Flood control scheduling optimization method for cascade reservoirs based on improved flood optimization algorithm

Abstract

The application discloses a kind of based on improved flood optimization algorithm's cascade reservoir group flood control scheduling optimization method, comprising: obtaining cascade reservoir group flood control scheduling basic data data;Determine initial calculation condition, and establish fitness function;Population initialization operation, obtain population containing several individuals and obtain population optimal individual;Population optimization operation, in turn through flood routing simulation operation, flood change simulation operation, elite reverse learning operation, longitudinal cross learning operation updates population and population optimal individual;Termination condition judging operation, and output final optimal individual as cascade reservoir group flood control scheduling optimization result.The application firstly introduces novel flood optimization algorithm into solving reservoir group optimization scheduling problem, proposes improved flood optimization algorithm based on elite reverse strategy and longitudinal cross strategy, with the advantages of fast convergence efficiency, high calculation precision, and has good popularization value and application prospect in solving reservoir group optimization scheduling problem.

Description

Technical Field

[0001] This invention relates to the field of reservoir group optimization scheduling technology, specifically to a method for optimizing flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm. Background Technology

[0002] Optimal flood control scheduling of cascade reservoir groups is a typical high-dimensional, nonlinear, multi-stage, and strongly constrained complex system optimization and control problem. With the continuous development of cascade reservoirs in river basins, the scale of reservoir groups along main and tributary rivers is becoming increasingly large, exacerbating the contradiction between the complexity of the problem and the limitations of existing solution methods, making optimization extremely difficult. To solve this optimization challenge, scholars both domestically and internationally have proposed various computational methods. While traditional dynamic programming can solve the optimal scheduling of a single reservoir, it faces the curse of dimensionality when dealing with reservoir groups. Improved methods, such as discrete differential dynamic programming and stepwise optimization, have been proposed to alleviate the curse of dimensionality to some extent. In recent years, a series of intelligent evolutionary algorithms have also been proposed, adding new ideas to the optimal scheduling of reservoir groups, including particle swarm optimization, genetic algorithms, difference algorithms, and quantum particle swarm optimization. However, each algorithm has its advantages and limitations, including difficulty in handling multiple constraints, long computation time, and susceptibility to local optima, which restricts its practical application and promotion.

[0003] The Flood Algorithm (FLA), proposed in June 2024, is a novel swarm intelligence optimization algorithm. Inspired by the study of the complex movement and flow patterns of floods, its optimization approach involves simulating flood evolution and changes based on initial population data, iteratively updating the population to ultimately obtain the optimal result. The Flood Algorithm boasts advantages such as clear principles, simple structure, and fast optimization speed; however, its application in engineering fields is currently very limited.

[0004] Therefore, the applicant considers proposing a new method for optimizing the scheduling of cascade reservoir groups based on flood optimization algorithms. Summary of the Invention

[0005] To overcome the shortcomings of the above-mentioned technologies, the purpose of this invention is to provide an optimization method for flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm. Based on the introduction of the standard flood optimization algorithm into the flood control optimization scheduling of cascade reservoir groups, the standard flood optimization algorithm is improved based on elite back learning and vertical cross learning strategies. It has the advantages of strong search ability and high calculation accuracy, and can quickly and accurately obtain the optimal scheduling scheme of cascade reservoir groups, thereby improving optimization efficiency.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An optimization method for flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm includes the following steps:

[0008] 1) Obtain basic data on flood control scheduling of the cascade reservoir group;

[0009] 2) Determine the initial calculation conditions and establish the objective function of the flood control optimization scheduling of the cascade reservoir group as the fitness function;

[0010] 3) Population initialization operation, to obtain a population containing a certain number of individuals and to obtain the best individual in the population;

[0011] 4) Population optimization operations: The population and the best individual in the population are updated sequentially through flood evolution simulation operation, flood change simulation operation, elite reverse learning operation, and vertical cross-learning operation.

[0012] 5) Terminate the condition judgment operation and output the final optimal individual as the flood control scheduling optimization scheme of the cascade reservoir group.

[0013] Preferably, in step 2), the initial calculation conditions include using the water level of each reservoir at each time period during the scheduling period as the decision variable, minimizing the sum of squares of the flow processes of each flood control object as the optimization objective, establishing an objective function for the optimal scheduling of flood control in the cascade reservoir group as the fitness function, and setting constraints.

