CN106372740B - Calculation method and system for pasturing area water-soil grass-livestock balance model - Google Patents
Calculation method and system for pasturing area water-soil grass-livestock balance model Download PDFInfo
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Abstract
The invention discloses a calculation method and a calculation system for a pastoral water-soil grass-livestock balance model, and relates to the technical field of mathematical model calculation. The method takes water resources, land resources and grassland resource bearing capacity as the bottom line, aims to achieve the maximum comprehensive benefit of economic benefit and ecological benefit, and reasonably determines the water and soil resource development scale, the farming and animal husbandry planting structure, the animal husbandry production mode and the appropriate livestock carrying capacity by taking the comprehensive balance between 'water-soil-grass-livestock' in the pastoral area as a criterion, so as to realize the sustainable utilization of water, soil and grass resources, the benign development of ecological environment and the sustainable development of social economy.
Description
Technical Field
The invention relates to the technical field of mathematical model calculation, in particular to a calculation method and a system of a pastoral water, soil, grass and livestock balance model.
Background
The pastoral area in China is dry and has little rain, water resource shortage, unmatched water and soil resources, outstanding contradiction of the balance of grasses and livestock, serious desertification degradation of the grassland, very fragile ecological environment, and overloading grazing and farming-assisted silkworm rearing are main human factors causing ecological degradation of the grassland.
The current pasturing area balance calculation has the following problems:
(1) most of the previous researches are water-grass-livestock balance calculation, and the consideration of soil which is an important influence factor for irrigating artificial grassland planting is insufficient;
(2) in the past, the economic benefit maximization is mostly used as the target for calculation;
(3) in the past, the available irrigation water is mostly restricted by the available irrigation water, the available irrigation water is a fixed value obtained by deducting the water consumption of other industries from the available water supply of water resources, and the available irrigation water is changed in different water configuration targets and schemes;
(4) previous forage-animal balance studies only considered quantitative balance, neglecting the mass balance between natural grass forage and artificial high-quality forage.
Disclosure of Invention
The embodiment of the invention provides a calculation method and a calculation system for a pasturing area water-soil grass-animal balance model, which are used for solving the problems in the prior art.
A method of calculating a pasture hydro-soil pasture balance model, the method comprising:
determining an objective function according to input parameters and a first preset relation between the parameters, wherein the objective function comprises a comprehensive benefit function and a water supply source priority function, and the comprehensive benefit function is the maximum value of the sum of economic benefit and ecological benefit;
Determining constraint conditions according to the parameters and a second preset relation between the parameters, wherein the constraint conditions comprise resource bearing capacity constraint conditions, supply and demand balance constraint conditions, life support constraint conditions, fairness constraint conditions and non-negative constraint conditions;
according to the livestock feeding mode, a plurality of groups of values of the parameters are set in a balanced mode from natural grazing to full-house feeding of the water and soil livestock according to an artificial supplementary feeding quota increasing mode, the value of each group of parameters is combined with the objective function and the constraint condition to form a scheme, and a plurality of schemes form a scheme set;
solving the scheme set to obtain an optimal solution set of each scheme;
according to the optimal solution sets obtained by calculation of different schemes, analyzing the limiting factors of regional development through multi-index comprehensive analysis and comparison, selecting the scheme most beneficial to regional development as the optimal scheme, and taking the optimal solution set of the optimal scheme as the regional water-soil-grassy-animal development threshold;
solving the solution set to obtain an optimal solution set of each solution comprises:
corresponding the solution of the objective function of each scheme to a [0, 1] interval to obtain the coding form of all solutions, wherein the coding form of the solutions is called as an individual;
Randomly generating a plurality of individuals, carrying out rationality test on each individual, reserving the individuals meeting the constraint condition as initial individuals, and forming an initial population by the initial individuals;
calculating the fitness of each initial individual in the initial population;
taking the initial individuals in the initial population as parent individuals, and generating corresponding child individuals according to the fitness of the parent individuals;
storing a set of n sub-generation individuals with the most advanced fitness generated by the first generation evolution as an existing non-inferior solution set, comparing the best n sub-generation individuals generated by each generation evolution with each solution in the existing non-inferior solution set one by one, and reserving a superior solution to replace an inferior solution to obtain a non-inferior solution set;
and when the evolution times reach the preset evolution times and the iteration times also reach the preset iteration times, reserving the non-inferior solution set obtained through replacement as an optimal solution set.
Preferably, when the iteration number does not reach the preset iteration number, the next iteration is performed again until the iteration number reaches the preset iteration number.
Preferably, the overall benefit function is determined according to the following formula:
fc＝Max(OBE+OBEN)
In the formula (f)cThe function of the comprehensive benefit is OBE, the economic benefit is OBE, and the ecological benefit is OBEN;
the economic benefit OBE is determined by the following formula:
OBE＝ANB+INB
wherein, ANB is the net benefit of agriculture and animal husbandry, INB is the net benefit of non-agriculture and animal husbandry;
the net benefits of farming and animal husbandry are determined by the following formula:
ANB＝ANBA+ANBL
in the formula, ANBA is the irrigation net benefit of the planting industry, and ANBL is the livestock feeding net benefit;
the net irrigation benefit of the planting industry is determined by the following formula:
wherein ACA (f) is the irrigation area of f-type planted crops, P (f), Y (f) and C (f) are the unit price, the average yield per mu and the planting cost of the f-type planted crops respectively, WP is the water price, WN (f) is the hair irrigation quota of the f-type planted crops;
the livestock raising net benefit is determined by the following formula:
in the formula, LSL is the livestock feeding amount, namely a standard sheep unit, P (l) and Y (l) are the yield and unit price of a type 1 product of the standard sheep unit of livestock respectively, omega is the livestock slaughtering rate, C is the cost of the standard sheep unit of livestock, and WNL is the drinking water quota of the standard sheep unit of livestock;
the non-farming-animal-husbandry net benefit INB is expressed by the industrial water net benefit as follows:
INB＝IAV·ψ·δ
in the formula, IAV is an industrial added value, psi is the proportion of an industrial net value to a total product value, and delta is an industrial water benefit allocation coefficient;
The ecological benefit OBEN is determined by the following formula:
in the formula, ANAkThe utilization AREA of the kth natural pasture, the OBEND is the ecological service value of the dynamic grassland, the AREA is the utilization AREA of the natural pasture, and the xi (k) is the conversion coefficient of the kth natural pasture under the corresponding feed intake rate;
the dynamic grassland ecological service value is determined by the following formula:
OBEND＝l·r·OBENS
in the formula, l is the relative willingness to pay, r is the scarcity degree of natural grassland resources, the value can be taken according to the degradation degree of the natural grassland, the value range is [0, 1], and OBENS is the ecological service value of the static grassland;
the relative willingness-to-pay expression is as follows:
in the formula, L is the maximum value of the relative willingness-to-pay L, represents the willingness-to-pay in an extremely rich stage, takes a value of 1, t is a time variable, represents the socioeconomic development stage, a and b are constants, take a value of 1, and e is a natural logarithm;
wherein the time variable t expression is:
in the formula, EnIs the Enger coefficient;
the static grassland ecological service value is determined by the following formula:
in the formula, AREAiIs the area of a natural grassland of the i-type, VPAiThe unit price of the grassland ecological service value under the natural state of the i-type natural grassland.
