Multi-objective flood control optimization method and device for large-scale reservoir groups

Abstract

This invention provides a method and apparatus for multi-objective flood control optimization of large-scale reservoir groups. It constructs a multi-objective flood control optimization model and initializes multiple sets of decision variables to obtain an initial population containing multiple individuals. Then, it initializes a corresponding objective vector and weight vector for each individual in the initial population. Based on the initial population and the objective and weight vectors corresponding to each individual, a preset dynamic cooperative regional evolutionary algorithm is used to iteratively solve the multi-objective flood control optimization model. When the evolutionary number meets a preset number, the iterative solution ends; otherwise, the iterative solution continues. The solution result at the end of the iterative solution is used as the set of non-dominated scheduling schemes for the reservoir group. This invention can alleviate the problem of low optimization efficiency in existing reservoir optimization scheduling methods when dealing with high-dimensional optimization problems of decision variables in large-scale reservoir groups.

Description

Technical Field

[0001] This invention relates to the field of flood control optimization technology for reservoir groups, and in particular to a method and apparatus for multi-objective flood control optimization for large-scale reservoir groups. Background Technology

[0002] The optimal scheduling model for reservoirs is a multi-stage decision problem that satisfies the principles of optimization, lack of aftereffects, and overlap, making it suitable for dynamic programming. However, when faced with the optimal scheduling problem of large-scale reservoir groups, the dimensionality of the optimization decision variables increases dramatically with the number of reservoirs and the optimization period for each reservoir. Whether using dynamic programming or heuristic algorithms, the "curse of dimensionality" in decision variables easily arises, making it impossible to obtain the optimal solution. To address the optimal scheduling problem of reservoir groups, existing techniques such as discrete differential dynamic programming, successive optimization algorithms, and stepwise dynamic programming can solve the multi-reservoir optimal scheduling problem to some extent, but they all have technical bottlenecks in handling large-scale reservoir group optimal scheduling and multi-objective problems.

[0003] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0004] (1) Existing methods for solving reservoir group optimization problems cannot handle the "curse of dimensionality" problem of decision variables faced by large-scale reservoir group optimization scheduling.

[0005] (2) Existing methods for optimizing reservoir groups cannot effectively solve multi-objective scheduling models in parallel, and cannot obtain non-dominated frontiers in large-scale reservoir group optimization scheduling.

[0006] The difficulty in solving the above problems and defects lies in the fact that large-scale reservoir group optimization scheduling faces high-dimensional decision variables in terms of both time and the number of reservoirs, and it is even more difficult to converge effectively when dealing with multi-objective problems. Therefore, the difficulty lies in the design of scheduling optimization variables, objective design, constraint design, and efficient solution methods for the model.

[0007] The significance of solving the above problems and shortcomings is that by inventing an efficient multi-objective optimization scheduling solution method for large-scale reservoir groups, it is possible to obtain the Pareto optimal scheduling scheme set for large-scale reservoir groups in watersheds and regions, which can provide strong technical support and decision support for actual flood control scheduling and operation. Summary of the Invention

[0008] In view of this, the purpose of the present invention is to provide a method and apparatus for multi-objective flood control optimization of large-scale reservoir groups, so as to alleviate the problem of low optimization efficiency of existing reservoir optimization scheduling methods when dealing with high-dimensional optimization problems of decision variables in large-scale reservoir groups.

[0009] In a first aspect, embodiments of the present invention provide a multi-objective flood control optimization method for large-scale reservoir groups, the method comprising the following steps:

[0010] Step 1: Using water level and / or downstream discharge as decision variables, construct a multi-objective flood control optimization model with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity used by tributaries. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation and scheduling rules of the reservoir group.

[0011] Step 2: Initialize multiple sets of decision variables based on the upper limit and lower limit of water level fluctuation of each reservoir in the reservoir group and the initial operation scheduling rules to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables;

[0012] Step 3: Based on the target number and population size, initialize the corresponding target vector and weight vector for each individual in the initial population; wherein the dimension of the target vector and weight vector are equal to the target number.

