Intelligent reservoir scheduling method based on HHO and MPA double optimization driving

Abstract

The application belongs to the technical field of reservoir dispatching, and specifically discloses a reservoir intelligent dispatching method based on HHO and MPA double optimization driving, which comprises the following steps: establishing a target function with the maximization of total power generation of cascade reservoir groups as an optimization target; setting constraint conditions of the target function, including equation constraints and inequality constraints meeting reservoir operation; solving the target function based on an improved predation strategy optimization algorithm to obtain the operation water level of each reservoir in the cascade reservoir group at different time points within a dispatching period; wherein the improved predation strategy optimization algorithm is realized by introducing the following operation in the search strategy selection stage of the HHO algorithm: based on the escape energy, the global exploration of the MPA algorithm and the local development of the HHO algorithm are adaptively switched. The application effectively makes up for the imbalance problem of the exploration and development process of the HHO algorithm in the joint optimization and dispatching application of the cascade reservoir group, not only realizes the effective balance of global search and local development, but also has strong robustness.

Description

Technical Field

[0001] This application belongs to the field of reservoir scheduling technology, and more specifically, relates to a reservoir intelligent scheduling method based on dual optimization driven by HHO and MPA. Background Technology

[0002] As the core facility of water conservancy projects, the scientific scheduling of reservoirs is not only related to the realization of basic functions such as flood control, irrigation, and water supply, but also directly affects the efficient allocation of water resources and the realization of comprehensive benefits. Especially in cascade reservoir systems, due to the dynamic correlation of hydrological elements and the intricate constraints, their optimal scheduling exhibits significant characteristics such as high-dimensional decision space, nonlinearity, and strong coupling constraints, constituting a highly challenging large-scale, multi-stage optimization problem.

[0003] Classic intelligent algorithms such as particle swarm optimization, ant colony optimization, and gray wolf optimization have been widely used in reservoir management, but technical bottlenecks still exist in terms of solution accuracy, convergence speed, and local optimum avoidance. In particular, as the number of cascade reservoirs increases, the spatiotemporal coupling effect intensifies, and the magnitude and dimensions of multiple constraints differ significantly, which places higher demands on the performance of optimization algorithms.

[0004] CN119168300A discloses a method and apparatus for ecological scheduling of cascade reservoirs based on chaotic enhanced HHO (Hybrid Homing Occurrence). By introducing a chaotic strategy into HHO, it effectively overcomes the problems of reduced individual diversity and low convergence accuracy in solving cascade reservoir ecological problems presented by the original HHO algorithm, increasing the diversity of individual generation and improving the algorithm's convergence accuracy. However, the problem of imbalance in the exploration and development of the HHO algorithm remains unresolved. Summary of the Invention

[0005] To address the aforementioned shortcomings of existing technologies, this application provides a reservoir intelligent scheduling method based on dual optimization driven by HHO and MPA, aiming to solve the problem of imbalance in the exploration and development process of traditional HHO algorithms in reservoir scheduling.

[0006] Firstly, this application provides a reservoir intelligent scheduling method based on dual optimization driven by HHO and MPA, including:

[0007] An objective function is established with the goal of maximizing the total power generation of the cascade reservoir group.

[0008] Set the constraints for the objective function, including equality constraints and inequality constraints that satisfy the reservoir operation requirements;

[0009] The objective function is solved based on the improved predation strategy optimization algorithm, and the operating water level of each reservoir in the cascade reservoir group at different times during the scheduling period is obtained.

[0010] The improved predator strategy optimization algorithm is achieved by introducing the following operations into the search strategy selection phase of the HHO algorithm: global exploration based on escape energy adaptive switching MPA algorithm and local development of HHO algorithm.

[0011] Secondly, this application also provides a reservoir intelligent scheduling device based on dual optimization driven by HHO and MPA, comprising:

[0012] The objective function establishment module is used to establish an objective function with the optimization objective of maximizing the total power generation of the cascade reservoir group.

[0013] The constraint setting module is used to set the constraints of the objective function, including equality constraints and inequality constraints that satisfy the reservoir operation.

[0014] The solution module is used to solve the objective function based on the improved predation strategy optimization algorithm and obtain the operating water level of each reservoir in the cascade reservoir group at different times during the scheduling period;

[0015] The improved predator strategy optimization algorithm is achieved by introducing the following operations into the search strategy selection phase of the HHO algorithm: global exploration based on escape energy adaptive switching MPA algorithm and local development of HHO algorithm.

[0016] Thirdly, this application also provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0017] Fourthly, this application also provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0018] Fifthly, this application also provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0019] The intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in this application effectively compensates for the imbalance between the exploration and development processes of the HHO algorithm in the joint optimization scheduling application of cascade reservoir groups by introducing the operation of global exploration of the MPA algorithm and local development of the HHO algorithm based on escape energy adaptive switching in the search strategy selection stage of the HHO algorithm. It not only achieves an effective balance between global search and local development, but also has strong robustness. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in this application or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is one of the flowcharts of the intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in the embodiments of this application;

[0022] Figure 2 This is the second flowchart of the intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in the embodiments of this application;

[0023] Figure 3 This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application at a 25% inflow frequency.

[0024] Figure 4 This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application at a 50% inflow frequency.

[0025] Figure 5 This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application at a 75% inflow frequency.

[0026] Figure 6 This is a schematic diagram of the maximum total power generation convergence process of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application at a 25% inflow frequency;

[0027] Figure 7 This is a schematic diagram of the maximum total power generation convergence process of the reservoir intelligent scheduling method based on HHO and MPA dual optimization drive provided in the embodiments of this application at a 50% inflow frequency.

