A reservoir group optimization scheduling method and system based on improved whale algorithm

Abstract

The present invention belongs to the technical field related to reservoir scheduling, and discloses a reservoir group optimization scheduling method and system based on an improved whale algorithm, wherein the method comprises: establishing a reservoir group optimization scheduling model; using the improved whale algorithm to solve the model; specifically comprising: setting algorithm parameters including population size, individual dimension and maximum number of iterations, initializing the population; introducing an adaptive probability critical value p 1 and random probability p , p 1 is between [0, 1] and gradually decreases with the increase of the number of iterations. p is a random number between [0, 1], judge p ≤ p 1 is established, if established, the population is updated according to the encirclement predation method or random search method in the whale algorithm, if not established, the population is updated according to the spiral movement method in the whale algorithm; if it is judged that the maximum number of iterations is reached, the global optimal solution is output as the optimal scheduling solution. The present invention constructs a more efficient and robust swarm intelligence optimization algorithm in the field of reservoir optimization scheduling.

Description

Technical Field

[0001] The present invention belongs to the technical field related to reservoir scheduling, and more specifically, relates to a reservoir group optimization scheduling method and system based on an improved whale algorithm. Background Art

[0002] As a complex large-scale, multi-stage, nonlinear optimization problem, the optimal operation of a group of reservoirs is characterized by high dimensions of decision variables, complex constraints between power stations, and significant dynamic correlation, which makes the solution of the optimal operation of a group of cascade reservoirs a very challenging task. Traditional solutions to the optimal operation of a group of reservoirs include linear and nonlinear programming, dynamic programming, and stepwise optimization algorithms. Although these methods have shown certain results in the optimal operation of a single reservoir, they are often limited by the high consumption of computing resources and the bottleneck of "dimensionality curse" when facing large-scale cascade reservoir systems, making it difficult to effectively deal with them. In recent years, emerging intelligent computing methods have the advantages of no gradient information, simple principles, and efficient calculations. These algorithms include swarm intelligence bionic algorithms that simulate group foraging behavior, genetic evolution algorithms that simulate natural selection evolution, and intelligent algorithms that simulate physical principles. They have been widely introduced and applied to the practice of reservoir group operation.

[0003] Although swarm intelligence bionic optimization algorithms have made significant progress in the field of reservoir optimization and scheduling, and classic algorithms such as particle swarm optimization algorithm, ant colony optimization algorithm, and grey wolf optimization algorithm have been widely adopted, existing methods still face technical bottlenecks such as insufficient accuracy, limited convergence speed, and easy to fall into local optimality. Summary of the invention

[0004] In view of the above defects or improvement needs of the prior art, the present invention provides a reservoir group optimization scheduling method and system based on the improved whale algorithm, which solves the technical bottlenecks of the existing group intelligent bionic optimization algorithms in the field of reservoir optimization scheduling, such as insufficient accuracy, limited convergence speed and easy to fall into local optimality, so as to more efficiently solve the problem of solving the reservoir optimization scheduling model.

[0005] To achieve the above object, according to a first aspect of the present invention, a reservoir group optimization scheduling method based on an improved whale algorithm is provided, comprising:

[0006] S1, establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include flow constraints, output constraints, water level constraints, water balance constraints, water level fluctuation constraints, and flow fluctuation constraints of each reservoir in the reservoir group;

[0007] S2, using the improved whale algorithm to solve the reservoir group optimization scheduling model and obtain the optimal scheduling plan;

[0008] Among them, S2 specifically includes:

[0009] S21, set the algorithm parameters, including population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of individuals in the population is the value of the objective function. The decision variable of the individual is the water level process of the reservoir group. The decision variable satisfies the constraints in S1.

[0010] S22, introduce adaptive probability threshold p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p 1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm.

[0011] S23, determine whether the maximum number of iterations has been reached. If not, increase the number of iterations and return to S22. If reached, output the global optimal solution as the optimal reservoir group optimization scheduling plan.

[0012] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the population initialization in S21 specifically includes:

[0013] A cubic chaotic array is generated according to the cubic chaotic mapping method, and the scale of the cubic chaotic array is consistent with the scale of the population; the individual values ​​in the cubic chaotic array are mapped to the value space of the decision variable to obtain the initial population.

[0014] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the adaptive probability critical value in S22 p 1 Specifically:

[0015] ;

[0016] in, m is the current iteration number, is the maximum number of iterations.

[0017] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, in S22, the population is optimized and updated according to the encirclement predation method or random search method in the whale algorithm, specifically including:

[0018] Further determine the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm. If not, the population is optimized and updated according to the random search method in the whale algorithm, where:

[0019] ;

[0020] ;

[0021] Where 𝑟 is a random vector in [0, 1], is the convergence factor, It decreases linearly from 2 to 0 during the iteration. m is the current iteration number, is the maximum number of iterations.

[0022] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm, including:

[0023] The differential evolution algorithm is used to improve the original encirclement and predation method in the whale algorithm, and the improved encirclement and predation method is used to optimize and update the population;

[0024] The improved encirclement and predation method is used to optimize and update the population as follows:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in, Indicates the current m The population individual vector at the iteration, Indicates The population individual vector at the iteration, is the current optimal solution position, is the coefficient, F is the mutation operator used to control the degree of disturbance, Get a random number between [0, 2], and The current m The random individuals 1 and 2 generated in the iterations are: The difference vector generated for the current random individual.

