CN114647944A - Interval uncertain water resource bearing capacity optimization evaluation method and device - Google Patents
Interval uncertain water resource bearing capacity optimization evaluation method and device Download PDFInfo
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Abstract
The invention provides a method and a device for optimizing and evaluating water resource bearing capacity based on interval uncertainty, wherein the method comprises the following steps: establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions; converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model; solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution; and determining the maximum population number, the maximum economic output value and the maximum grain yield range which can be borne by the water resource according to the optimal compromise. Through the technical scheme, the inaccuracy caused by the conventional method for evaluating the bearing capacity of the water resource can be effectively reduced.
Description
Technical Field
The disclosure relates to the technical field of water resource management, in particular to a method and a device for optimizing and evaluating water resource bearing capacity based on interval uncertainty.
Background
Water is the basis of existence and development of all lives and is one of the basic conditions for sustainable development of human society. With the rapid development of economic society and the continuous increase of population, the demand of water is continuously increased, and especially in arid regions with water shortage and fragile ecological environment, the shortage of water resources becomes a main factor for restricting the development of economic society. Currently, China supports 9% of arable land and 18% of people worldwide with 6% of water resources worldwide, and sustainable utilization of water resources is facing serious challenges. Therefore, how to scientifically evaluate the supporting capability of water resources on the economic society has become a hot problem in the field of water science research. The water resource bearing capacity reflects the supporting capacity of regional water resources on the development of the economic society, is an important index for measuring the coordinated development of the regional water resources and the economic society, provides basic measurement for the safety and sustainable utilization of the regional water resources, and provides a premise and a foundation for water resource planning and management. However, in a real-world water resource system, there are many unknown information and uncertainty factors, so that the conventional water resource bearing capacity assessment cannot accurately reflect the actual situation, thereby affecting the application of the water resource system in water resource planning and management.
Uncertainty is a ubiquitous property of a wide variety of natural, social phenomena, and engineering practices, as well as objective things. As a system in nature, water resource systems also have uncertainty. On the one hand, the natural formation process of water resources has uncertainty itself, such as random uncertainty of rainfall events and runoff process. On the other hand, the driving factors of the water change for socioeconomic development are uncertain in a certain range, such as population growth, economic development, policy change and the like. In addition, in the current scientific and technical level, human beings have insufficient cognition on the objective world, the constructed evaluation model is not complete, and uncertainty still exists in the parameter estimation aspect of the model. In conclusion, the evaluation result of the bearing capacity of the water resource is obviously influenced by the objective existence of various uncertain factors, and the accuracy and the reliability of the water resource planning and evaluation are further reduced. Therefore, how to scientifically evaluate the bearing capacity of water resources under uncertain conditions is a subject that needs intensive research for sustainable utilization of water resources.
The uncertainty optimization theory is an extension of the traditional optimization theory, and aims to be more in line with objective practice. The inherent complexity and uncertainty of the water resource system make the water resource bearing capacity assessment method higher than the conventional deterministic optimization method in nature. The uncertain optimization method begins in the last 50 th century at the earliest, and the summary of the current uncertain optimization method mainly comprises the following steps: stochastic programming (Stochastic programming), Fuzzy programming (Fuzzy programming), and Interval programming (Interval programming). Due to the solution of the stochastic programming or the fuzzy programming, the probability distribution rule or the fuzzy membership function of the uncertain parameters needs to be mastered. When an actual system is modeled, the two types of information are often difficult to obtain. The interval planning means that the uncertain parameters are expressed in an interval form, namely, only the upper and lower bounds of the parameters are needed to be known, and the accurate probability distribution or fuzzy membership function of the parameters is not needed to be known. Therefore, the invention provides the method for evaluating the bearing capacity of the water resource based on the interval uncertainty, which can practically provide the scale range of social economy borne by the water resource, provides an effective method for scientifically evaluating the bearing capacity of the water resource in the region under the uncertain condition, and has important practical significance for guiding the planning and management of the water resource in the region and realizing the sustainable utilization of the water resource.
Disclosure of Invention
In order to overcome the problems in the related art, the disclosure provides a method and a device for optimizing and evaluating the water resource bearing capacity based on interval uncertainty, a multi-target water resource bearing capacity optimization method based on interval uncertainty is constructed, an effective method is provided for scientifically evaluating the water resource bearing capacity under the uncertain condition, a scientific basis is also provided for guiding regional water resource allocation and planning, and therefore the inaccuracy caused by evaluating the water resource bearing capacity by a conventional method is reduced.