[0028] Figure 8 This is a schematic diagram of the maximum total power generation convergence process of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application at a 75% inflow frequency;

[0029] Figure 9 This is a schematic diagram of the structure of the intelligent reservoir scheduling device based on dual optimization drive of HHO and MPA provided in the embodiments of this application;

[0030] Figure 10This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0032] First, the technical terms used in the embodiments of this application will be explained in both Chinese and English.

[0033] HHO: Harris Hawks Optimization;

[0034] MPA: Marine Predators Algorithm;

[0035] HHONMPA: A dual-optimization driven algorithm based on HHO and MPA;

[0036] DBO: Dung Beetle Optimizer, a noise beetle optimization algorithm;

[0037] PSO: Particle Swarm Optimization.

[0038] PWLCM: Piecewise Linear Chaotic Map;

[0039] SPM: A new chaotic map that combines the Sine chaotic map and the PWLCM chaotic map.

[0040] The technical solutions provided in the embodiments of this application will be described below with reference to the accompanying drawings.

[0041] Figure 1 This is one of the flowcharts illustrating the intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in this application embodiment, such as... Figure 1 As shown, the method includes at least the following steps (Step):

[0042] S101. Establish an objective function with the goal of maximizing the total power generation of the cascade reservoir group.

[0043] Specifically, a model is constructed for the long-term optimal power generation scheduling problem of a cascade reservoir group. The solution to this problem can be represented by a state variable matrix consisting of the final operating water levels of each reservoir within the cascade reservoir group during different scheduling cycles within the scheduling period, as follows:

[0044] ;

[0045] in, This indicates the number of reservoirs in a cascade reservoir group; Indicates the first i The vector formed by the operating water levels at the end of all scheduling cycles of the reservoir. Indicates the first i The reservoir is in t The operating water level at the end of each scheduling cycle or at time [time missing] t The operating water level. Therefore, a system containing... The number of reservoirs and the number of scheduling cycles are: The dimensions of the long-term power generation optimization scheduling problem of a cascade reservoir group are: = .

[0046] The optimization objective of the long-term power generation optimization scheduling problem of a cascade reservoir group is to maximize the total power generation of the cascade reservoir group. Specifically, the objective function can be constructed as follows:

[0047] ;

[0048] in, This represents the total power generation of the cascade reservoir group. This indicates the number of reservoirs in a cascade reservoir group. Indicates the number of scheduling cycles. This represents the power output of the i-th reservoir during the t-th scheduling cycle. This indicates the time interval of the scheduling cycle. Specifically, satisfy:

[0049] ;

[0050] in, This represents the output coefficient of the i-th reservoir. This represents the head of the i-th reservoir during the t-th scheduling cycle. This represents the power generation flow of the i-th reservoir during the t-th scheduling cycle.

[0051] S102. Set the constraints for the objective function, including equality constraints and inequality constraints that satisfy the reservoir operation.

[0052] Specifically, while pursuing maximum power generation, the operation and scheduling of cascade reservoir groups also need to consider setting various equality and inequality constraints to satisfy reservoir operation. Taking into account the law of conservation of energy mass, safe operation rules, and ecological scheduling strategies, the specific constraints include:

[0053] ① Water balance constraint, satisfying:

[0054] ;

[0055] Among them, V i，t+1 V represents the storage capacity of the i-th reservoir at time t+1. i，t Let I represent the storage capacity of the i-th reservoir during the t-th scheduling cycle. i，t R i，t and q i，t U represents the inflow, outflow, and interval flow of the i-th reservoir during the t-th scheduling cycle. i R represents the number of upstream reservoirs directly hydraulically connected to the i-th reservoir. j，t This represents the inflow interval of the j-th upstream reservoir that is directly hydraulically connected to the i-th reservoir during the t-th scheduling cycle.

[0056] ② Head constraint, satisfying:

[0057] ;

[0058] in, This represents the head of the i-th reservoir during the t-th scheduling cycle. and Let these represent the upstream water level and the downstream water level of the i-th reservoir during the t-th scheduling cycle, respectively. This represents the water level in front of the dam of the i-th reservoir during the time period t-1.

[0059] ③ Water level constraint, satisfying:

[0060] ;

[0061] in, and Let represent the lowest and highest water levels of the i-th reservoir during the t-th scheduling cycle, respectively.

[0062] ④ Reservoir discharge constraints, satisfying:

[0063] ;

[0064] in, and Let represent the minimum and maximum discharge flows of the i-th reservoir during the t-th scheduling cycle, respectively.

[0065] ⑤ Water level fluctuation constraint, satisfying:

[0066] ;

[0067] in, This represents the maximum threshold value of the water level difference of the i-th reservoir during the scheduling cycle.

[0068] ⑥ Output constraints, satisfying:

[0069] ;

[0070] in, This represents the power output of the i-th reservoir during the t-th scheduling cycle. and Let represent the minimum and maximum output of the i-th reservoir during the t-th scheduling cycle, respectively.

[0071] ⑦ Ensure output constraints satisfy:

[0072] ;

[0073] in, This represents the guaranteed output of the i-th reservoir during the t-th scheduling cycle.

[0074] ⑧ Initial and final water level constraints, satisfying:

[0075] ;

[0076] in, and Let represent the initial water level and the final water level of the i-th reservoir during the overall scheduling period, respectively.

[0077] ⑨ Non-negativity constraint

[0078] All of the above variables are non-negative.