[0030] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the coefficient vector Is it true? If not, the population is updated and optimized according to the random search method in the whale algorithm, including:

[0031] Set the migration probability between (0, 1) to further determine the random number rand and the size of the migration probability, rand Represents a random number between (0, 1);

[0032] exist rand When it is greater than the migration probability, an adaptive weight is introduced , As the number of iterations increases, the nonlinearity decreases. The original random search method in the whale algorithm is weighted according to the adaptive weight, and the weighted random search method is used to optimize and update the population.

[0033] exist rand When it is less than or equal to the migration probability, the black kite optimization algorithm is introduced, and the black kite migration method is used to optimize and update the population.

[0034] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the weighted random search method is used to optimize and update the population specifically as follows:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] in, Indicates The population individual vector at the iteration, is current m The individuals randomly selected in the iterations are and represents the weights at the beginning and end of the iteration, k is the control factor used to control the shape of the curve. is the coefficient, Indicates the current m The population individual vector at the iteration, is the migration probability;

[0040] The specific optimization and update of the population by black-winged kite migration is as follows:

[0041] ;

[0042] in, Represents the current m The population individual vector at the iteration, represents the current optimal position, Represents random numbers from a Cauchy distribution.

[0043] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, in S22, the population is updated and optimized according to the spiral movement mode in the whale algorithm, specifically including:

[0044] Introducing adaptive weights , As the number of iterations increases, the nonlinearity decreases. The original spiral movement method in the whale algorithm is weighted according to the adaptive weight, and the weighted spiral movement method is used to update and optimize the population.

[0045] According to the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention, the weighted spiral movement method is used to update and optimize the population as follows:

[0046] ;

[0047] ;

[0048] ;

[0049] in, Indicates The population individual vector at the iteration, is the current optimal solution position, Represents the current m The population individual vector at the iteration, is the maximum number of iterations, and represents the weights at the beginning and end of the iteration, k is the control factor used to control the shape of the curve. is the distance between the current individual and the optimal individual, is a constant used to define the shape of the logarithmic spiral, is a random number in [-1, 1].

[0050] According to a second aspect of the present invention, a reservoir group optimization scheduling system based on an improved whale algorithm is provided, comprising:

[0051] The model building module is used to establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include the flow constraint, output constraint, water level constraint, water balance constraint, water level amplitude constraint and flow amplitude constraint of each reservoir in the reservoir group;

[0052] Model solving module, used to solve the reservoir group optimization dispatching model using improved whale algorithm to obtain the optimal dispatching plan;

[0053] The model solving module specifically includes:

[0054] The initialization module is used to set the algorithm parameters, including the population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of the individuals in the population is the value of the objective function, and the decision variables of the individuals are the water level process of the reservoir group. The decision variables meet the above constraints.

[0055] Optimization module for introducing adaptive probability thresholds p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p 1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm.

[0056] The output module is used to determine whether the maximum number of iterations has been reached. If not, the number of iterations is increased and returned to the optimization module. If reached, the global optimal solution is output as the optimal reservoir group optimization scheduling plan.

[0057] In general, compared with the prior art, the above technical solutions conceived by the present invention provide a reservoir group optimization scheduling method and system based on the improved whale algorithm:

[0058] 1. Through adaptive probability threshold p 1 to balance the global and local search capabilities. In the early stages of iteration, the adaptive probability threshold p 1 is larger, then when p ≤ p 1, the algorithm performs global search with higher probability and faster speed. It can perform global search according to the encirclement and predation method or random search method in the whale algorithm to improve the search efficiency and thus improve the convergence speed of the algorithm. As the iteration progresses, the adaptive probability critical value p 1 slowly decreases to close to 0, because at this timep > p 1. The algorithm will choose the spiral movement mode with a greater probability to update the leader position; by continuously updating the adaptive probability critical value, adjusting the local and global search capabilities of the algorithm, the whale group gradually approaches the optimal solution, thereby improving the convergence accuracy of the algorithm and avoiding falling into the local optimum; and then by using the whale algorithm improved by the adaptive probability critical value to solve the reservoir group optimization scheduling model, it is conducive to obtaining the optimal scheduling plan faster and more accurately;

[0059] 2. By deeply integrating the migration mechanism of the black-winged warbler algorithm and the unique advantages of differential mutation, the whale optimization algorithm was systematically improved, aiming to enhance the algorithm's exploration and development capabilities, and then build a more efficient and robust swarm intelligence optimization algorithm in the field of reservoir optimization and scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of the reservoir group optimization scheduling method based on the improved whale algorithm provided by the present invention.

[0061] Figure 2 It is a flow chart for solving the problem of optimal dispatching of cascade reservoir power generation in a specific embodiment provided by the present invention.

[0062] Figure 3 It is a schematic diagram of the solution process of different algorithms in 2017 (a normal water year) in the embodiment provided by the present invention.