According to a first aspect of the embodiments of the present disclosure, there is provided a method for optimizing and evaluating water resource bearing capacity based on interval uncertainty, the method including:
establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions;
converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and determining the interval range of the maximum population number, the maximum economic output value and the maximum grain yield which can be borne by the water resource according to the optimal compromise.
In one embodiment, preferably, the constraints on the amount of water suppliable include: the total water consumption interval value is not more than the sum of the regional water resource utilization interval value and the reclaimed water utilization interval value;
the constraints of the water consumption include: the total water consumption interval value is equal to the sum of a domestic water consumption interval value, an industrial water consumption interval value and an agricultural water consumption interval value, wherein the domestic water consumption interval value is equal to the product of a population interval value and a per capita domestic consumption interval value, and the industrial water consumption interval value is equal to the product of a GDP interval value and an industrial added value, namely the product of the GDP proportion and the ten thousand yuan industrial added value water consumption interval value;
the water use efficiency constraint conditions comprise: the grain yield interval value of single-side irrigation water production is not less than the minimum standard interval value;
the constraints of the welfare level include: the average human GDP interval value is not less than the minimum standard interval value.
In one embodiment, preferably, the multi-objective water resource bearing capacity optimization evaluation model with uncertain intervals comprises the following steps:
the constraint conditions include:
A±X±＝B±
X±≥0
wherein the content of the first and second substances,
respectively representing the population number, the economic output value and the grain output under the condition of uncertain intervals; c±Interval parameters of decision variables in the objective function are set; x±Deciding a variable for the interval; a. the±Interval parameters of decision variables in constraint conditions; b is±Is an interval parameter; a. the±∈{R±}m×n，B±∈{R±}m×1，C±∈{R±}1×nAnd X±∈{R±}n×1，R±Representing a set of interval numbers.
In one embodiment, preferably, the optimization model includes:
wherein the constraint condition comprises:
xj≥0
wherein, the first and the second end of the pipe are connected with each other,
representing the kth objective function;
and
respectively representing the upper limit value and the lower limit value of the k-th optimal value of the objective function,
the median value representing the optimum value of the k-th objective function,
αia satisfaction threshold representing the ith constraint;
the lower boundary of the coefficient representing the jth variable of the ith constraint,
an upper bound representing coefficients for the jth variable of the ith constraint;
the lower bound of the ith constraint is indicated,
representing the upper bound of the ith constraint.
In one embodiment, preferably, the method further comprises:
respectively solving a corresponding target interval value when each target function is used as a single target function according to an interval uncertainty two-step method;
acquiring a preset expected value corresponding to a single objective function;
determining the weight coefficient of each single target function according to the target interval value corresponding to each single target function and a preset expected value;
and solving the optimization model by adopting an interval multi-objective step-by-step tolerant constraint method according to the weight coefficient of each single objective function so as to determine the optimal compromise.
In one embodiment, preferably, solving the optimization model by using an interval multi-objective step-by-step tolerant constraint method according to the weight coefficient of each single objective function to determine an optimal compromise solution includes:
calculated by the following first calculation formula
The best optimum value of (c):
calculated by the following second calculation formula
Best difference of (c):
order to
The compromise solution X is calculated by the following third calculation formula:
wherein the constraint condition comprises:
X∈D0
xj≥0(j＝1,…,n)
in the formula (I), the compound is shown in the specification,
wherein
Is an interval vector CkMedian value of (2)
The euclidean norm of the vector, and
Okrepresenting a predetermined expected value, ε, corresponding to the kth objective functionkRepresents the maximum value of the weight coefficient of the k-th objective function,
represents the lower bound of the jth variable coefficient of the ith constraint,
representing the upper boundary of the jth variable coefficient of the ith constraint condition;
the lower bound of the ith constraint is indicated,
representing the upper bound of the ith constraint.