[0014] Preferably, the constraints include water balance constraints for each reservoir, water level constraints for each reservoir, outflow constraints for each reservoir, and discharge capacity constraints for each reservoir.

[0015] Preferably, in step 3), the population initialization operation includes randomly initializing individuals based on the basic information and constraints of the cascade reservoirs to obtain a population containing several individuals and then obtaining the optimal individual in the population; including the following steps:

[0016] (1) Encode and transform the water level of each reservoir for all time periods into the population individual variables: Set the population size to NP and the maximum number of iterations to G, then the population consists of NP D-dimensional individuals, each of which is... Where i = 1, 2, ..., NP, g = 0, 1, 2, ..., G, D = N × T;

[0017] Let the iteration number g = 0, and initialize the individual. as follows:

[0018]

[0019] in, The water levels of the first reservoir at different times. The water levels of the second reservoir at different times. Let N be the water level of the Nth reservoir at different times; Let be the j-th dimension variable of individual i in the g-th generation population, where i = 1, 2, ..., NP; j = 1, 2, ..., D. This refers to the water level of the s-th reservoir during the t-th time period, where s = 1, 2, ..., N; t = 1, 2, ..., T;

[0020] (2) Obtaining the optimal individual in the population: Select the individual with the smallest fitness value as the optimal individual in the population, denoted as x. best =(x best,1 ,x best,2 ,...,x best,D The fitness value is calculated by the fitness function f.

[0021] Preferably, in step 4), the flood evolution simulation operation, i.e., simulating conventional flood movement, includes the following steps:

[0022] (1) Perform iterative update operations on all individuals to obtain mutated individuals. The calculation formula is as follows:

[0023]

[0024] Where randn is a normally distributed random number; r1, r2, r3, and r4 are random numbers between 0 and 1; p j and q j These are the upper and lower limits of the j-th dimension variable for an individual, respectively; Let be the j-th dimension variable of an individual k randomly selected from the g-th generation population, k∈[1,NP] and k≠i; PK is the water consumption coefficient; PE i Let be the fitness coefficient value of individual i;

[0025] (2) Comparison of individuals and The fitness, if Then let Otherwise, no action is taken; where f is the fitness function;

[0026] (3) After all individuals have completed the flood evolution simulation operation, update the optimal individual x. best :

[0027]

[0028] Preferably, the formula for calculating the water consumption coefficient PK is:

[0029]

[0030] Preferably, the fitness coefficient value PE of individual i i The calculation formula is:

[0031]

[0032] in,

[0033] Preferably, in step 4), the flood change simulation operation, i.e., simulating the evaporation attenuation of floodwater, includes the following steps:

[0034] (1) By sorting the population after the flood evolution simulation operation, the NW worst individuals in the updated population were identified. Perform iterative updates to obtain the updated mutated individuals. The calculation formula is:

[0035]

[0036] In the formula, r5 and r6 are random numbers between 0 and 1; x best,j Let be the j-th dimension variable of the optimal individual after the flood evolution simulation operation update;

[0037] (2) Directly using the updated mutant individuals Replace the worse individuals in the updated population Immediately

[0038] (3) Repeat steps (1) and (2) of the flood change simulation operation. After all individuals have completed the flood change simulation operation, update the optimal individual x. best .

[0039] Preferably, NW is 10% of the population size NP.

[0040] Preferably, in step 4), the elite back-learning operation, that is, introducing an elite back-learning strategy on the basis of the standard flood optimization algorithm, includes the following steps:

[0041] (1) NE superior elite individuals in the population after the flood evolution simulation operation. Perform iterative updates to obtain the updated reverse individual. The calculation formula is:

[0042]

[0043] In the formula, r7 is a random number between 0 and 1;

[0044] (2) Compare individuals in the population after the flood evolution simulation operation. and the updated reverse individual The fitness, if Then let Otherwise, no action will be taken.

[0045] Preferably, NE is 10% of the population size NP.