Preferably, the water supply source priority function is determined according to the following formula:
In the formula (f)wAs a function of said priority of the water supply source, OBW being the priority of the water supply source, αiAnd betajThe water supply weight coefficient of the i industry and the water supply priority coefficient of the j water source are respectively, and WSL (i, j, t) is the water supply amount of the i industry j water source in the t period.
Preferably, the resource bearing capacity constraint condition comprises a water resource bearing capacity constraint condition, a grassland resource bearing capacity constraint condition and a land resource bearing capacity constraint condition;
the water resource bearing capacity constraint condition expression is as follows:
in the formula, WSG (t)maxFor the maximum water supply capacity of a water supply project in a time period t, WLL (j, t) is the available quantity of a water source in a time period j in the time period t, WTL (t) is the water regulating quantity outside the time period t, and WUI is a regional water total quantity control index;
the grassland resource bearing capacity constraint condition expression is as follows:
LSL·LNk·Tk≤ANAk·NCLk
LSL·ILNl·Tl≤IGAl·CLl
in the formula (I), LNkIs a unit feed ration of a k-class natural pasture sheep, TkDays of rearing in a natural pasture of the k-th class, NCLkFor hay production in natural pastures of the k-type, ILNlFor l-class irrigation artificial grassland sheep unit feed intake quota, TlDays of rearing on class I irrigated turf, IGAlIs the area of the class I irrigated grass land, CLlDry grass yield for class i irrigated grasslands;
the land resource bearing capacity constraint condition expression is as follows:
In the formula, ACA is the irrigation area of the planted crop, FCAmFor irrigation area of m-th grain crops, ECAnThe irrigation area of the nth cash crop, the AFL is the available cultivated land area, and the R is the multiple cropping index;
the supply and demand balance constraint condition comprises a water resource supply and demand balance constraint condition and a forage grass supply and demand balance constraint condition, and the expression of the water resource supply and demand balance constraint condition is as follows:
WRL(i，t)＝EI(i，t)·WN(i，t)
in the formula, WRL (i, t) is the water demand of the ith industry in the period t, EI (i, t) is the economic index of the ith industry in the period t, and WN (i, t) is the water demand quota of the ith industry in the period t;
the expression of the forage material supply and demand balance constraint condition is as follows:
LSL·ILNl·Tl＝IGAl·CLl；
the life support class constraint conditions comprise minimum constraint conditions of grain crops and basic number constraint conditions of livestock feed. The expression of the minimum constraint condition of the grain crops is as follows:
in the formula, FCDmThe yield per unit area of the m-th grain crops is PGD (plant growth data) which is the average grain demand, and POP (plant population data) which is the total number of mouths;
the expression of the constraint condition of the basic number of the livestock feed is as follows:
LSL≥LSLmin
in the formula, LSLminThe basic feeding quantity of livestock is calculated;
the expression of the fairness constraint condition is as follows:
EImin(i，t)≤EI(i，t)≤EImax(i，t)
WSLmin(i，j，t)≤WSL(i，j，t)≤WSLmax(i，j，t)
in the formula, EImin(i, t) is the lowest limit of the i-industry economic index in the t period, EI max(i, t) is the highest limit of the i industry economic index in the t period, WSLmin(i, j, t) is the lowest limit of the water supply of the j water source of the i industry in the t period, WSLmax(i, j, t) is the highest limit of the water supply of the water source j in the i industry in the t period.
Preferably, the encoded form of the solution is determined by the following formula:
x(j)＝a(j)+y(j)[(b(j)-a(j))] (j＝1，2，…，p)
in the formula, [ a (j), b (j) ] is an initial change interval of a j-th optimization variable x (j) which is preset, y (j) is a real number corresponding to [0, 1] and is called as a gene, and the coding form is expressed as (y (1), y (2), …, y (p)), wherein the optimization variable x (j) is a solution of the objective function corresponding to each scheme.
Preferably, the fitness of the initial individual is determined by the following formula:
in the formula: rt(i) Sequencing sequence number of ith individual in the initial population to the target function t, Ft(i) The fitness of the ith individual in the initial population to a target t is obtained, F (i) is the comprehensive fitness of the ith individual in the initial population to all target functions, k is a constant in (1, 2) and is used for increasing the individual fitness which shows the optimal performance and obtaining more participation opportunities, and n is the targetAnd the number of the functions is N, and N is the number of individuals in the initial population.