[0013] Step 4: Based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, the multi-objective flood control optimization model is iteratively solved using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector;

[0014] Step 5: When the number of evolutions meets the preset number, the iterative solution ends; otherwise, proceed to step 4 to continue the iterative solution.

[0015] Step 6: The solution results at the end of the iteration are used as the set of non-inferior scheduling schemes for the reservoir group.

[0016] Secondly, embodiments of the present invention also provide a multi-objective flood control optimization device for large-scale reservoir groups, the device comprising the following modules:

[0017] The model building module is used to construct a multi-objective flood control optimization model with water level and / or downstream discharge as decision variables, and with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity for tributary utilization. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation and scheduling rules of the reservoir group.

[0018] The first initialization module is used to initialize multiple sets of decision variables based on the upper limit and lower limit of water level fluctuation of each reservoir in the reservoir group and the initial operation scheduling rules, to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables;

[0019] The second initialization module is used to initialize a corresponding target vector and weight vector for each individual in the initial population according to the target number and population size; wherein the dimension of the target vector and the weight vector are equal to the target number.

[0020] The model solving module is used to iteratively solve the multi-objective flood control optimization model based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector; when the number of evolutions meets the preset number, the iteration ends, otherwise the iteration continues;

[0021] The non-dominated scheduling scheme set module is used to take the solution result at the end of the iteration as the non-dominated scheduling scheme set of the reservoir group.

[0022] This invention provides a method and apparatus for multi-objective flood control optimization of a large-scale reservoir group. Using water level and / or downstream discharge as decision variables, a multi-objective flood control optimization model is constructed with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity used by tributaries. Multiple sets of decision variables are initialized based on the upper and lower limits of water level fluctuations and initial operation scheduling rules for each reservoir in the reservoir group, resulting in an initial population containing multiple individuals. Based on the number of objectives and the population size, corresponding objective vectors and weight vectors are initialized for each individual in the initial population. Based on the initial population and the objective and weight vectors corresponding to each individual, a preset dynamic cooperative regional evolution algorithm is used to iteratively solve the multi-objective flood control optimization model. The iterative solution ends when the number of evolutions meets a preset number; otherwise, iterative solution continues. The solution result at the end of the iterative solution is used as the set of non-dominated scheduling schemes for the reservoir group. The above-mentioned technology provides an efficient solution for multi-objective optimization scheduling of large-scale reservoir groups, which can obtain a set of non-inferior scheduling schemes for large-scale reservoir groups in watersheds and regions, and can provide strong technical support and decision support for actual flood control scheduling operations.

[0023] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0025] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating a multi-objective flood control optimization method for a large-scale reservoir group according to an embodiment of the present invention;

[0027] Figure 2 This is a flowchart illustrating the dynamic cooperative region evolution algorithm in an embodiment of the present invention.

[0028] Figure 3 These are the non-dominated front graphs of the four algorithms in this embodiment of the invention;

[0029] Figure 4 This is an example diagram illustrating the water level and flow rate process of Longtan Reservoir, which has the lowest peak flow rate in Wuzhou, during a non-inferior scheduling method in this embodiment of the invention.

[0030] Figure 5 This is an example diagram illustrating the water level and flow rate process of the Datengxia Reservoir, which has the lowest peak flow rate in Wuzhou, under non-inferior scheduling in this embodiment of the invention.

[0031] Figure 6 This is an example diagram illustrating the water level and flow rate process of the Baise Reservoir, which has the lowest peak flow rate in Wuzhou, in a non-inferior scheduling scenario according to an embodiment of the present invention.

[0032] Figure 7 This is an example diagram of the flow process in Wuzhou in an embodiment of the present invention;

[0033] Figure 8 This is a schematic diagram of the structure of a multi-objective flood control optimization device for a large-scale reservoir group in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] To facilitate understanding of this embodiment, a detailed description of a multi-objective flood control optimization method for a large-scale reservoir group disclosed in this embodiment of the invention will be provided first. (See [link to relevant documentation]). Figure 1 As shown, the method may include the following steps:

[0036] Step S102: Using water level and / or downstream discharge as decision variables, a multi-objective flood control optimization model is constructed with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity used by tributaries. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation and scheduling rules of the reservoir group.