[0046] Preferably, in step 4), the vertical cross-learning operation, that is, introducing a vertical cross-learning strategy based on the standard flood optimization algorithm, includes the following steps:

[0047] (1) Cross-learning is performed on the individual dimensional information of the population obtained after updating through flood evolution simulation, flood change simulation, and elite back-learning operations, based on... The updated cross individuals are obtained from the j-dimensional and k-dimensional dimensions. The calculation formula is:

[0048]

[0049] Where r8 is a random number between 0 and 1; Let i be the k-th dimension variable of an individual i randomly selected from the g-th generation population after being updated through flood evolution simulation operation, flood change simulation operation, and elite reverse learning operation.

[0050] (2) Individuals in the population obtained after updating by comparing flood evolution simulation operation, flood change simulation operation, and elite back learning operation. and the updated cross individuals The fitness, if Then let Otherwise, no action will be taken;

[0051] (3) Repeat steps (1) and (2) of the longitudinal crossover learning operation. After all individuals have completed the longitudinal crossover learning operation, update the optimal individual x. best .

[0052] Preferably, in step 5), the termination condition judgment operation is to determine whether the current iteration number has reached the maximum iteration number. If g≤G, let g=g+1 and repeat step 4); otherwise, stop the iteration and output the optimal individual as the final flood control scheduling optimization result of the cascade reservoir group.

[0053] This invention also provides a flood control scheduling optimization system for a cascade reservoir group based on an improved flood optimization algorithm, used to implement the aforementioned flood control scheduling optimization method for a cascade reservoir group based on an improved flood optimization algorithm, comprising:

[0054] The initial condition setting module is used to determine the objective function, constraints, and decision variables for the optimal flood control scheduling of the cascade reservoir group.

[0055] The population initialization module is used to randomly initialize individuals according to the constraints of the cascade reservoir, obtain a population containing several individuals, and select the best individual by comparison.

[0056] The population optimization module is used to update the population and the best individuals in the population through flood evolution simulation, flood change simulation, elite back learning, and vertical cross learning.

[0057] The output module is used to repeatedly execute the population optimization module until the iteration stopping condition is met, obtain the optimal individual, and output it as the final calculation result of the flood control scheduling water level optimization of the cascade reservoir group.

[0058] Preferably, the population optimization module includes:

[0059] The flood evolution simulation operation submodule is used to simulate the movement of a normal flood and perform iterative updates on all individuals;

[0060] The flood change simulation operation submodule is used to simulate the evaporation decay of floods and iteratively update several poorly performing individuals.

[0061] The Elite Reverse Learning Operation Submodule is used to introduce an elite reverse learning strategy and iteratively update a number of elite individuals.

[0062] The vertical cross-learning operation submodule is used to introduce a vertical cross-learning strategy to perform cross-learning of information from each dimension of all individuals for iterative updates.

[0063] The present invention also provides a computer device, including a memory and a processor, wherein the memory is used to store at least one program, and the processor is used to load the at least one program to execute the above-described method for optimizing flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] The flood optimization algorithm used in this invention has the advantages of clear principle, simple structure and fast optimization speed. It mainly includes operations such as initialization, flood evolution simulation and flood change simulation. However, it has not yet been applied to the field of reservoir group scheduling. This invention is the first to introduce it into the research problem of optimal scheduling of cascade reservoir groups.

[0066] This invention incorporates elite back-learning and longitudinal cross-learning operations into the standard flood optimization algorithm, proposing an improved flood optimization algorithm. This algorithm not only realizes the interactive learning of information among populations, enabling the development and utilization of information for global search and avoiding local optima, but also realizes the communication and learning of information within individuals, enabling the deep utilization of information to escape local optima and improve computational accuracy.

[0067] This invention presents an optimization method for flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm. It features simple principle, few control parameters, strong convergence ability, and high computational accuracy, and can be applied to solving complex optimization problems with multiple variables, multiple constraints, and high dimensions.

[0068] This invention proposes an optimized flood control scheduling method for cascade reservoir groups based on an improved flood optimization algorithm. It has the advantages of strong search capability and effective avoidance of the "curse of dimensionality". It can quickly and effectively obtain the optimized scheduling scheme for cascade reservoir groups and has good promotion value and application prospects in solving the optimal scheduling problem of reservoir groups. Attached Figure Description

[0069] Figure 1 This is a flowchart of a flood control scheduling optimization method for a cascade reservoir group based on an improved flood optimization algorithm, according to the present invention.

[0070] Figure 2 This is a diagram showing the calculation results of flood control and lake recreation scheduling for Reservoir A in a cascade reservoir group under the condition of 1% inflow in 1998, as described in an embodiment of the present invention.

