A multi-objective scheduling method and system for water projects

Abstract

The present invention discloses a multi-objective scheduling method and system for water projects, which belongs to the technical field of water project optimization scheduling, including S1, based on basic information data of water projects, constructing a water project group optimization scheduling model with maximum power generation, maximum sediment discharge and minimum ecological water shortage as objective functions, and setting constraints for the water project group optimization scheduling model; S2, based on the water project group optimization scheduling model, using a dual-population optimization mechanism to solve the optimal scheduling plan for the water project; S3, outputting the optimal scheduling plan; the multi-objective scheduling method and system for water projects provided by the present invention can coordinate the relationship between water project power generation, sediment discharge and ecology, quickly provide a set of water project group scheduling plans, maximize the benefits of water projects, have the advantages of few calculation parameters, fast convergence speed, strong global optimization ability and not easy to fall into local optimality, etc., and provide a more effective technical method for solving complex multi-objective engineering problems of water projects.

Description

Technical Field

[0001] The present invention relates to the technical field of water project optimization scheduling, and in particular to a water project multi-objective scheduling method and system. Background Art

[0002] Optimal scheduling of water conservancy systems is a key means of achieving efficient utilization of water resources within a river basin and plays a crucial role in power generation and hydropower management. While ensuring the safe and stable operation of water conservancy projects and the power grid, scientific scheduling strategies can leverage the combined benefits of power generation, water supply, flood control, and navigation. Furthermore, with the diversification of water conservancy functional requirements, coordinating multiple objectives—power generation, flood control, navigation, water supply, and ecological conservation—has become a core issue in modern water conservancy scheduling.

[0003] Currently, there are two main approaches to solving multi-objective problems in water projects. Mathematical analytical algorithms, such as linear programming, nonlinear programming, and integer programming, have been widely used in scheduling projects due to their simplicity and ease of use. However, the sophistication of their model processing, the closed nature of their computational processes, and the complexity of their problem solving all affect their efficiency and reliability. Metaheuristic algorithms, such as NSGAII, MOEA / D, and LMOCSO, which mimic the behavior of biological populations and employ a dynamic optimization strategy to adjust the optimal solution, can effectively solve large-scale, complex optimization problems. However, these algorithms suffer from issues such as premature convergence, difficulty handling high-dimensional spaces, and unstable optimization results. Furthermore, existing optimization scheduling models focus on converting multi-objective optimization problems into single-objective ones, using single-objective optimization algorithms to solve them and obtain a unique scheduling solution. This makes them difficult to meet the actual scheduling solution adjustment requirements at different scheduling stages under the current comprehensive benefit-benefit objective, hindering the further development of multi-objective optimization algorithms.

[0004] Based on this, the present invention first constructs an optimal scheduling model for a water project group with the goals of maximizing power generation, maximizing sediment discharge and minimizing ecological water shortage, and at the same time adds constraints to the optimal scheduling model for the water project group; secondly, an adaptive multi-objective victory algorithm based on a dual-population optimization mechanism is proposed to solve the multi-objective optimization scheduling problem; further, it is applied to the multi-objective optimization scheduling problem of water projects with other excellent optimization algorithms, and the performance superiority and solution set reliability of the proposed method are proved through result analysis and scheme decision-making, providing a powerful tool for effectively solving the multi-dimensional objective collaborative optimization problem of water project groups. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective scheduling method and system for water projects to solve the problem that the existing water project models in the above background technology are insufficient in terms of scheduling solution efficiency, sand and silt removal, and ecological benefits.

[0006] To achieve the above object, the present invention provides a multi-objective scheduling method for water projects, comprising the following steps:

[0007] S1. Based on basic information data of water projects, a water project group optimization scheduling model is constructed with the objective functions of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage. At the same time, constraints are set for the water project group optimization scheduling model, the maximum number of iterations and population size are preset, and the outflow rate during the water project scheduling period is determined as the decision variable;

[0008] S2. Based on the water project group optimization scheduling model, a dual-population optimization mechanism is used to solve the optimal scheduling plan for water projects, including:

[0009] S21. Dual population initialization: In the initialization phase, two populations of equal size and uniform distribution are randomly generated in the optimization space. The fitness of the individuals in the populations is calculated simultaneously. The dominant population and the optimal individual in the dominant population are obtained based on the fast non-dominated sorting method.

[0010] S22, optimal mean search mechanism: using the mean of the current optimal solution to guide the population search direction;

[0011] S23, Elite Difference Search Mechanism: Increases population diversity by considering the differences between individuals in the population, thereby identifying new search areas in the optimization space;

[0012] S24, balanced median search mechanism: balances extreme individuals within the population to prevent excessive differences between individuals;

[0013] S25, adopt the worst mean search mechanism to increase the chance of exploring more favorable spaces and reduce the time of invalid search;

[0014] S26. Update the dominant population and the optimal position of individuals: Calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting method, update the dominant population, and then use the conventional update method to determine the optimal position of the individual. Use the adaptive jump out of the local optimal strategy to dynamically replace the optimal position of the individual;

[0015] S27, iterative update, if the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained, and the fitness value of the dominant population is output, otherwise return to step S22;

[0016] S3. Output the optimal scheduling plan.