[0079] As can be seen, the long-term power generation optimization scheduling problem of a cascade reservoir group is a very complex constrained optimization problem, and constraint handling strategies must be used in the application of optimization algorithms. Specifically, ε-constraint methods, penalty function methods, etc., can be selected.

[0080] The ε-constraint method works as follows: An ε value is set, and when an individual's violation degree is less than ε, it is considered a feasible solution; otherwise, it is considered an infeasible solution. Compared to the penalty function method, the ε-constraint method does not require any penalty factor or additional parameters, making it more advantageous in solving problems with complex constraints. Furthermore, it considers the information carried by infeasible solutions, which is more beneficial for finding the optimal solution to the objective function.

[0081] In the process of handling ε-constraints, for inequality constraints, the constrained optimization problem is transformed into an unconstrained optimization problem. The inequality constraints mainly include water level constraints, reservoir discharge constraints, and power output constraints, which are transformed into:

[0082] .

[0083] For equality constraints: transform equality constraints into inequality constraints, and then transform inequality constraints into an unconstrained problem. Equality constraints mainly include initial and final water level / reservoir capacity constraints and water balance constraints, which are transformed into:

[0084] .

[0085] The constraint violation function is as follows:

[0086] .

[0087] If an individual that violates the constraints still fails to meet the constraints after processing, a penalty function is applied, causing the individual to be eliminated.

[0088] S103. Solve the objective function based on the improved predation strategy optimization algorithm to obtain the operating water level of each reservoir in the cascade reservoir group at different times during the scheduling period.

[0089] The improved predator strategy optimization algorithm is achieved by introducing the following operations into the search strategy selection phase of the HHO algorithm: global exploration based on escape energy adaptive switching MPA algorithm and local development of HHO algorithm.

[0090] Specifically, the optimization process of the HHO algorithm includes three stages: global exploration, the transition from global exploration to local development, and local development. It has advantages such as fewer parameters to be tuned, simple implementation, and strong local search capabilities. The HHO algorithm performs well in the development stage by using different encirclement strategies for local development, but its efficiency is not high for complex optimization problems in the exploration stage, and it is prone to premature convergence. Therefore, this application's embodiments consider introducing the MPA algorithm to improve the update method of the HHO algorithm in the exploration stage, avoiding getting trapped in local optima during the exploration phase.

[0091] The reservoir intelligent scheduling method based on HHO and MPA dual optimization driving provided in this application proposes an intelligent optimization algorithm based on HHO and MPA dual optimization driving, and applies it to the long-term power generation optimization scheduling problem of cascade reservoir groups.

[0092] Figure 2 This is the second flowchart illustrating the intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in this application embodiment. Figure 2 As shown, the specific process of solving the objective function based on the improved predator strategy optimization algorithm in S103 is as follows:

[0093] Step a: Initialize the population in the search space based on the improved chaotic mapping strategy.

[0094] Specifically, an improved chaotic strategy is used to generate an initial population in the search space corresponding to the population, wherein the initial population is... The real-valued matrix, The dimension of the problem to be solved is denoted by , and N represents the number of individuals in the population. The problem to be solved is to optimize the power generation scheduling scheme of a cascade reservoir group. The individuals in the initial population correspond to the decision variables in the power generation optimization scheduling scheme of the cascade reservoirs, that is, the decision variables in solving the objective function. The dimension corresponds to the value of the decision variable. This decision variable can be any one of the following: the water level of the reservoir at a certain time period, the operating water level of the power station at a certain time period, or the outflow of the power station at a certain time period.

[0095] In some embodiments, step a specifically includes:

[0096] In the search space, N individual positions are randomly generated by combining the Sine chaotic map and the PWLCM chaotic map, and these N individual positions are determined as the initial population.

[0097] Specifically, the improved chaos strategy is the SPM chaotic map generated by combining the Sine chaotic map and the PWLCM chaotic map.

[0098] The Sine chaotic map is characterized by its simple expression, ease of implementation, and high computational efficiency. It can generate sequences with good chaotic properties. The Sine chaotic map function is as follows:

[0099] ;

[0100] in, and Let x be the iterative sequence value, x∈(0,1), and a be the control parameter.

[0101] The PWLCM chaotic map is composed of piecewise linear functions. It is simple, efficient, structurally simple, easy to implement, and has good chaotic properties. The PWLCM chaotic map function is as follows:

[0102] ;

[0103] in, and Let x be the iterative sequence value, x∈(0,1), and P∈(0,1) be the control parameter.

[0104] The Sine map exhibits a relatively small chaotic range, while the PWLCM chaotic map demonstrates good traversal. Therefore, a new chaotic map—the SPM chaotic map—is designed to complement the Sine and PWLCM chaotic maps, and the population is initialized accordingly. N individual positions are randomly generated in the search space using a combination of the Sine and PWLCM chaotic maps. For any given individual position, the SPM chaotic map represents the following:

[0105] ;

[0106] in, and For iterative individuals, ∈(0,1) is a control parameter. When r∈(0,1), the system is in a chaotic state, and r∈(0,1) is a random number.

[0107] Step b: Introduce an elite reverse learning strategy to optimize the initial population.

[0108] Specifically, backward learning refers to simultaneously considering the current solution and backward solutions in the search space to increase the probability of discovering a better solution. Elite individuals refer to the individuals with the highest fitness in the current population (usually set as the top k%), who carry superior search direction information. The elite backward learning strategy uses the distribution information of elite individuals to dynamically generate backward solutions, rather than a fixed interval, so that the backward solutions are closer to the potential optimal region.

