CN115713154A - Reservoir scheduling optimization method based on improved multi-target genetic algorithm - Google Patents
Reservoir scheduling optimization method based on improved multi-target genetic algorithm Download PDFInfo
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Abstract
The reservoir dispatching aims to improve the reservoir benefit to the maximum extent on the premise of ensuring safe operation of the reservoir, wherein the average output of the reservoir in the water supply period and the annual energy production of the reservoir are the keys for realizing stable operation of the reservoir dispatching and improving the power generation benefit. The invention designs a reservoir dispatching optimization method based on an improved multi-target genetic algorithm aiming at the problem that the average output and the annual energy production in the water supply period are difficult to be simultaneously optimized in the reservoir dispatching process, the average output and the annual energy production in the water supply period of the reservoir are taken as optimization targets, and the optimal water level value of each month in one year of the reservoir is solved by utilizing the improved multi-target genetic algorithm, so that the safe and stable operation of the reservoir is ensured, and the average output and the annual energy production in the water supply period of the reservoir are effectively improved.
Description
Technical Field
The invention designs a reservoir dispatching optimization method by utilizing an improved multi-objective genetic algorithm aiming at the characteristics of the reservoir dispatching process, and realizes the optimization of the water level in the reservoir dispatching process. The optimization of the reservoir water level is an important link for realizing the stable safe operation and the maximization of the economic benefit in the reservoir dispatching process, and belongs to the field of multi-target optimization of reservoir dispatching in the water conservancy industry.
Background
The purpose of reservoir scheduling is to promote average output and annual energy production of a reservoir water supply period as far as possible on the premise of ensuring safe operation of the reservoir, and achieve the optimal state of stable operation and reservoir benefit promotion. However, the optimization of the average output of the water supply period of the reservoir and the annual energy production of the reservoir is influenced by various factors, the relation is complex, the simultaneous optimization is difficult to realize, and the comprehensive benefit of reservoir scheduling is influenced. The reservoir dispatching optimization method based on the improved multi-objective genetic algorithm can guarantee safe and stable operation of reservoir dispatching, is beneficial to improving the power generation benefit of the reservoir, ensures that the generated energy meets the power grid planning value designed by the reservoir, and has obvious environmental and economic benefits. Therefore, the research result of the invention has wide application prospect.
The reservoir is an important project for realizing runoff regulation, has a complex relationship between water power and electric power, the average output and the generated energy of the water supply period of the reservoir conflict with each other, the difference between the front water level and the tail water level of the reservoir is adjusted by controlling the warehousing runoff and the delivery flow of the reservoir, the kinetic energy and the potential energy of water are effectively utilized, and the maximization of the power generation benefit is realized on the premise of ensuring the safe operation of the reservoir. Therefore, an effective average output in a water supply period and a reservoir power generation model are designed, and an efficient optimization algorithm is used for solving, so that the problem which needs to be solved urgently in reservoir optimization scheduling is formed, and the method has important practical significance.
The invention provides a reservoir dispatching optimization method based on an improved multi-target genetic algorithm. According to the method, the horizontal year data is used as an operation example, the water level value of the reservoir in each month is optimized, and therefore the guaranteed output and the generated energy of the reservoir are improved on the premise that the safe operation of the reservoir is guaranteed.
Disclosure of Invention
The invention obtains a reservoir dispatching optimization method based on an improved multi-target genetic algorithm, which deeply analyzes reservoir dispatching characteristics, determines a multi-target function for reservoir dispatching by considering two targets of average output in a reservoir water supply period and annual generated energy of a reservoir, adopts the improved multi-target genetic algorithm for optimization, completes optimization of a reservoir dispatching process according to a solved monthly reservoir water level value, and realizes the target of ensuring the maximum output and generated energy.