[0017] Preferably, the objective function in step S1 is specifically:

[0018] The objective function for maximizing power generation is expressed as:

[0019] ;

[0020] ;

[0021] in, is the number of water projects; is the hydraulic program number, ; is the number of time periods in the scheduling period; is the time period number, ; For the period The number of hours, in h; 、 、 Represents water projects In the period Output (kW), power flow (m 3 / s) and hydraulic head (m); Water project Output coefficient;

[0022] The objective function for maximizing sediment discharge is expressed as:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] in, 、 Water projects In the period Inbound and outbound traffic, m 3 / s; is the bed sand dry density; Water Project In the period The sediment discharge ratio; 、 Water projects In the period The sand content of the incoming and outgoing storage, kg / m 3 ; Water project In the period Storage capacity;

[0028] The objective function of minimizing ecological water shortage is expressed as:

[0029] ;

[0030] in, Water Project In the period Ecological water demand, m 3 / s.

[0031] Preferably, the constraints set in step S1 specifically include:

[0032] Initial and final water level constraints:

[0033] ;

[0034] ;

[0035] in, 、 Water projects Initial water level and expected final water level, m;

[0036] Water balance constraints:

[0037] ;

[0038] Water level constraint:

[0039] ;

[0040] in, Water Project In the period water level; 、 Water projects In the period The upper and lower limits of the water level; Under normal circumstances, The flood limit water level and normal high water level of the water intake project during the flood season and non-flood season respectively; Dead water level of the water intake project.

[0041] Power generation flow constraints:

[0042] ;

[0043] in, 、 Water projects In the period The upper and lower limits of the power generation flow are usually limited by the unit's overcurrent capacity, maintenance plan, etc.

[0044] Outbound flow constraints:

[0045] ;

[0046] in, 、 Water projects In the period The upper and lower limits of outbound flow; Under normal circumstances, The flood control safety requirements of water projects and their downstream areas need to be met; It is necessary to consider the comprehensive utilization needs of downstream irrigation, water supply, ecology, environment, etc.

[0047] Constraints on outbound traffic fluctuations:

[0048] ;

[0049] in, Water Project The outbound flow rate variation value, m 3 / s;

[0050] Output constraints:

[0051] ;

[0052] in, 、 Water projects In the period The upper and lower limits of output are mainly determined by factors such as the technical output requirements, maintenance capacity, and installed capacity of the water project.

[0053] Non-negativity constraint: All variables must be non-negative.

[0054] Preferably, step S21 specifically includes the following steps:

[0055] S211. In the initialization phase, two populations of the same size and uniform distribution in the optimization space are randomly generated as the optimization population. population and elite archive populations Arc :

[0056] ;

[0057] in, To generate a random number that is uniformly distributed within the upper and lower boundaries of the optimization space; are the total number of individuals in the population and the variable dimension respectively;

[0058] S212, in order to avoid repeated visits to the same individuals and excessive optimization time and other waste of computing resources, as the iteration process progresses, a class of population is randomly and dynamically selected for update to generate the offspring population. In the early stage of iteration, the focus is on optimizing the population. Population Global exploration update; as the optimization process progresses, the elite archive population ArcIt no longer just plays the role of storing the historical optimal individual set. The frequency of its selection as the offspring population is increased, further effectively improving the local optimization ability of the population on the Pareto frontier and improving the quality of the solution set. Among them, the update strategy is mainly based on the multi-dimensional adaptive optimization strategy:

[0059] ;

[0060] in, is a random function that takes random values ​​in the interval [0, 1); is the number of evaluations for the current iteration;

[0061] S213, Dual Population Iterative Update: Considering the characteristics of fitness value ranking, solution set distribution sparseness and randomness, the dual population selects and updates the next generation of dual population individuals based on the environmental selection function. Population based on Population and Offspring The collection is selected and updated, the elite population Arc based on Population and Arc The collection of is selected and updated, and the high-quality information sharing and collaboration of the two populations are fully carried out, effectively maintaining the diversity of population individuals and the efficiency of optimization, which is expressed as:

[0062] ;

[0063] in, For the Population population; For the Generation Arc population; is the environmental selection function, which means that after merging populations A and B, the individuals with better performance are selected using the reference-based environmental selection function; For the The offspring individuals generated by generations.

