of the individual decision variables; The small disturbance amplitude is set; To the first pair Applying perturbations to individual decision variable dimensions The solution vector after that; The target function value after disturbance; Is the original objective function value.
7. The multi-objective robust optimization method for treating Bay nutrient salt pollution in accordance with claim 1, wherein the specific process of step S6 is that based on normalizing the robust index data, an individual minimum distance index and a maximum regret index are calculated, the overall deviation degree of candidate solutions on all indexes and the relative disadvantages on the worst indexes are respectively evaluated, and then the overall robust level of each solution is judged by integrating the VIKOR comprehensive index, wherein the calculation formula of the individual minimum distance index is as follows: , wherein, Numbering the candidate solutions; Numbering the indexes; Is the total index number; To solve the comprehensive deviation degree of all indexes; Is the first The weight coefficient of each index; Is the first Optimal values of the individual indicators in all solutions; for a candidate solution In the first place A value on the individual index; Is the first The worst value of each index in all solutions; the calculation formula of the maximum regret index is as follows: , wherein, For the relative worst performance of the solution on the worst index; taking the worst value for all indexes; the calculation formula of the VIKOR comprehensive index is as follows: , wherein, Is VIKOR comprehensive index; is a decision preference coefficient; Is that Is the maximum value of (2); Is that Is the minimum of (2); Is that Is the maximum value of (2); Is that Is a minimum of (2).
8. The multi-objective robust optimization method for gulf nutrient salt pollution control as claimed in claim 1, wherein the objective function response performance in the non-original disturbance scenes in the step S7 is to put the representative solutions screened in the step S6 into other disturbance scenes except the original background thereof respectively for simulation operation, and the objective function performance of the representative solutions in all non-original disturbance scenes is obtained by repeatedly operating the nutrient salt partition simulation model and the reduction measure cost function in each disturbance scene, and the stability of the representative solutions in different disturbance scenes is verified, so that the optimal nutrient salt reduction scheme which still maintains good performance under various uncertainty conditions is identified.
9. The multi-objective robust optimization method for the treatment of the gulf nutrient salt pollution as claimed in claim 1, wherein the specific process of the step S8 is to check whether the concentration of the corresponding pollutant of each representative solution under all disturbance scenes meets the requirement of the water quality reaching the red line one by one and simultaneously meet the total cost of the pollution treatment within the acceptable budget range, and finally reserve solutions meeting the constraint condition of the multi-scene reaching the standard to form a feasible solution set as the optimal recommended scheme for the treatment of the gulf nutrient salt pollution in the watershed.

Description

Multi-objective robust optimization method for bay nutrient salt pollution treatment Technical Field The invention belongs to the technical field of environmental pollution control and management, and particularly relates to a multi-objective robust optimization method for bay nutrient salt pollution treatment. Background The input flux of the nutrient salt in the water body of the bay is increased, the ecological environment problems such as eutrophication of the water body, frequent red tide and the like are easily induced, and the health of the ecological system of the bay is seriously threatened. The gulf nutrient salt pollution presents the characteristics of multiple emission sources, strong sea Liu Ouge, complex pollution migration path and the like, the space coupling of pollution control and reduction strategies is high, the response uncertainty is large, and a scientific and reasonable pollution control scheme and space partition emission reduction strategy are needed to be formulated so as to improve the accuracy and the robustness of treatment. Most of the existing optimization methods for the treatment of the Bay pollution are based on the output result of a deterministic model, neglect the uncertainty of key parameters of a Bay nutritive salt simulation model, weaken the actual operability and robustness of a treatment scheme, and are difficult to meet the actual use requirements. Disclosure of Invention In order to solve the problems, the invention provides a multi-objective robust optimization method for the pollution treatment of the gulf nutrient salt, which solves the pollution control scheme with stable performance and strong space suitability under the complex uncertainty condition by constructing a full-chain technical framework of multi-disturbance simulation, multi-objective optimization and posterior robustness assessment, and remarkably improves the feasibility and ecological safety of a gulf nutrient salt reduction strategy. In order to achieve the above purpose, the present invention adopts the following technical scheme: a multi-objective robust optimization method for bay nutrient salt pollution control comprises the following steps: S1, identifying an uncertainty parameter set of a bay nutrient salt partition simulation model in a river basin, performing global sensitivity analysis by using a Sobol variance analysis method, and setting a threshold value to screen out high-sensitivity parameters; s2, generating a plurality of disturbance scene parameter combinations for the high-sensitivity parameters by using a Latin hypercube sampling method, and constructing a unified disturbance sample space for multi-scene simulation and optimization solution; s3, constructing a multi-objective optimization model for nutrient salt pollution treatment, defining a water quality optimization and treatment cost minimization objective, taking the implementation proportion of pollution treatment measures as a model decision variable, and setting upper and lower limits of the variable and total constraint conditions; s4, calling an NSGA-II algorithm to respectively solve the multi-objective optimization problem and obtain Pareto solution sets under different disturbance scenes; s5, performing posterior robustness evaluation on the candidate solution set, and calculating an expected value, a standard deviation and a gradient change rate of each solution under decision disturbance under a representative disturbance sample; S6, calculating comprehensive robust scores by using a VIKOR method, and evaluating the robustness of each candidate solution to obtain a representative solution set; S7, verifying response performance of each representative objective function in the non-original disturbance scene, and verifying stability performance of each representative objective function in different disturbance scenes; S8, screening out a feasible solution set based on the constraint of the standard reaching condition, and outputting an optimal solution for the gulf nutrient salt pollution treatment in the watershed. Preferably, the specific process of step S1 is: S11, analyzing and assuming uncertainty distribution of main parameters based on literature collection, field investigation data and reasonable assumption, and sampling by using a Latin hypercube sampling method to generate a plurality of groups of uncertainty parameter groups, wherein the main parameters comprise pollution source nutrient salt emission, biochemical process rate parameters and cost price; s12, inputting an uncertainty parameter set into a nutrient salt partition simulation model and a measure cost reduction function, and analyzing probability distribution of output results of the nutrient salt partition simulation model and the measure cost reduction function; S13, performing sensitivity analysis on key process parameters and reduction measure cost functions of the nutrient salt partition simulation model by using a Sobol variance