[0109] In some embodiments, step b specifically includes:

[0110] By using elite individuals in the population to generate reverse individuals, a reverse population can be constructed.

[0111] The initial population is expanded using a reverse population.

[0112] Specifically, for individuals whose fitness of the original solution is greater than that of the reverse solution, performing a reverse search on them is a waste of search time, and their original domain search should be strengthened; while for individuals whose fitness of the original solution is less than that of the reverse solution, performing a reverse search on them is more valuable than developing their original domain.

[0113] To address this, an elite strategy is introduced. This strategy leverages the fact that elite individuals contain more valuable information than ordinary individuals. It generates reverse individuals from the current population's elite individuals, thus constructing a reverse population to increase population diversity. The optimal individual is then selected from the new population formed by the current and reverse populations to serve as the next generation's elite for reverse learning, guiding the search process towards the optimal solution. For any given individual position, the specific manifestation is as follows:

[0114] ;

[0115] in, It is a reverse individual generated based on a reverse strategy. k It is a random number between 0 and 1. L and U These are the minimum and maximum values ​​of the current search region, respectively. For the current individual. The basic meaning of the above formula is: taking the current individual as an example. Centered on the population, and combining the distribution range [L, U] of elite individuals in the current population with the proportionality coefficient k, reverse individuals are generated. .

[0116] Step c: Update the individual's location based on its fitness.

[0117] Specifically, the individual's position is updated based on the relationship between the individual's fitness in the current fitness iteration and the individual's fitness in the next fitness iteration.

[0118] In some embodiments, step c specifically includes:

[0119] If the fitness of the original individual is greater than that of the reverse individual, then update the individual's position to the reverse individual's position;

[0120] If the fitness of the original individual is less than that of the reversed individual, then the original individual's position is retained.

[0121] Specifically, for any individual: Assume the first The position of the first individual, based on the fitness of that individual, is used to determine the position of the second individual. The method for updating the position of an individual is expressed as follows:

[0122] ;

[0123] in, and The fitness of the original individual and the reversed individual are respectively. The optimal individual selected during the optimization process.

[0124] In some embodiments, the fitness function The optimization objectives can be set based on the long-term power generation optimization scheduling problem of cascade reservoir groups.

[0125] Step d: Update the global optimal individual position and the historical extreme value individual position based on individual fitness.

[0126] Specifically, the globally optimal individual position is the position of the individual with the lowest fitness among all individuals during the current population iteration. For any individual, the historical extreme individual position is the position of the individual with the lowest fitness obtained by that individual during evolution. The globally optimal individual position is updated based on the individual position corresponding to the lowest fitness among all individuals. The historical extreme individual position is updated based on the individual position with the lowest fitness obtained during the individual's fitness iteration.

[0127] Specifically, the position of the individual with the lowest fitness among all individuals is taken as the globally optimal individual position, and the position of the individual with the lowest fitness obtained in the individual evolution process (i.e., the fitness iteration process) is taken as the historical extreme value individual position, as expressed in the following way:

[0128] ;

[0129] in, For the first The position of the globally optimal individual in the current population during each fitness iteration. For the first During the first fitness iteration, the... The historical extreme value location corresponding to each individual. For the first During the first fitness iteration, the... The fitness of an individual.

[0130] Step e: Global exploration of the MPA algorithm based on escape energy adaptive switching and local development of the HHO algorithm.

[0131] Specifically, different search strategies are selected based on escape energy to update the location of each individual.

[0132] The HHO algorithm divides the hunting process of the Harris Eagle into exploratory and exploitative behaviors based on its hunting habits, initially assigning a starting energy value. As the number of iterations increases, the prey's energy gradually decreases during its escape. Therefore, the prey escape energy is used to dynamically select between exploratory and exploitative hunting behaviors. The mathematical expression for the prey escape energy is as follows:

[0133] ;

[0134] in, For the escape energy of the prey, K represents the initial escape energy of the prey, K represents the maximum number of iterations for the population, and k represents the current number of iterations.

[0135] The improved predation strategy optimization algorithm draws inspiration from the cooperative hunting behavior of the Harris Eagle, dividing the optimization process into two key stages: global search and local exploitation. Breaking through the limitations of the traditional HHO framework, it introduces an innovative nonlinear energy decay model, enabling the algorithm to exhibit greater adaptability when exploring the solution space. As the iteration progresses, the escape energy of an individual decreases according to a specific pattern, and the algorithm intelligently switches its search strategy accordingly—performing wide-area exploration in high-energy states and precise localization in low-energy states. This dynamic equilibrium mechanism is represented by the following mathematical expression:

[0136] ;

[0137] in, For the escape energy of the prey, K represents the initial escape energy of the prey, K represents the maximum number of iterations for the population, and k represents the current number of iterations.

[0138] In some embodiments, the objective function is solved using an improved predation strategy optimization algorithm based on adaptive switching of escape energy, including:

[0139] When the absolute value of the escape energy is greater than or equal to 1, the dual-species cooperative MPA multi-strategy exploration mechanism is executed, and the improved MPA Brownian motion and Lévy flight are used for global search.

[0140] When the absolute value of the escape energy is less than 1, the improved HHO adaptive trapping strategy and adaptive jump strategy are executed, and different trapping strategies of the improved HHO are used for local search.

[0141] Specifically, when the escape energy is high (absolute value ≥ 1), the exploration phase begins, and a dual-species cooperative MPA multi-strategy exploration mechanism is implemented. The improved MPA Brownian motion and Levy flight are used for global search, and the individual global exploration strategy is implemented to update the position.