[0063] Figure 4 It is a schematic diagram of the solution process of different algorithms in 2018 (a flood year) in the embodiment provided by the present invention.

[0064] Figure 5 It is a schematic diagram of the solution process of different algorithms in 2021 (dry year) in the embodiment provided by the present invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0066] The whale algorithm is a mathematical model constructed to simulate the predation behavior of whales. The algorithm uses random or best search to simulate hunting behavior to chase prey, and uses spiral search to simulate the bubble net attack mechanism of humpback whales, foraging through encirclement predation, spiral bubble attack, and random hunting mechanisms. In the whale algorithm, the positions of all whales are feasible solutions to the problem. The calculation starts with a set of random solutions. In each iteration, the position of the new individual is updated according to the randomly selected individual or the best individual obtained so far. The position of the best individual is the optimal solution of the model. The whale algorithm includes three methods: encirclement predation, spiral bubble attack (spiral travel), and random search predation. The main process and principle of the original whale algorithm (WOA algorithm) are as follows:

[0067] a. Individual initialization

[0068] Randomly generate a population with individual dimension E and population size N, as shown in formula (4.1):

[0069]

[0070] in, represents the population individual vector under the current m iterations, Indicates Individual Dimension value, , and are the upper and lower bounds of the algorithm’s decision variables, exist Initialize according to formula (4.2):

[0071]

[0072] In the formula, Represents a random number randomly distributed in the interval [0, 1].

[0073] b. Surrounding the prey

[0074] In the whale algorithm, whales can identify the location of prey and surround it. At the beginning, the algorithm assumes that the current best candidate solution is the target prey location. After the target prey location is defined, other whales will try to surround the target prey location. The behavior of surrounding and preying on prey, that is, the surrounding prey method, is expressed in the following mathematical way:

[0075]

[0076] in, m is the current iteration number, A and C is the coefficient, X is the current solution position, is the current optimal solution position, is the distance vector and also the enclosing step length, 𝑟 is a random vector in [0, 1], is the convergence factor, which decreases linearly from 2 to 0 during the iteration process, as shown in formula (4.7):

[0077]

[0078] in, Indicates the maximum number of iterations.

[0079] c. Spiral bubble attack means spiral movement

[0080] In the process of spiral predation, whales gradually approach their prey in a spiral ascending manner and capture it by continuously shrinking the encirclement. The spiral bubble predation strategy of whales can be divided into: contraction encirclement and spiral renewal.

[0081] Contraction and encirclement: This behavior of the whale is mainly based on the linear convergence factor in formula (4.7) As the iteration process progresses, the parameters The value of gradually decreases, prompting individual whales to gradually adjust their positions and move closer to the prey, thus completing the encirclement.

[0082] Spiral update: As the whale gradually narrows the circle around its prey, it uses a spiral path to gradually approach the target, which can be expressed by the following mathematical formula:

[0083]

[0084] Indicates The population individual vector at the iteration, is the current optimal solution position, Represents the current m The population individual vector at the iteration, is the distance between the current individual and the optimal individual and is also the spiral update step length. is a constant that defines the shape of the logarithmic spiral, is a random number in [-1, 1].

[0085] In order to simulate the shrinking and surrounding mechanism and the spiral updating mechanism of the whale at the same time, it is assumed that there is a 50% probability of choosing between the shrinking and surrounding mechanism or the spiral updating mechanism, that is, the probability critical value is set to 0.5, and the mathematical expression is expressed as follows:

[0086]

[0087] in, is a random number between [0, 1].

[0088] d. Random search

[0089] In addition to the spiral bubble attack predation, humpback whales also randomly search for prey to balance the development and exploration phases of the algorithm. When When , the optimal individual is no longer selected to update the position vector, but a randomly selected whale is used to update the position. The mathematical expression is as follows:

[0090]

[0091] in, is a randomly selected whale individual, namely the current m The individuals randomly selected in the iterations are is the distance vector and also the random search step size, Indicates the current m The population individual vector at iterations.

[0092] See also Figure 1 This embodiment provides a reservoir group optimization scheduling method based on an improved whale algorithm, the method comprising:

[0093] S1, establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include flow constraints, output constraints, water level constraints, water balance constraints, water level fluctuation constraints, and flow fluctuation constraints of each reservoir in the reservoir group;

[0094] S2, using the improved whale algorithm to solve the reservoir group optimization scheduling model and obtain the optimal scheduling plan;

[0095] Among them, S2 specifically includes:

[0096] S21, set the algorithm parameters, including population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of individuals in the population is the value of the objective function. The decision variable of the individual is the water level process of the reservoir group. The decision variable satisfies the constraints in S1.

[0097] S22, introduce adaptive probability threshold p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm.

[0098] S23, determine whether the maximum number of iterations has been reached. If not, increase the number of iterations and return to S22. If reached, output the global optimal solution as the optimal reservoir group optimization scheduling plan.