[0064] Preferably, step S22 performs the optimal mean search mechanism specifically including:

[0065] Using the mean of the current optimal solution to guide the population search direction can smooth the search path of individuals in the population, reduce the randomness of the search, enable the algorithm to converge faster, and improve the stability and consistency of the solution. In addition, by guiding the population toward the mean of the elite individuals, the algorithm can effectively avoid over-exploring unnecessary solution areas, reduce computational overhead, and improve optimization efficiency:

[0066] ;

[0067] in, is a random function that takes random values ​​in the interval [0, 1); Search for the optimal mean solution; Indicates the The individual mean of the elite archive set in the iteration, the elite archive set is the individual that stores several Pareto frontier surfaces.

[0068] Preferably, step S23 performs the elite difference search mechanism and specifically includes:

[0069] By considering the differences between individuals in the population, we can increase population diversity, assist in identifying new search areas in the solution space, avoid premature convergence, and enhance the algorithm's optimization performance. In addition, by using information about differences between individuals, we can dynamically adjust the search strategy, allowing the algorithm to adaptively adjust the ratio of exploration and exploitation at different stages:

[0070] ;

[0071] in, Search for solutions for the elite difference; Indicates the The individuals selected from the elite archive set in the iteration, ind Randomly select from the integer set {1,2,…,NArc} the number of individuals in the elite population NArc.

[0072] Preferably, step S24 executes the balanced median search mechanism specifically including:

[0073] The median is the median or the value of some middle point in the population. It is used in multi-objective optimization to balance extreme individuals within the population, prevent excessive differences between individuals, enhance the robustness of the algorithm to noise and uncertainty, avoid the adverse effects of extreme individuals on the search direction of the population, and improve the stability and reliability of the optimization process:

[0074] ;

[0075] in, Search for the median solution; Indicates the The median individual selected from the elite archive set after sorting according to any target in the iteration; Represents random numbers that follow a normal distribution.

[0076] Preferably, step S25 adopts the worst mean search mechanism specifically as follows:

[0077] As individuals gradually approach the worst individual in the search space, the algorithm can dynamically adjust the search direction to avoid falling into a harsh search area, thereby increasing the chances of exploring more favorable spaces, reducing the time of ineffective searches, and improving the fitness of the individuals in the overall population, enabling the algorithm to find high-quality solutions more quickly:

[0078] ;

[0079] ;

[0080] in, is the worst mean away from the search solution; represents the mean position of the worst individual in the population; Indicates the presence of a target ; Represents an individual On target The worst performers A collection of individuals.

[0081] The present invention also provides a water project multi-objective scheduling system, comprising:

[0082] The model building module is configured to perform the following actions: based on the basic information data of the water projects, construct an optimal scheduling model for the water project group with the goals of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage, and at the same time add constraints to the optimal scheduling model for the water project group; preset the maximum number of iterations and population size, and determine the outflow flow during the water project scheduling period as the decision variable;

[0083] The water project group multi-objective scheduling victory method solution module includes an initialization unit, an optimal mean search mechanism unit, an elite difference search mechanism unit, an equilibrium median search mechanism unit, a worst mean principle search mechanism unit, an elite population and individual optimal position update unit, and a water project optimal scheduling plan acquisition unit.

[0084] Preferably, each unit in the water project group multi-objective scheduling success method solution module is specifically:

[0085] The initialization unit is configured to perform the following actions: based on a preset range of the decision variable, initialize the population, the optimal position of the individuals in the population, and the fitness of the individuals, and then obtain the dominant population and the optimal individual in the dominant population based on a fast non-dominated sorting method;

[0086] The optimal mean search mechanism unit is configured to perform the following actions: It uses the mean of the current optimal solution to guide the population search direction, smoothing the search paths of individuals in the population, reducing the randomness of the search, enabling the algorithm to converge faster, and improving the stability and consistency of the solution;

[0087] The elite difference search mechanism unit is configured to perform the following actions: increase population diversity by considering the differences between different individuals in the population, assist in identifying new search areas in the optimal solution space, avoid premature convergence, and enhance the algorithm's optimization performance.

[0088] The balanced median search mechanism unit is configured to perform the following actions: the median is the median or the value of some middle point in the population. It is used in multi-objective optimization to balance extreme individuals within the population, prevent excessive differences between individuals, enhance the robustness of the algorithm to noise and uncertainty, avoid the adverse effects of extreme individuals on the search direction of the population, and improve the stability and reliability of the optimization process.

[0089] The worst mean principle search mechanism unit is configured to perform the following actions: When an individual gradually approaches the worst individual in the search space, the algorithm can dynamically adjust the search direction to avoid being trapped in a harsh search area, thereby increasing the opportunity to explore more favorable spaces, reducing the time of invalid search, and improving the overall fitness of individuals in the population, allowing the algorithm to find high-quality solutions more quickly.