[0142] When the escape energy is low (absolute value < 1), the development phase begins, and the adaptive containment strategy and adaptive jump strategy of HHO are executed. Different containment strategies of improved HHO are adopted: soft containment, hard containment, gradual rapid dive and gradual circling containment. Four strategies are used to achieve local search, and the individual local development strategy is executed to update the position.

[0143] In some embodiments, when the absolute value of the escape energy is greater than or equal to 1, a dual-species cooperative multi-strategy exploration mechanism is implemented, employing Brownian motion and Lévy flight with improved MPA for global search, and updating the position using individual global exploration strategies, including:

[0144] For any individual in the two populations, if the individual is in the first half of the population and the current iteration count is less than one-third of the total iteration count, the main population will guide the execution of the MPA Brownian motion strategy to conduct a global exploration.

[0145] Unlike the original MPA algorithm, the location of the tracked individual It can be represented by a vector, as follows:

[0146] ;

[0147] in, Let be the position of the i-th tracked individual in the j-th dimension, and d be the dimension of the search space. The individual with the optimal fitness value is called the apex predator, as follows:

[0148] ;

[0149] in, X This is the current optimal individual vector, whose position vector guides other individuals in the population, promoting the algorithm to converge to the optimal solution.

[0150] The MPA Brownian motion strategy, guided by the main population, performs global exploration, as specifically expressed below:

[0151] ;

[0152] in, This represents the maximum time step of the algorithm iteration. n The total population. For the search step size, Let be a vector of random numbers following a Lévy distribution, used to represent Brownian motion. This is the term-by-term multiplication operator, where R is a random number between [0, 1] and P is a constant with a value of 0.5.

[0153] If the current iteration count is greater than or equal to one-third of the total iteration count, the improved MPA Lévy flight strategy is executed collaboratively by the two populations. This strategy integrates nonlinear inertial weights and adaptive crossover mutation operators to achieve dynamic information exchange between the master and slave populations. The mathematical model for this stage is described as follows:

[0154] ;

[0155] in, This represents the maximum time step of the algorithm iteration. n The total population. For the search step size, A vector of random numbers based on the Lévy distribution. For each term, CF is the adaptive parameter controlling the individual's step size—the nonlinear inertia weight parameter factor. The exponent Tp=2t is the parameter controlling the decay rate. P is a constant with a value of 0.5.

[0156] When an individual is in the latter half of the population, if the random number is greater than or equal to 0.5, the search is based on the population's random position; if the random number is less than 0.5, the search is based on the population's average position to update the individual's position. These two strategies utilize current position information and randomly selected individual position information, respectively. By combining these two strategies, the improved algorithm can extensively explore the search space to find potential optimal solutions. Its mathematical expression is as follows:

[0157] ;

[0158] ;

[0159] in, For individuals in the first The position vector in the next iteration. Let r1, r2, r3, r4, and q be the position vector of an individual randomly selected from the k-th iteration, and let r1, r2, r3, r4, and q be different random numbers uniformly distributed in the interval [0, 1]. Let be the position vector of the individual being tracked in the k-th iteration. Let N be the average position vector of the population in the k-th iteration, where N represents the number of individuals in the population.

[0160] When the escape energy is low (absolute value < 1), an individual exploitation strategy is implemented to update the individual's position, achieving localized precise search through adaptive encirclement and adaptive jump strategies. The selection of the individual exploitation strategy depends on the prey escape probability p, which is a random number between 0 and 1.

[0161] When p ≥ 0.5, the individual executes an adaptive containment strategy. Even though the individual may attempt to escape the current search area through random jumps, the algorithm triggers this adaptive containment strategy to constrain its behavior. This mechanism dynamically adjusts the search radius, gradually shrinking the target individual's activity space to form a progressive containment situation. As the containment area shrinks more precisely, the algorithm can more efficiently pinpoint the region containing the potential optimal solution. The mathematical expression is as follows:

[0162] ;

[0163] Where λ is a uniformly distributed random number in the interval [0.5, 1]. β(E) is the difference between the position of the individual with minimum fitness and the position of every individual in the current population, β(E) is an adaptive parameter that is adjusted as the escape energy E changes, and p is the escape probability of prey randomly generated in the interval [0,1].

[0164] When p < 0.5, the individual implements an adaptive jump strategy, enabling it to explore the search space more flexibly. This mechanism, by combining Lévy flight characteristics with the current escape energy level, provides the individual with multi-scale jump capabilities. As the search progresses, the jump behavior automatically adjusts its intensity and direction based on the energy parameters. Initially, it tends to explore a wide range to avoid getting trapped in local optima, while later it gradually shifts to a finer search to improve convergence accuracy, ensuring the quality of the optimal solution. Its mathematical expression is as follows:

[0165] ;

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] Where Y and Z are the temporary individual positions corresponding to the i-th individual position during the k-th fitness iteration, respectively. Let Y be the fitness of the temporary individual position Y corresponding to the i-th individual position during the k-th fitness iteration. Let u and v be the fitness of the temporary individual position Z corresponding to the k-th individual position during the k-th fitness iteration, where u and v are intervals. Uniformly distributed random numbers within the range. This is a constant term, which is taken as 1.5 in this embodiment. Let r be the gamma function and p be a randomly generated value in the interval [0,1]. The random numbers are generated by the Lévy distribution, γ is the intensity coefficient controlling the approach to the prey, S is the random jump vector, and the parameters δ and θ control the weight range and rate of change. In this embodiment, δ=1.5 and θ=2.