The invention also provides a calculation system of the pastoral water-soil grass-animal balance model, which comprises the following components:
The system comprises an objective function determining module, a first parameter setting module and a second parameter setting module, wherein the objective function determining module is used for determining an objective function according to input parameters and a first preset relation among the parameters, the objective function comprises a comprehensive benefit function and a water supply source priority function, and the comprehensive benefit function is the maximum value of the sum of economic benefits and ecological benefits;
the constraint condition determining module is used for determining constraint conditions according to the parameters and a second preset relation between the parameters, wherein the constraint conditions comprise resource bearing capacity constraint conditions, supply and demand balance constraint conditions, life support constraint conditions, fairness constraint conditions and non-negative constraint conditions;
the scheme set setting module is used for setting a plurality of groups of values of the parameters in a balanced manner from natural grazing to full-house feeding of the water and soil grasses and animals according to a livestock feeding mode and an artificial supplementary feeding quota increasing mode, the value of each group of parameters is combined with the objective function and the constraint condition to form a scheme, and a plurality of schemes form a scheme set;
the scheme set solving module is used for solving the scheme set to obtain an optimal solution set of each scheme;
the optimal scheme determining module is used for calculating an optimal solution set according to different schemes, analyzing limiting factors of regional development through multi-index comprehensive analysis and comparison, selecting a scheme most beneficial to regional development as an optimal scheme, and taking the optimal solution set of the optimal scheme as a regional water-soil livestock development threshold;
Wherein the solution set solving module comprises:
the individual coding submodule is used for corresponding the solution of the objective function of each scheme to a [0, 1] interval to obtain the coding form of all solutions, and the coding form of the solutions is called as an individual;
the population generation and initialization submodule is used for randomly generating a plurality of individuals, carrying out rationality test on each individual, reserving the individuals meeting the constraint condition as initial individuals, and forming an initial population by the initial individuals;
a fitness calculation submodule, configured to calculate a fitness of each initial individual in the initial population;
the child individual generation submodule is used for taking the initial individuals in the initial population as parent individuals and generating corresponding child individuals according to the fitness of the parent individuals;
a non-inferior solution set calculation submodule, configured to store a set of n descendant individuals, which are most advanced in fitness and generated by first generation evolution, as an existing non-inferior solution set, compare the best n descendant individuals generated by each generation of evolution with each solution in the existing non-inferior solution set one by one, and retain a good solution to replace a poor solution, so as to obtain a non-inferior solution set;
The optimal solution set calculation submodule is used for judging whether the iteration times reach the preset iteration times when the evolution times reach the preset evolution times, and if so, retaining the non-inferior solution set obtained through replacement as the optimal solution set; otherwise, carrying out the next iteration again until the iteration times reach the preset iteration times; after the optimal solution set of one scheme is obtained, the steps of evolution and iteration are repeated to calculate the optimal solution set of the next scheme.
The calculation method and the system of the pastoral area water-soil grass-livestock balance model in the embodiment of the invention take water resources, land resources and grassland resource bearing capacity as bottom lines, the maximum comprehensive benefit of economic benefit and ecological benefit is taken as a target, and the comprehensive balance between 'water-soil-grass-livestock' in the pastoral area is taken as a criterion, so that the development scale of the water-soil resources, the farming and animal husbandry planting structure, the animal husbandry production mode and the appropriate livestock carrying capacity are reasonably determined, and the sustainable utilization of the water, soil and grass resources in the pastoral area, the benign development of the ecological environment and the sustainable development of social economy are realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart illustrating steps of a method for calculating a water-soil livestock balance model in a pasturing area according to an embodiment of the present invention;
FIG. 2 is a flow chart of the steps of the solution set of FIG. 1;
fig. 3 is a functional block diagram of a computing system of a pasture water and soil livestock balance model according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 and 2, an embodiment of the present invention provides a method for calculating a water-soil and livestock balance model in a pasturing area, where the method includes:
The comprehensive benefit function is the maximum value of the sum of the economic benefit and the ecological benefit, namely:
fc＝Max(OBE+OBEN)
In the formula (f)cAnd the OBE is the economic benefit and the OBEN is the ecological benefit.
The economic benefit OBE is determined by the following formula:
OBE＝ANB+INB
wherein, ANB is the net benefit of agriculture and animal husbandry, and INB is the net benefit of non-agriculture and animal husbandry.
The net benefits of farming and animal husbandry are determined by the following formula:
ANB＝ANBA+ANBL
in the formula, ANBA is the irrigation net benefit of the planting industry, and ANBL is the livestock feeding net benefit.
The net irrigation benefit of the planting industry is determined by the following formula:
wherein ACA (f) is the irrigation area of the f-type planted crops, P (f), Y (f) and C (f) are the unit price, the average yield per mu and the planting cost of the f-type planted crops respectively, WP is the water price, and WN (f) is the hair irrigation quota of the f-type planted crops.
The livestock raising net benefit is determined by the following formula:
in the formula, LSL is the livestock feeding amount, namely the standard sheep unit, P (l) and Y (l) are respectively the yield and unit price of the type 1 products (mutton, cashmere, sheepskin and the like) of the standard sheep unit of livestock, omega is the livestock slaughtering rate, C is the cost of the standard sheep unit of livestock, and WNL is the drinking water quota of the standard sheep unit of livestock.
The non-farming-animal-husbandry net benefit INB is expressed by the industrial water net benefit as follows:
INB＝IAV·ψ·δ
in the formula, IAV is an industrial added value, psi is the proportion of an industrial net value to a total value, and delta is an industrial water benefit allocation coefficient.
The ecological benefit OBEN is determined by the following formula:
in the formula, ANAkThe method is characterized in that the method is used for determining the utilization AREA of a kth natural pasture, OBEND is the ecological service value of a dynamic grassland, AREA is the utilization AREA of the natural pasture, and xi (k) is a conversion coefficient of the kth natural pasture under the corresponding feed intake rate.
The dynamic grassland ecological service value is determined by the following formula:
OBEND＝l·r·OBENS
in the formula, l is the relative willingness to pay, r is the scarcity degree of natural grassland resources, the value can be taken according to the degradation degree of the natural grassland, the value range is [0, 1], and OBENS is the ecological service value of the static grassland.
The relative willingness-to-pay expression is as follows:
in the formula, L is the maximum value of the relative willingness-to-pay L, the willingness-to-pay in the extremely rich stage is represented, the value is 1, t is a time variable and represents the social and economic development stage, a and b are constants, the value is 1, and e is a natural logarithm.
Wherein the time variable t expression is:
in the formula, EnIs the Enger coefficient.
