A multi-objective optimization method for reservoir group dispatching interval under uncertain conditions

Abstract

The invention discloses a multi-objective optimization method for reservoir group dispatching interval under uncertain conditions, which belongs to the technical field of reservoir optimization dispatching. Firstly, an innovative multi-objective dispatching model for cascade reservoir groups is established; secondly, a dual-population dynamic collaborative interval optimization method is proposed to solve the proposed interval multi-objective dispatching model, and further obtain the optimal dispatching plan for the reservoir group; finally, the optimal dispatching plan set for the reservoir group is output; wherein the proposed optimization method organically combines a chaos-order mapping initialization strategy, a dynamic adaptive mutual promotion update strategy and an elite guidance optimization strategy, so as to quickly and efficiently optimize a set of reliable and accurate dispatching plan sets considering runoff uncertainty, and provides dispatching decision makers with an effective decision-making technical means for solving the multi-objective complex engineering problems of cascade reservoir group optimization, improves the intelligent level and comprehensive benefits of water resources management, and further enhances the ability of water resources system to cope with complex environment and uncertain factors.

Description

Technical Field

[0001] The invention belongs to the technical field of reservoir optimization and dispatching, and in particular relates to a multi-objective optimization method for reservoir group dispatching interval under uncertain conditions. Background Art

[0002] As an important means of regional water resources management, the joint operation of reservoir groups aims to meet multiple needs, such as water supply, flood control, power generation and ecological protection, by optimizing the reasonable allocation of reservoir capacity. However, climate change, frequent extreme weather and the complexity of hydrological processes have gradually increased the uncertainty of inflow, bringing unprecedented challenges to the operation of reservoir groups. Traditional operation methods are mainly based on deterministic inflow prediction and single-objective optimization, which are difficult to effectively adapt to the volatility of inflow and the complex balance between multi-objective demands.

[0003] The uncertainty of inflow runoff comes from a wide range of sources, including climate fluctuations, variability of surface runoff processes, and meteorological forecast errors. This uncertainty not only increases the difficulty of reservoir scheduling decisions, but also creates greater uncertainty risks in flood control scheduling during the flood season, water supply security during the dry season, and ecological maintenance during the normal period. For example, excessive inflow runoff prediction errors during the flood season will lead to unreasonable storage capacity allocation, thereby increasing the risk of floods; during the dry season, the stable water supply needs of agriculture, industry, and residents may not be met due to insufficient inflow; during the peak period of power generation demand, runoff fluctuations may affect the security and economy of power generation flow; in areas with high ecological demands, drastic fluctuations in runoff may also affect the health of the downstream ecological environment. Therefore, the scheduling challenges brought about by the uncertainty of inflow runoff have become an important issue affecting the operation of reservoir groups.

[0004] In this context, interval optimization and multi-objective optimization methods have been gradually introduced into reservoir group scheduling in recent years to better adapt to the complex flow volatility and the balance requirements of multiple objectives. The interval optimization method represents the uncertainty range of runoff by means of upper and lower bounds, and optimizes within this interval to improve the adaptability of scheduling. The advantage of this method is that it can take into account multiple scheduling requirements, especially improving the robustness of decision-making under uncertain conditions. However, the existing interval optimization methods are too simplified in the design of objective functions, and it is difficult to cover the dynamic balance between multiple needs such as water supply, flood control, power generation and ecology. Traditional multi-objective models are generally constructed only under certain static conditions, and it is difficult to achieve reasonable scheduling in actual scenarios where runoff changes dynamically.

[0005] In summary, the present invention provides a more robust and adaptive scheduling solution under the condition of uncertain inflow runoff by proposing a multi-objective optimization model and a dynamic optimization algorithm, and provides innovative technical support for the scientific management of a group of reservoirs. In addition, the innovation of the model of the present invention lies in the combination of multi-objective optimization methods and interval optimization strategies, which provides significant technical advantages in the balance of multiple objectives and the adaptive adjustment of scheduling strategies, and helps to improve the comprehensive benefits and safety of the scheduling of a group of reservoirs. Summary of the invention

[0006] The purpose of the present invention is to provide a multi-objective optimization method for the dispatching interval of a reservoir group under uncertain conditions, so as to solve the problem that the design of the objective function in the prior art is too simplified and it is difficult to cover the dynamic balance between multiple demands such as water supply, flood control, power generation and ecology. At the same time, traditional multi-objective models are generally only constructed under certain static conditions, and it is difficult to achieve reasonable dispatching problems in actual scenarios with dynamic changes in runoff.

[0007] To achieve the above object, the present invention provides a multi-objective optimization method for reservoir group dispatching interval under uncertain conditions, comprising the following steps:

[0008] Step 1: Based on the dispatching characteristics of the basin where the reservoir is located, a multi-objective dispatching model for the interval of the cascade reservoir group is constructed with the maximum flood control storage capacity safety guarantee criterion and the maximum total power generation criterion of the cascade reservoir group; at the same time, interval constraints are added to the multi-objective dispatching model for the interval of the cascade reservoir group, and the interval constraints include water balance constraints, outflow balance constraints, water storage capacity constraints, turbine flow constraints, outflow constraints and output constraints;

[0009] Step 2: Execute the dual-population dynamic collaborative interval optimization method to solve the optimal dispatching plan of the reservoir group;

[0010] Step 3: Output the optimal scheduling solution set for the reservoir group.

