Cascade reservoir multi-objective optimization scheduling method and system based on tree structure unbounded archiving

Abstract

The invention discloses a cascade reservoir multi-objective optimization scheduling method and system based on tree structure unbounded archiving, aims to solve the problem of complex multi-objective optimization under the action of high-dimensional multi-constraint coupling represented by cascade reservoir group joint optimization scheduling, and constructs a tree structure suitable for large-scale data storage and updating. According to the method, a tree structure is constructed, an unbounded archiving strategy based on the structure is provided, archiving scale limitation is cancelled, loss of potential effective solutions is avoided, the strategy is integrated into a multi-target particle swarm algorithm, and the multi-target particle swarm algorithm based on tree structure unbounded archiving is formed. The method comprises the steps of arrangement and analysis of scheduling data, establishment of a cascade reservoir multi-target optimization scheduling model, design of a tree structure and an unbounded archiving strategy, algorithm fusion, model solution and the like, and can be applied to cascade reservoir multi-target optimization scheduling to obtain a high-quality optimization scheduling scheme set, provide decision support for scheduling personnel and improve the scheduling efficiency. And the method has obvious practical application value.

Description

Technical Field

[0001] The present invention relates to the technical field of cascade reservoir multi-objective optimal operation, and particularly to a cascade reservoir multi-objective optimal operation method and system based on a tree-structured unbounded archive. Background Art

[0002] The joint optimal operation of cascade reservoir groups is an important topic in modern water resources management, which is restricted by many factors, including hydrological processes, power grid operation requirements, ecological needs, etc. Essentially, this is a complex multi-objective optimization problem under the coupling action of high-dimensional multiple constraints. With the successive completion and commissioning of reservoir groups in large river basins such as the Jinsha River and the Lancang River, and the continuous development of hydropower energy, the scale of cascade hydropower systems has been continuously expanding, and their topological structures have become increasingly complex. This makes the scheduling problem of cascade reservoirs more intractable and requires more refined management and optimization means.

[0003] Currently, the model solution of cascade reservoir optimal operation mainly relies on traditional dynamic programming methods. However, when facing large-scale, multi-objective optimization problems, these methods often have difficulty ensuring the timeliness of optimization and the effect of multi-objective collaborative optimization. Specifically, when dealing with the multi-objective optimal operation of cascade reservoirs, traditional dynamic programming methods have the following main problems: High computational complexity: As the number of cascade reservoirs increases, the state and decision spaces to be considered increase exponentially, resulting in a huge amount of calculation and making it difficult to achieve fast solution in practical applications.

[0004] Local optimal solutions: For complex optimization problems, improved dynamic programming methods such as stepwise optimization algorithms and successive approximation algorithms often can only find local optimal solutions and cannot guarantee global optimality.

[0005] Difficulty in multi-objective collaborative optimization: The scheduling objectives of cascade reservoirs usually include maximizing power generation, minimizing water abandonment, maximizing energy storage at the end of the scheduling period, minimizing water supply shortage rate, minimizing flood control risk, etc. These objectives are both interrelated and contradictory. Traditional methods often have difficulty taking into account each objective when dealing with such problems, resulting in less than ideal optimization results.

[0006] In order to overcome the deficiencies of traditional methods, scholars at home and abroad have conducted a large number of studies and proposed a variety of intelligent optimization algorithms. For example, multi-objective genetic algorithms, particle swarm algorithms, etc. have been widely applied to the multi-objective optimal operation problems of cascade reservoirs. These methods have improved the solution efficiency and accuracy to a certain extent, but there are still some problems, such as slow convergence speed and difficulty in balancing the solution efficiency and result quality.

[0007] A multi-objective optimal operation decision-making method for cascade reservoirs based on an improved MOFA (Multi-Objective Firefly Algorithm), as disclosed in CN117788208A, mainly includes the following steps: constructing a multi-objective operation model for cascade reservoirs, selecting objective functions (such as power generation, ecology, water supply, etc.) and setting constraint conditions; solving the model by the improved MOFA algorithm, and selecting a set number of solutions to form a set of operation plans; according to the decision index system, assigning index weights and selecting the best operation plan; among them, the improvement of the MOFA algorithm is mainly reflected in using the Singer mapping to generate the initial population of fireflies, and introducing the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution, abbreviated as the method of distance between superior and inferior solutions in China) method and the VIKOR (VlseKriterijumska Optimizacija Kompromisno Resenje, multi-criteria compromise solution ranking method) evaluation method to establish a decision model; the proposed improved MOFA algorithm is optimized in terms of time efficiency and complexity, but its algorithm complexity is still relatively high, resulting in low efficiency when solving the multi-objective optimal operation problem of large-scale cascade reservoirs.