[0071] Figure 3 This is a diagram showing the flood control optimization scheduling calculation results of Reservoir B in a cascade reservoir group under the condition of 1% inflow in 1998, according to an embodiment of the present invention. Detailed Implementation

[0072] To better explain the present invention, the main contents of the present invention are further illustrated below with reference to the accompanying drawings and specific embodiments, but the contents of the present invention are not limited to the following embodiments.

[0073] To reduce the flood control burden and flood losses downstream of reservoir groups, and to provide technical support for real-time flood control scheduling decisions, the maximum peak reduction criterion is widely used to construct the optimal scheduling objective function. Therefore, based on the maximum peak reduction criterion, the optimal flood control scheduling model for cascade reservoirs is generally described as follows: Given the initial water level, final water level, inflow flood process, and interval flood process of each reservoir during the scheduling period, and under the complex constraints of water level and flow rate of each reservoir and upstream and downstream protected objects, the optimization objective is to minimize the sum of squares of the flow processes of each flood protected object. The specific mathematical expression for the flood control benefit objective value is as follows:

[0074]

[0075] In the formula: W is the sum of squares of the flow process of the flood control object; N is the number of reservoirs; i is the reservoir number, i = 1, 2, ..., N; T is the total number of time periods during the scheduling period; j is the time period number, j = 1, 2, ..., T; O i,j Let m be the outflow from reservoir i during time period j. 3 / s); R i,j The interval flow (m³) from reservoir i to the downstream reservoir or downstream flood control section during time period j.3 / s).

[0076] The main constraints to be considered in the optimization calculation of flood control scheduling for a cascade reservoir group include:

[0077] (1) Water balance constraints of each reservoir:

[0078] (2) Hydraulic constraints of each reservoir:

[0079] (3) Water level constraints of each reservoir:

[0080] (4) Outflow constraints of each reservoir:

[0081] (5) Constraints on the discharge capacity of each reservoir:

[0082] (6) Initial and final water level constraints of each reservoir: Z i,0 =Z i,start Z i,T =Z i,end ;

[0083] (7) Non-negativity constraint: All variables are non-negative.

[0084] In the formula, V i,j Let m be the reservoir capacity of reservoir i at the end of time period j. 3 );I i,j Let m be the inflow rate of reservoir i during time period j. 3 / s); O i,j Let m be the outflow from reservoir i during time period j. 3 / s); Δt is the time interval length (h); and These represent the minimum outflow (m³) of reservoir i during time period j. 3 / s) and maximum outflow (m 3 / s); Z i,j Let be the water level (m) in front of the dam of reservoir i during time period j; and These represent the lowest and highest water levels (m) in front of the dam for reservoir i during time period j; O i,max (Z i,j () represents the water level Z corresponding to reservoir i during time period j. i,j Maximum discharge capacity (m) 3 / s); Z i,start and Z i,end These represent the initial reservoir water level (m) and the final control water level (m) of reservoir i during the scheduling period, respectively.

[0085] Analysis of the objective function and constraints reveals that the optimal scheduling of flood control in a cascade reservoir group involves numerous complex constraints such as water level, reservoir capacity, and flow rate. It is a significant, large-scale, high-dimensional, multi-stage, strongly constrained, and nonlinear complex control problem.

[0086] To efficiently solve the flood control optimization scheduling problem of a cascade reservoir group, this invention first analyzes the computational principle of the standard flood optimization algorithm, and then further considers elite back learning and vertical cross learning strategies to fully utilize search information, proposing an improved flood optimization algorithm. This algorithm has the advantages of strong search capability and effective avoidance of the "curse of dimensionality," and is a new method for efficiently solving the flood control optimization scheduling problem of a cascade reservoir group.

[0087] like Figure 1 As shown, the present invention provides a method for optimizing flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm, comprising the following steps:

[0088] 1) Obtain basic data on flood control scheduling of the cascade reservoir group;

[0089] The basic data includes the number of reservoirs N, the number of time periods T during the scheduling period, the characteristic parameters of each reservoir, the water level and storage capacity curves of each reservoir, the discharge capacity curves of each reservoir, and the data on different inflow floods into each reservoir.