The static grassland ecological service value is determined by the following formula:
in the formula, AREAiIs the area of a natural grassland of the i-type, VPAiThe unit price of the grassland ecological service value under the natural state of the i-type natural grassland.
The water supply source priority function is determined by the following formula:
In the formula (f)wAs a function of said priority of the water supply source, OBW being the priority of the water supply source, αiAnd betajThe water supply weight coefficient of the i industry and the water supply priority coefficient of the j water source are respectively, and WSL (i, j, t) is the water supply amount of the i industry j water source in the t period.
And 110, determining constraint conditions according to the parameters input by the user and the preset relation among the parameters, wherein the constraint conditions comprise resource bearing capacity constraint conditions, supply and demand balance constraint conditions, life support constraint conditions, fairness constraint conditions and non-negative constraint conditions.
The resource bearing capacity constraint conditions comprise water resource bearing capacity constraint conditions, grassland resource bearing capacity constraint conditions and land resource bearing capacity constraint conditions.
The water resource bearing capacity constraint condition expression is as follows:
in the formula, WSG (t)maxFor the maximum water supply capacity of the water supply project in the time period t, WLL (j, t) is the available quantity of a water source in the time period j in the time period t, WTL (t) is the water regulating quantity outside the time period t, and WUI is a regional water total quantity control index.
The grassland resource bearing capacity constraint condition expression is as follows:
LSL·LNk·Tk≤ANAk·NCLk
LSL·ILNl·Tl≤IGAl·CLl
in the formula (I), LNkIs a unit feed ration of a k-class natural pasture sheep, TkDays of rearing in a natural pasture of the k-th class, NCLkFor hay production in natural pastures of the k-type, ILN lFor l-class irrigation artificial grassland sheep unit feed intake quota, TlDays of rearing on class I irrigated turf, IGAlIs the area of the class I irrigated grass land, CLlIs the hay yield for class l irrigated grasses.
The land resource bearing capacity constraint condition expression is as follows:
in the formula, ACA is the irrigation area of the planted crop, FCAmFor irrigation area of m-th grain crops, ECAnThe irrigation area of the nth commercial crop, the AFL is the available cultivated land area, and the R is the multiple cropping index.
The supply and demand balance constraint conditions comprise water resource supply and demand balance constraint conditions and forage material supply and demand balance constraint conditions. The expression of the water resource supply and demand balance constraint condition is as follows:
WRL(i，t)＝EI(i，t)·WN(i，t)
in the formula, WRL (i, t) is the water demand of the ith industry in the period t, EI (i, t) is the economic index of the ith industry in the period t, and WN (i, t) is the water demand quota of the ith industry in the period t.
The expression of the forage material supply and demand balance constraint condition is as follows:
LSL·ILNl·Tl＝IGAl·CLl
the life support class constraint conditions comprise minimum constraint conditions of grain crops and basic number constraint conditions of livestock feed. The expression of the minimum constraint condition of the grain crops is as follows:
in the formula, FCDmThe yield per unit area of the m-th grain crops is PGD (plant growth data) which is the average grain demand, and POP (plant population data) which is the total population.
The expression of the constraint condition of the basic number of the livestock feed is as follows:
LSL≥LSLmin
in the formula, LSLminThe quantity of the livestock is based on the livestock breeding quantity.
The expression of the fairness constraint condition is as follows:
EImin(i，t)≤EI(i，t)≤EImax(i，t)
WSLmin(i，j，t)≤WSL(i，j，t)≤WSLmax(i，j，t)
in the formula, EImin(i, t) is the lowest limit of the i-industry economic index in the t period, EImax(i, t) is the highest limit of the i industry economic index in the t period, WSLmin(i, j, t) is the lowest limit of the water supply of the j water source of the i industry in the t period, WSLmax(i, j, t) is the highest limit of the water supply of the water source j in the i industry in the t period.
The above constraints are all non-negative constraints.
And step 130, solving and calculating the scheme set.
Specifically, the solution of the solution set includes a one-by-one solution of each solution in the solution set, and the solution calculation of each solution includes the following sub-steps:
and a substep 131 of individual coding, using a real number coding method, using the following linear transformation:
x(j)＝a(j)+y(j)[(b(j)-a(j))] (j＝1，2，…，p)
In the formula, [ a (j), b (j) ] is the preset j-th optimization variable x (j), namely the initial change interval of the solution of the objective function corresponding to each scheme, and y (j) is a real number corresponding to [0, 1] and is called as a gene. Genes corresponding to all variables of the optimization problem are connected together in sequence to form a coding form (y (1), y (2), …, y (p)) of the problem solution, which is called chromosome or individual. Through encoding, all optimized variables are unified to the interval of [0, 1], and various genetic operations are directly carried out on the gene forms of the optimized variables.
In the formula: rt(i) Sequence number of target function t for ith individual of population, Ft(i) And F (i) the fitness of the ith individual of the population to the target t, wherein F (i) is the comprehensive fitness of the ith individual of the population to all target functions, k is a constant in (1, 2) and is used for increasing the individual fitness with the optimal performance and obtaining more participation opportunities, N is the number of the target functions, and N is the number of the individuals in the initial population.
And a substep 134 of using the individuals in the initial population as parent individuals and generating child individuals according to the parent individuals.
The method for selecting the parent individuals is selection operation, and the method for generating the child individuals comprises cross operation and mutation operation.
The selection operation is specifically as follows: taking a proportional selection mode, the selection probability p of the ith parent y (j, i)s(i) Is composed of
Order to
The sequence { p (i) | i ═ 1, 2, …, n } would then be [0, 1]The interval is divided into n subintervals, and the subintervals correspond to the n parent individuals one by one. Generating a random number u if u is in the interval [ p (i-1), p (i)]Then the ith parent y (j, i) is selected.
The crossing operation specifically comprises the following steps: for a real number coding system, one gene represents an optimization variable, and in order to keep the diversity of the population, a pair of parent individuals y (j, i) is randomly selected according to the selection probability 1) And y (j, i)2) As parents and are randomly linearly combined as follows to generate a descendant individual y2(j，i)：
In the formula: u. of1，u2，u3Are random numbers, and a total of n generations of individuals are generated by such hybridization operations.