When the compromise solution X is determined as the optimal compromise solution by the decision maker, ending the process;
in one embodiment, preferably, solving the optimization model by using an interval multi-objective gradual tolerant constraint method according to the weight coefficient of each single objective function to determine an optimal compromise solution further includes:
when the compromise solution X is determined by a decision maker not to be the optimal compromise solution, the k-th median value of the objective function selected by the decision maker is determined
As an object of improvement, and determining an improvement distance
The target improvement level τ is calculated by the following fourth calculation formula*New compromise solution of lower correspondence
Wherein the constraint condition comprises:
X∈D0
xj≥0(j＝1,…,n)
according to the new compromise
And will be
And
and substituting the constraint condition into the third calculation formula to perform iterative calculation to obtain the optimal compromise solution.
According to a second aspect of the embodiments of the present disclosure, there is provided an interval uncertainty-based optimization and assessment apparatus for water resource bearing capacity, the apparatus comprising:
the modeling module is used for establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain output which can be borne by water resources as a multi-target function and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions;
the conversion module is used for converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
the solving module is used for solving the optimization model by adopting an interval multi-target gradual tolerance constraint method so as to determine an optimal compromise solution;
and the determining module is used for determining the maximum population number, the maximum economic output value and the interval range of the maximum grain yield which can be borne by the water resource according to the optimal compromise solution.
According to a third aspect of the embodiments of the present disclosure, there is provided an interval uncertainty-based optimization and assessment apparatus for water resource bearing capacity, the apparatus comprising:
a processor;
a memory for storing processor-executable instructions;
wherein the processor is configured to:
establishing a multi-target water resource bearing capacity optimization evaluation model with uncertain intervals, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions;
converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and determining the maximum population number, the maximum economic output value and the maximum grain yield range which can be borne by the water resource according to the optimal compromise.
According to a fourth aspect of embodiments of the present disclosure, there is provided a computer-readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any one of the first aspects.
The technical scheme provided by the embodiment of the disclosure can have the following beneficial effects:
in the embodiment of the invention, according to a system analysis method, a composite system formed by water resources, economy and society is used, on the premise of meeting water consumption of ecological environment, a multi-target water resource bearing capacity optimization evaluation model is established by taking the bearable population number, economic scale output value and grain yield as targets and taking water supply quantity, water consumption, water use efficiency, welfare level and the like as constraint conditions, and the bearing capacity of regional water resources is evaluated, so that the inaccuracy caused by the bearing capacity of the water resources in a conventional evaluation method is reduced, an effective method is provided for scientifically evaluating the bearing capacity of the water resources under uncertain conditions, and a scientific basis is provided for guiding regional water resource allocation and planning.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.
FIG. 1 is a flowchart illustrating a method for optimizing and evaluating water resource bearing capacity based on interval uncertainty multi-objective according to an exemplary embodiment.
FIG. 2 is a flow chart illustrating another interval uncertainty based single target water resource capacity optimization method according to an example embodiment.
FIG. 3 is a graph illustrating the level of improvement according to an exemplary embodiment
Median value in different objective functions
Schematic analysis of (a).
FIG. 4 is a block diagram illustrating an interval uncertainty-based water resource capacity optimization assessment apparatus, according to an exemplary embodiment.
FIG. 5 is a block diagram illustrating another interval uncertainty-based single-target optimization apparatus, according to an example embodiment.
Detailed Description
Reference will now be made in detail to the exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, like numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the exemplary embodiments below are not intended to represent all implementations consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.