[0011] Preferably, the maximum flood control reservoir capacity safety assurance criterion specifically takes the minimum occupancy of flood control reservoir capacity as the optimization goal, aiming to improve the comprehensive benefits and flood control safety of the reservoir by reducing the occupancy of flood control reservoir capacity. This goal can optimize the utilization efficiency of water resources and free up more reservoir capacity for water supply, power generation and other needs while ensuring flood control safety. At the same time, minimizing the occupancy of flood control reservoir capacity increases the flexibility of reservoir scheduling, allowing it to have greater operating space under different water conditions, better respond to meteorological and hydrological changes, reduce the impact of frequent flood discharges on the downstream economy and environment, reduce operating costs, and extend the service life of facilities. Overall, this optimization goal helps to achieve a coordinated balance of the multi-functions of the reservoir and ensure the optimal comprehensive benefits of reservoir operation. The objective function corresponding to the maximum flood control reservoir capacity safety assurance criterion is expressed as:

[0012] (1);

[0013] in, Indicates k The reservoir is j The flood control storage capacity occupied in each period; yes No. j The amount of time, ,in is an independent decision variable x In this scheduling model, the interval parameter represent m uncertainty interval for inflow and runoff; Indicates that the interval vector parameter Flood control target value under the influence.

[0014] The optimal criterion for the maximum total power generation of cascade reservoirs is to achieve efficient use of water resources, improved economic benefits of power generation, stable energy supply, and protection of the ecological environment through reasonable scheduling; this goal can promote the maximization of hydropower generation on the basis of full utilization of water resources, increase economic benefits and support the reliable supply of regional energy needs, reduce dependence on fossil fuels, and thus reduce carbon emissions and promote green and low-carbon development. In general, taking the maximization of the total power generation of cascade reservoirs as the optimization goal ensures the economic and social benefits of the reservoirs and promotes the sustainable use of resources. The corresponding objective function is expressed as:

[0015] (2 );

[0016] In the formula, To represent the interval vector parameter The total power generation of all cascade reservoirs under the influence, and Represent the number of reservoirs and the number of dispatching periods, respectively. It is The total number of hours in the period, , and Respectively represent The reservoir is Output, power generation flow and water head for each period, For the The output coefficient of a reservoir.

[0017] Preferably, the expressions of water balance constraint, outflow balance constraint, water storage capacity constraint, turbine flow constraint, outflow constraint and output constraint are as follows:

[0018] Water balance constraints:

[0019] (3);

[0020] In the formula, Representatives and k All upstream reservoirs directly connected to the reservoir, and Respectively represent k The reservoir is j The storage capacity and interval inflow of each period, interval parameters Representatives received m The impact of runoff in the reservoir with uncertainty intervals; Indicates k The reservoir is directly connected to The upstream reservoir is in j Outbound flow in the time period; Indicates k The reservoir is j Outbound flow in the time period;

[0021] Outflow balance constraint:

[0022] (4 );

[0023] In the formula, Representative k The reservoir is j The amount of water discarded during each period;

[0024] Water storage capacity constraints:

[0025] (5);

[0026] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the allowable storage capacity threshold for each time period;

[0027] Turbine flow constraints:

[0028] (6);

[0029] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the turbine's allowable overflow threshold for each period;

[0030] Outflow constraints:

[0031] (7);

[0032] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the discharge flow threshold for each time period;

[0033] Output constraints:

[0034] (8);

[0035] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the power generation threshold for each time period.

[0036] Preferably, the process of executing the dual-population dynamic collaborative interval optimization method in step 2 to solve the optimal scheduling plan for the reservoir group is as follows:

[0037] S201. Initialize basic parameters: Initialize the number of iterations t =1, determine the maximum number of iterations T , variable dimension J ;

[0038] S202, executing the chaos-order mapping initialization strategy: setting the outflow during the reservoir scheduling period as a decision variable, generating two initial scheduling scheme sets of chaos and order according to the chaos-order mapping initialization strategy, and calculating the objective function fitness of the initial scheduling scheme set;

[0039] S203, executing a dynamic adaptive mutual promotion update strategy, and performing a dynamic adaptive mutual promotion update strategy on the dual populations according to the current Pareto frontier optimization situation; wherein the chaotic population determines the number of offspring populations that need to be updated by comprehensively and fully measuring the optimization situation, iteration stage, and update index and other multi-dimensional parameters and updates them through an elite guidance optimization strategy; the order population relies on the global optimization performance of the genetic algorithm to maintain diversity at different stages of the algorithm operation to avoid premature convergence;

[0040] S204, execute elite guidance optimization strategy: based on the elite guidance optimization strategy, the individuals of the chaotic population make full use of the mean, optimality, and randomness high-quality information in the elite population, so that the optimization individuals can conduct a full global search in a large search space with a better optimization direction and convergence rate, avoiding the iteration from falling into the local optimal dilemma too early, so as to quickly and efficiently find a feasible optimal solution set;

[0041] S205, perform iterative update: if the preset maximum number of iterations is reached T , then the optimal reservoir dispatching scheme is obtained, and the fitness value of the elite dispatching scheme set is output to obtain the reservoir group dispatching scheme corresponding to the fitness value, otherwise, return to execute step S203.