[0008] Therefore, there is an urgent need to design a new optimization method to address the complex multi-objective optimization problem of the joint optimal operation of cascade reservoir groups, and quickly obtain a set of high-quality operation plan sets under the given computing resources, providing comprehensive and reliable decision support for dispatchers. Aiming at the deficiencies of the existing technology, the present invention proposes a multi-objective optimal operation method and system for cascade reservoirs based on a tree-structured unbounded archive, aiming to provide a more efficient, comprehensive and reliable solution for the joint optimal operation of cascade reservoir groups. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide a multi-objective optimal operation method and system for cascade reservoirs based on a tree-structured unbounded archive, and solve the complex multi-objective optimization problem in the field of joint optimal operation of cascade reservoir groups, especially when facing multiple operation objectives such as maximizing power generation, minimizing the amount of abandoned water, maximizing the end-of-scheduling energy storage, minimizing the water shortage rate of water supply, and minimizing the flood control risk, the technical problem that the correlation and contradiction between different objectives become increasingly intricate.

[0010] To solve the above technical problems, the technical solution adopted by the present invention is: a multi-objective optimal operation method for cascade reservoirs based on a tree-structured unbounded archive, including the following steps: Step 1: Organize and analyze the existing operation data of cascade reservoirs, determine the scheduling objectives and corresponding constraints, and establish a multi-objective optimal scheduling model for cascade reservoirs based on the scheduling objectives and constraints; Step 2: Design a tree structure suitable for storing archived data, and propose an unbounded archiving strategy based on the tree structure, where unbounded archiving means canceling the limit on the scale of the archive; Step 3: Incorporate the unbounded archiving strategy described in Step 2 into the multi-objective particle swarm optimization algorithm, and propose a multi-objective particle swarm algorithm based on unbounded archiving of the tree structure; Step 4: Use the improved multi-objective particle swarm algorithm to solve the multi-objective optimal scheduling model of cascade reservoirs and obtain a set of high-quality optimal scheduling schemes.

[0011] In the preferred scheme, the scheduling objectives in Step 1 include the maximum power generation of cascade reservoirs, the minimum water discharge, the maximum energy storage at the end of the scheduling period, the minimum water supply shortage rate, and the minimum flood control risk. Their calculation formulas are as follows: (1) (2) (3) (4) (5) In the formula, is the maximum power generation of cascade reservoirs, is the minimum water discharge, is the maximum energy storage at the end of the scheduling period, is the minimum water supply shortage rate, is the minimum flood control risk, n represents the number of hydropower stations, T represents the number of time periods, represents t the average output of hydropower station i in the time period, t represents i the average water discharge of hydropower station in the time period, j represents the unit time period length, represents the available water volume of hydropower station i at the end of the scheduling period, represents t the average outflow of the last-stage hydropower station in the time period, t represents the flow corresponding to the downstream water demand in the time period, representst The reservoir capacity of the hydropower station at the end of the period i , represents the reservoir capacity corresponding to the flood control limited water level of the hydropower station i , represents the reservoir corresponding to the highest flood interception water level of the hydropower station specified by the regulations i , is a custom intermediate variable i , j represent two different hydropower station numbers

[0012] In the preferred solution, the calculation formulas for the maximum power generation, minimum water discharge, maximum energy storage at the end of the operation period, minimum water supply shortage rate, and minimum flood control risk of the cascade reservoir are based on parameters such as the number of hydropower stations, number of periods, average output, average water discharge, unit period length, available water volume at the end of the operation period, available water volume - energy storage value function relationship, average outflow, downstream water demand corresponding flow, reservoir capacity, reservoir capacity corresponding to the flood control limited water level, and reservoir capacity corresponding to the highest flood interception water level

[0013] In the preferred solution, the constraint conditions in the above - mentioned Step1 include water level range, water level variation constraint, flow range, flow variation constraint, output range, output variation constraint, and reserved reservoir capacity constraint, and their calculation formulas are respectively (6) (7) (8) (9) In the formula , , and respectively represent t the average water level, minimum water level, maximum water level, and water level variation of the hydropower station in the period i , represents the average water level of the hydropower station in the period i , , , and respectively represent t the average outflow, minimum outflow, maximum outflow, and outflow variation of the hydropower station in the period i , represents the average outflow of the hydropower station in the period i , , respectively represent t the hydropower station in the period​​i The minimum output, maximum output, and output variation range Indicating the time period Hydropower station i The average output; Indicating t The sum of the storage capacities corresponding to the normal storage levels of the reservoirs with reserved storage capacity constraints during the time period; Indicating t The reserved storage capacity during the time period.

[0014] In the preferred solution, in the tree structure in Step2, each node includes information about the parent node, child nodes, the archived subset divided from the parent node, the maximum vertex and minimum vertex of the hypercube covering the target vector set corresponding to the archived subset.

[0015] In the preferred solution, the calculation process of the multi-objective particle swarm algorithm based on the tree-structured unbounded archive in Step3 includes: initializing the particle swarm and the tree-structured unbounded archive, initializing the individual optimal positions and global optimal positions of each particle, updating the velocities and positions of each particle based on the individual optimal positions and global optimal positions, correcting and mutating the individual positions, updating the archive set, individual optimal positions, and global optimal positions based on each particle after position update, and repeating the above steps until the maximum number of iterations or a given termination condition is reached.

[0016] In the preferred solution, the archive initialization operation in Step3 is that the archive set is initially empty. First, the first particle in the particle swarm is directly included in the archive, and subsequent operations are the same as the archive update operation, that is, using the particles in the particle swarm to update the archive, determining whether the particle meets the condition to enter the archive, and if so, inserting it into the tree structure.