[0090] The dominant population and individual optimal position update unit is configured to perform the following actions: calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting algorithm, update the dominant population, and then use the conventional update method to determine the optimal position of the individual, and then use the adaptive jump out of the local optimal strategy to dynamically replace the individual optimal position;

[0091] The water project optimal scheduling plan acquisition unit is configured to perform the following actions: perform iterative updates. If the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained and the fitness value of the dominant population is output; otherwise, the optimal mean search mechanism unit is returned.

[0092] Therefore, the present invention adopts the above-mentioned multi-objective scheduling method and system for water projects, which has the following beneficial effects:

[0093] (1) It has the advantages of simple implementation, fast convergence speed, strong global optimization ability, not easy to fall into local optimality, and wide application scenarios. It can comprehensively consider the comprehensive benefits of power generation, sedimentation and ecology in the optimization scheduling of water projects, providing a new way to solve the multi-objective optimization scheduling problem of water project groups;

[0094] (2) Considering the imbalance between convergence efficiency and particle diversity in the traditional single population during the iteration process, the dual population progressive optimization strategy is introduced, which makes the algorithm less likely to fall into the local optimum and can jump out of the local optimum, thus achieving a good balance between global exploration and local exploration;

[0095] (3) The number of input parameters is small, which avoids the complex parameter adjustment process and makes programming simple;

[0096] (4) It can realize the global optimization of the water project group scheduling problem, further improve the calculation efficiency and accuracy, and quickly and efficiently decide on the water project group scheduling plan set, thereby providing a more effective method for solving complex multi-objective engineering problems of water project groups and providing decision makers with the best plan selection.

[0097] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 This is a flow chart of a multi-objective scheduling method for water projects according to the present invention;

[0099] Figure 2 Schematic diagram of the average ranking of IGD and HV indicators of the embodiment of the present invention and the comparison algorithm, where (a) is ZDT, (b) is DTLZ-3, (c) is DTLZ-5, (d) is DTLZ-8, (e) is DTLZ-10, (f) is WFG-3, (g) is WFG-5, (h) is WFG-8, and (i) is WFG-10;

[0100] Figure 3 The HV variation diagram of three targets in the C-DTLZ and DC-DTLZ test problems according to an embodiment of the present invention, where (a) is C1_DTLZ1, (b) is C1_DTLZ3, (c) is C2_DTLZ2, (d) is C3_DTLZ4, (e) is DC1_DTLZ1, (f) is DC1_DTLZ3, (g) is DC3_DTLZ1, and (h) is DC3_DTLZ3;

[0101] Figure 4 The Pareto frontier diagram of the multi-objective scheduling model in the embodiment of the present invention, where (a) is a high-water year, (b) is a normal-water year, and (c) is a low-water year;

[0102] Figure 5 This is a typical annual scheduling result diagram drawn from the Pareto front solution set of an embodiment of the present invention, where (a) is a wet year (SMX), (b) is a normal year (SMX), (c) is a dry year (SMX), (d) is a wet year (XLD), (e) is a normal year (XLD), and (f) is a dry year (XLD). DETAILED DESCRIPTION

[0103] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0104] See also Figure 1 , a multi-objective scheduling method for water projects, comprising the following steps:

[0105] S1. Based on the basic information data of water projects, a water project group optimization scheduling model with the objective functions of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage is constructed, and constraints are set for the water project group optimization scheduling model;

[0106] S2. Based on the water project group optimization scheduling model, a dual-population optimization mechanism is used to solve the optimal scheduling plan for water projects, including:

[0107] S21. Dual population initialization: In the initialization phase, two populations of equal size and uniform distribution are randomly generated in the optimization space. The fitness of the individuals in the populations is calculated simultaneously. The dominant population and the optimal individual in the dominant population are obtained based on the fast non-dominated sorting method.

[0108] S22, optimal mean search mechanism: using the mean of the current optimal solution to guide the population search direction;

[0109] S23, Elite Difference Search Mechanism: Increases population diversity by considering the differences between individuals in the population, thereby identifying new search areas in the optimization space;

[0110] S24, balanced median search mechanism: balances extreme individuals within the population;

[0111] S25, using the worst mean search mechanism to reduce invalid search time;

[0112] S26. Update the dominant population and the optimal position of individuals: Calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting method, update the dominant population, and then use the conventional update method to determine the optimal position of the individual. Use the adaptive jump out of the local optimal strategy to dynamically replace the optimal position of the individual;

[0113] S27, iterative update, if the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained, and the fitness value of the dominant population is output, otherwise return to step S22;

[0114] S3. Output the optimal scheduling plan.