According to a first aspect of the embodiments of the present disclosure, there is provided a method for optimizing and evaluating water resource bearing capacity based on interval uncertainty, the method including:
FIG. 1 is a flowchart illustrating a method for optimizing and evaluating water resource bearing capacity based on multiple targets with uncertain intervals, according to an exemplary embodiment, where the method includes:
step S101, establishing a multi-target water resource bearing capacity optimization evaluation model with uncertain intervals, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain output which can be borne by water resources as a multi-target function, and takes water supply amount, water consumption amount, water use efficiency and welfare level as constraint conditions;
the objective function includes:
1) with maximum number of population to bear
Max Pop±
In the formula, Pop±The number of the bearable population intervals is ten thousand;
2) maximum target of supportable national production total value (GDP)
Max GDP±
In the formula, GDP±The bearing total value interval value of national production is ten thousand yuan;
3) the maximum yield of the bearable grain is a target
Max Grain_yield±
In the formula, gain _ yield±The grain yield interval value is ten thousand tons;
in one embodiment, preferably, the constraints on the amount of water suppliable include: the total water consumption interval value is not more than the sum of the regional water resource utilization interval value and the reclaimed water utilization interval value;
Total_WatUse±≤Wat_avail±+Wat_recy±
wherein Total _ WatUse±Means the total water consumption interval value of ten thousand meters3；Wat_avail±Indicates the interval value of available water supply (the minimum ecological water demand of a river is deducted from the regional water resource), ten thousand meters3；Wat_recy±Means interval value of reclaimed water utilization amount, ten thousand meters3。
The constraints of the water consumption include: the total water consumption interval value is equal to the sum of a domestic water consumption interval value, an industrial water consumption interval value and an agricultural water consumption interval value, wherein the domestic water consumption interval value is equal to the product of a population interval value and a per capita domestic consumption interval value, and the industrial water consumption interval value is equal to the product of a GDP interval value and an industrial added value, namely the product of the GDP proportion and the ten thousand yuan industrial added value water consumption interval value;
Total_WatUse±＝Dom_WatUse±+Ind_WatUse±+Agr_WatUse±
wherein Dom _ WatUse±Means interval value of water consumption for daily use, ten thousand meters3；Ind_WatUse±Means the interval value of industrial water consumption, ten thousand meters3；Agr_WatUse±Means interval value of water consumption for agriculture, ten thousand meters3。
The interval value of the industrial water consumption is equal to the GDP interval value multiplied by the proportion of the industrial added value to the GDP, and then multiplied by the interval value of the ten thousand yuan industrial added value water consumption.
Ind_WatUse±＝GDP±×Rate_Ind_GDP×Quota_Ind±
In the formula, Rate _ Ind _ GDP means that the industrial added value accounts for the proportion of GDP,%; quota _ Ind±Indicates the water consumption interval value of ten thousand yuan of industry added value, m3Per ten thousand yuan.
The agricultural water consumption interval value is equal to the grain yield interval value multiplied by the proportion of the irrigation area to the cultivated land area and then divided by the grain yield interval value produced by single irrigation water.
Agr_WatUse±＝Grain_yield±×Rate_irrg_area/Grain_per_Wat±
In the formula, Rate _ irrg _ area±The proportion of irrigation area to the cultivated land area is percent; gain _ per _ Wat±Indicates the grain yield interval value of the single irrigation water production, kg/m3。
The water use efficiency constraint conditions comprise: the grain yield interval value of single-side irrigation water production is not less than the minimum standard interval value;
Grain_per_Wat±≥MinGrain_per_Wat±
in the formula, MinGrain _ per _ Wat±Indicates the minimum standard interval value of grain yield, kg/m, of single irrigation water production3。
The constraints on the welfare level include: the average human GDP interval value is not less than the minimum standard interval value.
GDP_per_Pop±≥MinGDP_per_Pop±
In the formula，MinGDP_per_Pop±The minimum standard interval value of GDP is the average number of people, ten thousand yuan per person.
Step S102, converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
step S103, solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and step S104, determining the maximum population number, the maximum economic total value and the interval range of the maximum grain yield which can be borne by the water resource according to the optimal compromise.
In one embodiment, preferably, the interval uncertain multi-objective water resource bearing capacity optimization evaluation model comprises:
the constraint conditions include:
A±X±＝B± (1-d)
X±≥0 (1-e)
wherein the content of the first and second substances,
respectively representing the population number, the economic output value and the grain yield under the uncertain condition of the interval; c±Interval parameters of decision variables in the objective function are set; x±Deciding a variable for the interval; a. the±Interval parameters of decision variables in constraint conditions; b is±Is an interval parameter; a. the±∈{R±}m×n，B±∈{R±}m×1，C±∈{R±}1×nAnd X±∈{R±}n×1，R±Representing a set of interval numbers.
In one embodiment, preferably, the optimization model includes:
wherein the constraint condition comprises:
xj≥0(2-f)
wherein the content of the first and second substances,
representing the kth objective function;
and
respectively representing the upper limit value and the lower limit value of the optimal value of the k-th objective function,
the median value representing the optimum value of the k-th objective function,
αia satisfaction threshold representing the ith constraint;
represents the lower bound of the jth variable coefficient of the ith constraint,
representing the upper boundary of the jth variable coefficient of the ith constraint condition; (ii) a
The lower bound of the ith constraint is indicated,
representing the upper bound of the ith constraint.
To complete the solution of the interval multi-objective optimization problem of the formula (1), the optimal interval value of the single-objective problem needs to be obtained first.