[0017] In the preferred solution, the method for obtaining the dominance relationship between the particle and the archive set in Step3 includes: comparing the particle with the particle set corresponding to the nodes in the archive tree structure, first comparing the dominance relationship with the maximum vertex and minimum vertex of the hypercube corresponding to the node, and deciding whether the particle joins the archive or conducts further comparisons based on the comparison results.

[0018] In the preferred solution, the update operation of the global optimal position of each particle in Step3 includes: first setting an empty set as the candidate set for the global optimal position, preferentially selecting marginal particles and particles located in the sparse area from the archive set to join the candidate set, and finally selecting the global optimal position of each particle from the candidate set through the form of binary tournament.

[0019] The cascade reservoir multi-objective optimal scheduling system based on tree-structured unbounded archive is a system for implementing the cascade reservoir multi-objective optimal scheduling method based on tree-structured unbounded archive described in any one of the above, including: A model establishment module, which is used to determine the scheduling objectives and corresponding constraint conditions of cascade reservoirs in different periods, and establish a cascade reservoir multi-objective optimal scheduling model based on the scheduling objectives and constraint conditions; An unbounded archive strategy design module, which is used to design a tree structure suitable for storing archive data and propose an unbounded archive strategy based on the tree structure; A multi-objective particle swarm algorithm design module, which is used to integrate the unbounded archive strategy into the multi-objective particle swarm optimization algorithm and propose a multi-objective particle swarm algorithm based on tree-structured unbounded archive; A solution module, which is used to solve the cascade reservoir multi-objective optimal scheduling model by using the improved multi-objective particle swarm algorithm and obtain an optimal scheduling solution set.

[0020] In the preferred solution, the system further includes a user interface module, which is used to display the optimal scheduling solution set and provide user interaction functions to select and adjust the scheduling solution.

[0021] The cascade reservoir multi-objective optimal scheduling method and system based on tree-structured unbounded archive provided by the present invention have the following beneficial effects: 1. The unbounded archive strategy proposed by the present invention effectively solves the problem that potential effective solutions are lost due to the limitation of the archive scale in the traditional archive strategy. This strategy cancels the hard limit of the archive scale, ensuring that all non-dominated solutions generated during the optimization process can be retained to provide a high-density Pareto front with good distribution characteristics; 2. The present invention designs a tree structure suitable for storing large-scale archive data. This structure has clear hierarchy and good scalability, and can efficiently manage a large number of non-dominated solutions generated during the optimization process, making the access, update and maintenance of archive data simpler and more efficient; 3. By combining the unbounded archive strategy, the tree structure and the multi-objective particle swarm optimization algorithm, the present invention forms a new multi-objective particle swarm algorithm based on tree-structured unbounded archive. This improvement significantly enhances the overall performance of the algorithm, and can quickly search for high-quality non-dominated solution sets in complex solution spaces, providing a powerful tool for solving practical engineering problems; 4. The technical solution of the present invention can effectively solve the complex multi-objective optimization problem under the coupling action of high-dimensional multiple constraints in the joint optimal scheduling of cascade reservoir groups, and provide a high-quality optimal scheduling solution set for schedulers; 5. With the expansion of the scale of cascade hydropower systems and the complexity of their topological structures, traditional dynamic programming methods can no longer meet the requirements of timeliness and multi-objective collaborative optimization for cascade system optimization. The present invention effectively overcomes this limitation and provides a new solution idea for the optimal operation of cascade reservoir groups; 6. By introducing the unbounded archive strategy and the tree-structured archive, the present invention effectively solves the problems of redundant dominance relationship comparison and potential loss of effective solutions existing in traditional archive strategies when managing and utilizing non-dominated solutions in the optimization process. This improvement improves the efficiency of archive update and maintenance and ensures the quality of the solution results; 7. The technical solution of the present invention significantly improves the quality of the solution results for the multi-objective optimal operation problem of cascade reservoirs. By providing a set of high-quality optimal operation plans, it provides a more accurate and reliable decision-making basis for dispatchers; 8. The technical solution of the present invention has been successfully applied to the dispatch operation of cascade power stations in the upper reaches of the Yangtze River and achieved remarkable results. This successful application proves the practical value and broad application prospects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is the calculation flow chart of the multi-objective particle swarm optimization algorithm based on the tree-structured unbounded archive of the present invention; Figure 2 is the flow chart of archive update based on the tree structure of the present invention; Figure 3 is the flow chart of updating the global optimal position of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] The technical solutions in the present invention will be further described below with reference to the drawings and embodiments: Embodiment 1 As Figures 1 to 3 shown, this embodiment provides a multi-objective optimal operation method for cascade reservoirs based on a tree-structured unbounded archive, and the steps are as follows: 1. Organize and analyze the existing dispatching operation data of cascade reservoirs, determine the dispatching objectives and corresponding constraint conditions of cascade reservoirs in different periods, and establish a multi-objective optimal operation model for cascade reservoirs based on the dispatching objectives and constraint conditions; The dispatching objectives include maximizing the power generation of cascade reservoirs , minimizing the water abandonment , maximizing the energy storage at the end of the dispatching period , minimizing the water supply shortage rate and minimizing the flood control risk , and their calculation formulas are as follows: (1) (2) (3) (4) (5) In the formula, n represents the number of hydropower stations, T represents the number of time periods, represents t the average output of the hydropower station in the time period i ; represents t the average water discharge of the hydropower station in the time period i ; represents the unit time period length, represents the available water volume of the hydropower station j at the end of the dispatching period, represents the relationship between the available water volume and the energy storage value function of the hydropower station i ; represents t the average discharge of the last - stage hydropower station in the time period ; t represents the flow corresponding to the water demand downstream in the time period ; t represents the storage capacity of the hydropower station i at the end of the time period, represents the storage capacity corresponding to the flood - limit water level of the hydropower station i ; represents the storage corresponding to the highest flood - control water level of the hydropower station specified by the regulations i ; is a custom intermediate variable, i , j represent two different hydropower station numbers.