The mutation operation specifically comprises: any parent individual y (j, i) has a smaller fitness function value F (i) and a smaller selection probability ps(i) The smaller the probability p of mutating the individualm(i) The larger should be. Thus, the mutation operation is performed using p random numbers and pm(i)＝1-ps(i) The probability of (c) is used to replace the individual y (j, i), thereby obtaining the offspring individual y3(j，i)，j＝1，2，…，p。
Wherein u (j) 1, 2.. p) and umIs [0, 1 ]]Uniform random number between pm(i) Is the mutation probability.
And a sub-step 135 of calculating a non-inferior solution set.
According to the characteristic that each generation in the genetic algorithm has a large number of feasible solutions, namely, offspring individuals generate, the approach of the final non-inferior solution set is achieved by considering the method of mutually comparing and eliminating inferior solutions among the feasible solutions. The method comprises the steps of firstly storing n feasible solutions with the best fitness, which are generated by the first generation of evolution, as the existing non-inferior solution set, comparing the n feasible solutions with the non-inferior solution set one by one, and keeping the superior solution to replace the inferior solution to obtain the non-inferior solution set.
And a substep 136 of calculating an optimal solution set.
And when the evolution times reach the preset evolution times, judging whether the iteration times reach the preset iteration times, if so, keeping the non-inferior solution set obtained through replacement as the optimal solution set. Otherwise, go back to substep 132 until the number of iterations reaches the preset number of iterations. After the optimal solution set of one scheme is obtained, the above substeps 131 to 136 are repeated to calculate the optimal solution set of the next scheme.
And 140, calculating the obtained optimal solution set according to different schemes, analyzing the limiting factors of regional development by comprehensively analyzing and comparing multiple indexes such as comprehensive benefits, total water consumption, single water benefits, livestock feeding level, ecological economic coordination development degree and the like, selecting a scheme most beneficial to regional development as an optimal scheme, and taking the optimal solution set of the optimal scheme as a regional water-soil livestock development threshold. The development threshold comprises the development and utilization degree of natural grassland, water consumption, single water benefit, land development scale, irrigation forage land planting scale, livestock breeding mode, livestock breeding amount and the like.
Based on the same inventive concept, the embodiment of the invention provides a computing system of a pastoral area water and soil and grass and livestock balance model, as shown in fig. 3, as the principle of the system for solving the technical problem is similar to a computing method of the pastoral area water and soil and grass and livestock balance model, the implementation of the system can refer to the implementation of the method, and repeated parts are not repeated.
An objective function determining module 200, configured to determine an objective function according to input parameters and a first preset relationship between the parameters, where the objective function includes a comprehensive benefit function and a water supply source priority function, and the comprehensive benefit function is a maximum value of a sum of economic benefits and ecological benefits;
a constraint condition determining module 210, configured to determine constraint conditions according to the parameters and a second preset relationship between the parameters, where the constraint conditions include a resource carrying capacity constraint condition, a supply and demand balance constraint condition, a life support constraint condition, a fairness constraint condition, and a non-negative constraint condition;
the scheme set setting module 220 is used for setting a plurality of groups of parameters from naturally grazing to totally-confined aquatic livestock in a balanced manner according to the livestock feeding mode and an artificial supplementary feeding quota increasing manner, each group of parameters forms a scheme by combining the objective function and the constraint condition, and a plurality of schemes form a scheme set;
and the scheme set solving module 230 is configured to solve the scheme set to obtain an optimal solution set of each scheme. The solution set solving module 230 includes:
the individual coding submodule 231 is used for corresponding the solution of the objective function of each scheme to the [0, 1] interval to obtain the coding form of all solutions, and the coding form of the solutions is called as an individual;
A population generation and initialization submodule 232, configured to randomly generate a plurality of individuals, perform rationality inspection on each individual, keep the individuals satisfying the constraint condition as initial individuals, and form an initial population by the plurality of initial individuals;
a fitness calculation submodule 233, configured to calculate a fitness of each initial individual in the initial population;
the child individual generation submodule 234 is configured to use the initial individuals in the initial population as parent individuals, and generate corresponding child individuals according to fitness of the initial individuals;
a non-inferior solution set calculation submodule 235, configured to store n feasible solutions with the highest fitness generated by the first generation of evolution as an existing non-inferior solution set, compare the best n feasible solutions generated by each generation of evolution with each solution in the existing non-inferior solution set one by one, and retain the superior solution to replace the inferior solution, so as to obtain the non-inferior solution set;
and the optimal solution set calculating submodule 236 is configured to judge whether the iteration number reaches the preset iteration number when the evolution number reaches the preset evolution number, and if so, keep the non-inferior solution set obtained through replacement as the optimal solution set. Otherwise, the next iteration is carried out again until the iteration times reach the preset iteration times. After the optimal solution set of one scheme is obtained, the steps of evolution and iteration are repeated to calculate the optimal solution set of the next scheme.
And the optimal solution determining module 240 is used for calculating an optimal solution set according to different schemes, analyzing the limiting factors of regional development through multi-index comprehensive analysis and comparison, selecting a scheme most beneficial to regional development as an optimal scheme, and taking the optimal solution set of the optimal scheme as a regional water-soil livestock development threshold.