The invention adopts the following technical scheme and implementation steps:
1. a reservoir dispatching optimization method based on an improved multi-objective genetic algorithm comprises the following steps:
(1) Designing the average output N of the water supply period of the reservoir and the annual generated energy E of the reservoir as an optimization objective function:
(1) acquiring basic information data of a reservoir, including a reservoir level capacity relation, a reservoir discharge flow and tail level relation and a reservoir monthly average warehousing flow;
(2) establishing a multi-objective optimization scheduling mathematical model considering water balance, unit output, discharge capacity and generating capacity constraint conditions according to the basic information data, wherein an objective function is an objective function established by average output N of a reservoir water supply period and annual generating capacity E of the reservoir:
objective function 1: average output N of reservoir water supply period
Wherein N is average output of the reservoir in water supply period, the unit is kw, K is output coefficient of the reservoir, the output coefficient is basic parameter of the reservoir, the output coefficient is obtained by reservoir engineering plan, Q is monthly power generation quotation flow of the reservoir, and the unit is m 3 S is obtained from the water balance equation (2), Z u The upstream water level of the reservoir at the end of each month and month is m and Z d The value of the downstream water level of the monthly and monthly ends of the reservoir is read from the tail water level characteristic curve of the lower discharge flow of the reservoirThe position is m, the water supply period of the reservoir is 5 months, 6 months and 12 months of the open water year and 1-4 months of the next year, the total period is 7 months, and a is more than or equal to 1 and less than or equal to 7.
Wherein Q is the monthly power generation flow rate of the reservoir and the unit is m 3 And/s, I is the monthly warehousing runoff of the reservoir, namely the measured reservoir runoff data, and the unit is m 3 /s，V t+1 The storage capacity of the reservoir in the unit of m in the t +1 th month 3 ，V t The storage capacity of the reservoir in the unit of m in the t month 3 And the delta t is the scheduling days of each month, and the unit of calculation time is converted into seconds.
Objective function 2: annual energy production E of reservoir
Wherein E is the annual generating capacity of the reservoir, namely the generating benefit of the reservoir, and the unit is kwh, K is the output coefficient of the reservoir, the output coefficient is the basic parameter of the reservoir and is obtained by a reservoir engineering plan, Q is the monthly generating reference flow of the reservoir, and the unit is m 3 /s，Z u The upstream water level of the reservoir at the end of each month and month is m and Z d The numerical value of the downstream water level of the monthly and the monthly ends of the reservoir is read from a characteristic curve of the tail water level of the lower discharge of the reservoir, the unit is m, delta t is the scheduling days of each month, and the unit is converted into seconds during calculation.
(2) The multi-objective optimization method for optimizing the average output N of the reservoir water supply period and the annual energy production E of the reservoir is designed, and specifically comprises the following steps:
(1) setting parameters of the multi-target genetic algorithm and initializing the population, setting the population scale of the multi-target genetic algorithm to NP, the maximum evolution algebra T and initializing the cross probability P c And the mutation probability P m Generating a first generation parent population P of population size NP using regression chaotic mapping t ：
First, a set of chaotic sequences ranging from [0,1] is generated using a regression chaotic map:
x 1 ＝rand (4)
x p+1 ＝μx p (1-x 1 ) (5)
x＝(x 1 ,x 2 ,...,x p ,...,x 11 ) (6)
wherein x is 1 For the first value of the sequence, rand is a random number function, randomly generating a range of [0,1]]Mu is a regression chaotic mapping parameter, random generation satisfies the conditions that mu is more than or equal to 3.569945627 and less than or equal to 4, p is more than or equal to 1 and less than or equal to 10, x satisfies the range of [0,1]]Of the chaotic sequence of (a).
Generating an actual reservoir water level value at the end of each month according to the regression chaos mapping:
Z u ＝Z min +(Z max -Z min )x(7)
wherein Z is u Storing the water level value at the end of the month of 1-11 months in m for initializing individuals of the population, wherein the value range meets the interval [ Z min Z max ]，Z min Minimum constraint, Z, representing reservoir operating level max A maximum constraint value representing the water level of the reservoir in operation, x being a value satisfying the range [0,1]]Of the chaotic sequence of (a).
