Multi-objective optimization method and system for joint emergency dispatch of cascade reservoirs based on improved NSGA-II algorithm

Abstract

The application discloses a kind of based on improved NSGA-II algorithm's cascade reservoir joint emergency dispatching multi-objective optimization method and system, the method includes: obtaining the hydrological data of cascade reservoir system, reservoir capacity data, discharge capacity data and downstream ecological base flow data;Multi-objective optimization model is constructed with the maximization flood control effect index and minimization downstream ecological flow process form deviation index as target;Improved NSGA-II algorithm is used to solve the model, and the Pareto target solution set is obtained;Improved NSGA-II algorithm adopts adaptive constraint dominance relationship instead of penalty function method in constraint processing, and the penalty weight of constraint violation degree is dynamically adjusted according to the proportion of feasible solution in current population;In ecological target modeling, downstream ecological flow process form deviation index is constructed, which is used to quantify the difference between the flow process generated by the scheduling scheme and the natural flow process in form;The application can improve the feasibility and ecological friendliness of scheduling scheme.

Description

Technical Field

[0001] This invention relates to multi-objective optimization methods and systems, specifically to a multi-objective optimization method and system for joint emergency dispatch of cascade reservoirs based on an improved NSGA-II algorithm. Background Technology

[0002] Existing reservoir emergency dispatching methods, such as conventional dispatching charts and dynamic programming, are typically single-objective-oriented under conditions of above-standard floods, making it difficult to simultaneously consider flood control safety and downstream ecological needs. For example, while conventional dispatching charts can effectively control floods in specific situations, they often overlook the potential ecological impacts of flood control dispatching. For instance, the non-rapid decline in reservoir water levels can cause localized changes in ecological water levels, thus affecting the stability and health of the ecosystem. In contrast, with the development of multi-objective evolutionary algorithms, such as the Non-Dominated Sorting Genetic Algorithm (NSGA-II), they have gradually entered the field of water conservancy dispatching.

[0003] However, existing methods have some shortcomings in addressing the following issues. Regarding constraint handling, actual reservoir scheduling involves multiple complex constraints such as reservoir capacity, discharge capacity, scheduling rules, and downstream ecological baseflow. Traditional NSGA-II uses the penalty function method to handle these constraints, which easily leads to scarce feasible solutions or unstable convergence. In terms of multi-scenario adaptability, there is still a lack of modeling for comprehensive indicators under multiple scenario conditions. Regarding ecological objective modeling, existing research or applications are still limited to applying simple ecological flow lower bound constraints, lacking detailed modeling of flow process morphology. These shortcomings limit the widespread application and development of multi-objective optimization algorithms in water conservancy scheduling. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization method and system for joint emergency scheduling of cascade reservoirs based on an improved NSGA-II algorithm, in order to solve the problems in the prior art where constraint processing relies on fixed penalty weights and ecological objective modeling ignores the similarity of flow process morphology.

[0005] According to one aspect of the present invention, a multi-objective optimization method for joint emergency dispatch of cascade reservoirs based on an improved NSGA-II algorithm is provided, the method comprising: Acquire hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system; A multi-objective optimization model is constructed based on the hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data. The multi-objective optimization model aims to maximize the flood control effect index and minimize the downstream ecological flow process morphological deviation index. The improved NSGA-II algorithm was used to solve the multi-objective optimization model to obtain the Pareto optimal solution set; The improved NSGA-II algorithm includes: in the constraint processing step, a constraint non-dominated ordering relation is used to replace the penalty function method, and the constraint non-dominated ordering relation dynamically adjusts the penalty weight of constraint violation according to the proportion of feasible solutions in the current population; in the ecological goal modeling step, a downstream ecological flow process morphological deviation index is constructed, and the downstream ecological flow process morphological deviation index is used to quantify the difference in morphology between the flow process generated by the scheduling scheme and the natural flow process.