[0115] In order to achieve multi-objective coordinated scheduling of cascade water projects, this embodiment evaluates the pros and cons of the alternative plans by comparing the size of the multi-objective benefit values ​​of the alternative plans with the requirements of the decision makers and the objective characteristics of each indicator. The present invention uses power generation, sediment discharge and ecological water shortage rate as evaluation indicators, among which power generation is a benefit-type indicator. This value can reflect the performance level of the water project in terms of revenue. The larger the indicator value, the stronger the profitability of the water project and the higher the operation level. Sediment discharge and ecological water shortage rate are cost-type benefit indicators. This value can reflect the performance level of the water project in terms of operation and maintenance costs. The larger the indicator value, the higher the operation and maintenance costs of the water project and the poorer the operation level. The calculation expressions of the three indicators are the same as the corresponding objective function expressions in the scheduling model, and the values ​​of each indicator are the corresponding values ​​of the model optimization solution results.

[0116] The traditional AHP method relies too much on experts to judge the relative importance of each item, making it difficult to ensure fairness and consistency in the evaluation of each item. Therefore, the ambiguity of the traditional AHP method in reflecting expert evaluations needs to be improved, and the results of the originally uncertain evaluation indicators are too absolute. At the same time, the consistency of the judgment matrix in the traditional AHP method is difficult to ensure, and the judgment indicator CR < 0.1 lacks a certain scientific basis. This study introduces fuzzy interval theory to consider the ambiguity of the importance between indicators, forming the fuzzy AHP method (FAHP). The specific steps are as follows:

[0117] First, set the evaluation index to set , triangular fuzzy numbers are introduced to construct the judgment matrix, the formula is as follows:

[0118] ;

[0119] in, Respectively represent indicators Relative to the indicator The upper and lower bounds of relative importance. A 9-scale method is used to quantify the relative importance of each indicator to provide more accurate and detailed comparison results. Specific criteria are shown in Table 1.

[0120] Table 1 Relative importance quantification table

[0121] ;

[0122] The relative importance of the evaluation indicators is judged to form a judgment matrix, as shown in the formula.

[0123] ;

[0124] Calculate the initial weight of each indicator:

[0125] ;

[0126] A method for comparing the relative importance of two indicators.

[0127] ;

[0128] Finally, the data is normalized to obtain the subjective weight of each indicator. .

[0129] First, determine the set of solutions to be evaluated , where the set of indicators used for evaluation in each scheme is The indicator value corresponding to the scheme set is determined by the entropy value. The greater the importance of the indicator, the higher the entropy value, and the greater its influence on the comprehensive evaluation, that is, the greater the weight. The formula for calculating the entropy value of each evaluation indicator is as follows:

[0130] ;

[0131] ;

[0132] ;

[0133] in: For the Among the plans The information entropy of each indicator; is the number of scheduling scheme sets; when season In the traditional entropy weight method, the weight of each indicator is calculated based on the degree of difference in the whole, that is, the proportion of the entropy value of each indicator to the overall entropy value. Weight of each indicator for:

[0134] ;

[0135] Fuzzy the indicator values ​​of each scheme, that is, About indicators The index value is fuzzy , forming an interval fuzzy matrix. The normalized matrix is ​​obtained as shown in the formula.

[0136] ;

[0137] make , which means that in the indicator The smaller the sum of the degrees of separation of all candidate solutions, the smaller the indicator's ability to distinguish between the solutions, and the smaller the weight of the indicator in the evaluation; conversely, the greater the indicator's ability to distinguish between the solutions, the greater the weight of the indicator in the evaluation. Indicates the indicator The total difference of all the options. The choice of weight vector The difference between all alternatives under all indicators should be maximized, as shown in the formula.

[0138] ;

[0139] The optimal weight matrix The solution is shown in Eq.

[0140] ;

[0141] The basic idea of ​​the combined weighting method based on game theory is to regard the different weight results obtained by the subjective and objective weighting methods as non-cooperative players in a game that competes with each other, and to transform the optimal comprehensive weighting problem into a multi-person optimization problem. The goal is to obtain an equilibrium solution between the subjective and objective weighting methods so that the deviation between each weight result and the optimal weight combination is minimized. Then, based on the equilibrium solution, the subjective and objective weighting methods are combined to obtain the combined weight of each indicator. The specific calculation method is as follows:

[0142] ;

[0143] Where: G is the comprehensive weight; s is the number of weighting methods to be combined; For the t The linear weight coefficient of the weighting method; For the t The transposed matrix of the weighting method.

[0144] Comprehensive weight G Will follow the linear weight coefficient changes with the changes, when Get the optimal weight coefficient When the comprehensive weight G At the same time, obtain the optimal comprehensive weight Therefore, the idea of ​​game theory is used to optimize the linear weight coefficient, and the objective function is the comprehensive weight G With each weight method The sum of the deviations is minimum.