Repeating the above initialization operation formulas (4) - (7) to obtain a first generation parent population P with a population size NP t 。
(2) The multi-target genetic algorithm is used for rapid non-dominated sorting and congestion degree calculation:
for the first generation parent population P t Non-dominant sorting is performed, and then the population selection, variable intensity crossover and variable intensity variation operations are performed to produce a progeny population Q with a population size NP t The population P t And a population Q t Merging into population R with population size of 2NP t . For population R t Carrying out non-dominated sorting, carrying out crowding calculation after layering of the population, and screening the optimal individual by adopting an elite retention strategy to obtain a new generation population P with the population size of NP t+1 . The population fitness calculation formula is as follows:
f t,i,j ＝(N t,i (Z u )，E t,i (Z u ))(8)
wherein f is t,i,j Representing the fitness of the jth target of the ith individual in the tth generation population, N t,i (Z u ) Calculated by the formula (1), the average output of the reservoir water supply period is represented by kw, E t,i (Z u ) Calculated by the formula (3), the annual energy production of the reservoir is represented by kwh and Z u Are individuals of the population.
(3) Selecting operation of the multi-target genetic algorithm:
randomly selecting two individuals to compare fitness values, directly entering the next generation when the individuals with high fitness values are selected, eliminating the individuals with low fitness values, selecting parent individuals to enter a hybridization pool, and stopping when the number of the individuals reaches NP.
(4) Multi-target genetic algorithm cross operation:
firstly, normalizing and summing the fitness values of all individuals in the population for each target, then arranging in descending order, and calculating the average value of the fitness values of the first half:
wherein f is t,i Represents the normalized fitness value, f t,i,j Representing the fitness of the jth target of the ith individual in the tth generation population, f t,i,j max Represents the maximum fitness of the jth target of the ith individual in the tth generation population, f t,i,j min Represents the minimum fitness of the jth target of the ith individual in the tth generation population, f t,ave The mean value of the fitness values of the first half of the descending order of the population is shown, and NP is the size of the population.
Secondly, designing the number of genes participating in the cross operation:
n min ＝0(11)
wherein n is min Indicates the minimum number of genes involved in crossover operation, n max The number of the maximum genes participating in the cross operation is represented, D represents the total number of the genes of the individual, the value is 11, T represents the maximum evolution algebra, and t represents the current iteration number.
And finally, designing a crossover operator operation with adaptively adjustable crossover strength based on a hyperbolic tangent activation function in the neural network. The crossover operator is:
wherein n is t,i Indicates the number of genes participating in crossover of the ith individual in the t-th generation, n max Represents the maximum number of genes involved in crossover operation, n min Represents the minimum number of genes involved in crossover operation.
λ＝f t,i -f t,ave (14)
Wherein f is t,i Representing the normalized fitness value, f t,ave And expressing the average value of the fitness values of the first half of the descending order of the population, wherein lambda is the difference between the fitness value of the individual in the population and the average fitness value of the first half of the individual in the population, and e is a natural logarithm.
(5) Performing multi-target genetic algorithm mutation operation:
designing the number of genes involved in mutation operation:
m min ＝0(15)
wherein m is min Represents the minimum number of genes involved in mutation operation, m max The maximum number of genes participating in mutation operation is shown, D represents the total number of genes of an individual, the value is 11, and T represents the maximum evolution algebra.
Designing a mutation operator operation with adaptively adjustable mutation strength based on a Sigmoid activation function in a neural network. The mutation operator is:
wherein m is t,i Represents the number of genes in which the ith individual participates in crossover operation in the t generation, m min Represents the minimum number of genes involved in mutation operation, m max Represents the maximum number of genes involved in mutation operation, and e is the natural logarithm.