FIG. 2 is a flow diagram illustrating another two-step solution to a problem based on interval uncertainty single-objective optimization, according to an exemplary embodiment. As shown in fig. 2, in one embodiment, preferably, the method further comprises:
step S201, the interval uncertain single-target linear programming model has the following standard formula:
min F±＝C±X (3-a)
the constraint conditions are as follows:
A±X±≤B± (3-b)
X±≥0 (3-c)
the specific parameters in the formula are as above.
Step S202, a fuzzy linear programming model is constructed to solve the formula (3), so that the uncertainty of the interval is reduced, and the following formula is specifically adopted.
Maxλ± (4-a)
The constraint conditions are as follows:
A±X±≤B±-λ±·[B+-B-] (4-c)
0≤λ±≤1 (4-d)
X±≥0 (4-e)
in the formula (I), the compound is shown in the specification,
and
respectively representing the upper and lower limits of the optimal value of the objective function. Lambda [ alpha ]±Are the control variables that correspond to the satisfaction (membership) of the fuzzy decision. The interval fuzzy linear optimization model can be decomposed into two submodels for solving,
step S203, firstly, solving an interval fuzzy linear programming upper limit sub-model, which is as follows: max lambda+ (5-a)
The constraint conditions are as follows:
0≤λ+≤1 (5-d)
in the formula (I), the compound is shown in the specification,
represents the interval variable in which the objective function coefficient in the formula (3) is positive,
represents an interval variable in which the objective function coefficient is negative in formula (3). | aijL is coefficient aijAbsolute value of (a), Sign (a)±) Is a coefficient aijThe sign function of (a).
And step S204, determining the optimal upper limit value of the single objective function and a corresponding solution thereof. By solving the equation (5),
and
can be obtained.
Step S205, the second step, solving the interval fuzzy linear programming lower limit sub-model, as follows:
Maxλ- (6-a)
the constraint condition is
0≤λ-≤1 (6-d)
And step S206, determining the optimal upper limit value of the single objective function and a corresponding solution thereof. Can be obtained by the formula (6)
And
and
can be obtained.
Step S207, determining the optimal interval value of the single objective function and the corresponding interval solution thereof. The results of step S204 and step S206 are combined so as to correspond to λ±Interval solution of (2) X±＝[X-,X+]And the optimal interval value f of the objective function±＝[f-,f+]Can be obtained.
On the basis of completing the interval single-target optimization, the interval multi-target problem can be solved. In one embodiment, preferably, solving the optimization model by using an interval multi-objective gradual tolerant constraint method according to the weight coefficient of each single objective function to determine an optimal compromise solution includes:
calculated by the following first calculation formula
The best optimum value of (c):
calculated by the following second calculation formula
Best difference of (c):
order to
The compromise solution X is calculated by the following third calculation formula:
wherein the constraint condition comprises:
X∈D0 (9-c)
xj≥0(j＝1,…,n) (9-e)
in the formula (I), the compound is shown in the specification,
wherein
Is an interval vector CkMedian value of (2)
The euclidean norm of the vector, and
Okrepresenting a predetermined expected value, ε, corresponding to the kth objective functionkRepresenting weight coefficients of the kth objective functionThe maximum value of the number of the first and second,
represents the lower bound of the jth variable coefficient of the ith constraint,
representing the upper boundary of the jth variable coefficient of the ith constraint condition;
the lower bound of the ith constraint is indicated,
representing the upper bound of the ith constraint.
When the compromise solution X is determined as the optimal compromise solution by the decision maker, ending the process;
in one embodiment, preferably, solving the optimization model by using an interval multi-objective gradual tolerant constraint method according to the weight coefficient of each single objective function to determine an optimal compromise solution further includes:
when the compromise solution X is determined by a decision maker not to be the optimal compromise solution, the k-th median value of the objective function selected by the decision maker is determined
As an object of improvement, and determining an improvement distance
The target improvement level τ is calculated by the following fourth calculation formula*New compromise solution of lower correspondence
Wherein the constraint condition comprises:
X∈D0 (10-c)
xj≥0(j＝1,…,n) (10-f)
according to the new compromise
And will be
And
and substituting the constraint condition into the third calculation formula to perform iterative calculation to obtain the optimal compromise solution.