[0006] According to another aspect of the present invention, a multi-objective optimization system for joint emergency dispatch of cascade reservoirs based on an improved NSGA-II algorithm is provided, comprising: The data acquisition module is used to acquire hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system. The model building module is used to construct a multi-objective optimization model based on the hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data, with the objectives of maximizing flood control performance indicators and minimizing downstream ecological flow process morphological deviation indicators. The optimization solution module is used to solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain the Pareto optimal solution set; The improved NSGA-II algorithm includes: in the constraint processing step, a constraint non-dominated ordering relation is used to replace the penalty function method, and the constraint non-dominated ordering relation dynamically adjusts the penalty weight of constraint violation according to the proportion of feasible solutions in the current population; in the ecological goal modeling step, a downstream ecological flow process morphological deviation index is constructed, and the downstream ecological flow process morphological deviation index is used to quantify the difference in morphology between the flow process generated by the scheduling scheme and the natural flow process.

[0007] Compared with existing technologies, this invention has the following significant advantages: 1. By adopting a constraint non-dominated ordering relation instead of a penalty function method with fixed penalty weights, the penalty weights for constraint violations can be dynamically adjusted according to the proportion of feasible solutions in the population, significantly improving the search efficiency and the uniformity of the Pareto front distribution under complex constraints; 2. By constructing a downstream ecological flow process morphological deviation index, the morphological differences between the flow process generated by the scheduling scheme and the natural flow process are quantified, making up for the shortcomings of traditional ecological objectives that only focus on total flow or suitability, enabling the scheduling scheme to better maintain the natural hydrological rhythm of the river ecosystem; 3. By introducing multi-scenario adaptive modeling and adaptive crossover mutation probability, the robustness and global search capability of the algorithm under different flood scenarios are enhanced, providing more comprehensive and reliable decision support for the joint emergency scheduling of cascade reservoirs. Attached Figure Description

[0008] Figure 1This is a schematic diagram of the improved NSGA-II algorithm provided in an embodiment of the present invention;

[0009] Figure 2 This is a Pareto front scatter plot provided in an embodiment of the present invention;

[0010] Figure 3 This is a schematic diagram of HV index values ​​provided in an embodiment of the present invention;

[0011] Figure 4 This is a schematic diagram of GD index values ​​provided in an embodiment of the present invention. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0013] Example 1

[0014] This embodiment provides a multi-objective optimization method for joint emergency dispatch of cascade reservoirs based on the improved NSGA-II algorithm, including the following steps:

[0015] S1. Obtain hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system, which may include upstream and downstream reservoirs.

[0016] Specifically, the inflow flood sequence of the reservoir under multiple flood scenarios and the engineering parameters of the two cascade reservoirs required to construct the joint operation model of the reservoirs are obtained, and the Muskingen calculation parameters of the downstream river channels of the two reservoirs are set.

[0017] Hydrological data can include inflow flood sequences, interval inflow data, and historical flood event data for upstream and downstream reservoirs. This data can be collected in real time through hydrological monitoring network or retrieved from historical databases. Reservoir capacity data can include parameters such as water level-capacity curves, dead storage capacity, flood control capacity, and beneficial storage capacity. These parameters are typically provided by reservoir design data. Discharge capacity data can include water level-discharge capacity curves, discharge curves of discharge facilities such as floodgates, spillways, and spillways, reflecting the maximum discharge capacity of the reservoir at different water levels. Downstream ecological baseflow data can include the minimum flow threshold required to maintain the basic functions of the downstream river ecosystem, which can be determined based on river ecological protection objectives.

[0018] S2. Based on hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data, a multi-objective optimization model is constructed with the goal of maximizing flood control performance indicators and minimizing downstream ecological flow process morphological deviation indicators.

[0019] Specifically, the scheduling scheme is encoded as a real vector X=[ of length 2T. Q 1(1),..., Q 1(T), Q 2(1),..., Q 2(T)] represents the outflow from the two reservoirs at different time periods. A multi-objective optimization model is constructed using a series of inflow floods over several time periods (T) as input data and the outflow process of the cascade reservoir system over T time periods as output data. The model aims to maximize the flood control effect and minimize the morphological deviation of the downstream ecological flow process.