[0099] This embodiment converts the optimization scheduling problem of the reservoir group into a mathematical calculation problem by establishing a reservoir group optimization scheduling model, and solves the scheduling model based on the whale algorithm to obtain the optimal scheduling plan. The objective function in the scheduling model is to maximize the total power generation of the reservoir group during the scheduling period, that is, to maximize the total power generation of all reservoirs; each individual in the population is a scheduling plan, and the individual is composed of decision variables. The population size is the number of individuals in the population, and the individual dimension is the number of decision variables in each individual.

[0100] For example, the dispatch period can be 1 year, and the individual dimension can be 36. Each individual includes 36 decision variables, that is, 36 water level processes, that is, 1 year is divided into 36 time periods, and the 36 water level processes form a 1-year water level process. The 36 water level processes in each individual form the water level dispatching plan for the entire dispatching period. Among them, the water level process is the water level process of the reservoir group, that is, the water level process formed by multiple reservoirs, which reflects the water level regulation process of the reservoir group. The water level process needs to meet various constraints set in the dispatching model.

[0101] Furthermore, the present embodiment has found through research that the original whale algorithm (WOA algorithm) sets the probability threshold value of 0.5 to synchronize the encirclement and spiral movement processes. P The hunting strategy is selected by comparing the value with the probability critical value. As the number of iterations increases, this equal-probability hunting method will cause the algorithm to fall into local optimal problems.

[0102] Based on this, this embodiment proposes an optimization algorithm that improves the original whale algorithm by using an adaptive probability critical value. p 1 to balance the global and local search capabilities. In the early stages of iteration, the adaptive probability threshold p 1 is larger, then when p ≤ p 1, the algorithm performs global search with higher probability and faster speed. It can perform global search according to the encirclement and predation method or random search method in the whale algorithm to improve the search efficiency and thus improve the convergence speed of the algorithm. As the iteration progresses, the adaptive probability critical value p 1 slowly decreases to close to 0, because at this time p >p 1. The algorithm will choose the spiral movement mode with a greater probability to update the leader position; by continuously updating the adaptive probability critical value, adjusting the local and global search capabilities of the algorithm, the whale group gradually approaches the optimal solution, thereby improving the convergence accuracy of the algorithm and avoiding falling into the local optimum; and then by using the whale algorithm improved by the adaptive probability critical value to solve the reservoir group optimization scheduling model, it is conducive to obtaining the optimal scheduling plan faster and more accurately.

[0103] The improvement and optimization of the whale algorithm in this embodiment also includes the following aspects:

[0104] a. Chaos initialization

[0105] The characteristics of chaotic mapping are that it has a mixture of randomness, sensitivity and determinism, which helps to increase the global search performance of the algorithm. There are many ways of chaotic mapping, such as Chebyshev chaotic mapping, circular chaotic mapping, cubic chaotic mapping, tent chaotic mapping, logistic chaotic mapping, discrete chaotic mapping, etc. Among the many chaotic mapping methods, cubic chaotic mapping has better chaotic ergodicity. This embodiment uses cubic chaotic mapping to initialize the population, so that the position of the population generated by initialization is more uniform. Cubic chaotic mapping first generates a chaotic sequence according to the following formula:

[0106]

[0107] In the formula, rand is a random number between (0, 1), a =2.595 chaos parameter, cubic chaos mapping has good ergodicity between (0, 1). Then map the chaotic sequence to the value space of the decision variable in the problem to be optimized. The specific steps are as follows:

[0108] According to the cubic chaos mapping method, a set of N E-dimensional population individuals is generated, where a =2.595, the two-dimensional individual expression of the cubic chaotic array mapped by formula (4.13) is:

[0109]

[0110] in , Representative The individual The cubic chaotic array value of dimensions, Generated by formula (4.13).

[0111] Then follow the formula:

[0112]

[0113] Map the individual values ​​in the cubic chaotic array to the value space of the decision variable to obtain the initial population. and are the upper and lower limits of the decision variables, respectively. Represents the cubic chaotic map i The individual j The cubic chaotic array value of dimensions, For the i The individual j dimensional decision variables.

[0114] That is, the population initialization in S21 specifically includes:

[0115] A cubic chaotic array is generated according to the cubic chaotic mapping method, and the scale of the cubic chaotic array is consistent with the scale of the population; the individual values ​​in the cubic chaotic array are mapped to the value space of the decision variable to obtain the initial population.

[0116] b. Adaptive weights Adaptive probability threshold

[0117] The original whale optimization algorithm does not have corresponding weights to adjust the update formula when it is locally developed in the later stage. As the search process deepens, it may cause the whale individual to stay near the theoretical position or even fall into a local extreme value. Based on the above problems, the present invention uses adaptive weight values ​​to adjust the update formula and proposes an adaptive probability critical value to balance the global and local search capabilities.

[0118] The corresponding adaptive weight The expression is as follows:

[0119]

[0120] In the formula, m is the current iteration number, represents the maximum number of iterations, and Represents the weights at the beginning and end of the iteration, for example , k is the control factor, controlling the shape of the curve, and taking k =0.6.