It should be understood that the computing system of the pasture water and soil and livestock balance model includes only modules for logical division according to the functions implemented by the system, and in practical application, the modules can be stacked or split. The functions of the calculation system for the pasturing area water-soil livestock balance model provided by this embodiment correspond to the calculation method for the pasturing area water-soil livestock balance model provided by the above embodiment one by one, and for the more detailed processing flow implemented by this system, the detailed description is already given in the above method embodiment, and the detailed description is not repeated here.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (5)
1. A calculation method of a pasture water and soil livestock balance model is characterized by comprising the following steps:
Determining an objective function according to input parameters and a first preset relation between the parameters, wherein the objective function comprises a comprehensive benefit function and a water supply source priority function, and the comprehensive benefit function is the maximum value of the sum of economic benefit and ecological benefit;
determining constraint conditions according to the parameters and a second preset relation between the parameters, wherein the constraint conditions comprise resource bearing capacity constraint conditions, supply and demand balance constraint conditions, life support constraint conditions, fairness constraint conditions and non-negative constraint conditions;
according to the livestock feeding mode, a plurality of groups of values of the parameters are set in a balanced mode from natural grazing to full-house feeding of the water and soil livestock according to an artificial supplementary feeding quota increasing mode, the value of each group of parameters is combined with the objective function and the constraint condition to form a scheme, and a plurality of schemes form a scheme set;
solving the scheme set to obtain an optimal solution set of each scheme;
according to the optimal solution sets obtained by calculation of different schemes, analyzing the limiting factors of regional development through multi-index comprehensive analysis and comparison, selecting the scheme most beneficial to regional development as the optimal scheme, and taking the optimal solution set of the optimal scheme as the regional water-soil-grassy-animal development threshold;
Solving the solution set to obtain an optimal solution set of each solution comprises:
corresponding the solution of the objective function of each scheme to a [0, 1] interval to obtain the coding form of all solutions, wherein the coding form of the solutions is called as an individual;
randomly generating a plurality of individuals, carrying out rationality test on each individual, reserving the individuals meeting the constraint condition as initial individuals, and forming an initial population by the initial individuals;
calculating the fitness of each initial individual in the initial population;
taking the initial individuals in the initial population as parent individuals, and generating corresponding child individuals according to the fitness of the parent individuals;
storing a set of n sub-generation individuals with the most advanced fitness generated by the first generation evolution as an existing non-inferior solution set, comparing the best n sub-generation individuals generated by each generation evolution with each solution in the existing non-inferior solution set one by one, and reserving a superior solution to replace an inferior solution to obtain a non-inferior solution set;
when the evolution times reach preset evolution times and the iteration times also reach preset iteration times, reserving the non-inferior solution set obtained through replacement as an optimal solution set;
Wherein the overall benefit function is determined according to the following formula:
fc＝Max(OBE+OBEN)
in the formula (f)cThe function of the comprehensive benefit is OBE, the economic benefit is OBE, and the ecological benefit is OBEN;
the economic benefit OBE is determined by the following formula:
OBE＝ANB+INB
wherein, ANB is the net benefit of agriculture and animal husbandry, INB is the net benefit of non-agriculture and animal husbandry;
the net benefits of farming and animal husbandry are determined by the following formula:
ANB＝ANBA+ANBL
in the formula, ANBA is the irrigation net benefit of the planting industry, and ANBL is the livestock feeding net benefit;
the net irrigation benefit of the planting industry is determined by the following formula:
wherein ACA (f) is the irrigation area of f-type planted crops, P (f), Y (f) and C (f) are the unit price, the average yield per mu and the planting cost of the f-type planted crops respectively, WP is the water price, WN (f) is the hair irrigation quota of the f-type planted crops;
the livestock raising net benefit is determined by the following formula:
in the formula, LSL is the livestock feeding amount, namely a standard sheep unit, P (l) and Y (l) are the yield and unit price of a type 1 product of the standard sheep unit of livestock respectively, omega is the livestock slaughtering rate, C is the cost of the standard sheep unit of livestock, and WNL is the drinking water quota of the standard sheep unit of livestock;
the non-farming-animal-husbandry net benefit INB is expressed by the industrial water net benefit as follows:
INB＝IAV·ψ·δ
in the formula, IAV is an industrial added value, psi is the proportion of an industrial net value to a total product value, and delta is an industrial water benefit allocation coefficient;
The ecological benefit OBEN is determined by the following formula:
in the formula, ANAkThe utilization AREA of the kth natural pasture, the OBEND is the ecological service value of the dynamic grassland, the AREA is the utilization AREA of the natural pasture, and the xi (k) is the conversion coefficient of the kth natural pasture under the corresponding feed intake rate;
the dynamic grassland ecological service value is determined by the following formula:
OBEND＝l·r·OBENS
in the formula, l is the relative willingness to pay, r is the scarcity degree of natural grassland resources, the value can be taken according to the degradation degree of the natural grassland, the value range is [0, 1], and OBENS is the ecological service value of the static grassland;
the relative willingness-to-pay expression is as follows:
in the formula, L is the maximum value of the relative willingness-to-pay L, represents the willingness-to-pay in an extremely rich stage, takes a value of 1, t is a time variable, represents the socioeconomic development stage, a and b are constants, take a value of 1, and e is a natural logarithm;
wherein the time variable t expression is:
in the formula, EnIs the Enger coefficient;
the static grassland ecological service value is determined by the following formula:
in the formula, AREAiIs the area of a natural grassland of the i-type, VPAiThe grassland ecological service value unit price of the i-type natural grassland in the natural state is obtained;
determining the water supply source priority function according to the following formula:
In the formula (f)wAs a function of said priority of the water supply source, OBW being the priority of the water supply source, αiAnd betajThe water supply weight coefficient of the i industry and the water supply priority coefficient of the j water source are respectively set, and WSL (i, j, t) is the water supply amount of the j water source of the i industry in the t period;
the resource bearing capacity constraint condition comprises a water resource bearing capacity constraint condition, a grassland resource bearing capacity constraint condition and a land resource bearing capacity constraint condition;