[0024] The constraint conditions include: Water level range and water level amplitude constraint: (6) In the formula, , , and respectively represent t the average water level, the lowest water level, the highest water level and the water level amplitude of the hydropower station i in the time period, represents the time period of the hydropower station i ; Flow range and flow amplitude constraint: (7) In the formula, , , and respectively represent t the average discharge flow, minimum discharge flow, maximum discharge flow and discharge flow variation range of the hydropower station during a time period, i represents the time period hydropower station i average discharge flow; Output range and output variation range constraints: (8) In the formula, and respectively represent t the minimum output, maximum output and output variation range of the hydropower station during a time period, i represents the time period hydropower station i average output; Reserved storage capacity constraint: (9) In the formula, represents t the sum of the storage capacities corresponding to the normal storage levels of the reservoirs with reserved storage capacity constraints during a time period; represents t the reserved storage capacity during a time period.

[0025] 2. Design a tree structure suitable for archived data storage and propose an unbounded archiving strategy based on the tree structure; The unbounded archiving strategy is to cancel the limit on the archiving scale. The specific definition of the tree structure suitable for archived data storage is as follows: In the tree structure, each node includes a parent node ( Parent ), a child node ( Child ), an archived subset divided from the parent node ( W ), and the maximum vertex and minimum vertex of the hypercube covering the target vector set corresponding to the archived subset ( and ) these five parts of information.

[0026] 3. Incorporate the unbounded archiving strategy proposed in step 2 into the multi-objective particle swarm optimization algorithm. On this basis, propose a multi-objective particle swarm algorithm based on unbounded archiving of the tree structure; The calculation process of the multi-objective particle swarm algorithm based on unbounded archiving of the tree structure is as follows: (1) Initialize the particle swarm , where m represents the population size, and the current position of the j th particle is denoted as , , ; (2) Initialize the unbounded archive based on the tree structure F ; (3) Initialize the individual best position of each particle to its current position; (4) Initialize the global best position of each particle; (5) Based on the individual best position and the global best position, update the velocity and position of each particle. At the same time, according to the constraint conditions of the cascade reservoir, correct and mutate the individual position to ensure search within the feasible region; (6) Based on each particle after position update, update the archive set, and then update the individual best position and the global best position of each particle; (7) Repeat steps (5) and (6) until the maximum number of iterations is reached or the given termination condition is met.

[0027] For the archive initialization and update operations in steps (2) and (6), specifically: Archive initialization operation: The archive set is initially empty. First, include the first particle in the archive, and then the subsequent operations are the same as the archive update operation; Archive update operation: Use a certain particle p to update the archive, which can be denoted as . First, determine whether the particle meets the condition to enter the archive. If the particle p is not weakly dominated by any particle in the archive, it can enter the archive and be inserted into the tree structure; otherwise p it cannot enter the archive. Perform the above operation for each particle to complete the archive update; To obtain the dominance relationship between the particle p and the archive set, let the particle p be compared with the particle set corresponding to the node in the archive tree structure W (starting from the root node first). This operation is denoted as . The specific process is as follows: First, compare the particle p with the maximum vertex and the minimum vertex of the hypercube corresponding to the node , to compare the dominance relationship. If the particle p is weakly dominated, then p is weakly dominated by the archive set, that is, p cannot enter the archive; if the particle p weakly dominates , then the particle p dominates the archive subset corresponding to the node W . Include the particle p in the archive; if the particle p and , If they are all non-dominated with each other, then p it is non-dominated with any particle in the archive set, and p it will be included in the archive; if none of the above situations are met, determine whether the node is at the bottom layer of the tree. If the node is at the bottom layer of the tree, then let the particle p compare with each particle in the set W in turn for domination relationship. Otherwise, let the particle p compare with the child nodes of this node in turn for judgment, and the method is the same as the above operation; During the comparison process, if a particle or a set of particles in the archive dominated by the particle p is found, it will be deleted from the tree structure to ensure the non-domination of the archive set. If it is judged that the particle p can be included in the archive, then p it will be inserted into the node currently compared with it, and the archive subset corresponding to the node W as well as the maximum vertex and the minimum vertex of the hypercube , will be updated.