[0037] Water level constraints are:

[0038]

[0039] Among them, Z i，t Let be the water level of the i-th reservoir during the t-th time period. and These are the lower and upper limits of the water level of the i-th reservoir during the t-th time period, respectively.

[0040] The water balance constraint is:

[0041] V i，t =V i，t -1+(I i，t -Q i，t )Δt

[0042] Among them, V i，t I i，t and Q i，t These represent the reservoir capacity, inflow, and outflow of the i-th reservoir during the t-th time period;

[0043] The evolution of river flow is as follows:

[0044] I 1，t+Δt =C0Q 0，t+Δt +C1Q 0，t +C2I 1，t

[0045]

[0046]

[0047] C2 = 1 - C0 - C1

[0048] Among them, Q 0，t and I 1，tQ represents the flow rates at the upstream and downstream outlet sections at time t, respectively. 0，t+Δt and I 1，t+Δt C0, C1, and C2 are the flow rates at the upstream and downstream outlet sections at time interval t+Δt, respectively. C0, C1, and C2 are functions of K, x, and Δt, respectively. K is the river segment propagation time under steady flow conditions, x is the flow rate weight factor, and Δt is the time interval.

[0049] The discharge capacity constraint is:

[0050]

[0051] Among them, Q i，t Let be the discharge flow of the i-th reservoir during the t-th time period. For the i-th reservoir at water level Z t Discharge capacity at that time;

[0052] The reservoir discharge flow constraint is:

[0053]

[0054] |Q i，t -Q i，t-1 |≤ΔQ i

[0055] Among them, Q i，t Let be the discharge flow of the i-th reservoir during the t-th time period. and Let ΔQ be the lower limit and upper limit of the discharge flow of the i-th reservoir in the t-th time period. i This represents the upper limit of the flow variation of the i-th reservoir;

[0056] The flow constraint at the flood control point is:

[0057]

[0058] Among them, Q′ t (t) represents the outflow from the reservoir during the t-th time period, calculated from the river channel to the i-th downstream flood control point, Δq. i (t) represents the inflow between the upstream reservoir group and the i-th flood control point during the t-th time period. Let be the upper limit of the flow rate at the i-th flood control point.

[0059] Step S104: Initialize multiple sets of decision variables based on the upper limit and lower limit of water level fluctuation of each reservoir in the reservoir group and the initial operation scheduling rules to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables.

[0060] Step S106: Based on the target number and population size, initialize the corresponding target vector and weight vector for each individual in the initial population; wherein the dimension of the target vector and weight vector are equal to the target number.

[0061] Step S108: Based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, the multi-objective flood control optimization model is iteratively solved using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector.

[0062] Step S110: If the number of evolutions meets the preset number, the iterative solution ends; otherwise, proceed to step S108 to continue the iterative solution.

[0063] Step S112: The solution results at the end of the iteration are used as the set of non-inferior scheduling schemes for the reservoir group.

[0064] This invention provides a multi-objective flood control optimization method for large-scale reservoir groups. Using water level and / or downstream discharge as decision variables, and minimizing the maximum discharge at downstream flood control sections and the maximum storage capacity of tributaries as objectives, a multi-objective flood control optimization model is constructed. Multiple sets of decision variables are initialized based on the upper and lower limits of water level fluctuations and initial operation scheduling rules for each reservoir in the reservoir group, resulting in an initial population containing multiple individuals. Based on the number of objectives and the population size, corresponding objective vectors and weight vectors are initialized for each individual in the initial population. Based on the initial population and the objective and weight vectors corresponding to each individual, a preset dynamic cooperative regional evolution algorithm is used to iteratively solve the multi-objective flood control optimization model. The iterative solution ends when the number of evolutions meets a preset number; otherwise, iterative solution continues. The solution result at the end of the iterative solution is used as the set of non-dominated scheduling schemes for the reservoir group. The above-mentioned technology provides an efficient solution for multi-objective optimization scheduling of large-scale reservoir groups, which can obtain a set of non-inferior scheduling schemes for large-scale reservoir groups in watersheds and regions, and can provide strong technical support and decision support for actual flood control scheduling operations.