[0121] Weight It decreases nonlinearly with the increase of the number of iterations. In the early stage of the algorithm, the larger weight coefficient gives it a strong global search ability; as the number of iterations increases, the weight coefficient gradually decreases. At this time, the algorithm uses a smaller weight coefficient to perform a fine search in the neighborhood of the optimal solution through a spiral movement method, thereby avoiding falling into the local optimum. Adaptive weights are used to improve the shortcomings of random search and spiral predation stages, which are prone to falling into local extreme values ​​when performing local searches in the later stages. The weighted spiral movement method is the improved formula of formula (4.8) as shown in the following (4.17), and the weighted random search method is the improved formula of formula (4.11) as shown in the following (4.18):

[0122]

[0123] Adaptive probability threshold in S22 p 1The expression is as follows:

[0124]

[0125] In the formula, at the beginning of the iteration, the adaptive probability critical value p 1 is larger, then when When , the algorithm performs global search with higher probability and faster speed. As the iteration progresses, the probability threshold slowly decreases to close to 0. , the algorithm will choose the spiral movement mode with a higher probability to update the leader position. By continuously updating the adaptive probability threshold and adjusting the local and global search capabilities of the algorithm, the whale group gradually approaches the optimal solution, thereby improving the convergence accuracy of the algorithm.

[0126] Specifically, in S22, the population is updated and optimized according to the spiral movement method in the whale algorithm, including:

[0127] Introducing adaptive weights , As the number of iterations increases, the nonlinearity decreases. The original spiral movement method in the whale algorithm is weighted according to the adaptive weight, and the weighted spiral movement method (Formula 4.17) is used to update and optimize the population.

[0128] c. Improvements based on the migration behavior of black-winged kites

[0129] The Black Kite Optimization Algorithm (BKA) is an optimization algorithm that simulates the migration and predation behavior of black kites. Each black kite represents a feasible solution. The main update mechanisms include: attack behavior and migration behavior. The attack behavior mechanism is used for global search, and the migration strategy can dynamically select excellent optimal solutions to ensure the success of migration. Based on the migration principle of black kites, the present invention improves the original whale optimization algorithm, takes part of the migration behavior mechanism as a step in the whale update mechanism, and strengthens the local search ability of the original whale optimization algorithm. The calculation formula for the update of the migration behavior of black kites is as follows:

[0130]

[0131] In the formula, Represents the current position, that is, the current m The population individual vector at the iteration, represents the current optimal position, Represents random numbers from a Cauchy distribution.

[0132] In the Black Kite algorithm, the premise of selecting the above update mechanism is that the fitness value of the randomly generated individual is greater than the current fitness value. The current individual will be eliminated and the leader individual will be replaced to continue the update. The advantage of this method is that it can allow the poorer individuals to move towards the better individuals, increasing the optimization efficiency and convergence ability of the algorithm. This update method is applied to the random search stage of the whale optimization algorithm. At the same time, in order to balance the random search in the random search stage and the ability to avoid falling into the local optimal value, a probabilistic update mechanism is adopted for the random search stage. The update formula is:

[0133]

[0134] In the formula, rand represents a random number between (0, 1), is the migration probability, here we take At this point, the algorithm has a certain probability of performing a black kite migration update, otherwise, it will continue to perform a whale algorithm update.

[0135] Specifically, in S22, the population is optimized and updated according to the encirclement predation method or random search method in the whale algorithm, including:

[0136] Further determine the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm. If not, the population is optimized and updated according to the random search method in the whale algorithm.

[0137] Further determine the coefficient vector Is it true? If not, the population is updated and optimized according to the random search method in the whale algorithm, including:

[0138] Set the migration probability between (0, 1) to further determine the random number rand and the size of the migration probability, rand Represents a random number between (0, 1);

[0139] exist rand When it is greater than the migration probability, an adaptive weight is introduced , As the number of iterations increases, the nonlinearity decreases. The original random search method in the whale algorithm is weighted according to the adaptive weight, and the weighted random search method, i.e., formula (4.21), is used to optimize and update the population;

[0140] exist rand When it is less than or equal to the migration probability, the black kite optimization algorithm is introduced, and the black kite migration method, i.e., formula (4.22), is used to optimize and update the population.

[0141] d. Improvements based on differential mutation

[0142] Differential evolution algorithm is an evolutionary computing technology, which includes three main operations: mutation, crossover, and selection. The mutation operation uses the difference vectors between different individuals to perturb the individuals, which can effectively improve the search ability of the algorithm. There are many mutation strategies. This paper combines the mutation method of the differential algorithm mutation strategy (DE / current-to-best / 1) to improve the contraction and encirclement stage of the original whale. The differential algorithm mutation strategy (DE / current-to-best / 1) is expressed as follows:

[0143]

[0144] Where F is the mutation operator, which controls the degree of disturbance. For the current individual, is the difference variable between the optimal individual and the current individual, is the difference vector generated by a random individual.

[0145] In order to improve the shortcomings of the original whale algorithm in the process of shrinking and surrounding, such as poor search ability and easy to fall into the local optimum, the formula (4.3) is improved by adding differential variables and mutation operators for perturbation, which can improve the population diversity and global search ability. The improved formula is as follows:

[0146]

[0147] In the formula, Take a random number between [0, 2], and the improved formula adds a mutation difference vector on the basis of the original formula The perturbation effectively improves the algorithm's optimization ability. and The current m The random individuals 1 and 2 generated in the iterations are: The difference vector generated for the current random individual.