[0145] ;

[0146] According to the differential properties of the matrix, the above objective function is transformed to obtain the optimal linear weight coefficient , normalize it and substitute it into the optimized comprehensive weight G .

[0147] .

[0148] A multi-objective scheduling system for water projects, comprising:

[0149] The model building module is configured to perform the following actions: based on the basic information data of the water projects, construct an optimal scheduling model for the water project group with the goals of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage, and at the same time add constraints to the optimal scheduling model for the water project group; preset the maximum number of iterations and population size, and determine the outflow flow during the water project scheduling period as the decision variable;

[0150] The module for solving the successful method of multi-objective scheduling of water project groups includes:

[0151] The initialization unit is configured to perform the following actions: based on a preset range of the decision variable, initialize the population, the optimal position of the individuals in the population, and the fitness of the individuals, and then obtain the dominant population and the optimal individual in the dominant population based on a fast non-dominated sorting method;

[0152] The optimal mean search mechanism unit is configured to perform the following actions: It uses the mean of the current optimal solution to guide the population search direction, smoothing the search paths of individuals in the population, reducing the randomness of the search, enabling the algorithm to converge faster, and improving the stability and consistency of the solution;

[0153] The elite difference search mechanism unit is configured to perform the following actions: increase population diversity by considering the differences between different individuals in the population, assist in identifying new search areas in the optimal solution space, avoid premature convergence, and enhance the algorithm's optimization performance.

[0154] The balanced median search mechanism unit is configured to perform the following actions: the median is the median or the value of some middle point in the population. It is used in multi-objective optimization to balance extreme individuals within the population, prevent excessive differences between individuals, enhance the robustness of the algorithm to noise and uncertainty, avoid the adverse effects of extreme individuals on the search direction of the population, and improve the stability and reliability of the optimization process.

[0155] The worst mean principle search mechanism unit is configured to perform the following actions: When an individual gradually approaches the worst individual in the search space, the algorithm can dynamically adjust the search direction to avoid being trapped in a harsh search area, thereby increasing the opportunity to explore more favorable spaces, reducing the time of invalid search, and improving the overall fitness of individuals in the population, allowing the algorithm to find high-quality solutions more quickly.

[0156] The dominant population and individual optimal position update unit is configured to perform the following actions: calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting algorithm, update the dominant population, and then use the conventional update method to determine the optimal position of the individual, and then use the adaptive jump out of the local optimal strategy to dynamically replace the individual optimal position;

[0157] The water project optimal scheduling plan acquisition unit is configured to perform the following actions: perform iterative updates. If the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained and the fitness value of the dominant population is output; otherwise, the optimal mean search mechanism unit is returned.

[0158] In this example, a water project in a certain basin is selected as the research object to carry out a water-sediment-ecological multi-objective scheduling study of the water project. At the same time, four scheduling methods are adopted with annual scale as the scheduling period and monthly scale as the scheduling period to solve the multi-objective scheduling model under different typical annual scheduling scenarios of the research object, such as Figure 2-Figure 5 As shown in Table 2, the multi-objective scheduling solution results are shown in Table 2;

[0159] Table 2 Test results of the present invention on actual scheduling problems

[0160] ;

[0161] It can be seen that: Table 2 shows the scheduling results of the present invention and the comparative algorithm in different typical years (flood year, normal flood year, dry year). A comprehensive analysis is conducted from three perspectives (single target priority, average value of different targets and median value of different targets). Combined with the Pareto level of each algorithm in different year types, a comprehensive evaluation of its scheduling effect is conducted. It can be seen that: (1) Under the conditions of each typical year, the present invention shows the best scheduling performance. Its power generation, sediment discharge and ecological water shortage rate are close to or reach the optimal target. In particular, in terms of sediment discharge and ecological water shortage rate, the present invention shows excellent balancing ability. Compared with the present invention, the performance of NSGA-II and NSGA-III is slightly inferior. The MOEAD algorithm performs the worst. Although the power generation of the comparative algorithm is close to the power generation of the present invention, the performance of the two algorithms is slightly compromised in terms of sediment discharge and ecological water shortage rate. (2) In the multi-objective scheduling problem, the present invention is obviously the best choice. In particular, its scheduling advantage is more prominent in the context of strict ecological constraints. For different optimization requirements, NSGA-III and NSGA-II can be used as alternatives.