[0065] As one possible implementation, step S102 above may include:

[0066] (11) Based on the flow rate of the downstream flood control section after the upstream reservoir scheduling at each time period, construct a first objective function with the objective of minimizing the maximum flow rate of the downstream flood control section:

[0067]

[0068] Where f1 is the maximum flow rate at the downstream flood control section. Let T be the flow rate at the downstream flood control section after the upstream reservoir has been regulated during the t-th time period, and T be the total regulation time.

[0069] (12) Based on the flood control capacity utilized by each reservoir in each time period, construct a second objective function with the goal of minimizing the maximum capacity utilized by the tributaries:

[0070]

[0071] Where f2 is the maximum storage capacity used by the branch, ΔV i，t Let t represent the flood control capacity used by the i-th reservoir in the t-th time period, n represent the number of tributary reservoirs, and T represent the total scheduling duration.

[0072] (13) Combine the first objective function and the second objective function to form a multi-objective flood control optimization model.

[0073] As one possible implementation, step S104 above may include:

[0074] (21) The water level values ​​of each reservoir in the next period are calculated based on the upper limit of water level fluctuation of each reservoir in the reservoir group, the initial water level of the current period, water level constraints and flow constraints, and the calculated water level values ​​of each reservoir in each period are initialized as the first set of decision variables.

[0075] (22) The water level values ​​of each reservoir in the next period are calculated based on the lower limit of the water level fluctuation of each reservoir in the reservoir group, the initial water level of the current period, the water level constraint and the flow constraint, and the calculated water level values ​​of each reservoir in each period are initialized as the second set of decision variables.

[0076] (23) Simulate the operation of each reservoir according to the initial operation scheduling rules of each reservoir in the reservoir group, and initialize the water level values ​​of each reservoir at each time period obtained during the simulation operation as the third set of decision variables.

[0077] (24) Generate decision variables other than the first group, the second group, and the third group by randomly sampling within the preset upper and lower limit range of decision variables.

[0078] As one possible implementation, step S106 above may include:

[0079] (31) Based on the population size, initialize a weight vector uniformly for each individual in the initial population within a space range where the number of dimensions is equal to the number of targets.

[0080] For example, based on the population size N, a region vector (i.e., weight vector) λ can be initialized for each individual j in the population within an m-dimensional space. j =(λ j，1 ,...λ j，i ,...λ j，m) T , ..., m, where m is the number of targets, λ j，i ≥0, and

[0081] (32) Calculate the target value for each individual in the initial population and initialize the target value of each individual into a target vector.

[0082] For example, the decision variables contained in each individual in the initial population can be substituted into the above multi-objective flood control optimization model to obtain the corresponding objective value, and then all the objective values ​​corresponding to each individual can be combined into an objective vector.

[0083] As one possible implementation, step S108 may include:

[0084] (41) Determine the region to which each individual in the initial population belongs based on the vertical distance between each individual in the initial population and its corresponding weight vector.

[0085] For each individual in the population, and for each new individual generated subsequently, the region to which the individual belongs can be determined by the perpendicular distance from the individual to the region vector. The perpendicular distance between an individual and its corresponding weight vector is defined as follows:

[0086]

[0087]

[0088] Where d(x, λ) j Let λ be an individual x and its corresponding weight vector λ. j The vertical distance between them, x = (x1, ..., x2) n ) T Let F(x) be an n-dimensional decision variable, where F(x) = (f1(x), f2(x), ..., f... m (x)) T Let m be the target vector corresponding to individual x, and m be the number of targets. Let be a vector within an m-dimensional space. It is the minimum value of the i-th objective corresponding to all populations;

[0089] The weight vector with the smallest vertical distance to an individual is defined as the region to which the individual belongs, as shown in the following formula:

[0090]

[0091] Where r is the region to which individual x belongs.