(6) Judging the termination condition of the improved multi-target genetic algorithm, if T is less than T, returning to the step (2) to continue circulation, otherwise, terminating the calculation, and outputting the result of the reservoir water level optimization set value;
(3) And calculating the reservoir dispatching process according to the solved reservoir water level optimization set value to obtain the reservoir output and the generated energy.
The invention is mainly characterized in that:
(1) The method takes the average output N of a water supply period and the annual energy production E in the reservoir scheduling process as targets, adopts a water quantity scheduling optimization method based on an improved multi-target genetic algorithm, realizes the solution of the optimal water level value of the reservoir, and has the characteristics of high optimization speed, good algorithm stability and the like;
(2) The invention designs an initial solution generation mechanism based on regression chaotic mapping, generates a population which traverses a search space and is uniformly distributed, and increases the diversity of initial solution distribution. Secondly, designing a hyperbolic tangent activation function-based cross strength self-adaptive adjustment mechanism, dynamically adjusting the number of genes participating in cross operation according to the fitness information of the population, and guiding an algorithm to quickly enter an effective search space. And finally, designing a variation strength self-adaptive adjustment mechanism based on a Sigmoid growth activation function, so that the algorithm can jump out of local optimum, the computing resource in an invalid search space is saved, and the optimization speed is increased.
Drawings
FIG. 1 is a reservoir scheduling process
FIG. 2 is a diagram of reservoir water level process
FIG. 3 is a diagram of the output process of a reservoir
FIG. 4 is a diagram of the power generation process of a reservoir
Detailed Description
The invention takes the Longyang strait reservoir as a research object, selects the average output N and the annual energy production E of the reservoir water supply period as optimization targets, and adopts the following technical scheme and implementation steps.
The reservoir dispatching optimization method based on the improved multi-target genetic algorithm comprises the following specific steps:
1. a reservoir dispatching optimization method based on an improved multi-objective genetic algorithm comprises the following steps:
according to the warehousing runoff of the Longyang fynit reservoir, the monthly reservoir water level Z in the scheduling process is optimized u The upstream and downstream water levels of the reservoir are coordinated to realize the maximization of the target benefit of the reservoir, and the reservoir dispatching process is as shown in figure 1;
(1) Designing the average output N of the water supply period of the reservoir and the annual generated energy E of the reservoir as an optimization objective function:
(1) acquiring basic information data of a reservoir, wherein the basic information data comprises a reservoir level and reservoir capacity relation, a reservoir discharge flow and tail water level relation and an actually measured monthly average reservoir inlet flow of the reservoir;
(2) establishing a multi-objective optimization scheduling mathematical model considering water balance, unit output, discharge capacity and generating capacity constraint conditions according to the basic information data, wherein an objective function is an objective function established by average output N of a reservoir water supply period and annual generating capacity E of the reservoir:
objective function 1: average output N in water supply period of reservoir
Wherein N is the average output of the reservoir in the water supply period, the unit is kw, K is the output coefficient of the reservoir, is the basic parameter of the reservoir, is obtained by the reservoir engineering plan book, the value is 8.8, Q is the monthly power generation flow rate of the reservoir, and the unit is m 3 S, obtained from the equation of water balance (2), Z u Is the upstream water level of the reservoir at the end of each month in m,Z d the value of the downstream water level of the monthly and the end of the month of the reservoir is read from a characteristic curve of the tail water level of the lower discharge of the reservoir, the unit is m, the water supply period of the reservoir is 5 months, 6 months and 12 months of the flat year and 1-4 months of the next year, the total period is 7 months, and a is more than or equal to 1 and less than or equal to 7.
Wherein Q is the monthly power generation flow of the reservoir and the unit is m 3 The I is the monthly warehousing runoff of the reservoir, namely the measured runoff data of the reservoir, and the unit is m 3 /s，V t+1 The storage capacity of the reservoir in the t +1 th month is m 3 ，V t The storage capacity of the reservoir in unit of m in the t month 3 And the delta t is the scheduling days of each month, and the unit of calculation is converted into seconds.