[0162] Further analysis of the scheduling scheme of the present invention: (1) The power generation in the wet year increased by 580 million kW·h compared with the actual scheme, an increase of 5%, reducing the original ecological water shortage rate of 2.01% to 0.84%, but sacrificing about 98 million tons of sediment discharge. This shows that the wet year can bring more economic benefits under the present invention while better protecting the ecological benefits of the downstream water project. (2) In the actual scheduling scheme, the average water year, due to the pursuit of high power generation efficiency, caused the sediment discharge and ecological target benefit values ​​to be significantly reduced. In comparison, the average water year in the present invention achieves an effective improvement in ecological benefits by reducing power generation and sediment discharge, and to a certain extent optimizes the balanced utilization of water resources for multiple objectives. (3) The power generation in the dry year increased from 6.673 billion kW·h to 7.968 billion kW·h, significantly alleviating the problem of low power generation in the dry season. The ecological water shortage rate was significantly reduced, but even less than the ecological water shortage rate in the actual scheduling wet year. However, the ecological sediment discharge continued to decrease, indicating that the present invention can effectively alleviate the problems of insufficient hydropower generation and serious ecological interruption in the dry year through reasonable optimization scheduling.

[0163] Table 3 Comparison between the actual scheduling scheme and the present invention

[0164] ;

[0165] Table 3 is a comparison table between the actual scheduling scheme and the present invention. In summary, compared with the actual scheduling scheme, the multi-objective balanced allocation of water resources and the overall comprehensive benefits of the present invention are significantly improved.

[0166] Therefore, the present invention adopts the above-mentioned multi-objective scheduling method and system for water projects, which can coordinate the relationship between water project power generation, sand discharge and ecology, quickly provide a set of scheduling plans for water project groups, and maximize the benefits of water projects. It has the advantages of few calculation parameters, fast convergence speed, strong global optimization ability and not easy to fall into local optimality, providing a more effective technical method for solving complex multi-objective engineering problems of water projects.

[0167] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-objective scheduling method for water projects, characterized in that: The following steps are involved: S1. Based on the basic information data of water projects, a water project group optimization scheduling model with the objective functions of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage is constructed, and constraints are set for the water project group optimization scheduling model; S2. Based on the water project group optimization scheduling model, a dual-population optimization mechanism is used to solve the optimal scheduling plan for water projects, including: S21. Dual population initialization: In the initialization phase, two populations of equal size and uniform distribution are randomly generated in the optimization space. The fitness of the individuals in the populations is calculated simultaneously. The dominant population and the optimal individual in the dominant population are obtained based on the fast non-dominated sorting method. S22, optimal mean search mechanism: using the mean of the current optimal solution to guide the population search direction; S23, Elite Difference Search Mechanism: Increases population diversity by considering the differences between individuals in the population, thereby identifying new search areas in the optimization space; S24, balanced median search mechanism: balances extreme individuals within the population; S25, using the worst mean search mechanism to reduce invalid search time; S26. Update the dominant population and the optimal position of individuals: Calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting method, update the dominant population, and then use the conventional update method to determine the optimal position of the individual. Use the adaptive jump out of the local optimal strategy to dynamically replace the optimal position of the individual; S27, iterative update, if the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained, and the fitness value of the dominant population is output, otherwise return to step S22; S3. Output the optimal scheduling plan.

2. A multi-objective scheduling method for water projects according to claim 1, characterized in that: The objective function in step S1 is specifically: The objective function for maximizing power generation is expressed as: ； ； in, is the number of water projects; is the hydraulic program number, ; is the number of time periods in the scheduling period; is the time period number, ; For the period The number of hours, in h; 、 、 Represents water projects In the period output, power generation flow and water head; Water project Output coefficient; The objective function for maximizing sediment discharge is expressed as: ； ； ； ； in, 、 Water projects In the period Inbound and outbound traffic; is the bed sand dry density; Water Project In the period The sediment discharge ratio; 、 Water projects In the period The sand content of incoming and outgoing storage; Water project In the period Storage capacity; The objective function of minimizing ecological water shortage is expressed as: ； in, Water Project In the period ecological water demand.

3. A multi-objective scheduling method for water projects according to claim 2, characterized in that: The constraints set in step S1 specifically include: Initial and final water level constraints: ； ； in, 、 Water projects Initial water level and expected final water level; Water balance constraints: ； Water level constraint: ； in, Water Project In the period water level; 、 Water projects In the period Upper and lower limits of water level; Power generation flow constraints: ； in, 、 Water projects In the period The upper and lower limits of power generation flow; Outbound flow constraints: ； in, 、 Water projects In the period The upper and lower limits of outbound flow; Constraints on outbound traffic fluctuations: ； in, Water Project The outbound flow rate variation value; Output constraints: ； in, 、 Water projects In the period The upper and lower limits of output; Non-negativity constraint: All variables must be non-negative.