[0173] In some embodiments, the FADs mechanism of adaptive MPA is introduced to enhance search efficiency. By adaptively controlling parameters, the exploration and development capabilities of the algorithm are balanced, and an effective balance between global search and local fine search is achieved.

[0174] Step f: In each iteration, continuously iterate the individual fitness and update the individual position until the preset maximum number of iterations is reached, and obtain the latest global optimal individual position.

[0175] Specifically, the current iteration count is recorded and it is determined whether the maximum iteration count has been reached. If it has, the globally optimal individual position is output as the optimal power generation scheduling scheme for the cascade reservoirs. Otherwise, the process returns to the beginning and repeats the iteration calculation based on the fitness of each individual to update the position of each individual until the maximum iteration count is reached.

[0176] In some embodiments, before S102, the algorithm further includes: initializing key input parameters of the algorithm, specifically including initial escape energy, number of individuals in the population, maximum number of iterations K, maximum number of repeated runs of the algorithm, etc.

[0177] The reservoir intelligent scheduling method based on HHO and MPA dual optimization provided in this application first initializes the population in the search space through an improved SPM chaotic strategy and introduces an elite reverse learning strategy to improve population diversity. On this basis, the predation behavior of Harris eagles is integrated with the search mechanism of marine predators. The algorithm adaptively selects different search strategies based on escape energy and updates the position of each individual: in the global exploration phase, a dual-population collaborative MPA multi-strategy exploration mechanism is executed; in the local development phase, a fine search is performed through an improved HHO adaptive confinement strategy and an adaptive jump strategy; finally, when the fitness iteration count reaches the maximum iteration count, the updated global optimal individual position is obtained based on the updated position of each individual.

[0178] Furthermore, to verify the effectiveness of the above technical solution, four cascade reservoirs in a certain watershed were selected as case studies for analysis. To comprehensively iterate the performance of the Harris Eagle-Marine Predator hybrid algorithm (HHONMPA) in the optimal scheduling of cascade reservoir groups, based on historical runoff sequence data from 1999 to 2022, three typical hydrological years—2020 (high-water year), 2015 (normal-water year), and 2016 (dry-water year)—were selected as test scenarios to construct representative hydrological scenario combinations.

[0179] The experiment adopted an annual scheduling cycle, with ten-day periods as the basic time unit, totaling 36 scheduling periods. This time scale ensured both the granularity of the scheduling scheme and the need for computational efficiency. To scientifically verify the superiority of the HHONMPA algorithm, four mainstream optimization algorithms—HHO, MPA, DBO, and PSO—were selected as control groups. Regarding parameter configuration, each algorithm used a maximum of 1000 evaluation runs, a population size of 50, and dimensions corresponding to the 36 scheduling periods. Twenty independent runs were performed to ensure the reliability of the statistical results. Convergence criteria were set as either the change in the optimal value being less than 1E-6 over 50 consecutive generations or reaching the maximum number of evaluation runs.

[0180] Through systematic comparative analysis from multiple dimensions such as optimization results, convergence speed, solution stability and computational efficiency, experimental results show that the HHONMPA hybrid algorithm has significant advantages in terms of solution quality, convergence characteristics and computational efficiency, especially in dealing with optimization problems under complex constraints such as dry years.

[0181] Figure 3 This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application under a 25% inflow frequency. Figure 4This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application under a 50% inflow frequency. Figure 5 This is a schematic diagram of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application under a 75% inflow frequency. Figure 6 This is a schematic diagram illustrating the convergence process of the maximum total power generation of the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application under a 25% inflow frequency. Figure 7 This is a schematic diagram illustrating the convergence process of the maximum total power generation under a 50% inflow frequency using the reservoir intelligent scheduling method based on dual optimization driven by HHO and MPA, as provided in the embodiments of this application. Figure 8 This is a schematic diagram illustrating the convergence process of the maximum total power generation under a 75% inflow frequency for the reservoir intelligent scheduling method based on HHO and MPA dual optimization driven by embodiments of this application. Figures 3 to 8 The intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA provided in the embodiments of this application is analyzed, as shown in Table 1:

[0182] Table 1

[0183]

[0184] As shown in Table 1, compared with other control algorithms, the HHONMPA hybrid optimization algorithm proposed in this application demonstrates significant advantages in most evaluation metrics. Specifically, at a 25% water inflow frequency, the optimal values ​​obtained by the HHONMPA algorithm are improved by 0.9%, 1.15%, 6.97%, and 5.59% compared to HHO, MPA, DBO, and GWO, respectively, with standard deviations reduced by 88.5%, 89.7%, 90.3%, and 78.3%. Similar advantages are maintained at 50% and 75% water inflow frequencies.

[0185] It is worth noting that although the HHONMPA algorithm achieved good performance in various statistical indicators (including optimal value, median, mean, and worst value), the standard deviation increased slightly at a 75% water inflow frequency. This indicates that the algorithm discovered more potential optimal solutions in the search space, demonstrating its stronger exploration ability and solution diversity. Overall, the optimization results of the HHONMPA algorithm are significantly better than other control algorithms, exhibiting superior search performance.

[0186] To further verify the effectiveness and reliability of the HHONMPA algorithm, statistical analysis was performed on 20 independent runs of the five algorithms under different water inflow frequencies. The results show that, under all water inflow frequencies, HHONMPA consistently finds a higher quality and more stable solution compared to other mature optimization algorithms, a conclusion that is highly consistent with the statistical results in Table 1.