[0090] 2) Determine the initial calculation conditions, including taking the water level of each reservoir at each time period during the scheduling period as the decision variable, taking the minimum of the sum of squares of the flow process of each flood control object as the optimization objective, establishing the fitness function f, that is, the optimization scheduling objective function W mentioned above, and setting various constraints such as water level, flow, and reservoir capacity;

[0091] 3) Population initialization operation, including random initialization of individuals based on the basic information and constraints of the cascade reservoirs, resulting in a population containing a certain number of individuals. Setting the population size to NP and the maximum number of iterations to G, the population consists of NP D-dimensional individuals, each of which is... Where i = 1, 2, ..., NP, g = 0, 1, 2, ..., G, D = N × T; let the iteration number g = 0, and initialize the individual.

[0092]

[0093] in, The water levels of the first reservoir at different times. The water levels of the second reservoir at different times. Let N be the water level of the Nth reservoir at different times; Let be the j-th dimension variable of individual i in the g-th generation population, where i = 1, 2, ..., NP; j = 1, 2, ..., D. It represents the water level of the s-th reservoir at the t-th time period, where s = 1, 2, ..., N; t = 1, 2, ..., T. In other words, an individual represents the water level of each reservoir at all time periods, thus completing the encoding conversion from water level to individual population variables.

[0094] At the same time, the individual with the smallest fitness value is selected as the optimal individual in the population, denoted as x. best =(x best,1 ,x best,2 ,...,x best,D The fitness value is calculated by the fitness function f().

[0095] 4) Population optimization operations: The population and the best individual in the population are updated sequentially through flood evolution simulation operation, flood change simulation operation, elite reverse learning operation, and vertical cross-learning operation.

[0096] 4.1) Flood evolution simulation operation, i.e., simulating conventional flood movement.

[0097] (1) Perform iterative update operations on all individuals to obtain mutated individuals. The calculation formula is:

[0098]

[0099] Where randn is a normally distributed random number; r1, r2, r3, and r4 are random numbers between 0 and 1; p j and q j These represent the upper and lower limits of the reservoir water level for the individual's j-th dimension variable; Let be the j-th dimension variable of an individual k randomly selected from the g-th generation population, where k∈[1,NP] and k≠i; PK is the water consumption coefficient, calculated using the following formula:

[0100]

[0101] PE i The fitness coefficient value of individual i is calculated using the following formula:

[0102]

[0103] Where f() is the individual fitness calculation function;

[0104] (2) Comparison of individuals and The fitness, if Then let Otherwise, no action will be taken.

[0105] (3) After all individuals have completed the flood evolution simulation operation, update the optimal individual x.best :

[0106]

[0107] 4.2) Flood change simulation operation, that is, simulating the evaporation decay of flood.

[0108] (1) By sorting the population after the flood evolution simulation operation, the NW worst individuals in the updated population were identified. Iterative updates are performed, with NW typically set to around 10% of NP, to obtain the updated mutant individuals. The calculation formula is:

[0109]

[0110] (2) Directly using the updated mutant individuals To replace the worse individuals in the updated population Immediately

[0111] (3) Repeat steps (1) and (2) of the flood change simulation operation. After all individuals have completed the flood change simulation operation, update the optimal individual x. best .

[0112] 4.3) Elite back-learning operation, that is, introducing an elite back-learning strategy on the basis of the standard flood optimization algorithm.

[0113] (1) In addition to iteratively updating the poor individuals, further consideration is given to updating the NE superior elite individuals in the population after the flood evolution simulation operation. Iterative updates are performed, with NE typically taken as about 10% of NP, to obtain the updated reverse individual. The calculation formula is:

[0114]

[0115] Where r7 is a random number between 0 and 1.

[0116] (2) Compare individuals in the population after the flood evolution simulation operation. and the updated reverse individual The fitness, if Then let Otherwise, no action will be taken.

[0117] 4.4) Vertical cross-learning operation, that is, based on the standard flood optimization algorithm, in addition to information exchange between individuals, a vertical cross-learning strategy is further introduced to consider cross-learning of information of each individual in various dimensions.

[0118] (1) Cross-learning is performed on the individual dimensional information of the population obtained after updating through flood evolution simulation, flood change simulation, and elite reverse learning operations, based on... The j-dimensional and k-dimensional cross individuals are obtained. The calculation formula is:

[0119]

[0120] Where r8 is a random number between 0 and 1; Let be the k-th dimension variable of an individual i randomly selected from the g-th generation population after being updated through flood evolution simulation, flood change simulation, and elite reverse learning operations.