[0148] Specifically, further determine the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm, including:

[0149] The differential evolution algorithm is used to improve the original encirclement and predation method in the whale algorithm, and the improved encirclement and predation method, namely formula (4.24), is used to optimize and update the population.

[0150] In another embodiment, the present invention further provides a reservoir group optimization scheduling system based on the improved whale algorithm, which is used to implement the reservoir group optimization scheduling method based on the improved whale algorithm in any of the above embodiments, and the system includes:

[0151] The model building module is used to establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include the flow constraint, output constraint, water level constraint, water balance constraint, water level amplitude constraint and flow amplitude constraint of each reservoir in the reservoir group;

[0152] Model solving module, used to solve the reservoir group optimization dispatching model using improved whale algorithm to obtain the optimal dispatching plan;

[0153] The model solving module specifically includes:

[0154] The initialization module is used to set the algorithm parameters, including the population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of the individuals in the population is the value of the objective function, and the decision variables of the individuals are the water level process of the reservoir group. The decision variables meet the above constraints.

[0155] Optimization module for introducing adaptive probability thresholds p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm.

[0156] The output module is used to determine whether the maximum number of iterations has been reached. If not, the number of iterations is increased and returned to the optimization module. If reached, the global optimal solution is output as the optimal reservoir group optimization scheduling plan.

[0157] According to the above improvement strategies, this embodiment proposes a reservoir group optimization scheduling method based on the migration difference variation whale algorithm (BDWOA algorithm), referring to Figure 2 , the algorithm solves the problem of optimal dispatching of cascade reservoir power generation as follows:

[0158] Step 1: Set the algorithm parameters, the population size is N, the individual dimension is E, and the number of algorithm iterations is , the migration probability is , the weights at the beginning and end of the iteration and , adaptive weight control factor k Read the basic data of the hydropower station, including the water level storage capacity curve, the discharge flow curve, the inflow flow of each power station, the inflow and outflow flow of each power station during the dispatch period, etc., and input various flow, output, water level and other constraints of the cascade reservoir power generation dispatch model:

[0159] flow The constraints are: , and Reservoirs are i Minimum and maximum outbound flow limits for a period of time;

[0160] contribute The constraints are: , and The power stations are i Minimum and maximum output limits for each time period;

[0161] Water Level The constraints are: , and Reservoirs are i Minimum and maximum water level limits for each time period;

[0162] The water balance constraint is: , and Reservoirs are i Period and i- 1 Period: Storage capacity at the end of the period; For the reservoir i The average inbound flow during the period, For the reservoir i Average outbound flow during the period; The duration of a single period;

[0163] Water level / flow range constraints: , and are the maximum variation constraints of water level and flow in adjacent time periods respectively.

[0164] The objective function is set to maximize the power generation during the scheduling period, and the formula is: , where T is the total number of time periods in the scheduling period, No. i The fitness of the algorithm is the objective function value, that is, the total power generation of the cascade reservoirs, and the decision variable is the water level process in each period, that is, the population individual of the algorithm.

[0165] Step 2: Generate N whale individuals through cubic chaos mapping using formula (4.15), that is, the initialization population of N individuals. Each individual represents the water level process of a cascade reservoir. Calculate the individual fitness F , evaluate the fitness of the initial population, record the individual optimal value and the global optimal value. Determine whether the water level process generated by initialization meets the constraints. If so, proceed to the next step; if not, correct the water level.

[0166] Step 3: Calculate the whale convergence factor , coefficient vector , , adaptive threshold , adaptive weight And random probability . judge Is it true? If so, proceed to the next step; if not, according to the spiral predation update mechanism, combined with the adaptive weight Value, use formula (4.17) to update the individual position.

[0167] Step 4: Determine the coefficient vector Is it true? If true, enter the shrinking and encircling stage and calculate the differential mutation operator , effectively increasing the diversity of the original population, and calculating the distance vector D according to formula (4.4), taking , update the individual position according to formula (4.24); if it does not hold, proceed to the next step.

[0168] Step 5: Generate random numbers When performing random search, the individuals generated in the random search stage cannot be guaranteed to be excellent individuals. The black kite migration mechanism can make the randomly generated individuals move towards better individuals, improving the algorithm's optimization performance. At the same time, the migration probability is introduced , balancing the algorithm's optimization and random search capabilities. Is it true? If so, the black kite migration mechanism is used to update the individual position according to formula (4.22); if not, the whale's random search mechanism is used to update the individual position according to the calculated adaptive weight And formula (4.21) to update individual positions.

[0169] Step6: After updating the individual positions according to Step3, Step4, and Step5, a new generation of individuals is obtained, the fitness values ​​of the new individuals are calculated, and the individual optimal positions and the global optimal positions are updated.

[0170] Step 7: Determine whether the maximum number of iterations has been reached If it is not reached, increase the number of iterations and return to Step 3 to iterate again; if the maximum number of iterations is reached , then the global optimal position is determined and the global optimal solution is output as the solution for optimal operation of cascade reservoirs.