[0187] From the perspective of convergence performance, the DBO algorithm performs poorly at a 25% inflow frequency, and only moderately at 50% and 75% inflow frequencies. The HHO and MPA algorithms exhibit moderate performance across all three inflow frequencies. In contrast, the HHONMPA algorithm demonstrates the fastest convergence speed and highest solution accuracy across all three inflow frequencies. This fully demonstrates the effectiveness and efficiency of this hybrid optimization algorithm, making it a reliable optimization tool.

[0188] The HHONMPA hybrid algorithm proposed in this application effectively overcomes the technical difficulties of insufficient population diversity, local optimum trapping, and imbalance of exploration and development capabilities in solving the optimal scheduling problem of cascade reservoir groups by the single HHO algorithm. It significantly improves the population quality, search balance, and global exploration capability of the algorithm, and has important engineering application value and promotion significance.

[0189] The following describes the intelligent reservoir scheduling device based on dual optimization driven by HHO and MPA provided in this application. The intelligent reservoir scheduling device based on dual optimization driven by HHO and MPA described below can be referred to in correspondence with the intelligent reservoir scheduling method based on dual optimization driven by HHO and MPA described above.

[0190] Figure 9 This is a schematic diagram of the structure of the intelligent reservoir scheduling device based on dual optimization drive of HHO and MPA provided in the embodiments of this application, as shown below. Figure 9 As shown, the device includes at least:

[0191] Objective function establishment module 901 is used to establish an objective function with the optimization objective of maximizing the total power generation of the cascade reservoir group.

[0192] The constraint setting module 902 is used to set the constraint conditions of the objective function, including equality constraints and inequality constraints that satisfy the operation of the reservoir.

[0193] The solution module 903 is used to solve the objective function based on the improved predation strategy optimization algorithm and obtain the operating water level of each reservoir in the cascade reservoir group at different times during the scheduling period;

[0194] The improved predator strategy optimization algorithm is achieved by introducing the following operations into the search strategy selection phase of the HHO algorithm: global exploration based on escape energy adaptive switching MPA algorithm and local development of HHO algorithm.

[0195] In some embodiments, the solver module 903 is specifically used for:

[0196] When the absolute value of the escape energy is greater than or equal to 1, the dual-species cooperative MPA multi-strategy exploration mechanism is executed, and the improved MPA Brownian motion and Lévy flight are used for global search.

[0197] When the absolute value of the escape energy is less than 1, the improved HHO adaptive trapping strategy and adaptive jump strategy are executed, and different trapping strategies of the improved HHO are used for local search.

[0198] In some embodiments, different encirclement strategies for improved HHO are employed for local search, including:

[0199] When the probability of prey escaping is less than or equal to 0.5, the individual executes an adaptive entrapment strategy;

[0200] When the probability of prey escaping is greater than 0.5, the individual executes an adaptive jumping strategy.

[0201] In some embodiments, global search is performed using Brownian motion and Lévy flight with improved MPA, including:

[0202] For any individual in the two populations, if the individual is in the first half of the population and the current iteration number is less than one-third of the total iteration number, the main population guides the execution of the MPA Brownian motion strategy; if the current iteration number is greater than or equal to one-third of the total iteration number, the two populations cooperate to execute the improved MPA Levy flight strategy.

[0203] When an individual is in the latter half of the population, if the random number is greater than or equal to 0.5, the search is based on the random position of the population; if the random number is less than 0.5, the search is based on the average position of the population.

[0204] In some embodiments, the solver module 903 is specifically used for:

[0205] The population is initialized in the search space based on an improved chaotic mapping strategy. Individuals in the population correspond to decision variables in solving the objective function. The decision variables are any one of the following: reservoir water level, power station water level, and power station outflow.

[0206] An elite reverse learning strategy is introduced to optimize the initial population;

[0207] Update individual location based on individual fitness;

[0208] Update the global optimal individual position and the historical extreme value individual position based on individual fitness;

[0209] Global exploration of the MPA algorithm based on escape energy adaptive switching and local development of the HHO algorithm;

[0210] In each iteration, the individual fitness is continuously iterated and the individual position is updated until the preset maximum number of iterations is reached, and the latest global optimal individual position is obtained.

[0211] In some embodiments, initializing the population in the search space based on an improved chaotic mapping strategy includes:

[0212] In the search space, N individual positions are randomly generated by combining the Sine chaotic map and the PWLCM chaotic map, and these N individual positions are determined as the initial population.

[0213] In some embodiments, N individual positions are randomly generated in the search space by combining the Sine chaotic map and the PWLCM chaotic map, satisfying:

[0214] ;

[0215] in, and For iterative individuals, ∈(0,1) is a control parameter. When r∈(0,1), the system is in a chaotic state, and r∈(0,1) is a random number.

[0216] In some embodiments, an elite reverse learning strategy is introduced to optimize the initial population, including:

[0217] By using elite individuals in the population to generate reverse individuals, a reverse population can be constructed.

[0218] The initial population is expanded using a reverse population.

[0219] In some embodiments, updating an individual's location based on its fitness includes:

[0220] If the fitness of the original individual is greater than that of the reverse individual, then update the individual's position to the reverse individual's position;

[0221] If the fitness of the original individual is less than that of the reversed individual, then the original individual's position is retained.

[0222] In some embodiments, the objective function satisfies:

[0223] ;

[0224] in, This represents the total power generation of the cascade reservoir group. This indicates the number of reservoirs in a cascade reservoir group. Indicates the number of scheduling cycles. Let the output of the i-th reservoir during the t-th scheduling cycle satisfy: , This represents the output coefficient of the i-th reservoir. This represents the head of the i-th reservoir during the t-th scheduling cycle. This represents the power generation flow of the i-th reservoir during the t-th scheduling cycle. This indicates the time interval of the scheduling cycle.