The objective function 2: annual energy production E of reservoir
Wherein E is the annual energy production of the reservoir, namely the power generation benefit of the reservoir, the unit is kwh, b is more than or equal to 1 and less than or equal to 12, K is the output coefficient of the reservoir, is the basic parameter of the reservoir, is obtained by a reservoir engineering plan, the value is 8.8, Q is the monthly power generation reference flow of the reservoir, and the unit is m 3 /s，Z u The upstream water level of the monthly and the monthly ends of the reservoir is m, Z d The numerical value of the downstream water level of the monthly and the monthly ends of the reservoir is read from a characteristic curve of the tail water level of the lower discharge of the reservoir, the unit is m, delta t is the scheduling days of each month, and the unit is converted into seconds during calculation.
(2) The multi-objective optimization method for optimizing the average output N of the water supply period of the reservoir and the annual energy production E of the reservoir is designed, and specifically comprises the following steps:
(1) setting parameters of a multi-target genetic algorithm and initializing a population, setting the population scale of the multi-target genetic algorithm NP =100, setting the maximum evolution algebra T =1000, and initializing the cross probability P c =0.9 and mutation probability P m =0.1, using regression chaotic mapping to produce a first generation parent population P of population size NP t ：
First, a set of chaotic sequences ranging from [0,1] is generated using a regression chaotic map:
x 1 ＝rand (21)
x p+1 ＝μx p (1-x 1 ) (22)
x＝(x 1 ,x 2 ,...,x p ,...,x 11 ) (23)
wherein x is 1 For the first value of the sequence, rand is a random number function, randomly generating a range of [0,1]]Mu is a regression chaotic mapping parameter, random generation satisfies 3.569945627-mu 4, 1-p 10, x satisfies the range [0,1 ≤]Of the chaotic sequence of (a).
Generating an actual reservoir water level value at the end of each month according to regression chaos mapping:
Z u ＝Z min +(Z max -Z min )x(24)
wherein Z is u Storing the water level value at the end of the month of 1-11 months in m for initializing individuals of the population, wherein the value range meets the interval [2530,2600]，Z min The minimum constraint value of the reservoir operation water level is 2530 max The maximum restriction value of the water level in the reservoir operation is 2600, x is the satisfied range of [0,1]]Of the chaotic sequence of (a).
Repeating the above initialization operation formulas (4) - (7) to obtain a first generation parent population P with a population size NP t 。
(2) The multi-target genetic algorithm is used for rapid non-dominated sorting and congestion degree calculation:
for the first generation parent population P t Non-dominant sorting is performed, and then the population selection, variable intensity crossover and variable intensity variation operations are performed to produce a progeny population Q with a population size NP t The population P t And a population Q t Merging into population R with population size of 2NP t . For population R t Performing non-dominated sorting, calculating crowdedness after layering of the population, and screening the optimal individual by adopting an elite retention strategy to obtain the speciesGroup size NP is a new generation parent group P t+1 . The population fitness calculation formula is as follows:
f t,i,j ＝(N t,i (Z u )，E t,i (Z u ))(25)
wherein f is t,i,j Represents the fitness of the jth target of the ith individual in the tth generation population, N t,i (Z u ) Calculated by the formula (18), the average output in kw, E is the mean time of the reservoir supply t,i (Z u ) Calculated by the formula (20), the annual energy production of the reservoir is represented by kwh and Z u Is an individual of the population.
(3) Selecting operation of the multi-target genetic algorithm:
randomly selecting two individuals to compare fitness values, directly entering the next generation when the individuals with high fitness values are selected, eliminating the individuals with low fitness values, selecting parent individuals to enter a hybridization pool, and stopping when the number of the individuals reaches NP.