[0042] Preferably, the expression for executing the chaos-order mapping initialization strategy in S202 is as follows:

[0043] (9);

[0044] (10);

[0045] (11);

[0046] In the formula, , , , is a random parameter, where and Follows standard normal distribution, and Obeys uniform distribution between [0,1]; and Representative solution Medium Variable j The upper and lower thresholds; , Respectively represent the chaotic and order-initialized populations obtained by initializing each individual and decision variable in the population based on chaos and order mapping, where, , Represents the first Individual j decision variables, , N and D are the number of individuals in the population and the number of decision variables respectively; Represents the elite initial population obtained by selecting the chaotic and orderly populations based on the reference point environment.

[0047] Preferably, the specific process of S203 is as follows:

[0048] S203-1. Determine the number of updated offspring populations: The chaotic population and the ordered population determine the number of offspring populations that need to be updated by comprehensively and fully measuring the optimization situation, iteration stage, and update index and other multi-dimensional parameters. The expression is as follows:

[0049] (12);

[0050] (13);

[0051] (14);

[0052] (15);

[0053] (16);

[0054] In the formula, , are the number of individuals that need to be updated in the chaotic population and the orderly population, and the initial number is set to ; N is the number of individuals in the chaotic population and the orderly population, and is also the number of individuals in the update population; Adjust the parameter for the starting ratio, the default setting is 0.4; , are the numbers of optimal solutions of chaotic population and dual population on the first Pareto frontier respectively; The judgment matrix for determining whether to change the number of individuals in the two-group optimization The number of times the number of optimization individuals changes during the entire optimization process; is the judgment matrix Calculation parameters of Indicates the current iteration number; Represents the population and population After merging, the individuals in the first level of Pareto are selected as the size of the population;

[0055] S203-2. Population update: updated offspring population set It is composed of individuals updated by elite guided optimization strategy and simulated binary crossover and polynomial mutation strategy based on genetic algorithm. Chaotic population, orderly population and elite population are based on environmental selection function. Determine, as shown below:

[0056] (17);

[0057] (18);

[0058] (19);

[0059] (20);

[0060] In the formula, and Respectively indicate t Generation Chaos Population and ordered population Separately with the offspring population set After environmental selection, the t +1) generation of chaotic and orderly populations; Expressing the t Elite population The first ( t +1) generation of elite population; Select a function for the environment; Select the function for the environment that only takes the first Pareto frontier; , Provide elite guidance and optimization strategies Ego and the crossover mutation strategy used in genetic algorithms, where p and q are sets of random integers, , . The simulated binary crossover and polynomial mutation strategy based on genetic algorithm for the ordered population is called as the individual optimization update strategy, and the crossover mutation parameters are , in order to maintain diversity at different stages of the algorithm operation and avoid premature convergence.

[0061] Preferably, the elite guidance optimization strategy is executed in S204. In order to further enhance the efficient convergence and quality reliability of the optimal solution set, the chaotic population individuals make full use of the high-quality information such as mean, optimality, and randomness in the elite population based on the elite guidance optimization strategy, so that the optimization individuals can perform a full global search in a large search space with a better optimization direction and convergence rate, avoid the iteration from falling into the local optimal dilemma too early, and thus quickly and efficiently find a feasible optimal solution set. The specific expression is as follows:

[0062] (twenty one);

[0063] (twenty two);

[0064] (twenty three);

[0065] (twenty four);

[0066] In the formula, Indicates that through the population The t+1th generation update population obtained by using the elite guided optimization strategy, Indicates t The first generation of chaotic population The individual j The value of a variable, Indicated in The elite population mean guidance information obtained during the iteration; is a random number that follows a standard normal distribution; For the tThe mean of the elite population of the first generation The value of the decision variable; Indicates the number of individuals in population 1 participating in the optimization update; Indicated in The first The individual j The optimal individual guidance information of a population of decision variables; Indicates t The mean of the individuals on the first Pareto frontier in population 1 in the iteration j decision variables; Indicated in The first The individual j The global and current optimal population joint guiding factors of the decision variables; Indicated in t The first generation of elite population randomly selects an individual The value of the decision variable, is a random integer number, .