By comparing the median values of the objective functions
And expected value of OkThe decision maker selects the kth target for improvement. The decision maker sets the maximum improvement distance, if any
If the maximum improvement distance is not known to the decision maker
Can pass through
The distance that needs improvement is calculated. To achieve a gradual compromise between conflicting objectives, a level of improvement is required to the extent possible
Median value in different objective functions
The feedback of (2) is analyzed as shown in fig. 3.
By solving equation (10), a series of stable interval forms [ tau ]i,τi+1]Can be obtained. Based on these values, the decision maker can select a certain improvement level τ*As a reasonable level of improvement. Once τ is selected*The decision maker will get a new compromise solution
Then will be
And
added to equation (9) as a new constraint. This iterative process is repeated until the decision maker considers each objective function value to be an acceptable objective function, and the iterative calculation is stopped. Alpha is more than or equal to 0 in satisfaction degree thresholdiCorresponding solution X in the range of less than or equal to 1±＝[X-,X+]I.e. the interval solution, the corresponding optimal interval target
The interval range of the maximum population, GDP and grain yield borne by water resources.
In order to further demonstrate the feasibility of the solution process of the interval uncertain multi-objective optimization problem proposed by the present disclosure, the proposed interactive multi-objective interval optimization algorithm is verified by using a specific two-objective example.
Constraint conditions are as follows:
firstly, the interval optimal solution of each objective function and the corresponding function interval value are solved by using the interval single-objective two-step method, as shown in table 1.
TABLE 1
Presetting the expected value O of the 1 st objective function1Expectation value O of the 2 nd objective function of-202Is 55. The payment table for the values of the objective function and the expected values is shown in table 2.
TABLE 2
According to the formula (7), the formula (8) and the formula (9), the following results can be obtained by calculation:
P1 u＝0.78645 P1 l＝0.11665
φ1＝0.19801 φ2＝0.21407π1＝0.48051 π2＝0.51949
let alpha1＝α2＝α3＝α40.8, the following optimization model was calculated according to the interactive method under uncertain conditions:
minε1+ε2 (12-a)
the constraint conditions include:
-0.19046-0.02381x1+0.03333x2≤ε1 (12-b)
0.71344-0.04216x1-0.03243x2≤ε2 (12-c)
-6.64x1+3.58x2≤9.2 (12-d)
3.16x1+5.4x2≤70.4 (12-e)
x1≤13.2 (12-f)
x2≤8.2 (12-g)
xj≥0 (12-m)
through the first optimization calculation, the solution of equation (12) is obtained as: x is the number of1＝13.2，x2The median of the objective function is 2.82: f. of1 c＝23.14557，
If the decision maker is acceptable as a reasonable solution to the above result, the calculation will terminate. Otherwise, the decision maker picks one of the targets for improvement. Where f is selected1 cThe improvement is made as an objective function requiring improvement. If the decision maker does not know the distance measure Δ that needs to be improved1Can be represented by1＝|O1-f1 c(X1) Calculated as | -20- (23.14557) | ═ 43.14557.
The compromise iterative calculation is performed using the following equation (13).
minε1+ε2 (13-a)
The constraint conditions include:
-0.19046-0.02381x1+0.03333x2≤ε1 (13-b)
0.71344-0.04216x1-0.03243x2≤ε2 (13-c)
-6.64x1+3.58x2≤9.2 (13-d)
3.16x1+5.4x2≤70.4 (13-e)
x1≤13.2 (13-f)
x2≤8.2 (13-g)
2.5x1-3.5x2＝-20+43.14557τ (13-h)
xj≥0 (13-n)
f1 ±(X) and
the compromise calculation procedure is shown in table 3.
TABLE 3 median value f of objective function for different T1 c(X) and
when τ is 0.3, the decision maker considers f1 c(X)＝-7.05633,
Is an acceptable value of the objective function, at which the corresponding x1＝8.48110，x28.07402. Obviously, with the above method, a decision maker can easily perform compromise calculation between multiple uncertain targets. By utilizing the interactive method, not only can the range of the solved interval be mastered, but also the gradual compromise analysis among multiple targets can be obtained, and a decision maker can conveniently make a decision on a scheme.
FIG. 4 is a block diagram illustrating an interval uncertainty-based water resource capacity optimization assessment apparatus, according to an exemplary embodiment.