the water resource bearing capacity constraint condition expression is as follows:
in the formula, WSG (t)maxFor the maximum water supply capacity of a water supply project in a time period t, WLL (j, t) is the available quantity of a water source in a time period j in the time period t, WTL (t) is the water regulating quantity outside the time period t, and WUI is a regional water total quantity control index;
the grassland resource bearing capacity constraint condition expression is as follows:
LSL·LNk·Tk≤ANAk·NCLk
LSL·ILNl·Tl≤IGAl·CLl
in the formula (I), LNkIs a unit feed ration of a k-class natural pasture sheep, TkDays of rearing in a natural pasture of the k-th class, NCLkFor hay production in natural pastures of the k-type, ILNlFor l-class irrigation artificial grassland sheep unit feed intake quota, TlDays of rearing on class I irrigated turf, IGAlIs the area of the class I irrigated grass land, CLlDry grass yield for class i irrigated grasslands;
the land resource bearing capacity constraint condition expression is as follows:
in the formula, ACA is the irrigation area of the planted crop, FCA mFor irrigation area of m-th grain crops, ECAnThe irrigation area of the nth cash crop, the AFL is the available cultivated land area, and the R is the multiple cropping index;
the supply and demand balance constraint condition comprises a water resource supply and demand balance constraint condition and a forage grass supply and demand balance constraint condition, and the expression of the water resource supply and demand balance constraint condition is as follows:
WRL(i，t)＝EI(i，t)·WN(i，t)
in the formula, WRL (i, t) is the water demand of the ith industry in the period t, EI (i, t) is the economic index of the ith industry in the period t, and WN (i, t) is the water demand quota of the ith industry in the period t;
the expression of the forage material supply and demand balance constraint condition is as follows:
LSL·ILNl·Tl＝IGAl·CLl；
the life support class constraint conditions comprise grain crop minimum constraint conditions and livestock feed basic number constraint conditions; the expression of the minimum constraint condition of the grain crops is as follows:
in the formula, FCDmThe yield per unit area of the m-th grain crops is PGD (plant growth data) which is the average grain demand, and POP (plant population data) which is the total number of mouths;
the expression of the constraint condition of the basic number of the livestock feed is as follows:
LSL≥LSLmin
in the formula, LSLminThe basic feeding quantity of livestock is calculated;
the expression of the fairness constraint condition is as follows:
EImin(i，t)≤EI(i，t)≤EImax(i，t)
WSLmin(i，j，t)≤WSL(i，j，t)≤WSLmax(i，j，t)
in the formula, EImin(i, t) is the lowest limit of the i-industry economic index in the t period, EImax(i, t) is the highest limit of the i industry economic index in the t period, WSL min(i, j, t) is the lowest limit of the water supply of the j water source of the i industry in the t period, WSLmax(i, j, t) is tAnd the section i industry j is the highest limit of the water supply amount of the water source.
2. The method of claim 1, wherein when the number of iterations does not reach the preset number of iterations, the next iteration is resumed until the number of iterations reaches the preset number of iterations.
3. The method of claim 1, wherein the encoded form of the solution is determined by the following equation:
x(j)＝a(j)+y(j)[(b(j)-a(j))] (j＝1，2，…，p)
in the formula, [ a (j), b (j) ] is an initial change interval of a j-th optimization variable x (j) which is preset, y (j) is a real number corresponding to [0, 1] and is called as a gene, and the coding form is expressed as (y (1), y (2), …, y (p)), wherein the optimization variable x (j) is a solution of the objective function corresponding to each scheme.
4. The method of claim 1, wherein the fitness of the initial individual is determined by the formula:
in the formula: rt(i) Sequencing sequence number of ith individual in the initial population to the target function t, Ft(i) And F (i) the fitness of the ith individual in the initial population to the target t, wherein k is a constant in (1, 2) and is used for increasing the individual fitness which shows the optimal performance and obtaining more participation opportunities, N is the number of the target functions, and N is the number of the individuals in the initial population.
5. A computing system for a pasture hydro-soil livestock balancing model, the system comprising:
the system comprises an objective function determining module, a first parameter setting module and a second parameter setting module, wherein the objective function determining module is used for determining an objective function according to input parameters and a first preset relation among the parameters, the objective function comprises a comprehensive benefit function and a water supply source priority function, and the comprehensive benefit function is the maximum value of the sum of economic benefits and ecological benefits;
the constraint condition determining module is used for determining constraint conditions according to the parameters and a second preset relation between the parameters, wherein the constraint conditions comprise resource bearing capacity constraint conditions, supply and demand balance constraint conditions, life support constraint conditions, fairness constraint conditions and non-negative constraint conditions;
the scheme set setting module is used for setting a plurality of groups of values of the parameters in a balanced manner from natural grazing to full-house feeding of the water and soil grasses and animals according to a livestock feeding mode and an artificial supplementary feeding quota increasing mode, the value of each group of parameters is combined with the objective function and the constraint condition to form a scheme, and a plurality of schemes form a scheme set;
the scheme set solving module is used for solving the scheme set to obtain an optimal solution set of each scheme;
The optimal scheme determining module is used for calculating an optimal solution set according to different schemes, analyzing limiting factors of regional development through multi-index comprehensive analysis and comparison, selecting a scheme most beneficial to regional development as an optimal scheme, and taking the optimal solution set of the optimal scheme as a regional water-soil livestock development threshold;
wherein the solution set solving module comprises:
the individual coding submodule is used for corresponding the solution of the objective function of each scheme to a [0, 1] interval to obtain the coding form of all solutions, and the coding form of the solutions is called as an individual;
the population generation and initialization submodule is used for randomly generating a plurality of individuals, carrying out rationality test on each individual, reserving the individuals meeting the constraint condition as initial individuals, and forming an initial population by the initial individuals;
a fitness calculation submodule, configured to calculate a fitness of each initial individual in the initial population;
the child individual generation submodule is used for taking the initial individuals in the initial population as parent individuals and generating corresponding child individuals according to the fitness of the parent individuals;
a non-inferior solution set calculation submodule, configured to store a set of n descendant individuals, which are most advanced in fitness and generated by first generation evolution, as an existing non-inferior solution set, compare the best n descendant individuals generated by each generation of evolution with each solution in the existing non-inferior solution set one by one, and retain a good solution to replace a poor solution, so as to obtain a non-inferior solution set;