[0171] Specifically, the Xiluodu, Xiangjiaba, Three Gorges and Gezhouba reservoirs were selected as case study objects, 2018, 2017 and 2021 were selected as three typical years of wet and dry seasons, the whole year was used as the scheduling period, and the ten days were used as the scheduling period. A total of 36 scheduling periods were divided, and the maximum power generation of cascade hydropower stations was used as the objective function. An optimal scheduling model for cascade reservoirs was established, and the whale algorithm based on migration differential mutation (BDWOA algorithm) was used for solution calculation. Then, four algorithms, including the whale algorithm (WOA), particle swarm algorithm (PSO), improved migration mechanism whale algorithm (BWOA), and improved cubic chaos particle swarm algorithm (CPSO), were used as comparison models. The above models were independently run 30 times for solution, and the solution results were statistically analyzed to verify the optimization ability of the migration differential mutation whale algorithm provided by the present invention in solving the optimal scheduling model of cascade reservoirs.

[0172] Set algorithm parameters for the model. In the above five algorithms, in order to unify the comparison results, the population size is set , individual dimension , maximum number of iterations In the migration differential mutation whale algorithm, the spiral update coefficient b=10, the migration probability , chaos coefficient ; In the migration mechanism whale algorithm, , the rest of the parameters are the same as those of the migration differential mutation whale algorithm; in the whale algorithm, the parameter settings are the same as those of the migration differential mutation whale algorithm; in the particle swarm algorithm, the constant ; In the chaotic particle swarm algorithm, the chaos coefficient , and the other parameters are consistent with the particle swarm algorithm.

[0173] Analyze the solution results and use the average value, maximum value, and standard deviation to analyze the results of the model operation. The average value and maximum value can reflect the algorithm's optimization ability, and the standard deviation can reflect the stability of the algorithm's operation. An excellent algorithm should have the characteristics of fast convergence and finding a better solution;

[0174] .

[0175] According to the dispatching results of the five algorithms in Table 1, the following conclusions can be drawn: The migration differential mutation whale algorithm shows significant advantages in reservoir dispatching problems for different hydrological years. Specifically, in the calculation of 2018 (flood year), the migration differential mutation whale algorithm improved the average power generation and maximum power generation results by 5.2% and 2.1% respectively compared with the whale algorithm; in the calculation of 2017 (normal water year), the migration differential mutation whale algorithm improved the average power generation and maximum power generation results by 3.8% and 0.8% respectively compared with the whale algorithm; in the calculation of 2021 (dry year), the migration differential mutation whale algorithm improved the average power generation and maximum power generation results by 8.5% and 0.9% respectively compared with the whale algorithm. The average power generation and maximum power generation of the migration differential mutation whale algorithm are higher than those of the other four algorithms, indicating that its optimization ability is better than the unimproved whale algorithm and several other algorithms. In addition, the standard deviation of power generation of the migration differential mutation whale algorithm is the smallest, indicating that the results during the algorithm operation have good stability and reference value.

[0176] Further observation Figure 3 , Figure 4 and Figure 5 From the convergence process shown, it can be intuitively found that the migration differential mutation whale algorithm can converge to the optimal solution at a faster speed in typical years of wet and dry seasons. This feature not only reflects its efficient optimization mechanism, but also lays a solid foundation for its practical application in complex reservoir scheduling problems.

[0177] In summary, the convergence speed, optimization effect and stability of the migration differential mutation whale algorithm are higher than those of the other four algorithms. It shows significant advantages in solving the reservoir optimization scheduling model, has good optimization results, and provides an efficient method for solving the scheduling plan.

[0178] The purpose of this invention is to propose a reservoir optimization scheduling method based on the migration differential mutation whale algorithm (BDWOA) to more efficiently solve the problem of solving the reservoir optimization scheduling model. This invention systematically improves the whale optimization algorithm by deeply integrating the migration mechanism of the black-winged warbler algorithm and the unique advantages of differential mutation, aiming to enhance the algorithm's exploration and development capabilities, and then build a more efficient and robust swarm intelligence optimization algorithm in the field of reservoir optimization scheduling.