4. A multi-objective scheduling method for water projects according to claim 1, characterized in that: Step S21 specifically includes the following steps: S211. In the initialization phase, two populations of the same size and uniform distribution in the optimization space are randomly generated as the optimization population. population and elite archive populations Arc : ； in, To generate a random number that is uniformly distributed within the upper and lower boundaries of the optimization space; are the total number of individuals in the population and the variable dimension respectively; S212. As the iterative process progresses, a population is randomly and dynamically selected for update to generate a subpopulation. The update strategy is mainly a multi-dimensional adaptive optimization strategy: ； in, is a random function that takes random values ​​in the interval [0, 1); is the number of evaluations for the current iteration; S213, Dual population iterative update: The dual population selects and updates the next generation of dual population individuals based on the environmental selection function, where the optimal population Population based on Population and Offspring The collection is selected and updated, the elite archive population Arc based on Population and Arc The collection of is selected and updated, which is expressed as: ； in, For the generation Population population; For the generation Arc population; is the environmental selection function, which means that after merging populations A and B, the individuals with better performance are selected using the reference-based environmental selection function; For the The offspring individuals generated by generations.

5. A multi-objective scheduling method for water projects according to claim 1, characterized in that: Step S22 executes the optimal mean value search mechanism, specifically including: The mean of the current optimal solution is used to guide the population search direction. In addition, the population is guided towards the mean of the elite individuals: ； in, is a random function that takes random values ​​in the interval [0, 1); Search for the optimal mean solution; Indicates the The individual mean of the elite archive set in the iteration, the elite archive set is the individual that stores several Pareto frontier surfaces.

6. A multi-objective scheduling method for water projects according to claim 5, characterized in that: Step S23 executes the elite difference search mechanism, specifically including: By considering the differences between different individuals in the population, we can increase population diversity and assist in identifying new search areas in the optimal solution space. In addition, we can dynamically adjust the search strategy by using the difference information between individuals: ； in, Search for solutions for elite differences; Indicates the The individuals selected from the elite archive set in the iteration, ind Randomly select from the integer set {1,2,…,NArc} the number of individuals in the elite population NArc.

7. A multi-objective scheduling method for water projects according to claim 1, characterized in that: Step S24 executes the balanced median search mechanism, specifically including: The median is the middle value or some kind of midpoint value in a population: ； in, Search for the median solution; Indicates the The median individual selected from the elite archive set after sorting according to any target in the iteration; Represents random numbers that follow a normal distribution.

8. A multi-objective scheduling method for water projects according to claim 7, characterized in that: Step S25 adopts the worst mean search mechanism specifically as follows: ； ； in, is the worst mean away from the search solution; represents the mean position of the worst individual in the population; Indicates the presence of a target ; Represents an individual On target The worst performers A collection of individuals.

9. A water project multi-objective scheduling system, applied to a water project multi-objective scheduling method according to any one of claims 1 to 8, characterized in that: include: The model building module is configured to perform the following actions: based on the basic information data of the water projects, build an optimal scheduling model for the water project group with the goals of maximizing power generation, maximizing sediment discharge, and minimizing ecological water shortage, and at the same time add constraints to the optimal scheduling model for the water project group; The maximum number of iterations and population size are preset, and the outflow during the water project scheduling period is determined as the decision variable; The water project group multi-objective scheduling victory method solution module includes an initialization unit, an optimal mean search mechanism unit, an elite difference search mechanism unit, an equilibrium median search mechanism unit, a worst mean principle search mechanism unit, an elite population and individual optimal position update unit, and a water project optimal scheduling plan acquisition unit.

10. A multi-objective scheduling system for water projects according to claim 9, characterized in that: The various units in the water project group multi-objective scheduling success method solution module are as follows: The initialization unit is configured to perform the following actions: based on a preset range of the decision variable, initialize the population, the optimal position of the individuals in the population, and the fitness of the individuals, and then obtain the dominant population and the optimal individual in the dominant population based on a fast non-dominated sorting method; The optimal mean search mechanism unit is configured to perform the following actions: using the mean of the current optimal solution to guide the population search direction; The elite difference search mechanism unit is configured to perform the following actions: increase the diversity of the population by considering the differences between different individuals in the population, and assist in identifying new search areas in the optimal solution space; The balanced median search mechanism unit is configured to perform the following actions: the median is the median or some kind of middle point value in the population, which is used to balance extreme individuals in the population in multi-objective optimization; The worst mean principle search mechanism unit is configured to perform the following actions: when an individual gradually approaches the worst individual in the search space, the algorithm dynamically adjusts the search direction; The dominant population and individual optimal position update unit is configured to perform the following actions: calculate the fitness of the current population and the dominant population, obtain the dominance relationship of the solution set based on the fast non-dominated sorting algorithm, update the dominant population, and then use the conventional update method to determine the optimal position of the individual, and then use the adaptive jump out of the local optimal strategy to dynamically replace the individual optimal position; The water project optimal scheduling plan acquisition unit is configured to perform the following actions: perform iterative updates. If the preset maximum number of iterations is reached, the optimal scheduling plan for the water project is obtained and the fitness value of the dominant population is output; otherwise, the optimal mean search mechanism unit is returned.

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