(4) Multi-target genetic algorithm cross operation:
firstly, normalizing and summing the fitness value of each target of all individuals in the population, then arranging in descending order and counting
Calculating the average value of the first half fitness value:
wherein, f t,i Representing the normalized fitness value, f t,i,j Representing the fitness of the jth target of the ith individual in the tth generation population, f t,i,j max Represents the maximum fitness of the jth target of the ith individual in the tth generation population, f t,i,j min Represents the minimum fitness of the jth target of the ith individual in the tth generation population, f t,ave The average value of the fitness value of the first half of the descending order of the population is shown, and NP represents the size of the population.
Secondly, designing the number of genes participating in the cross operation:
n min ＝0(28)
wherein n is min Indicates the minimum number of genes involved in the crossover operation, n max The number of the maximum genes participating in the cross operation is represented, D represents the total number of the genes of the individual, the value is 11, T represents the maximum evolution algebra, and t represents the current iteration number.
Finally, designing a cross with adaptively adjustable cross strength based on hyperbolic tangent activation function in neural network
And (5) operating an operator. The crossover operator is:
wherein n is t,i Indicates the number of genes participating in crossover of the ith individual in the t-th generation, n max Indicates the maximum number of genes involved in crossover operation, n min Represents the minimum number of genes involved in crossover operation.
λ＝f t,i -f t,ave (31)
Wherein f is t,i Representing the normalized fitness value, f t,ave The average value of the fitness values of the first half of the population in descending order is shown, lambda is the difference between the fitness value of the individual in the population and the average fitness value of the individual in the first half of the population, and e is a natural logarithm.
(5) Performing multi-target genetic algorithm mutation operation:
designing the number of genes involved in mutation operation:
m min ＝0(32)
wherein m is min Indicating participationMinimum number of genes for mutation manipulation, m max The number of the maximum genes participating in mutation operation is represented, D represents the total number of the genes of the individual, the value is 11, T represents the maximum evolution algebra, and t represents the current iteration number.
Designing a mutation operator operation with adaptively adjustable mutation strength based on a Sigmoid activation function in a neural network. The mutation operator is:
wherein m is t,i Represents the number of genes in which the ith individual participates in crossover operation in the t generation, m min Represents the minimum number of genes involved in mutation operation, m max Represents the maximum number of genes involved in mutation operation, and e is the natural logarithm.
(6) And (4) judging the termination condition of the improved multi-target genetic algorithm, if T is less than T, returning to the step (2) to continue circulation, otherwise, terminating the calculation, and outputting the result of the reservoir water level optimization set value.
(3) And calculating the reservoir dispatching process according to the solved reservoir water level optimization set value to obtain the variation process of the output and the generated energy of the reservoir. Fig. 2 shows the reservoir water level change process, X-axis: time, in units of months, Y-axis: water level value Z at the end of the reservoir month u The unit is meter; fig. 3 shows the course of the reservoir output, X-axis: time, in units of months, Y-axis: the output value of the reservoir is megawatt; fig. 4 shows the variation of reservoir power generation, X-axis: time, in units of months, Y-axis: the power generation of the reservoir is billion kilowatts per hour; the design value of the average output of the water supply period of the Longyang isthmus reservoir is 558 megawatts, the design value of the annual energy generation of the reservoir is 57 hundred million kilowatts/hour, the average output of the water supply period of the Longyang isthmus reservoir is 621 megawatts according to the optimized scheduling result, the annual energy generation of the reservoir is 59.9 hundred million kilowatts/hour, the average output is increased by 11.2% and 5% respectively, and the result proves the effectiveness of the method.