[0028] For the initialization and update operations of the global optimal positions of each particle in steps (4) and (6), specifically: The initialization and update operations of the global optimal positions of each particle are the same. Denote the candidate set of the global optimal position gbest as . Before each round of updating the global optimal position of the particle, first update the set . The specific process is as follows: First, empty the set , and add the marginal particles in the archive set to ; then select the particles in the sparse area of the archive and add them to . Starting from the root node of the archive tree structure, check the scale of the set W corresponding to each node layer by layer. If it is less than 3, then directly include the set W corresponding to the node in ; otherwise, take the ratio of the size of the hypercube corresponding to the node (the distance between and ) to the set scale as the crowding coefficient, and include the set W with the larger crowding coefficient in ; The update operation of the global optimal position of a certain particle p can be denoted as . The specific process is as follows: Randomly select two particles from . If only one of them is a marginal particle, then select this particle as the global optimal position; otherwise, if only one of them dominates the particle p, then select this particle as the global optimal position; if none of the above conditions are met, randomly select a particle as the global optimal position.

[0029] 4. Use the improved multi-objective particle swarm optimization algorithm to solve the multi-objective optimal operation model of cascade reservoirs and obtain a set of high-quality optimal operation schemes.

[0030] Taking the cascade power stations composed of four series-connected hydropower stations A, B, C, and D in the upper reaches of the Yangtze River as the object, two examples are designed to verify the effectiveness of the multi-objective optimal operation method of cascade reservoirs based on tree-structured unbounded archives provided in this embodiment. The cascade power stations are, from upstream to downstream, Power Station A, Power Station B, Power Station C, and Power Station D. Except for Power Station D, the other power stations have strong regulation capabilities.

[0031] The first example takes the inflow from January to April during the drawdown period of a typical year as the input, with the scheduling scale being ten-day periods. The scheduling objectives are to maximize the power generation of the cascade reservoirs, minimize the water discharge, maximize the energy storage at the end of the scheduling period, and minimize the water supply shortage rate. Select the multi-objective particle swarm optimization algorithm based on tree-structured unbounded archives proposed in this embodiment as the solution algorithm, and select the classical algorithms NSGA-II (Non-dominated Sorting Genetic Algorithm-II) and MOPSO (Multi-objective Particle Swarm Optimization) as the comparison algorithms. Compare the calculation results of different algorithms, and use the hypervolume index to evaluate the quality of the non-dominated solution sets obtained by the algorithms. The closer the index value is to 1, the better the result quality. Its definition is as follows: (10) In the formula, W represents the set to be evaluated; r represents the reference point set in the objective space; λ represents the Lebesgue measure; H ( W , r ) represents a region in the objective space Z such that any point z in this region satisfies f ( w ) ≤ z ≤ r , w is a point belonging to the set W .

[0032] The second example uses the water inflow from August 1st to August 31st during the flood season of a typical year as the input, with a daily scheduling scale. The scheduling objectives are to maximize the power generation of cascade reservoirs, minimize the water discharge, maximize the energy storage at the end of the scheduling period, and minimize the flood control risk. The multi-objective particle swarm optimization algorithm based on a tree-structured unbounded archive proposed in this embodiment is selected as the solution algorithm, and the classical algorithms NSGA-II and MOPSO are selected as the comparison algorithms to compare the calculation results of different algorithms. The hypervolume index I H is used as the evaluation index for the non-dominated solution set obtained by the algorithm calculation.

[0033] The calculation programs are all written in JAVA and the calculations are completed on a workstation with an Intel Core i7-12700, 12 cores, and 64GB of memory. The parameter settings of the algorithm are as follows: the population size is set to 100, and the size of the bounded archive is set to 100; the parameters related to velocity update are set to w = 0.4, r 1 = r 2 = 2; the maximum number of iterations of the algorithm is 50, and the results are shown in Tables 1 - 3.

[0034] It can be seen from Table 1 that for Examples 1 and 2, the calculation results of the multi-objective particle swarm optimization algorithm based on a tree-structured unbounded archive proposed in this embodiment are significantly better than those of the traditional algorithms NSGA-II and MOPSO. It can be seen from Table 2 that in Example 1, for the set of scheduling schemes obtained by the algorithm calculation in this embodiment, the corresponding cascade power generation is 38.981 - 43.507 billion kWh, and the water supply shortage rate is 9.56e-4 - 2.32e-3. The upper and lower limits of the corresponding objectives are better than those of NSGA-II and MOPSO. It can be seen from Table 3 that in Example 2, for the set of scheduling schemes obtained by the algorithm calculation in this embodiment, the corresponding cascade power generation is 30.881 - 32.375 billion kWh, the cascade water discharge is 3.801 - 6.028 billion m 3 , and the flood control risk value is 53.72 - 66.89. The upper and lower limits of the corresponding objectives are better than those of NSGA-II and MOPSO.