[0067] Therefore, the present invention adopts the above-mentioned multi-objective optimization method for reservoir group dispatching interval under uncertain conditions, which has the following beneficial effects:

[0068] (1) The interval multi-objective optimization method proposed in the present invention shows significant algorithmic advantages in reservoir group scheduling. First, the method introduces an interval multi-objective optimization strategy, which effectively addresses the uncertainty of inflow runoff during reservoir group scheduling. By setting reasonable upper and lower limit intervals in each objective function, the algorithm can optimize each target demand within the flow fluctuation range, thereby ensuring the robustness of scheduling under uncertain conditions. The present invention makes scheduling decisions more flexible, avoids the decision-making deviation caused by runoff uncertainty in traditional optimization methods, and ensures the comprehensive balance of flood control and power generation goals under various flow conditions;

[0069] (2) The present invention has better solution set coverage and balance, especially in dealing with multi-objective optimization problems. Compared with traditional algorithms, the present invention guides solution set search through multiple strategies, which can better distribute solution sets on the Pareto frontier to meet multi-objective requirements. When faced with different traffic conditions, conflicts between various objective requirements are often difficult to avoid. However, the present invention can still maintain the diversity and stability of the solution set, providing multiple high-quality solutions for scheduling;

[0070] (3) The present invention also enhances the dynamic adjustment capability, making the dispatching process more flexible. Through the dynamically updated interval optimization mechanism, the algorithm can quickly respond to flow changes, especially under extreme weather conditions during the flood or dry seasons, to provide decision makers with timely and reliable dispatching solutions. This flexible feedback mechanism is particularly effective in solving the changing dispatching needs of reservoir groups, improving the overall robustness of the system;

[0071] (4) The model construction of the present invention enables the algorithm to effectively combine the multi-dimensional objectives of reservoir scheduling needs. It ensures the coordination of various objectives under uncertain conditions, especially when the inflow fluctuates, so that the scheduling system can maintain a multi-objective balance, providing practical and efficient support for solving the problem of reservoir group scheduling.

[0072] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is an overall flow chart of a multi-objective optimization method for reservoir group dispatching interval under uncertain conditions of the present invention;

[0074] Figure 2 It is the HV index variation trend diagram of the present invention and the comparative method;

[0075] Figure 3 It is the Pareto front graph obtained by the present invention in the scheduling engineering problem of the present invention;

[0076] Figure 4 It is the Pareto front graph obtained by the present invention and NSGAII in the scheduling engineering problem of the present invention;

[0077] Figure 5 It is the Pareto front diagram obtained by the present invention and MOEA / D in the scheduling engineering problem of the present invention;

[0078] Figure 6 It is the Pareto front diagram obtained by all methods in the scheduling engineering problem of the present invention. DETAILED DESCRIPTION

[0079] 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 invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] See also Figure 1-Figure 6 , a multi-objective optimization method for reservoir group dispatching interval under uncertain conditions, comprising the following steps:

[0081] Step 1: Based on the dispatching characteristics of the basin where the reservoir is located, a multi-objective dispatching model for the interval of cascade reservoirs is constructed with the maximum flood control storage capacity safety guarantee criterion and the maximum total power generation criterion of the cascade reservoir group; at the same time, interval constraints are added to the multi-objective dispatching model for the interval of cascade reservoirs, and the interval constraints include water balance constraints, outflow balance constraints, water storage capacity constraints, turbine flow constraints, outflow constraints and output constraints; the maximum flood control storage capacity safety guarantee criterion is specifically to take the minimum occupation of flood control storage capacity as the optimization goal, aiming to improve the comprehensive benefits and flood control safety of the reservoir by reducing the occupation of flood control storage capacity. This goal can optimize the utilization efficiency of water resources and free up more storage capacity for water supply, power generation and other needs under the premise of ensuring flood control safety. At the same time, minimizing the occupation of flood control storage capacity increases the flexibility of reservoir dispatching, giving it a larger operating space under different water conditions, better responding to meteorological and hydrological changes, reducing the impact of frequent flood discharges on the downstream economy and environment, reducing operating costs, and extending the service life of facilities. In general, this optimization goal helps to achieve a coordinated balance of the reservoir's multiple functions and ensure the optimal comprehensive benefits of reservoir operation. The objective function corresponding to the maximum flood control storage capacity safety guarantee criterion is expressed as:

[0082] (1);

[0083] in, Indicates k The reservoir is j The flood control storage capacity occupied in each period; yes No. j The amount of time, ,in is an independent decision variable x In this scheduling model, the interval parameter represent m uncertainty interval for inflow and runoff; Indicates that the interval vector parameter Flood control target value under the influence.

[0084] The maximum total power generation criterion of cascade reservoirs aims to achieve efficient use of water resources, improved economic benefits of power generation, stable energy supply and protection of the ecological environment through reasonable scheduling; this goal can promote the maximization of hydropower generation on the basis of full utilization of water resources, increase economic benefits and support the reliable supply of regional energy needs, reduce dependence on fossil fuels, and thus reduce carbon emissions and promote green and low-carbon development. In general, taking the maximization of the total power generation of cascade reservoirs as the optimization goal ensures the economic and social benefits of the reservoirs and promotes the sustainable use of resources. The corresponding objective function is expressed as:

[0085] (2 );

[0086] In the formula, To represent the interval vector parameter The total power generation of all cascade reservoirs under the influence, and Represent the number of reservoirs and the number of dispatching periods, respectively. It is The total number of hours in the period, , and Respectively represent The reservoir is Output, power generation flow and water head for each period, For the The output coefficient of a reservoir.