Claims (1)
1. A reservoir dispatching optimization method based on an improved multi-objective genetic algorithm is characterized by comprising the following steps:
(1) Designing the average output N of the water supply period of the reservoir and the annual energy production E of the reservoir as an optimization objective function:
(1) acquiring basic information data of a reservoir, including a reservoir level capacity relation, a reservoir discharge flow and tail level relation and a reservoir monthly average warehousing flow;
(2) establishing a multi-objective optimization scheduling mathematical model considering water balance, unit output, discharge capacity and generating capacity constraint conditions according to the basic information data, wherein an objective function is an objective function established by average output N of a reservoir water supply period and annual generating capacity E of the reservoir:
objective function 1: average output N of reservoir water supply period
Wherein N is the average output of the reservoir in the water supply period, the unit is kw, K is the output coefficient of the reservoir, the output coefficient is the basic parameter of the reservoir, the output coefficient is obtained by the reservoir engineering plan book, Q is the monthly power generation quotation flow of the reservoir, and the unit is m 3 S is obtained from the water balance equation (2), Z u The upstream water level of the monthly and the monthly ends of the reservoir is m, Z d The downstream water level of the monthly end of the reservoir is read from a characteristic curve of the tail water level of the lower discharge flow of the reservoir, the unit is m, the water supply period of the reservoir is 5 months, 6 months and 12 months of the horizontal year and 1-4 months of the next year, the total period is 7 months, and a is more than or equal to 1 and less than or equal to 7;
wherein Q is the monthly power generation flow rate of the reservoir and the unit is m 3 The I is the monthly warehousing runoff of the reservoir, namely the measured runoff data of the reservoir, and the unit is m 3 /s，V t+1 The storage capacity of the reservoir in the t +1 th month is m 3 ，V t The storage capacity of the reservoir in unit of m in the t month 3 Derived from the reservoir capacity of the reservoir, Δ tFor the scheduling days of each month, the unit of calculation time is converted into second;
objective function 2: annual energy production E of reservoir
Wherein E is the annual generating capacity of the reservoir, namely the generating benefit of the reservoir, the unit is kwh, K is the output coefficient of the reservoir, the basic parameter of the reservoir is obtained by a reservoir engineering plan book, Q is the monthly generating reference flow of the reservoir, and the unit is m 3 /s，Z u The upstream water level of the monthly and the monthly ends of the reservoir is m, Z d Reading the value of the downstream water level of the monthly and the end of the month of the reservoir from a characteristic curve of the tail water level of the lower discharge of the reservoir, wherein the unit is m, delta t is the scheduling days of each month, and the unit of calculation time is converted into seconds;
(2) The multi-objective optimization method for optimizing the average output N of the water supply period of the reservoir and the annual energy production E of the reservoir is designed, and specifically comprises the following steps:
(1) setting parameters of the multi-target genetic algorithm and initializing the population, setting the population scale of the multi-target genetic algorithm to NP, the maximum evolution algebra T and initializing the cross probability P c And probability of mutation P m Generating a first generation parent population P of population size NP using recursive chaotic mapping t ：
First, a set of chaotic sequences ranging from [0,1] is generated using a regression chaotic map:
x 1 ＝rand (4)
x p+1 ＝μx p (1-x 1 ) (5)
x＝(x 1 ,x 2 ,...,x p ,...,x 11 )(6)
wherein x is 1 For the first value of the sequence, rand is a random number function, randomly generating a range of [0,1]]Mu is a regression chaotic mapping parameter, random generation satisfies the conditions that mu is more than or equal to 3.569945627 and less than or equal to 4, p is more than or equal to 1 and less than or equal to 10, x satisfies the range of [0,1]]The chaotic sequence of (a);
generating an actual reservoir water level value at the end of each month according to the regression chaos mapping:
Z u ＝Z min +(Z max -Z min )x(7)
wherein, Z u Storing the water level value at the end of the month of 1-11 months in the unit of m for initializing individuals of the population, wherein the value range meets the interval [ Z ] min Z max ]，Z min Minimum constraint, Z, representing reservoir operating level max The maximum constraint value of the water level in the reservoir operation is represented, and x is the satisfying range of [0,1]]The chaotic sequence of (a);
repeating the above initialization operation formulas (4) - (7) to obtain a first generation parent population P with a population size NP t ；