[0179] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A reservoir group optimization scheduling method based on improved whale algorithm, characterized in that: include: S1, establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include flow constraints, output constraints, water level constraints, water balance constraints, water level fluctuation constraints, and flow fluctuation constraints of each reservoir in the reservoir group; S2, using the improved whale algorithm to solve the reservoir group optimization scheduling model and obtain the optimal scheduling plan; Among them, S2 specifically includes: S21, set the algorithm parameters, including population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of individuals in the population is the value of the objective function. The decision variable of the individual is the water level process of the reservoir group. The decision variable satisfies the constraints in S1. S22, introduce adaptive probability threshold p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p 1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm. S23, judging whether the maximum number of iterations has been reached, if not, increasing the number of iterations and returning to S22, if reached, outputting the global optimal solution as the optimal reservoir group optimization dispatching plan; In S22, the population is optimized and updated according to the encirclement predation method or random search method in the whale algorithm, including: Further determine the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm. If not, the population is optimized and updated according to the random search method in the whale algorithm, where: ； ； Where 𝑟 is a random vector in [0, 1], is the convergence factor, It decreases linearly from 2 to 0 during the iteration. m is the current iteration number, is the maximum number of iterations; Further determine the coefficient vector Is it true? If so, the population is optimized and updated according to the encirclement and predation method in the whale algorithm, including: The differential evolution algorithm is used to improve the original encirclement and predation method in the whale algorithm, and the improved encirclement and predation method is used to optimize and update the population; The improved encirclement and predation method is used to optimize and update the population as follows: ； ； ； ； in, Indicates the current m The population individual vector at the iteration, Indicates The population individual vector at the iteration, is the current optimal solution position, D is the bracketing step length, is the mutation difference vector, is the coefficient, is the mutation operator used to control the degree of disturbance, Get a random number between [0, 2], and The current m The random individuals 1 and 2 generated in the iterations are: The difference vector generated for the current random individual; Further determine the coefficient vector Is it true? If not, the population is updated and optimized according to the random search method in the whale algorithm, including: Set the migration probability between (0, 1) to further determine the random number rand and the size of the migration probability, rand Represents a random number between (0, 1); exist rand When it is greater than the migration probability, an adaptive weight is introduced ω , ω As the number of iterations increases, the nonlinearity decreases. The original random search method in the whale algorithm is weighted according to the adaptive weight, and the weighted random search method is used to optimize and update the population. exist rand When it is less than or equal to the migration probability, the black kite optimization algorithm is introduced, and the black kite migration method is used to optimize and update the population.

2. The reservoir group optimization scheduling method based on the improved whale algorithm according to claim 1 is characterized in that: Initializing the population in S21 specifically includes: The cubic chaotic array is generated according to the cubic chaotic mapping method, and the scale of the cubic chaotic array is consistent with the scale of the population; The individual values ​​in the cubic chaotic array are mapped to the value space of the decision variables to obtain the initial population.

3. The reservoir group optimization scheduling method based on the improved whale algorithm according to claim 1 is characterized in that: Adaptive probability threshold in S22 p 1 Specifically: ； in, m is the current iteration number, is the maximum number of iterations.

4. The reservoir group optimization scheduling method based on the improved whale algorithm according to claim 1 is characterized in that: The weighted random search method is used to optimize and update the population as follows: ； ； ； ； in, Indicates The population individual vector at the iteration, is current m The individuals randomly selected in the iterations are is the random search step size, and represents the weights at the beginning and end of the iteration, k is the control factor used to control the shape of the curve. is the coefficient, Indicates the current m The population individual vector at the iteration, is the migration probability; The specific optimization and update of the population by black-winged kite migration is as follows: ； in, Represents the current m The population individual vector at the iteration, represents the current optimal position, Represents random numbers from a Cauchy distribution.

5. The reservoir group optimization scheduling method based on the improved whale algorithm according to any one of claims 1 to 3, characterized in that: In S22, the population is updated and optimized according to the spiral movement method in the whale algorithm, including: Introducing adaptive weights ω , ω As the number of iterations increases, the nonlinearity decreases. The original spiral movement method in the whale algorithm is weighted according to the adaptive weight, and the weighted spiral movement method is used to update and optimize the population.

6. The reservoir group optimization scheduling method based on the improved whale algorithm according to claim 5 is characterized in that: The weighted spiral movement method is used to update and optimize the population as follows: ； ； ； in, Indicates The population individual vector at the iteration, is the current optimal solution position, Represents the current m The population individual vector at the iteration, is the maximum number of iterations, and represents the weights at the beginning and end of the iteration, k is the control factor used to control the shape of the curve. is the distance between the current individual and the optimal individual, is a constant used to define the shape of the logarithmic spiral, is a random number in [-1, 1].

7. A reservoir group optimization dispatching system based on improved whale algorithm, characterized in that: The reservoir group optimization scheduling method based on the improved whale algorithm for implementing any one of claims 1 to 6 above comprises: The model building module is used to establish a reservoir group optimization scheduling model, where the objective function of the model is to maximize the total power generation of the reservoir group during the scheduling period, and the constraints include the flow constraint, output constraint, water level constraint, water balance constraint, water level amplitude constraint and flow amplitude constraint of each reservoir in the reservoir group; Model solving module, used to solve the reservoir group optimization dispatching model using improved whale algorithm to obtain the optimal dispatching plan; The model solving module specifically includes: The initialization module is used to set the algorithm parameters, including the population size, individual dimension and maximum number of iterations, and initialize the population. The fitness of the individuals in the population is the value of the objective function, and the decision variables of the individuals are the water level process of the reservoir group. The decision variables meet the above constraints. Optimization module for introducing adaptive probability thresholds p 1 and random probability p , p 1 is a quantity between [0, 1] related to the number of iterations. As the number of iterations increases p 1 gradually decreases, p is a random number between [0, 1], judge p ≤ p 1. Is it true? If so, the population is optimized and updated according to the encirclement and predation method or random search method in the whale algorithm. If not, the population is optimized and updated according to the spiral movement method in the whale algorithm. The output module is used to determine whether the maximum number of iterations has been reached. If not, the number of iterations is increased and returned to the optimization module. If reached, the global optimal solution is output as the optimal reservoir group optimization scheduling plan.

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