As shown in fig. 4, according to a second aspect of the embodiments of the present disclosure, there is provided an optimized evaluation device for water resource bearing capacity based on interval uncertainty, the device comprising:
the modeling module 41 is used for establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, the total economic value and the grain yield which can be borne by water resources as a multi-target function, and takes the available water supply amount, the water consumption amount, the water use efficiency and the welfare level as constraint conditions;
the conversion module 42 is used for converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
a solving module 43, configured to solve the optimization model by using an interval multi-objective gradual tolerant constraint method to determine an optimal compromise solution;
and the determining module 44 is configured to determine, according to the optimal compromise solution, a maximum population number, a maximum economic total value, and an interval range of a maximum grain yield that can be borne by the water resource.
FIG. 5 is a block diagram illustrating another interval uncertainty-based single-target optimization apparatus, according to an example embodiment.
As shown in fig. 5, in one embodiment, preferably, the apparatus further comprises:
the interval single-target modeling module 51 is used for establishing an interval uncertain single-target model, including a target function and a constraint condition;
the fuzzy linear programming module 52 is used for constructing an interval fuzzy linear programming module corresponding to the single target model;
a two-step method module 53, configured to sequentially solve, according to the interval uncertainty two-step method, a corresponding target interval value when each of the fuzzy linear programming submodels is used as a single objective function;
and a solution determining module 54, configured to determine a single-target interval solution and an optimal function interval value corresponding to the single-target interval solution according to the interval solution obtained by the two-step method. According to a third aspect of the embodiments of the present disclosure, there is provided an interval uncertainty-based optimization and assessment apparatus for water resource bearing capacity, the apparatus comprising:
a processor;
a memory for storing processor-executable instructions;
wherein the processor is configured to:
establishing a multi-target water resource bearing capacity optimization evaluation model with uncertain intervals, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, the total economic value and the grain yield which can be borne by water resources as a multi-target function, and takes the available water supply amount, the water consumption amount, the water use efficiency and the welfare level as constraint conditions;
converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and determining the maximum population number, the maximum economic total value and the maximum grain yield range which can be borne by the water resource according to the optimal compromise.
According to a fourth aspect of embodiments of the present disclosure, there is provided a computer-readable storage medium having stored thereon computer instructions which, when executed by a processor, implement the steps of the method of any one of the first aspects.
It is further to be understood that while operations are depicted in the drawings in a particular order, this is not to be understood as requiring that such operations be performed in the particular order shown or in serial order, or that all illustrated operations be performed, to achieve desirable results. In certain environments, multitasking and parallel processing may be advantageous.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.
Claims (10)
1. An interval uncertainty-based optimization evaluation method for bearing capacity of water resources is characterized by comprising the following steps:
establishing a multi-target water resource bearing capacity optimization evaluation model with uncertain intervals, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions;
converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and determining the interval range of the maximum population number, the maximum economic output value and the maximum grain yield which can be borne by the water resource according to the optimal compromise.
2. The method of claim 1, wherein the constraints on the amount of water that can be supplied include: the total water consumption interval value is not more than the sum of the regional water resource utilization interval value and the reclaimed water utilization interval value;
the constraints of the water consumption include: the total water consumption interval value is equal to the sum of a domestic water consumption interval value, an industrial water consumption interval value and an agricultural water consumption interval value, wherein the domestic water consumption interval value is equal to the product of a population interval value and a per capita domestic consumption interval value, and the industrial water consumption interval value is equal to the product of a GDP interval value and an industrial added value, namely the product of the GDP proportion and the ten thousand yuan industrial added value water consumption interval value;
the water use efficiency constraint conditions comprise: the grain yield interval value of single-side irrigation water production is not less than the minimum standard interval value;
the constraints of the welfare level include: the average human GDP interval value is not less than the minimum standard interval value.
3. The method of claim 1, wherein the multi-objective water resource bearing capacity optimization assessment model with uncertain intervals comprises:
the constraint conditions include:
A±X±＝B±
X±≥0
wherein, f1 ±，f2 ±，f3 ±Respectively representing the population number, the economic output value and the grain output under uncertain conditions; c±Interval parameters of decision variables in the objective function are set; x±Deciding a variable for the interval; a. the±Interval parameters of decision variables in constraint conditions; b is±Is an interval parameter; a. the±∈{R±}m×n，B±∈{R±}m×1，C±∈{R±}1×nAnd X±∈{R±}n×1，R±Representing a set of interval numbers.