[0035] Through the above example analysis, it can be concluded that the application of the unbounded archive strategy based on a tree structure in the multi-objective optimization algorithm can significantly improve the overall performance of the algorithm. Through the unbounded archive scale and the hierarchy and scalability of the tree structure, the strategy realizes the effective management and utilization of a large number of non-dominated solutions generated during the optimization process. Compared with the classical multi-objective optimization algorithms, it has obvious advantages and competitiveness in dealing with complex multi-objective optimization problems represented by the multi-objective optimal scheduling of cascade reservoirs.

[0036] Table 1 Comparison of hypervolume index values of different algorithms

[0037] Table 2 Example 1 Target value ranges of different algorithms

[0038] Table 3 Example 2 Target value ranges of different algorithms

[0039] Example 2 In another preferred embodiment, based on the above Embodiment 1, a cascade reservoir multi-objective optimal operation system based on a tree-structured unbounded archive is a system for implementing the method for multi-objective optimal operation of cascade reservoirs based on a tree-structured unbounded archive described in Embodiment 1, and includes: A model establishment module, configured to determine the operation objectives and corresponding constraint conditions of the cascade reservoir in different periods, and establish a multi-objective optimal operation model of the cascade reservoir based on the operation objectives and constraint conditions; An unbounded archive strategy design module, configured to design a tree structure suitable for storing archive data, and propose an unbounded archive strategy based on the tree structure; A multi-objective particle swarm algorithm design module, configured to integrate the unbounded archive strategy into the multi-objective particle swarm optimization algorithm, and propose a multi-objective particle swarm algorithm based on a tree-structured unbounded archive; A solution module, configured to use the improved multi-objective particle swarm algorithm to solve the multi-objective optimal operation model of the cascade reservoir, and obtain an optimal operation plan set.

[0040] In this embodiment, the system further includes a user interface module, configured to display the optimal operation plan set, and provide user interaction functions to select and adjust the operation plan.

[0041] In a preferred solution, the operation objectives in Step1 include the maximum power generation of the cascade reservoir, the minimum water discharge, the maximum energy storage at the end of the operation period, the minimum water supply shortage rate, and the minimum flood control risk; the above settings are aimed at realizing the efficient utilization and comprehensive management of water resources. By precisely regulating the water storage and release strategies of the reservoir, not only the stability of power supply and the benefits of the power plant are ensured, but also the multi-faceted balance of flood control safety, water supply demand, and ecological environment is taken into account.

[0042] In the preferred solution, the calculation formulas for the maximum power generation, minimum water abandonment, maximum energy storage at the end of the scheduling period, minimum water supply shortage rate, and minimum flood control risk of the cascade reservoir are based on parameters such as the number of hydropower stations, the number of time periods, average output, average water abandonment flow rate, unit time period length, available water volume at the end of the scheduling period, the functional relationship between available water volume and energy storage value, average discharge flow rate, the flow rate corresponding to downstream water demand, reservoir capacity, the reservoir capacity corresponding to the flood limit water level, and the reservoir capacity corresponding to the highest flood control water level. With the above settings, the comprehensive benefits of the cascade reservoir can be comprehensively evaluated, ensuring the optimal scheduling of power generation, water storage, water supply, and flood control under different working conditions, improving the water resource utilization efficiency, and ensuring the economic and social development within the basin and the safety of the lives and property of the people.

[0043] In the preferred solution, the constraint conditions in Step1 include water level range, water level amplitude constraint, flow rate range, flow rate amplitude constraint, output range, output amplitude constraint, and reserved reservoir capacity constraint. With the above settings, it is aimed to ensure that the hydropower station operates within a safe and efficient range, avoid damage to equipment caused by extreme working conditions, and at the same time ensure the stability and flexibility of power supply to meet the grid scheduling requirements and ecological water use requirements.

[0044] In the preferred solution, the calculation process of the multi-objective particle swarm optimization algorithm based on the tree-structured unbounded archive in Step3 includes: initializing the particle swarm and the tree-structured unbounded archive, initializing the individual optimal position and the global optimal position of each particle, updating the velocity and position of each particle based on the individual optimal position and the global optimal position, correcting and mutating the individual positions, updating the archive set, individual optimal position, and global optimal position based on each particle after position update, and repeating the above steps until the maximum number of iterations or a given termination condition is reached. With the above settings, it can ensure the effective convergence of the algorithm in complex multi-objective optimization problems, and at the same time use the tree-structured unbounded archive to record the historical optimal solutions, enhance the exploration ability and solution set diversity of the algorithm, and finally obtain high-quality optimization results.

[0045] In the preferred solution, the archive initialization operation in Step3 is that the archive set is empty at the beginning. First, the first particle in the particle swarm is directly included in the archive, and the subsequent operations are the same as the archive update operation, that is, using the particles in the particle swarm to update the archive, judging whether the particle meets the condition to enter the archive, and if it meets, inserting it into the tree structure. With the above settings, it can ensure that the archive always stores representative particles, improve the search efficiency, and remove the dominated particles during archive update to maintain the effectiveness of the archive.