[0020] The function expression that aims to maximize the flood control effect index is as follows: ;

[0021] in, Indicates the maximum peak reduction rate. This represents the peak value of the natural inflow calculated to the control section without scheduling. This indicates the peak value of the control section under the current scheduling scheme.

[0022] The function expression for minimizing the morphological deviation index of downstream ecological flow process is as follows: ; ; ;

[0023] in, Indicates the minimum ecological deviation. This indicates the flow rate of the reservoir at the downstream ecological control section during time period t. This represents the flow rate of the reservoir at the end of time period t at the downstream ecological control section. This represents the natural flow process at the same cross-section during time period t without reservoir regulation. This represents the natural flow process at the same cross-section at the end of time period t without reservoir regulation. , This represents the weighting coefficient.

[0024] S3. The improved NSGA-II algorithm is used to solve the multi-objective optimization model to obtain the Pareto optimal solution set. The constraints of the multi-objective optimization model include water balance constraints, water level upper and lower limit constraints, flow rate upper and lower limit constraints, and non-negativity constraints.

[0025] The expression for the water balance constraint is: ;

[0026] in, This represents the water storage capacity of reservoir i at the beginning of time period t. This represents the water storage capacity of reservoir i at the end of time period t. This represents the average inflow rate of reservoir i during time period t. This represents the average outflow from reservoir i during time period t;

[0027] The expressions for the upper and lower limits of water level constraints are: ;

[0028] in, This represents the water level of reservoir i during time period t. Indicates the lower limit of the reservoir's water level. Indicates the upper limit of the reservoir's water level;

[0029] The expressions for the upper and lower limits of flow are: ;

[0030] in, This represents the outflow from reservoir i. This indicates the lower limit of the reservoir's outflow. This indicates the upper limit of the reservoir's outflow.

[0031] The nonnegativity constraint requires that all variables be nonnegative.

[0032] The improved NSGA-II algorithm includes: in the constraint processing step, the constraint non-dominated ordering relation is used to replace the penalty function method, and the constraint non-dominated ordering relation dynamically adjusts the penalty weight of constraint violation according to the proportion of feasible solutions in the current population; in the ecological goal modeling step, a downstream ecological flow process morphological deviation index is constructed, which is used to quantify the morphological difference between the flow process generated by the scheduling scheme and the natural flow process.

[0033] Specifically, the population is first initialized by setting the iteration number k=1 and randomly generating the initial parent population. P k Each individual in the population consists of a 2T-dimensional real vector X, and each individual represents a scheduling scheme, namely the sequence of discharge decisions for the upstream and downstream reservoirs within the scheduling cycle. Initially, individuals are generated with a probability of 0.48, scaled according to the inflow ratio; the rest are generated uniformly and randomly. A repair function is executed on each individual, sequentially performing static boundary trimming, ramp limiting (two corrections in both forward and backward directions), and multi-scenario reservoir capacity hard repair (adjusting outflow based on water balance to prevent capacity overflow). Ramp limiting and hard repair are then performed again to ensure dynamic physical constraints are met.

[0034] During each generation of evolution, the algorithm performs selection, crossover, and mutation operations to generate the offspring population. In the constraint handling step, the algorithm replaces the traditional penalty function method with a constraint non-dominated ordering relation. Specifically, in each generation, the proportion of feasible solutions is calculated, i.e., the proportion of individuals satisfying all constraints out of the total population. When the proportion of feasible solutions is below a first threshold, it indicates that feasible solutions are scarce in the population, and the algorithm increases the penalty weight for constraint violations to guide the search towards the feasible region. When the proportion of feasible solutions is above a second threshold, it indicates that feasible solutions are abundant in the population, and the algorithm decreases the penalty weight for constraint violations to allow the algorithm to explore non-dominated solutions more freely within the feasible region. This adaptive mechanism avoids the problem of fixed penalty weights causing search stagnation in the early stages of optimization or over-constraint in the later stages of optimization, thereby improving the convergence and uniformity of the Pareto front.