4. The method of claim 1, wherein the optimization model comprises:
wherein the constraint condition comprises:
xj≥0
wherein the content of the first and second substances,
the k-th objective function is represented as,
and
respectively representing the upper limit value and the lower limit value of the optimal value of the k-th objective function,
the median value representing the optimum value of the kth objective function,
αia satisfaction threshold representing the ith constraint;
represents the lower bound of the jth variable coefficient of the ith constraint,
represents the jth variable coefficient of the ith constraint conditionAn upper boundary of (d);
the lower bound of the ith constraint is indicated,
representing the upper bound of the ith constraint.
5. The method of claim 4, further comprising:
respectively solving a corresponding target interval value when each target function is used as a single target function according to an interval uncertain two-step method;
acquiring a preset expected value corresponding to a single objective function;
determining a weight coefficient of each single target function according to the target interval value corresponding to each single target function and a preset expected value;
and solving the optimization model by adopting an interval multi-objective gradual tolerant constraint method according to the weight coefficient of each single objective function so as to determine the optimal compromise solution.
6. The method of claim 5, wherein solving the optimization model using an interval multi-objective step-by-step tolerant constraint method according to the weight coefficients of the single objective functions to determine an optimal compromise solution comprises:
calculated by the following first calculation formula
Best optimum value of (c):
calculated by the following second calculation formula
Best difference of (c):
order to
The compromise solution X is calculated by the following third calculation formula:
wherein the constraint condition comprises:
X∈D0
xj≥0(j＝1,…,n)
in the formula (I), the compound is shown in the specification,
wherein
Is an interval vector CkMedian value of (2)
The euclidean norm of the vector, and
Okrepresenting a predetermined expected value, ε, corresponding to the kth objective functionkRepresents the maximum value of the weight coefficient of the k-th objective function,
represents the lower bound of the jth variable coefficient of the ith constraint,
representing the upper boundary of the jth variable coefficient of the ith constraint condition;
the lower bound of the ith constraint is indicated,
an upper bound representing the ith constraint;
and when the compromise solution X is determined as the optimal compromise solution by the decision maker, ending the process.
7. The method of claim 6, wherein the optimization model is solved using an interval multi-objective gradual tolerant constraint method according to the weight coefficients of the single objective functions to determine an optimal compromise solution, further comprising:
when the compromise solution X is determined by a decision maker to be not the optimal compromise solution, selecting the k-th median value of the objective function selected by the decision maker
As an object of improvement, and determining an improvement distance
The target improvement level τ is calculated by the following fourth calculation formula*New compromise solution of lower correspondence
Wherein the constraint condition comprises:
X∈D0
xj≥0(j＝1,…,n)
according to the new compromise
And will be
And
and substituting the constraint condition into the third calculation formula to perform iterative calculation to obtain the optimal compromise solution.
8. An interval uncertainty-based optimization and evaluation device for water resource bearing capacity, which is characterized by comprising:
the modeling module is used for establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes the available water supply amount, water consumption amount, water use efficiency and welfare level as constraint conditions;
the conversion module is used for converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
the solving module is used for solving the optimization model by adopting an interval multi-target gradual tolerance constraint method so as to determine the optimal compromise solution;
and the determining module is used for determining the maximum population number, the maximum economic output value and the maximum grain output range which can be borne by the water resource according to the optimal compromise.
9. An interval uncertainty-based optimization and assessment device for water resource bearing capacity, which is characterized by comprising:
a processor;
a memory for storing processor-executable instructions;
wherein the processor is configured to:
establishing an uncertain multi-target water resource bearing capacity optimization evaluation model, wherein the multi-target water resource bearing capacity optimization evaluation model takes the population number, economic output value and grain yield which can be borne by water resources as a multi-target function, and takes available water supply, water consumption, water use efficiency and welfare level as constraint conditions;
converting the multi-target water resource bearing capacity optimization evaluation model into an equivalent optimization model;
solving the optimization model by adopting an interval multi-target gradual tolerant constraint method to determine an optimal compromise solution;
and determining the interval range of the maximum population number, the maximum economic output value and the maximum grain yield which can be borne by the water resource according to the optimal compromise.
10. A computer-readable storage medium having stored thereon computer instructions, which, when executed by a processor, carry out the steps of the method according to any one of claims 1 to 7.
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