[0225] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0226] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0227] Based on the methods described in the above embodiments, this application provides an electronic device. The device may include at least one memory for storing a program and at least one processor for executing the program stored in the memory. When the program stored in the memory is executed, the processor performs the methods described in the above embodiments.

[0228] Figure 10 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application, such as... Figure 10 As shown, the electronic device may include a processor 1001, a communications interface 1002, a memory 1003, and a communication bus 1004, wherein the processor 1001, the communications interface 1002, and the memory 1003 communicate with each other via the communication bus 1004. The processor 1001 can call software instructions in the memory 1003 to execute the methods described in the above embodiments.

[0229] Furthermore, the logical instructions in the aforementioned memory 1003 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application.

[0230] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0231] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0232] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0233] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0234] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0235] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0236] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A reservoir intelligent scheduling method based on dual optimization driven by HHO and MPA, characterized in that, include: An objective function is established with the goal of maximizing the total power generation of the cascade reservoir group. The constraints of the objective function are set, including equality constraints and inequality constraints that satisfy the operation of the reservoir; The objective function is solved based on the improved predation strategy optimization algorithm to obtain the operating water level of each reservoir in the cascade reservoir group at different times during the scheduling period; The improved predation strategy optimization algorithm is implemented by introducing the following operations in the search strategy selection stage of the HHO algorithm: global exploration based on escape energy adaptive switching MPA algorithm and local development of HHO algorithm; The escape energy decreases nonlinearly with increasing iteration, as shown in the following formula: in, For the escape energy of the prey, K represents the initial escape energy of the prey, K represents the maximum number of iterations for the population, and k represents the current number of iterations. Solving the objective function based on the improved predation strategy optimization algorithm includes: When the absolute value of the escape energy is greater than or equal to 1, the dual-species cooperative MPA multi-strategy exploration mechanism is executed, and the improved MPA Brownian motion and Lévy flight are used for global search. When the absolute value of the escape energy is less than 1, the improved HHO adaptive trapping strategy and adaptive jump strategy are executed, and different trapping strategies of the improved HHO are used for local search. The local search employing different encirclement strategies for improved HHO includes: When the probability of prey escaping is less than or equal to 0.5, the individual executes an adaptive entrapment strategy; When the probability of prey escaping is greater than 0.5, the individual executes an adaptive jumping strategy; The global search using Brownian motion and Lévy flight with improved MPA includes: For any individual in the two populations, if the individual is in the first half of the population and the current iteration number is less than one-third of the total iteration number, the main population guides the execution of the MPA Brownian motion strategy; if the current iteration number is greater than or equal to one-third of the total iteration number, the two populations cooperate to execute the improved MPA Levy flight strategy. When an individual is in the latter half of the population, if the random number is greater than or equal to 0.5, the search is based on the random position of the population; if the random number is less than 0.5, the search is based on the average position of the population.

2. The intelligent reservoir scheduling method according to claim 1, characterized in that, The objective function to be solved includes: The population is initialized in the search space based on an improved chaotic mapping strategy. Individuals in the population are used to solve the decision variables of the objective function. The decision variables are any one of the following: reservoir water level, power station water level, and power station outflow. An elite reverse learning strategy is introduced to optimize the initial population; Update individual location based on individual fitness; Update the global optimal individual position and the historical extreme value individual position based on individual fitness; Global exploration of the MPA algorithm based on escape energy adaptive switching and local development of the HHO algorithm; In each iteration, the individual fitness is continuously iterated and the individual position is updated until the preset maximum number of iterations is reached, and the latest global optimal individual position is obtained.

3. The intelligent reservoir scheduling method according to claim 2, characterized in that, The initialization of the population in the search space based on the improved chaotic mapping strategy includes: In the search space, N individual positions are randomly generated by combining the Sine chaotic map and the PWLCM chaotic map, and these N individual positions are determined as the initial population.

4. The intelligent reservoir scheduling method according to claim 3, characterized in that, The method involves randomly generating N individual positions in the search space using a combination of Sine chaotic mapping and PWLCM chaotic mapping, satisfying the following: ； in, and For iterative individuals, ∈(0,1) is a control parameter. When r∈(0,1), the system is in a chaotic state, and r∈(0,1) is a random number.

5. The intelligent reservoir scheduling method according to claim 2, characterized in that, The introduction of an elite reverse learning strategy to optimize the initial population includes: By using elite individuals in the population to generate reverse individuals, a reverse population can be constructed. The initial population is expanded using the reverse population.

6. The intelligent reservoir scheduling method according to claim 5, characterized in that, The method of updating individual location based on individual fitness includes: If the fitness of the original individual is greater than that of the reverse individual, then update the individual's position to the reverse individual's position; If the fitness of the original individual is less than that of the reversed individual, then the original individual's position is retained.

7. The intelligent reservoir scheduling method according to claim 1, characterized in that, The objective function satisfies: ； in, This represents the total power generation of the cascade reservoir group. This indicates the number of reservoirs in a cascade reservoir group. Indicates the number of scheduling cycles. Let the output of the i-th reservoir during the t-th scheduling cycle satisfy: , This represents the output coefficient of the i-th reservoir. This represents the head of the i-th reservoir during the t-th scheduling cycle. This represents the power generation flow of the i-th reservoir during the t-th scheduling cycle. This indicates the time interval of the scheduling cycle.

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