(2) The fast non-dominated sorting and crowding degree calculation of the multi-target genetic algorithm are as follows:
for the first generation parent population P t Non-dominated sorting is performed, and then the population selection, variable intensity crossover and variable intensity mutation operations are performed to produce a progeny population Q of population size NP t The population P t And group Q t Merging into a population R with a population size of 2NP t (ii) a For population R t Carrying out non-dominated sorting, carrying out crowding calculation after layering of the population, and screening the optimal individual by adopting an elite retention strategy to obtain a new generation population P with the population size of NP t+1 (ii) a The population fitness calculation formula is as follows:
f t,i,j ＝(N t,i (Z u )，E t,i (Z u ))(8)
wherein f is t,i,j Representing the fitness of the jth target of the ith individual in the tth generation population, N t,i (Z u ) Calculated by the formula (1), the average output of the reservoir water supply period is represented by kw, E t,i (Z u ) Calculated by the formula (3), the annual energy production of the reservoir is represented by kwh and Z u Is an individual of a population;
(3) selecting operation of the multi-target genetic algorithm:
randomly selecting two individuals for fitness value comparison, directly entering the next generation with the individuals with large fitness value, eliminating the individuals with small fitness, selecting the individuals of the parent generation to enter a hybridization pool, and stopping when the number of the individuals reaches NP;
(4) multi-target genetic algorithm cross operation:
firstly, normalizing and summing the fitness values of all individuals in the population for each target, then arranging in descending order, and calculating the average value of the fitness values of the first half:
wherein f is t,i Represents the normalized fitness value, f t,i,j Representing the fitness of the jth target of the ith individual in the tth generation population, f t,i,j max Represents the maximum fitness of the jth target of the ith individual in the tth generation population, f t,i,j min Represents the minimum fitness of the jth target of the ith individual in the tth generation population, f t,ave Representing the average value of the fitness values of the first half of the descending order arrangement of the population, and NP representing the size of the population;
secondly, designing the number of genes participating in the cross operation:
n min ＝0(11)
wherein n is min Indicates the minimum number of genes involved in crossover operation, n max Representing the maximum number of genes participating in cross operation, D representing the total number of genes of an individual, with the value of 11, T representing the maximum evolution algebra, and t representing the current iteration number;
finally, designing a crossover operator operation with adaptively adjustable crossover strength based on a hyperbolic tangent activation function in the neural network; the crossover operator is:
wherein n is t,i Indicates the number of genes participating in crossover of the ith individual in the t-th generation, n max Represents the maximum number of genes involved in crossover operation, n min Represents the minimum number of genes involved in the crossover operation;
λ＝f t,i -f t,ave (14)
wherein f is t,i Representing the normalized fitness value, f t,ave Expressing the average value of fitness values of the first half of the population descending order, wherein lambda is the difference between the fitness value of the individual in the population and the average fitness value of the individual in the first half of the population, and e is a natural logarithm;
(5) performing multi-target genetic algorithm mutation operation:
designing the number of genes involved in mutation operation:
m min ＝0(15)
wherein m is min Represents the minimum number of genes involved in mutation operation, m max Representing the maximum number of genes participating in mutation operation, D representing the total number of genes of an individual, the value is 11, and T representing the maximum evolution algebra;
designing a mutation operator operation with adaptively adjustable mutation intensity based on a Sigmoid activation function in a neural network; the mutation operator is:
wherein m is t,i Represents the number of genes participating in crossover operation of the ith individual in the t-th generation, m min Represents the minimum number of genes involved in mutation operation, m max Representing the maximum number of genes participating in mutation operation, wherein e is a natural logarithm;
(6) judging the termination condition of the improved multi-target genetic algorithm, if T is less than T, returning to the step (2) to continue circulation, otherwise, terminating the calculation, and outputting the result of the reservoir water level optimization set value;
(3) And calculating the reservoir dispatching process according to the solved reservoir water level optimal set value to obtain the reservoir output and the generated energy.
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