[0087] The expressions of water balance constraint, outflow balance constraint, water storage capacity constraint, turbine flow constraint, outflow constraint and output constraint are as follows:

[0088] Water balance constraints:

[0089] (3);

[0090] In the formula, Representatives and k All upstream reservoirs directly connected to the reservoir, and Respectively represent k The reservoir is j The storage capacity and interval inflow of each period, interval parameters Representatives received m The impact of runoff in the reservoir with uncertainty intervals; Indicates k The reservoir is directly connected to l The upstream reservoir is in j Outbound flow in the time period; Indicates k The reservoir is j Outbound flow in the time period;

[0091] Outflow balance constraint:

[0092] (4 );

[0093] In the formula, Representative k The reservoir is j The amount of water discarded during each period;

[0094] Water storage capacity constraints:

[0095] (5);

[0096] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the allowable storage capacity threshold for each time period;

[0097] Turbine flow constraints:

[0098] (6);

[0099] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the turbine's allowable overflow threshold for each period;

[0100] Outflow constraints:

[0101] (7);

[0102] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the discharge flow threshold for each time period;

[0103] Output constraints:

[0104] (8);

[0105] In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the power generation threshold for each time period.

[0106] Step 2: Execute the dual-population dynamic collaborative interval optimization method to solve the optimal scheduling plan for the reservoir group; the specific process is as follows:

[0107] S201. Initialize basic parameters: Initialize the number of iterations t =1, determine the maximum number of iterations T , variable dimension J ;

[0108] S202, execute the chaos-order mapping initialization strategy: set the outflow during the reservoir operation period as the decision variable, generate two initial scheduling scheme sets of chaos and order according to the chaos-order mapping initialization strategy, and calculate the objective function fitness of the initial scheduling scheme set; among them, iterative chaotic map with infinite collapse (ICMIC) has stronger sensitivity to the initial value of iteration, wider chaos range, better traversal, lower computational cost and better mapping accuracy. Combined with the "uniform in the middle and high frequency at the boundary" Logistic chaotic mapping sequence, the chaos mapping initialization strategy enables the optimal population to fully traverse the search space based on the ICMIC-Logistic combined mapping principle to complete the initialization of the chaotic population, as shown in formula (9). In addition, the order mapping initialization strategy realizes the uniform initialization of the order population in the global search space based on the uniform distribution principle. The initialization of the elite population is based on the environmental selection function of the reference point and is selected from the initialized dual population; the expression for executing the chaos-order mapping initialization strategy is as follows:

[0109] (9);

[0110] (10);

[0111] (11);

[0112] In the formula, , , , is a random parameter, where and Follows standard normal distribution, and Obeys uniform distribution between [0,1]; and Represents the upper and lower limits of the threshold of variable j in solution i; , Respectively represent the chaotic and order-initialized populations obtained by initializing each individual and decision variable in the population based on chaos and order mapping, where, , Represents the first Individual j decision variables, , N and D are the number of individuals in the population and the number of decision variables respectively; Represents the elite initial population obtained by selecting the chaotic and orderly populations based on the reference point environment.

[0113] S203, execute the dynamic adaptive mutual promotion update strategy, and perform the dynamic adaptive mutual promotion update strategy on the dual populations according to the current Pareto frontier optimization situation; the chaotic population determines the number of offspring groups that need to be updated by comprehensively and fully measuring the optimization situation, iteration stage, update index and other multi-dimensional parameters and updates them through the elite guidance optimization strategy; the order population relies on the global optimization performance of the genetic algorithm to maintain diversity at different stages of the algorithm operation to avoid premature convergence; the specific process is as follows:

[0114] S203-1. Determine the number of updated offspring populations: The chaotic population and the ordered population determine the number of offspring populations that need to be updated by comprehensively and fully measuring the optimization situation, iteration stage, and update index and other multi-dimensional parameters. The expression is as follows:

[0115] (12);

[0116] (13);

[0117] (14);

[0118] (15);

[0119] (16);

[0120] In the formula, , are the number of individuals that need to be updated in the chaotic population and the orderly population, and the initial number is set to ; N is the number of individuals in the chaotic population and the orderly population, and is also the number of individuals in the update population; Adjust the parameter for the starting ratio, the default setting is 0.4; , are the numbers of optimal solutions of chaotic population and dual population on the first Pareto frontier respectively; A judgment matrix for determining whether to change the number of individuals in the two groups; The number of times the number of optimization individuals changes during the entire optimization process; is the judgment matrix Calculation parameters of Indicates the current iteration number; Represents the population and population After merging, the individuals in the first level of Pareto are selected as The number of populations.