[0035] Preferably, the constraint non-dominated ordering relation follows the following logic: feasible solutions dominate infeasible solutions; when both are infeasible solutions, the one with the smaller violation degree dominates the one with the larger violation degree; when both are feasible solutions, the Pareto dominance relation is determined according to the objective function value.

[0036] Calculate the crowding degree (i.e., k-nearest neighbor Euclidean distance) of each individual within the frontier as an indicator of diversity preservation. For n individuals within the frontier, let: ;

[0037] For individual p, calculate and sort the Euclidean distances to the remaining points: ;

[0038] The congestion level is determined by the distance to the k-th nearest neighbor: ;

[0039] Where k represents the nearest neighbor order, and n represents the current number of non-dominated frontier individuals. This represents the Euclidean distance between individuals p and q. z p , z q For individuals p and q, a two-dimensional normalization point is formed. Indicates the degree of crowding.

[0040] In the ecological target modeling step, the algorithm constructs a downstream ecological flow process morphology deviation index, which is based on a shape similarity measure of the flow process. By calculating the differences in these shape characteristics between the scheduled flow process and the natural flow process and assigning different weights, a comprehensive morphology deviation index can be obtained. This index can more comprehensively assess the impact of scheduling schemes on the natural hydrological conditions of the river ecosystem, avoiding focusing solely on the total flow while ignoring the ecological significance of the process morphology.

[0041] In crossover and mutation operations, the improved NSGA-II algorithm can employ adaptive crossover and mutation probabilities. The adaptive crossover probability can be dynamically adjusted based on the number of generations of population evolution. For example, in the early stages of evolution, higher crossover and mutation probabilities can be set to enhance population diversity and global search capabilities; in the later stages, crossover and mutation probabilities can be gradually reduced to strengthen local search capabilities and promote algorithm convergence. The adaptive mutation probability can be dynamically adjusted based on population diversity. For example, when population diversity is below a preset threshold, the mutation probability can be increased to introduce new genes and prevent premature convergence. In some embodiments, the adaptive crossover and mutation probabilities can also be adjusted at the individual level based on the individual's fitness value or crowding distance, giving individuals with lower fitness a higher mutation probability to increase their chances of improvement. For example, individuals with higher fitness or larger crowding distances can be assigned lower crossover and mutation probabilities to protect superior individuals; individuals with lower fitness or smaller crowding distances can be assigned higher crossover and mutation probabilities to promote their improvement. This adaptive adjustment method can further improve the search efficiency and optimization performance of the improved NSGA-II algorithm.

[0042] In the multi-scenario adaptive modeling step, the improved NSGA-II algorithm can construct a comprehensive index under multiple scenarios. This index is used to evaluate the overall performance of the scheduling scheme under different flood scenarios. Specifically, multiple flood scenarios can be designed, such as flood processes with different return periods, as well as flood processes with different durations and peak types. For each scheduling scheme, its objective function value under each flood scenario is calculated, and then the comprehensive index is obtained through weighted summation or Pareto ranking.

[0043] After obtaining the Pareto objective solution set, this set is output for decision-makers to choose from. Each solution in the Pareto objective solution set represents a non-dominated scheduling scheme, meaning that improving one objective will at least worsen another. Decision-makers can select a compromise solution from the Pareto frontier as the final scheduling scheme based on their actual preferences, such as a greater emphasis on flood control security or ecological protection.