The optimal solution set calculation submodule is used for judging whether the iteration times reach the preset iteration times when the evolution times reach the preset evolution times, and if so, retaining the non-inferior solution set obtained through replacement as the optimal solution set; otherwise, carrying out the next iteration again until the iteration times reach the preset iteration times; after obtaining the optimal solution set of one scheme, repeating the steps of evolution and iteration to calculate the optimal solution set of the next scheme;
wherein the overall benefit function is determined according to the following formula:
fc＝Max(OBE+OBEN)
in the formula (f)cThe function of the comprehensive benefit is OBE, the economic benefit is OBE, and the ecological benefit is OBEN;
the economic benefit OBE is determined by the following formula:
OBE＝ANB+INB
wherein, ANB is the net benefit of agriculture and animal husbandry, INB is the net benefit of non-agriculture and animal husbandry;
the net benefits of farming and animal husbandry are determined by the following formula:
ANB＝ANBA+ANBL
in the formula, ANBA is the irrigation net benefit of the planting industry, and ANBL is the livestock feeding net benefit;
the net irrigation benefit of the planting industry is determined by the following formula:
wherein ACA (f) is the irrigation area of f-type planted crops, P (f), Y (f) and C (f) are the unit price, the average yield per mu and the planting cost of the f-type planted crops respectively, WP is the water price, WN (f) is the hair irrigation quota of the f-type planted crops;
The livestock raising net benefit is determined by the following formula:
in the formula, LSL is the livestock feeding amount, namely a standard sheep unit, P (l) and Y (l) are the yield and unit price of a type 1 product of the standard sheep unit of livestock respectively, omega is the livestock slaughtering rate, C is the cost of the standard sheep unit of livestock, and WNL is the drinking water quota of the standard sheep unit of livestock;
the non-farming-animal-husbandry net benefit INB is expressed by the industrial water net benefit as follows:
INB＝IAV·ψ·δ
in the formula, IAV is an industrial added value, psi is the proportion of an industrial net value to a total product value, and delta is an industrial water benefit allocation coefficient;
the ecological benefit OBEN is determined by the following formula:
in the formula, ANAkThe utilization AREA of the kth natural pasture, the OBEND is the ecological service value of the dynamic grassland, the AREA is the utilization AREA of the natural pasture, and the xi (k) is the conversion coefficient of the kth natural pasture under the corresponding feed intake rate;
the dynamic grassland ecological service value is determined by the following formula:
OBEND＝l·r·OBENS
in the formula, l is the relative willingness to pay, r is the scarcity degree of natural grassland resources, the value can be taken according to the degradation degree of the natural grassland, the value range is [0, 1], and OBENS is the ecological service value of the static grassland;
the relative willingness-to-pay expression is as follows:
in the formula, L is the maximum value of the relative willingness-to-pay L, represents the willingness-to-pay in an extremely rich stage, takes a value of 1, t is a time variable, represents the socioeconomic development stage, a and b are constants, take a value of 1, and e is a natural logarithm;
Wherein the time variable t expression is:
in the formula, EnIs the Enger coefficient;
the static grassland ecological service value is determined by the following formula:
in the formula, AREAiIs the area of a natural grassland of the i-type, VPAiThe grassland ecological service value unit price of the i-type natural grassland in the natural state is obtained;
determining the water supply source priority function according to the following formula:
in the formula (f)wAs a function of said priority of the water supply source, OBW being the priority of the water supply source, αiAnd betajThe water supply weight coefficient of the i industry and the water supply priority coefficient of the j water source are respectively set, and WSL (i, j, t) is the water supply amount of the j water source of the i industry in the t period;
the resource bearing capacity constraint condition comprises a water resource bearing capacity constraint condition, a grassland resource bearing capacity constraint condition and a land resource bearing capacity constraint condition;
the water resource bearing capacity constraint condition expression is as follows:
in the formula, WSG (t)maxFor the maximum water supply capacity of a water supply project in a time period t, WLL (j, t) is the available quantity of a water source in a time period j in the time period t, WTL (t) is the water regulating quantity outside the time period t, and WUI is a regional water total quantity control index;
the grassland resource bearing capacity constraint condition expression is as follows:
LSL·LNk·Tk≤ANAk·NCLk
LSL·ILNl·Tl≤IGAl·CLl
in the formula (I), LNkIs a unit feed ration of a k-class natural pasture sheep, T kDays of rearing in a natural pasture of the k-th class, NCLkFor hay production in natural pastures of the k-type, ILNlFor l-class irrigation artificial grassland sheep unit feed intake quota, TlDays of rearing on class I irrigated turf, IGAlIs the area of the class I irrigated grass land, CLlDry grass yield for class i irrigated grasslands;
the land resource bearing capacity constraint condition expression is as follows:
in the formula, ACA is the irrigation area of the planted crop, FCAmIs the irrigation area of the m-th class grain crops,ECAnthe irrigation area of the nth cash crop, the AFL is the available cultivated land area, and the R is the multiple cropping index;
the supply and demand balance constraint condition comprises a water resource supply and demand balance constraint condition and a forage grass supply and demand balance constraint condition, and the expression of the water resource supply and demand balance constraint condition is as follows:
WRL(i，t)＝EI(i，t)·WN(i，t)
in the formula, WRL (i, t) is the water demand of the ith industry in the period t, EI (i, t) is the economic index of the ith industry in the period t, and WN (i, t) is the water demand quota of the ith industry in the period t;
the expression of the forage material supply and demand balance constraint condition is as follows:
LSL·ILNl·Tl＝IGAl·CLl；
the life support class constraint conditions comprise grain crop minimum constraint conditions and livestock feed basic number constraint conditions; the expression of the minimum constraint condition of the grain crops is as follows:
in the formula, FCD mThe yield per unit area of the m-th grain crops is PGD (plant growth data) which is the average grain demand, and POP (plant population data) which is the total number of mouths;
the expression of the constraint condition of the basic number of the livestock feed is as follows:
LSL≥LSLmin
in the formula, LSLminThe basic feeding quantity of livestock is calculated;
the expression of the fairness constraint condition is as follows:
EImin(i，t)≤EI(i，t)≤EImax(i，t)
WSLmin(i，j，t)≤WSL(i，j，t)≤WSLmax(i，j，t)
in the formula, EImin(i, t) is the lowest limit of the i-industry economic index in the t period, EImax(i, t) is the highest limit of the i industry economic index in the t period, WSLmin(i, j, t) is the lowest limit of the water supply of the j water source of the i industry in the t period, WSLmax(i, j, t) is the highest limit of the water supply of the water source j in the i industry in the t period.
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