[0121] S203-2. Population update: updated offspring population set It is composed of individuals updated by elite guided optimization strategy and simulated binary crossover and polynomial mutation strategy based on genetic algorithm. Chaotic population, orderly population and elite population are based on environmental selection function. Determine, as shown below:

[0122] (17);

[0123] (18);

[0124] (19);

[0125] (20);

[0126] In the formula, and Respectively indicate t Generation Chaos Population and ordered population Separately with the offspring population set After environmental selection, the t +1) generation of chaotic and orderly populations; Expressing the t Elite population The first ( t +1) generation of elite population; Select a function for the environment; Select the function for the environment that only takes the first Pareto frontier; , Provide elite guidance and optimization strategies Ego and the crossover mutation strategy used in the genetic algorithm, where p and q are sets of random integers, , . The simulated binary crossover and polynomial mutation strategy based on genetic algorithm for the ordered population is called as the individual optimization update strategy, and the crossover mutation parameters are , in order to maintain diversity at different stages of the algorithm operation and avoid premature convergence.

[0127] S204, execute elite guidance optimization strategy: Chaotic population individuals make full use of the mean, optimality, randomness and other high-quality information in the elite population based on the elite guidance optimization strategy, so that the optimization individuals can perform full global search in a large search space with a better optimization direction and convergence rate, avoid the iteration falling into the local optimal dilemma too early, and thus quickly and efficiently find a feasible optimal solution set; wherein, the elite guidance optimization strategy is executed. In order to further enhance the efficient convergence and quality reliability of the optimal solution set, the chaotic population individuals make full use of the mean, optimality, randomness and other high-quality information in the elite population based on the elite guidance optimization strategy, so that the optimization individuals can perform full global search in a large search space with a better optimization direction and convergence rate, avoid the iteration falling into the local optimal dilemma too early, and thus quickly and efficiently find a feasible optimal solution set. The specific expression is as follows:

[0128] (twenty one);

[0129] (twenty two);

[0130] (twenty three);

[0131] (twenty four);

[0132] In the formula, Indicates that through the population The first ( t +1) generation to update the population, Indicates t The first generation of chaotic population Individual j the value of the variable, Indicated in The elite population mean guidance information obtained during the iteration; is a random number that follows a standard normal distribution; For the t The mean of the elite population of the first generation The value of the decision variable; Indicates the number of individuals in population 1 participating in the optimization update; Indicated in The first The individual j The optimal individual guidance information of a population of decision variables; Indicates t The mean of the individuals on the first Pareto frontier in population 1 in the iteration j decision variables; Indicated in The first The individual j The global and current optimal population joint guiding factors of the decision variables; Indicated in t The first generation of elite population randomly selects an individual The value of the decision variable, is a random integer number, .

[0133] S205, perform iterative update: if the preset maximum number of iterations is reached T , then the optimal reservoir dispatching scheme is obtained, and the fitness value of the elite dispatching scheme set is output to obtain the reservoir group dispatching scheme corresponding to the fitness value, otherwise, return to execute step S203.

[0134] Step 3: Output the optimal scheduling solution set for the reservoir group, where the optimal scheduling solution set is when the maximum number of iterations is reached. T , output the current elite population Arc , Arc Represents the final set of scheduling solutions.

[0135] Example

[0136] For the interval two-objective optimization scheduling model of cascade reservoirs for flood control and power generation, the present invention, NSGAII and MOEA / D are used to schedule the typical flood scenario of four cascade reservoirs in a basin, involving 20 scheduling periods, each of which has a scale of 1 day. The constraint variables include water level limit, final water level limit, total flood control storage capacity limit and other constraints. According to the scheduling model, each decision scheme of the multi-objective scheduling optimization problem has 80 decision variables. In addition, this study considers a 5% interval inflow runoff forecast scenario, and sets 10 random inflow runoff schemes for this scenario. Considering the constraint destruction caused by the fluctuation of the inflow interval forecast runoff, strong constraints will be set for different runoff scenarios to ensure that the risk requirements are met under all runoff fluctuation schemes. Taking the 10 runoff schemes generated by the interval forecast as an example, each decision scheme has 1723 constraint variables. For all solution methods, the number of iterations is 500 times, the population size is 100, so the total number of evaluations is 50,000.

[0137] In order to compare and analyze the solution set coverage, balance and optimality of the present invention and the comparative algorithms such as NSGAII in the actual multi-objective scheduling problem of reservoirs, the multi-objective scheduling problem was calculated 10 times independently, its HV index was calculated, and the calculation result with the best HV value was selected to draw the Pareto frontier diagram for analysis. It should be noted that the real Pareto frontier (PF) is almost impossible to obtain in actual scheduling. Therefore, in this case, the exact value of the HV index cannot be obtained, but this is not what we care about. We are concerned about the relative ranking of the HV index obtained by each algorithm. Because no matter which algorithm is used as the standard, their relative order will not change. Therefore, the extreme points obtained by each algorithm in each target dimension are set as standard reference points to normalize the solution set obtained by the method. The HV index calculated by this method can evaluate the relative performance of different actual situations. Therefore, the Pareto front obtained by each method and the ideal Pareto front are standardized to calculate the hypervolume (HV) index. HV can measure the convergence and distribution of the solution set, especially for problems with unknown Pareto fronts. The larger the HV, the better the distribution of the scheduling solution set obtained by this method, so as to compare their differences in practical applications. Secondly, the Spread index is used to measure the degree of propagation achieved between the obtained solutions. The smaller the Spread value, the better the distribution uniformity of the non-dominated solutions. When this metric value is 0, it means that all individual spacings in the Pareto optimal set are equal. Finally, the FR index is used to evaluate whether the solution set satisfies the constraints. When the FR index is 1, it means that the solution set is all feasible solutions.