[0044] For example, refer to Figure 1 A binary tournament selection method (first comparing non-dominant rank, then crowding) is used to select the parent, and crossover and mutation operators are applied to generate the offspring population. Q k (The same repair process will be performed after generation); the parent generation will be... P k and offspring Q k merged into R k , with a scale of 2 Np ;right R k Perform a constrained non-dominated sort again to obtain the hierarchical front; add the entire front to the new parent generation one by one in front order. P k+1 until it reaches or exceeds N p If the last addition to the frontier results in an overcrowding, then individuals within that frontier are sorted in descending order of crowding (i.e., k-nearest neighbor distance), and the individual with the largest distance is selected to fill the gap. N p To ensure a stable population size; starting from the new paternal generation. P k+1 The same selection, crossover, and mutation operations are used to generate a new generation of offspring. Q k+1 (All are repaired), let k = k + 1; iterate until convergence: repeat the merging, sorting, filtering and generation of the next generation until the number of iterations k = K; finally, the population... P k The first non-dominated frontier is the Pareto optimal solution set. This application is applicable to one or more flood scenarios, and the objective function indices under multiple flood scenarios are all obtained by arithmetic mean.

[0045] refer to Figure 1 A binary tournament selection method (first comparing non-dominant rank, then crowding) is used to select the parent, and crossover and mutation operators are applied to generate the offspring population. Q k (The same repair process will be performed after generation); the parent generation will be... P k and offspring Q k merged into R k , with a scale of 2 N p ;right R k Perform a constrained non-dominated sort again to obtain the hierarchical front; add the entire front to the new parent generation one by one in front order. P k+1 until it reaches or exceeds N p If the last addition to the frontier results in an overcrowding, then individuals within that frontier are sorted in descending order of crowding density (k-nearest neighbor distance), and the individual with the largest distance is selected to fill the gap. N p To ensure a stable population size; starting from the new paternal generation. P k+1 The same selection, crossover, and mutation operations are used to generate a new generation of offspring. P k+1(All are repaired), let; iterate until convergence: repeat the steps of merging, sorting, filtering and generating the next generation of offspring until the number of iterations k=K; the final population P k The first non-dominated frontier is the desired set of non-dominated solutions for the multi-objective problem (Pareto optimal solution set). This code is applicable to one or more flood scenarios, and the indices of the multi-objective optimization model under multiple flood scenarios are all obtained by taking the arithmetic mean.

[0046] Example 2

[0047] This embodiment provides a multi-objective optimization system for joint emergency dispatch of cascade reservoirs based on the improved NSGA-II algorithm, including a data acquisition module, a model building module, and an optimization solution module.

[0048] The data acquisition module is used to acquire hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system.

[0049] The data acquisition module may include multiple data interfaces for receiving relevant data from the two reservoirs from external data sources or sensor networks. Specifically, the data acquisition module may include a hydrological data interface, a reservoir capacity data interface, a discharge capacity data interface, and a downstream ecological baseflow data interface. The hydrological data interface can be used to acquire hydrological data from the two reservoirs, such as the inflow process, interval flow process, and natural flow process of the upstream and downstream reservoirs. The reservoir capacity data interface can be used to acquire reservoir capacity data from the two reservoirs, such as the water level-capacity relationship curves, dead water level, normal storage level, and flood control limit level of the upstream and downstream reservoirs. The discharge capacity data interface can be used to acquire discharge capacity data from the two reservoirs, such as the flood discharge facility type, discharge capacity curve, and upper limit of discharge capacity of the upstream and downstream reservoirs. The downstream ecological baseflow data interface can be used to acquire downstream ecological baseflow data from the two reservoirs, such as the minimum ecological flow requirement and suitable ecological flow range of the downstream river channel.

[0050] The model building module constructs a multi-objective optimization model based on the data acquired by the data acquisition module. This multi-objective optimization model can include multiple objective functions and multiple constraints. The objective functions include maximizing the flood control effect index and minimizing the downstream ecological flow process morphological deviation index. The constraints include water balance constraints, upper and lower water level constraints, upper and lower flow rate constraints, and non-negativity constraints. The model building module encodes these objective functions and constraints in the form of mathematical expressions, forming an optimization problem that can be processed by the optimization solution module.