[0046] In a preferred solution, the method for obtaining the domination relationship between the particles and the archive set in Step3 includes: comparing the particles with the particle sets corresponding to the nodes in the archive tree structure. First, compare the domination relationship between the particles and the maximum and minimum vertices of the hypercube corresponding to the nodes. According to the comparison results, determine whether the particles are added to the archive or further comparisons are carried out. The above settings can effectively reduce unnecessary domination relationship comparisons, achieve rapid discrimination of the domination relationship, and improve the efficiency of the algorithm.

[0047] In a preferred solution, the update operation of the global optimal position of each particle in Step3 includes: first, set an empty set as the candidate set for the global optimal position. Prioritize selecting marginal particles and particles located in sparse regions from the archive set and add them to the candidate set. Finally, select the global optimal position of each particle from the candidate set through the form of binary tournament. The above settings aim to balance the exploration and exploitation capabilities of the algorithm, avoid premature convergence, ensure that the algorithm can both deeply explore the current region and widely search the unexplored region in the search space, so as to balance the search efficiency and the diversity of solutions.

[0048] In a preferred solution, the system further includes a user interface module, which is used to display the set of optimized scheduling plans and provide user interaction functions to select and adjust the scheduling plans. The above settings enable users to intuitively view the effects of different scheduling plans and customize and adjust the plans through simple operations, greatly improving the flexibility of the system and the user experience.

[0049] In summary, the cascade reservoir multi-objective optimization scheduling method and system based on a tree structure unbounded archive proposed by the present invention effectively solve the technical problem that traditional optimization algorithms cannot balance the timeliness of solution and the quality of calculation results when facing the complex multi-objective optimization problem under the coupling action of high-dimensional multiple constraints in the joint optimization scheduling of cascade reservoir groups.

[0050] First of all, the present invention designs a tree structure suitable for storing large-scale archive data. This structure not only has clear hierarchy and scalability, but also can efficiently manage a large number of non-dominated solutions generated during the optimization process, improving the efficiency of data access and processing. Based on this, the present invention first applies the tree structure to the archive strategy, proposes an unbounded archive strategy based on the tree structure, cancels the limit on the archive scale, thus avoiding the deletion or replacement of potentially effective solutions, providing a high-density Pareto front with good distribution characteristics, and at the same time using the tree structure to ensure the efficiency of archive data management and maintenance.

[0051] Compared with traditional archiving strategies, the unbounded archiving strategy has significant advantages. Traditional strategies are often limited by the archiving scale. When the archive reaches the preset scale, new valid solutions may be deleted or replaced, resulting in a decline in the quality of the archive and causing the Pareto approximate front to decline and oscillate. The unbounded archiving strategy, on the other hand, ensures that all valid solutions can be retained by dynamically expanding the archive space, thereby improving the reliability of the solution results.

[0052] To further improve the solution performance, the present invention integrates a tree structure and an unbounded archiving strategy into a multi-objective particle swarm optimization algorithm, forming a multi-objective particle swarm algorithm based on a tree-structured unbounded archive. When solving the multi-objective optimal operation problem of cascade reservoirs, this algorithm can significantly improve the quality of the solution results, quickly search for high-quality non-dominated solution sets in a complex solution space, and provide a powerful tool for solving practical engineering problems.

[0053] The method and system for multi-objective optimal operation of cascade reservoirs based on a tree-structured unbounded archive proposed by the present invention have significant advantages in solving complex multi-objective optimization problems represented by the joint optimal operation of cascade reservoir groups. By innovatively applying the tree structure and the unbounded archiving strategy, this method optimizes the overall performance of the multi-objective particle swarm algorithm, improving the accuracy and reliability of the solution results. This invention provides a new solution idea and strong support for solving the problem of cascade reservoir optimal operation.

Claims

1. A multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archives, characterized in that: The following steps are involved: Step 1: Sort out and analyze the existing dispatching and operation data of cascade reservoirs, determine the dispatching objectives and corresponding constraints, and establish a multi-objective optimization dispatching model for cascade reservoirs based on the dispatching objectives and constraints; Step 2: Design a tree structure suitable for archiving data storage, and propose an unbounded archiving strategy based on the tree structure, where unbounded archiving removes restrictions on the size of the archive; Step 3: Integrate the unbounded archiving strategy described in Step 2 into the multi-objective particle swarm optimization algorithm, and propose a multi-objective particle swarm optimization algorithm based on tree-structured unbounded archiving; Step 4: Use the improved multi-objective particle swarm algorithm to solve the multi-objective optimization scheduling model of cascade reservoirs and obtain a high-quality set of optimization scheduling solutions.

2. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 1 is characterized in that: The scheduling objectives in Step 1 include maximum power generation of cascade reservoirs, minimum water abandonment, maximum energy storage at the end of the scheduling period, minimum water shortage rate and minimum flood control risk, and the calculation formulas are: （1）； （2）； （3）； （4）； （5）； In the formula, The cascade reservoirs have the largest power generation capacity. To minimize the amount of discarded water, The energy storage is maximum at the end of the dispatch period. To minimize water shortage rate, To minimize flood risk, n represents the number of hydropower stations, T Indicates the number of time periods, express t Time-limited hydropower station i The average output of express t Time-limited hydropower station i The average water discharge rate, Indicates the length of the unit time period, Indicates hydropower station j The amount of water available at the end of the dispatch period, Indicates hydropower station i The available water-energy storage value function relationship, express t The average outflow of the last hydropower station in the period, express t The flow rate corresponding to the downstream water demand during the period, express t Hydropower station at the end of the period i The storage capacity, Indicates hydropower station i The reservoir capacity corresponding to the flood limit water level is Indicates that the regulations stipulate that hydropower stations i The reservoir capacity corresponding to the highest flood control level is For custom intermediate variables, i , j Indicates two different hydropower station numbers.

3. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 2 is characterized in that: The calculation formula for the cascade reservoirs to achieve maximum power generation, minimum water abandonment, maximum energy storage at the end of the scheduling period, minimum water supply shortage rate and minimum flood control risk is based on parameters such as the number of hydropower stations, number of time periods, average output, average water abandonment flow, unit time period length, available water at the end of the scheduling period, available water-energy storage value function relationship, average outflow flow, flow corresponding to downstream water demand, reservoir capacity, reservoir capacity corresponding to flood limit water level and reservoir capacity corresponding to maximum flood control level.

4. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 1 is characterized in that: The constraints in Step 1 include water level range, water level amplitude constraint, flow range, flow amplitude constraint, output range, output amplitude constraint, and reserved storage capacity constraint, and their calculation formulas are: （6）； （7）； （8）； （9）； In the formula, , , and Respectively t Time-limited hydropower station i The average water level, minimum water level, maximum water level and water level fluctuation range, Indicates time period Hydropower Station i The average water level; , , and Respectively t Time-limited hydropower station i The average outbound flow, minimum outbound flow, maximum outbound flow and outbound flow variation, Indicates time period Hydropower Station i Average outbound flow rate; , Respectively t Time-limited hydropower station i The minimum output, maximum output and output amplitude, Indicates time period Hydropower Station i The average output of express t The sum of the storage capacities corresponding to the normal water storage levels of the reservoirs with reserved storage capacity constraints during the time period; express t Reserved storage capacity for a period of time.

5. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 1 is characterized in that: In the tree structure in Step 2, each node includes information about a parent node, a child node, an archive subset obtained by dividing the parent node, and the maximum vertex and minimum vertex of a hypercube covering the archive subset corresponding to the target vector set.

6. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 1 is characterized in that: The calculation process of the multi-objective particle swarm algorithm based on tree-structured unbounded archives in Step 3 includes: initializing the particle swarm and the tree-structured unbounded archives, initializing the individual optimal position and the global optimal position of each particle, updating the speed and position of each particle based on the individual optimal position and the global optimal position, correcting and mutating the individual position, updating the archive set, the individual optimal position and the global optimal position based on each particle after the position update, and repeating the above steps until the maximum number of iterations is reached or a given termination condition is given.

7. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 6 is characterized by: The archive initialization operation in Step 3 is that the archive set is empty at the beginning, and the first particle in the particle group is directly included in the archive. The subsequent operations are consistent with the archive update operation, that is, the archive is updated using the particles in the particle group to determine whether each particle meets the conditions for entering the archive. If so, it is inserted into the tree structure.

8. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 7 is characterized in that: The method for obtaining the dominance relationship between the particle and the archive set in Step 3 includes: comparing the particle with the particle set corresponding to the node in the archive tree structure, firstly comparing the dominance relationship with the maximum vertex and the minimum vertex of the hypercube corresponding to the node, and deciding whether to add the particle to the archive or conduct further comparison based on the comparison result.

9. The multi-objective optimization scheduling method for cascade reservoirs based on tree-structured unbounded archive according to claim 6 is characterized in that: The updating operation of the global optimal position of each particle in Step 3 includes: firstly setting an empty set as a candidate set of the global optimal position, preferentially selecting marginal particles and particles located in sparse areas from the archive set to add to the candidate set, and finally selecting the global optimal position of each particle from the candidate set in the form of a binary tournament.

10. A multi-objective optimization dispatching system for cascade reservoirs based on tree-structured unbounded archives, characterized in that: A system for implementing the multi-objective optimization scheduling method of cascade reservoirs based on tree-structured unbounded archiving as described in any one of claims 1 to 9, the system comprising: The model building module is used to determine the dispatching objectives and corresponding constraints of cascade reservoirs in different periods, and to establish a multi-objective optimization dispatching model of cascade reservoirs based on the dispatching objectives and constraints; Unbounded archiving strategy design module, used to design a tree structure suitable for archiving data storage and propose an unbounded archiving strategy based on the tree structure; The multi-objective particle swarm algorithm design module is used to integrate the unbounded archiving strategy into the multi-objective particle swarm optimization algorithm, and propose a multi-objective particle swarm algorithm based on tree-structured unbounded archiving; The solution module is used to solve the multi-objective optimization scheduling model of cascade reservoirs using the improved multi-objective particle swarm algorithm to obtain the optimal scheduling solution set.

11. The multi-objective optimization scheduling system for cascade reservoirs based on tree-structured unbounded archive according to claim 10 is characterized in that: The system further includes a user interface module for displaying the optimized scheduling solution set and providing a user interaction function for selecting and adjusting a scheduling solution.

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