[0121] (2) Individuals in the population obtained after updating by comparing flood evolution simulation operation, flood change simulation operation, and elite back learning operation. and the updated cross individuals The fitness, if Then let Otherwise, no action will be taken.

[0122] (3) Repeat steps (1) and (2) of the longitudinal crossover learning operation. After all individuals have completed the longitudinal crossover learning operation, update the optimal individual x. best .

[0123] 5) Termination condition judgment operation, that is, to determine whether the current iteration number has reached the maximum iteration number. If g≤G, let g=g+1 and repeat step 4); otherwise, stop the iteration and output the optimal individual as the final flood control scheduling optimization result of the cascade reservoir group.

[0124] This invention also provides a flood control scheduling optimization system for a cascade reservoir group based on an improved flood optimization algorithm, used to implement the aforementioned flood control scheduling optimization method for a cascade reservoir group based on an improved flood optimization algorithm, comprising:

[0125] The initial condition setting module is used to determine the objective function, constraints, and decision variables for the optimal flood control scheduling of the cascade reservoir group.

[0126] The population initialization module is used to randomly initialize individuals according to the constraints of the cascade reservoir, obtain a population containing several individuals, and select the best individual by comparison.

[0127] The population optimization module is used to update the population and its best individuals through flood evolution simulation, flood change simulation, elite back-learning, and vertical cross-learning operations. The module includes: a flood evolution simulation submodule, used to simulate conventional flood movement and perform iterative updates on all individuals; a flood change simulation submodule, used to simulate flood evaporation and attenuation and perform iterative updates on several weaker individuals; an elite back-learning submodule, used to introduce an elite back-learning strategy and perform iterative updates on several elite individuals; and a vertical cross-learning submodule, used to introduce a vertical cross-learning strategy and perform cross-learning of information from various dimensions of all individuals for iterative updates.

[0128] The output module is used to repeatedly execute the population optimization module until the iteration stopping condition is met, obtain the optimal individual, and output it as the final calculation result of the flood control scheduling water level optimization of the cascade reservoir group.

[0129] The present invention also provides a computer device, including a memory and a processor, wherein the memory is used to store at least one program, and the processor is used to load the at least one program to execute the above-described method for optimizing flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm.

[0130] The technical solution of the present invention will be further explained by taking three large cascade reservoirs on a tributary of a certain upper reaches of a certain river as an example.

[0131] Two flood control reservoirs, A and B, have been built sequentially in the middle and lower reaches of the river basin. Combined with the overall planning of the basin and flood control, these cascade reservoirs form a unified system for joint flood control operations, with a total flood control capacity of 2.5 billion cubic meters. 3 They play a crucial role in flood control within the watershed. Taking the actual flood, the 1% flood, and the 2% design flood of 1998 as examples, the optimal flood control scheduling of this cascade reservoir group was conducted. The method of this invention and the Power of Accounting (POA) were used to perform the optimal flood control scheduling calculations for the cascade reservoir group. The specific calculation results are shown in Table 1.

[0132] Table 1: Comparison of calculation results between the method of the present invention and other optimization algorithms

[0133]

[0134]

[0135] Table 1 shows the following findings regarding the water inflow process in the three scenarios:

[0136] (1) Compared with the calculation results of the differential evolution algorithm, the standard flood optimization algorithm is slightly worse. Although the standard flood optimization algorithm can be applied to the flood control optimization scheduling of cascade reservoir groups, its search capability needs to be improved and effective improvements are required.

[0137] (2) Compared with the standard flood optimization algorithm and the differential evolution algorithm, the method of this invention has a smaller target value in the calculation results, indicating that the cascade reservoirs have achieved good interception and storage effects for all three floods, and also demonstrating that the proposed improvement strategy is effective. The method of this invention provides an efficient and practical approach to address the optimal scheduling of large-scale complex reservoir groups.

[0138] like Figures 2-3 The figure shows the calculation results of the optimized flood control scheduling of cascade reservoirs under the condition of 1% inflow in 1998, using the method of the present invention. The scheduling results all meet the constraints of water level, reservoir capacity, and flow. The outflow from both reservoirs is relatively stable, indicating that the method of the present invention has excellent flood interception, peak reduction, and peak staggering effects. The method of the present invention can quickly obtain optimized flood control scheduling schemes for cascade reservoir groups.