[0051] The optimization solution module employs an improved NSGA-II algorithm to solve the multi-objective optimization model constructed by the model building module. The improved NSGA-II algorithm can be achieved by replacing the traditional penalty function method with a constraint non-dominated ranking relation in the constraint handling step. The constraint non-dominated ranking relation dynamically adjusts the penalty weights for constraint violations based on the proportion of feasible solutions in the current population. This avoids the inefficiency caused by fixed penalty weights and improves the uniformity and convergence of the Pareto front.

[0052] In the implementation of the constraint non-dominated ordering relation, according to one embodiment of the present invention, the proportion of feasible solutions can be calculated in each generation of the population. When the proportion of feasible solutions is lower than a first threshold, the penalty weight for constraint violation can be increased; when the proportion of feasible solutions is higher than a second threshold, the penalty weight for constraint violation can be decreased. The first and second thresholds can be preset values, which can be dynamically adjusted according to the constraint complexity and population size of the specific problem.

[0053] In the ecological target modeling step, the optimization solution module can construct a downstream ecological flow process morphology deviation index. This index can be used to quantify the morphological differences between the flow process generated by the scheduling scheme and the natural flow process. By introducing this index, the impact of the scheduling scheme on the river ecosystem can be more comprehensively assessed, avoiding the problem of focusing only on the total flow or a single suitability index while ignoring the morphological changes of the flow process.

[0054] The optimization solution module can also employ adaptive crossover and mutation probabilities in crossover and mutation operations. These probabilities can be dynamically adjusted based on the number of generations or population diversity. For example, higher crossover and mutation probabilities can be set in the early stages of evolution to increase population diversity; lower probabilities in the later stages can accelerate convergence. This balances global and local search capabilities, improving the algorithm's optimization efficiency. In some embodiments, the optimization solution module may also include a Pareto solution set post-processing unit for filtering, sorting, and visualizing the obtained Pareto objective solution set to assist decision-makers in selecting the final scheduling scheme. The data flow between the data acquisition module, model building module, and optimization solution module can form a closed loop, realizing a complete process from data input to scheme output.

[0055] This embodiment calls relevant tables to load data and sets various parameters and algorithm parameters for the cascade reservoir system. For each scenario, the downstream natural flow process is obtained through Muskingen calculus, with inflows considered as simultaneous outflows from both reservoirs (without scheduling). The process is then executed sequentially, including population initialization, repair operator, objective and constraint calculation, non-dominated sorting, congestion distance calculation, environment selection, crossover and mutation, and result output. (Reference) Figures 3-4 Each generation records the HV (relative to the reference point) and GD (relative to the final generation's first frontier) for the first frontier, writing them to hv_history.csv and gd_history.csv respectively. The decision variables and objective values ​​for the final generation's first frontier are written to pareto_F_timestamp.csv and pareto_X_timestamp.csv, and a Pareto frontier scatter plot is plotted, as shown below. Figure 2 As shown.