[0138] Result analysis:

[0139] First, the average HV index and Spread of the three methods are compared, as shown in Table 1 and Figure 2 , it can be seen that the average HV index and Spread of the present invention in the actual scheduling scenario are better than the comparison algorithm. Therefore, the optimality, balance and optimization breadth of the present invention have significant advantages over the comparison algorithms in the interval multi-objective optimization scheduling problem, indicating that the present invention can better balance the comprehensive aspects such as solution set convergence effect, distribution uniformity, distribution breadth, etc. in dealing with complex problems, and the algorithm has reliable comprehensive performance and excellent optimization performance. Therefore, the present invention has stronger exploration ability, search efficiency and solution efficiency for solving the interval multi-objective optimization problem of cascade reservoirs.

[0140] Table 1 Evaluation index values ​​obtained by different algorithms

[0141] ;

[0142] Secondly, to further verify the effectiveness of the method of the present invention, the Pareto frontier is plotted for the solutions corresponding to the best HV values ​​obtained by various algorithms in 10 experiments. Figure 3-Figure 6 The results show that, compared with the Pareto frontier distribution of the present invention, NSGAII and MOEA / D, the non-inferior solution set obtained by the algorithm of the present invention has outstanding performance advantages in terms of solution set quality and distribution breadth, proving that it has better global convergence ability. At the same time, the point distribution in space is more uniform, indicating that its solution is more diverse and more representative. Therefore, the present invention performs well in terms of convergence and distribution.

[0143] Therefore, the present invention adopts the above-mentioned multi-objective optimization method of reservoir group dispatching interval under uncertain conditions, coordinates two different flood control objectives, and through the optimization results, the dispatching plan decision maker can not only obtain a better dispatching plan, but also have an intuitive interval to provide decision support, and provide a plan that is conducive to the optimal allocation of water resources and risk prevention; in addition, multiple results comparisons show that the proposed solution method has better solution results. Therefore, this method is of great significance for improving the feasibility of the optimal results of water resources management, and can achieve more scientific, reasonable and efficient water resources management.

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. 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 solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-objective optimization method for reservoir group dispatching interval under uncertain conditions, characterized in that: The following steps are involved: Step 1: Based on the dispatching characteristics of the basin where the reservoir is located, a multi-objective dispatching model for the interval of the cascade reservoir group is constructed with the maximum flood control storage capacity safety guarantee criterion and the maximum total power generation criterion of the cascade reservoir group; at the same time, interval constraints are added to the multi-objective dispatching model for the interval of the cascade reservoir group, and the interval constraints include water balance constraints, outflow balance constraints, water storage capacity constraints, turbine flow constraints, outflow constraints and output constraints; Step 2: Execute the dual-population dynamic collaborative interval optimization method to solve the optimal dispatching plan of the reservoir group; Step 3: Output the optimal dispatching plan set of the reservoir group; The process of executing the dual-population dynamic cooperative interval optimization method to solve the optimal scheduling plan for the reservoir group in step 2 is as follows: S201. Initialize basic parameters: Initialize the number of iterations t =1, determine the maximum number of iterations T , variable dimension J ; S202, executing the chaos-order mapping initialization strategy: setting the outflow during the reservoir scheduling period as a decision variable, generating two initial scheduling scheme sets of chaos and order according to the chaos-order mapping initialization strategy, and calculating the objective function fitness of the initial scheduling scheme set; S203, executing a dynamic adaptive mutual promotion update strategy, and performing a dynamic adaptive mutual promotion update strategy on the dual populations according to the current Pareto frontier optimization situation; S204, executing the elite guidance optimization strategy: based on the elite guidance optimization strategy, the individuals of the chaotic population use the mean, optimality, and randomness high-quality information in the elite population to enable the optimization individuals to perform a global search in the search space with the optimization direction and convergence rate to find the optimal solution set; S205, perform iterative update: if the preset maximum number of iterations is reached T , then the optimal reservoir dispatching scheme is obtained, and the fitness value of the elite dispatching scheme set is output to obtain the reservoir group dispatching scheme corresponding to the fitness value, otherwise, return to execute step S203.

2. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 1 is characterized by: The maximum flood control reservoir capacity safety guarantee criterion specifically takes the minimum flood control reservoir capacity occupancy as the optimization target. The objective function corresponding to the maximum flood control reservoir capacity safety guarantee criterion is expressed as: (1)； in, Indicates k The reservoir is j The flood control storage capacity occupied in each period; yes No. j The amount of time, ,in is an independent decision variable x In this scheduling model, the interval parameter represent m uncertainty interval for inflow runoff; Indicates that the interval vector parameter Flood control target value under the influence.

3. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 2 is characterized in that: The objective function corresponding to the maximum criterion of total power generation of cascade reservoirs is expressed as: (2 )； In the formula, To represent the interval vector parameter The total power generation of all cascade reservoirs under the influence, and Represent the number of reservoirs and the number of dispatching periods, respectively. It is The total number of hours in the period, , and Respectively represent The reservoir is Output, power generation flow and water head for each period, For the The output coefficient of a reservoir.

4. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 3 is characterized by: The expressions of water balance constraint, outflow balance constraint, water storage capacity constraint, turbine flow constraint, outflow constraint and output constraint are as follows: Water balance constraints: (3)； In the formula, Representatives and k All upstream reservoirs directly connected to the reservoir, and Respectively represent k The reservoir is j The storage capacity and interval inflow of each period, interval parameters Representatives received m The impact of runoff in the reservoir with uncertainty intervals; Indicates k The reservoir is directly connected to The upstream reservoir is in j Outbound flow in the time period; Indicates k The reservoir is j Outbound flow in the time period; Outflow balance constraint: (4 )； In the formula, Representative k The reservoir is j The amount of water discarded during each period; Water storage capacity constraints: (5)； In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the allowable storage capacity threshold for each time period; Turbine flow constraints: (6)； In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the turbine's allowable overflow threshold for each period; Outflow constraints: (7)； In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the discharge flow threshold for each time period; Output constraints: (8)； In the formula, and Respectively represent k The reservoir is j The upper and lower limits of the power generation threshold for each time period.

5. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 4 is characterized by: The expression for executing the chaos-order mapping initialization strategy in S202 is as follows: (9)； (10)； (11)； In the formula, , , , is a random parameter, where and Follows standard normal distribution, and Obeys uniform distribution between [0,1]; and Representative The variables of the solution j The upper and lower thresholds; , Respectively represent the chaotic and order-initialized populations obtained by initializing each individual and decision variable in the population based on chaos and order mapping, where, , Represents the first Individual j decision variables, , N and D are the number of individuals in the population and the number of decision variables respectively; Represents the elite initial population obtained by selecting the chaotic and orderly populations based on the reference point environment.

6. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 5 is characterized in that: The specific process of S203 is as follows: S203-1. Determine the number of updated offspring populations: The chaotic population and the ordered population determine the number of offspring populations that need to be updated by measuring the optimization situation, the iteration stage, and the multi-dimensional parameters of the update index. The expression is as follows: (12)； (13)； (14)； (15)； (16)； In the formula, , are the number of individuals that need to be updated in the chaotic population and the orderly population, and the initial number is set to ; N is the number of individuals in the chaotic population and the orderly population, and is also the number of individuals in the update population; Adjust the parameter for the starting ratio, the default setting is 0.4; , are the numbers of optimal solutions of chaotic population and dual population on the first Pareto frontier respectively; A judgment matrix for determining whether to change the number of individuals in the two groups; The number of times the number of optimization individuals changes during the entire optimization process; is the judgment matrix Calculation parameters of Indicates the current iteration number; Represents the population and population After merging, the individuals in the first level of Pareto are selected as the size of the population; S203-2. Population update: updated offspring population set It is composed of individuals updated by elite guided optimization strategy and simulated binary crossover and polynomial mutation strategy based on genetic algorithm. Chaotic population, orderly population and elite population are based on environmental selection function. Determine, as shown below: （17）； （18）； （19）； （20）； In the formula, and Respectively indicate t Generation Chaos Population and ordered population Separately with the offspring population set After environmental selection, the t +1) generation of chaotic and orderly populations; Indicates t Elite population The first ( t +1) generation of elite population; Select a function for the environment; Select the function for the environment that only takes the first Pareto frontier; , Provide elite guidance and optimization strategies Ego and the crossover mutation strategy used in genetic algorithms, where p and q are sets of random integers, , .

7. The multi-objective optimization method for reservoir group dispatching interval under uncertain conditions according to claim 6 is characterized in that: The specific expression for executing the elite guidance optimization strategy in S204 is as follows: (21)； (22)； (23)； (24)； In the formula, Indicates that through the population The first t +1 generation to update the population, Indicates t The first generation of chaotic population Individual j the value of the variable, Indicated in The elite population mean guidance information obtained during the iteration; is a random number that follows a standard normal distribution; For the t The mean of the elite population of the first generation The value of the decision variable; Indicates the number of individuals in population 1 participating in the optimization update; Indicated in The first The individual j The optimal individual guidance information of a population of decision variables; Indicates t The mean of the individuals on the first Pareto frontier in population 1 in the iteration j decision variables; Indicated in The first The individual j The global and current optimal population joint guiding factors of the decision variables; Indicated in t The first generation of elite population randomly selects an individual The value of the decision variable, is a random integer number, .

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