[0139] In summary, this invention pioneered the introduction of flood optimization methods into the optimal scheduling problem of cascade reservoir groups. However, similar to population-based iterative intelligent algorithms, it was found that population diversity declines in the later stages, leading to a tendency to get trapped in local optima, necessitating further improvements in global search capabilities. Therefore, based on an analysis of the computational mechanism of flood optimization algorithms, two improved operations are coupled: first, elite back-learning is proposed for superior individuals to enhance the algorithm's ability to escape local optima; second, learning information from various dimensions of the individual and updating it through an effective information exchange mechanism improves the algorithm's ability to avoid premature convergence.

[0140] This invention proposes an optimized flood control scheduling method for cascade reservoir groups based on an improved flood optimization algorithm. It has the advantages of strong search capability and effective avoidance of the "curse of dimensionality". It can quickly and effectively obtain the optimized scheduling scheme for cascade reservoir groups and has good promotion value and application prospects in solving the optimal scheduling problem of reservoir groups.

[0141] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A flood control scheduling optimization method for a cascade reservoir group based on an improved flood optimization algorithm, characterized in that: Includes the following steps: 1) Obtain basic data on flood control scheduling of the cascade reservoir group; 2) Determine the initial calculation conditions and establish the objective function of the flood control optimization scheduling of the cascade reservoir group as the fitness function, and set the constraints; the initial calculation conditions include taking the water level of each reservoir at each time period during the scheduling period as the decision variable, and taking the minimum of the sum of squares of the flow process of each flood control object as the optimization objective; 3) Population initialization operation, to obtain a population containing a certain number of individuals and to obtain the best individual in the population; 4) Population optimization operations: The population and the best individual in the population are updated sequentially through flood evolution simulation operation, flood change simulation operation, elite reverse learning operation, and vertical cross-learning operation. The elite reverse learning operation includes the following steps: (1) In the population updated after flood evolution simulation operation A superior elite individual Perform iterative updates to obtain the updated reverse individual. The calculation formula is: ； In the formula, A random number between 0 and 1; and Individual number Upper and lower limits of a dimensional variable; For the first Individuals in a generation The Dimensional variables; , , Where D is the maximum number of iterations, N is the total number of individual dimensions, T is the number of reservoirs, and T is the number of scheduling periods. (2) Compare individuals in the population after the flood evolution simulation operation update. and the updated reverse individual The fitness, if Then let Otherwise, no action will be taken; f The fitness function; The vertical cross-learning operation includes the following steps: (1) Cross-learning is performed on the individual dimensional information of the population obtained after updating through flood evolution simulation operation, flood change simulation operation, and elite reverse learning operation, based on... of peacekeeping The updated cross individuals are obtained. The calculation formula is: ； in, A random number between 0 and 1; To update the [number]th [flood] through flood evolution simulation, flood change simulation, and elite back-learning operations. Individuals randomly selected from the population The Dimensional variable; NP represents the population size; (2) Individuals in the population obtained after updating by comparing flood evolution simulation operation, flood change simulation operation, and elite back learning operation. and the updated cross individuals The fitness, if Then let Otherwise, no action will be taken; (3) Repeat steps (1) and (2) of the longitudinal crossover learning operation. After all individuals have completed the longitudinal crossover learning operation, update the optimal individual. ; 5) Perform a termination condition judgment operation and output the final optimal individual as the flood control scheduling optimization scheme for the cascade reservoir group.

2. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 1, characterized in that: The constraints include water balance constraints for each reservoir, water level constraints for each reservoir, outflow constraints for each reservoir, and discharge capacity constraints for each reservoir.

3. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 1, characterized in that: In step 3), the population initialization operation includes randomly initializing individuals based on the basic information and constraints of the cascade reservoirs to obtain a population containing a number of individuals and then obtaining the optimal individual in the population; including the following steps: (1) Perform encoding conversion of water levels in all time periods of each reservoir to population individual variables: Set the population size to 1. The maximum number of iterations is Then the population is NP indivual Composed of dimensional individuals, each individual is ,in , , ; Let the number of iterations Initialized individuals as follows: ； in, ... The water levels of the first reservoir at different times. ... For the water levels of the second reservoir at different times, ... ... For the first N Water levels of each reservoir at different times; For the first Individuals in a generation The dimensional variables, ; j =1,2,......, D , It is the first The first reservoir Water level at different times ; (2) Obtaining the optimal individual in the population: Select the individual with the smallest fitness value as the optimal individual in the population, denoted as . The fitness value is determined by the fitness function. f Obtained through calculation.

4. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 3, characterized in that: In step 4), the flood evolution simulation operation, i.e., simulating conventional flood movement, includes the following steps: (1) Perform iterative update operations on all individuals to obtain mutated individuals. The calculation formula is as follows: in, These are normally distributed random numbers. r 1 , r 2 , r 3 and r 4 These are random numbers between 0 and 1; and Individual number Upper and lower limits of a dimensional variable; For from the first Individuals randomly selected from the population The dimensional variables, and ; This is the water consumption coefficient; For individuals The fitness coefficient value; (2) Comparison of individuals and The fitness, if Then let Otherwise, no action will be taken; (3) After all individuals have completed the flood evolution simulation operation, update the optimal individual. : 。 5. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 4, characterized in that: The formula for calculating the water consumption coefficient PK is as follows: 。 6. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 4, characterized in that: The individual fitness coefficient value The calculation formula is: ； in, ; .

7. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 4, characterized in that: Step 4), the flood change simulation operation, namely simulating the evaporation attenuation of floodwater, includes the following steps: (1) By sorting the population after the flood evolution simulation operation, the population in the updated population is sorted. A poorer individual Perform iterative updates to obtain the updated mutated individuals. The calculation formula is: ； In the formula, r 5 and r 6 represents a random number between 0 and 1; x best,j The optimal individual after the flood evolution simulation operation is updated. Dimensional variables; (2) Directly using the updated mutant individuals Replace the worse individuals in the updated population , that is to say ; (3) Repeat steps (1) and (2) of the flood change simulation operation. After all individuals have completed the flood change simulation operation, update the optimal individual. .

8. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 7, characterized in that: The value is the population size. 10%.

9. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 1, characterized in that: The value is the population size. 10%.

10. The method for optimizing flood control scheduling of a cascade reservoir group according to claim 4, characterized in that: In step 5), the termination condition judgment operation, that is, judging whether the current iteration count has reached the maximum iteration count, if... g ≤ G ,make g=g +1, repeat step 4); otherwise, stop the iteration and output the optimal individual as the final flood control scheduling optimization result of the cascade reservoir group.

11. A flood control scheduling optimization system for a cascade reservoir group based on an improved flood optimization algorithm, characterized in that: The method for optimizing flood control scheduling of cascade reservoir groups based on an improved flood optimization algorithm, as described in any one of claims 1 to 10, includes: The initial condition setting module is used to determine the objective function, constraints, and decision variables for the optimal flood control scheduling of the cascade reservoir group. The population initialization module is used to randomly initialize individuals according to the constraints of the cascade reservoir, obtain a population containing several individuals, and select the best individual by comparison. The population optimization module is used to update the population and the best individuals in the population through flood evolution simulation, flood change simulation, elite back learning, and vertical cross learning. The output module is used to repeatedly execute the population optimization module until the iteration stopping condition is met, obtain the optimal individual, and output it as the final calculation result of the flood control scheduling water level optimization of the cascade reservoir group.

12. The cascade reservoir group flood control scheduling optimization system according to claim 11, characterized in that: The population optimization module includes: The flood evolution simulation operation submodule is used to simulate the movement of a normal flood and perform iterative updates on all individuals; The flood change simulation operation submodule is used to simulate the evaporation decay of floods and iteratively update several poorly performing individuals. The Elite Reverse Learning Operation Submodule is used to introduce an elite reverse learning strategy and iteratively update a number of elite individuals. The vertical cross-learning operation submodule is used to introduce a vertical cross-learning strategy to perform cross-learning of information from each dimension of all individuals for iterative updates.

13. A computer device, characterized in that: The system includes a memory and a processor, wherein the memory is used to store at least one program, and the processor is used to load the at least one program to execute the flood control scheduling optimization method for a cascade reservoir group based on an improved flood optimization algorithm as described in any one of claims 1 to 10.

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