[0056] The above embodiments are merely illustrative of several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A multi-objective optimization method for joint emergency dispatch of cascade reservoirs based on an improved NSGA-II algorithm, characterized in that, The method includes: acquiring hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system; constructing a multi-objective optimization model based on the hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data, wherein the multi-objective optimization model aims to maximize the flood control effect index and minimize the downstream ecological flow process morphology deviation index; solving the multi-objective optimization model using an improved NSGA-II algorithm to obtain a Pareto optimal solution set; wherein the improved NSGA-II algorithm includes: in the constraint processing step, replacing the penalty function method with a constraint non-dominated ranking relation, wherein the constraint non-dominated ranking relation dynamically adjusts the penalty weight of constraint violation according to the proportion of feasible solutions in the current population; in the ecological objective modeling step, constructing the downstream ecological flow process morphology deviation index, wherein the downstream ecological flow process morphology deviation index is used to quantify the morphological difference between the flow process generated by the scheduling scheme and the natural flow process; in the crossover and mutation operations, using adaptive crossover probability and adaptive mutation probability, wherein the adaptive crossover probability and the adaptive mutation probability are dynamically adjusted according to the population evolution generation or population diversity. The constraint non-dominated ranking relationship is implemented in the following way: In each generation of the population, the proportion of feasible solutions is calculated. When the proportion of feasible solutions is lower than a first threshold, the penalty weight of the constraint violation is increased; when the proportion of feasible solutions is higher than a second threshold, the penalty weight of the constraint violation is decreased. The constraint non-dominated ranking relationship follows the following logic: feasible solutions dominate infeasible solutions; when both are infeasible solutions, the one with lower violation value dominates the one with higher violation value; when both are feasible solutions, the Pareto dominance relationship of the objective function value is used for determination. The function expression for minimizing the morphological deviation index of downstream ecological flow process is as follows: ； ； ； in, Indicates the minimum ecological deviation. This indicates the flow rate of the reservoir at the downstream ecological control section during time period t. This represents the flow rate of the reservoir at the end of time period t at the downstream ecological control section. This represents the natural flow process at the same cross-section during time period t without reservoir regulation. This represents the natural flow process at the same cross-section at the end of time period t without reservoir regulation. and This represents the weighting coefficient.

2. The method according to claim 1, characterized in that, The function expression with the objective of maximizing flood control effectiveness is as follows: ； in, Indicates the maximum peak reduction rate. This represents the peak value of the natural inflow calculated to the control section without scheduling. This indicates the peak value of the control section under the current scheduling scheme.

3. The method according to claim 1, characterized in that, The cascade reservoir system includes upstream and downstream reservoirs, and the constraints of the multi-objective optimization model include water balance constraints, upper and lower limits of water level, upper and lower limits of flow, and non-negative constraints.

4. The method according to claim 3, characterized in that, The expression for the water balance constraint is: ； in, This represents the water storage capacity of reservoir i at the beginning of time period t. This represents the water storage capacity of reservoir i at the end of time period t. This represents the average inflow rate of reservoir i during time period t. This represents the average outflow from reservoir i during time period t; The expressions for the upper and lower limits of the water level are: ； in, This represents the water level of reservoir i during time period t. Indicates the lower limit of the reservoir's water level. Indicates the upper limit of the reservoir's water level; The expressions for the upper and lower limits of the flow rate are: ； in, This represents the outflow from reservoir i. This indicates the lower limit of the reservoir's outflow. This indicates the upper limit of the reservoir's outflow. The nonnegativity constraint requires that all variables be nonnegative.

5. A multi-objective optimization system for joint emergency dispatching of two reservoirs based on an improved NSGA-II algorithm, used to execute the method as described in claim 1, characterized in that, include: The data acquisition module is used to acquire hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data of the cascade reservoir system. The model building module is used to construct a multi-objective optimization model based on the hydrological data, reservoir capacity data, discharge capacity data, and downstream ecological base flow data, with the objectives of maximizing flood control performance indicators and minimizing downstream ecological flow process morphological deviation indicators. The optimization solution module is used to solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain the Pareto optimal solution set; The improved NSGA-II algorithm includes: in the constraint processing step, a constraint non-dominated ordering relation is used to replace the penalty function method, and the constraint non-dominated ordering relation dynamically adjusts the penalty weight of constraint violation according to the proportion of feasible solutions in the current population; in the ecological goal modeling step, a downstream ecological flow process morphological deviation index is constructed, and the downstream ecological flow process morphological deviation index is used to quantify the difference in morphology between the flow process generated by the scheduling scheme and the natural flow process.

6. The system according to claim 5, characterized in that, The constraint non-dominated ordering relation is implemented in the following way: in each generation of the population, the proportion of feasible solutions is calculated. When the proportion of feasible solutions is lower than a first threshold, the penalty weight of the constraint violation is increased; when the proportion of feasible solutions is higher than a second threshold, the penalty weight of the constraint violation is decreased.

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