[0092] (42) Separate the decision variables corresponding to the same reservoir contained in each individual in the initial population as a set of decision variables, and form a subpopulation by combining all the separated sets of decision variables corresponding to the same reservoir.

[0093] For example, an individual in the initial population (i.e., a set of decision variables for the entire reservoir group) x = (x1, ..., x2) can be represented as an individual in the initial population. n ) T The decision variables of the i-th reservoir included in the data are treated as a new individual (i.e., a new set of decision variables). By separating them and so on, all the new individuals corresponding to the i-th reservoir separated in this way can be combined into a subpopulation.

[0094] (43) Based on the region to which each individual in each subpopulation belongs, each subpopulation is iteratively optimized; in each iteration, the corresponding decision variables are substituted into the multi-objective flood control optimization model to obtain the corresponding target value.

[0095] For example, for each subpopulation, the following steps are performed based on a preset initial time-series transformation parameter and a negative time-series transformation parameter step size:

[0096] (431) Based on the current time series transformation parameters, divide each individual in the current subpopulation into multiple groups of transformation decision variables according to the order of time periods.

[0097] (432) Determine the parent population pool from the neighborhood of the region corresponding to each individual in the current subpopulation, and generate offspring through crossover mutation. Then update the parent population pool by comparing the parent and offspring. Each offspring and each parent is a set of transformation decision variables.

[0098] (433) Use a preset time series transformation function to transform all transformation decision variables corresponding to each individual in the current subpopulation into corresponding decision variables.

[0099] (434) Take the decision variable corresponding to the current subpopulation as the decision variable to be optimized, and take the decision variables corresponding to other subpopulations outside the current subpopulation as fixed values, and substitute them into the multi-objective flood control optimization model to calculate the target value.

[0100] (435) Iterate through (431) to (434) until the number of iterations reaches the preset number of iterations, then end the iteration and take the iteration result of the decision variable to be optimized at the end of the iteration as the optimization decision variable corresponding to the subpopulation.

[0101] (44) Based on the iterative optimization results of each subpopulation, the multi-objective flood control optimization model is solved iteratively; wherein, the iterative optimization results of each subpopulation include the corresponding optimization decision variables and objective values.

[0102] For example, the optimization decision variables corresponding to all subpopulations can be substituted into a multi-objective flood control optimization model for iterative solution.

[0103] For ease of understanding, (43) and (44) above are described as follows by way of example.

[0104] The above (43) and (44) mainly involve the following three mechanisms:

[0105] 1) Dynamic time-series transformation mechanism.

[0106] To address the increased dimensionality of decision variables to be optimized due to the extended optimization period in large-scale reservoir groups, a dynamic time-series transformation mechanism can be introduced. This mechanism, based on the non-aftereffect nature of runoff time series, can transform the decision variables of the i-th reservoir to be optimized according to the chronological order of time periods. Middle 2 k Grouping the continuous decision variables into a group, thus transforming the original n... i The decision variables are divided into γ groups:

[0107]

[0108] Where k is the timing transformation parameter, n i Let represent the number of decision variables to be optimized for the i-th reservoir, and ceil() is the floor function;

[0109] Each set of decision variables for the i-th reservoir can be associated with a single transformed decision variable g. i ={g1, ..., g γ Given a set of n i dimensional decision vector v i The time-series transformation function ψ can be used to transform all the transformation decision variables g of the i-th reservoir. i Transformed into decision vector x i The mathematical expression is as follows:

[0110]

[0111] Using the time series transformation function described above, all γ-dimensional transformation decision variables of the same reservoir can be transformed into corresponding n-dimensional transformations. iSince the actual decision variables are dimensional, in the evolutionary algorithm process, by first optimizing the transformed decision variables and then converting the optimized transformed decision variables back into actual decision variables, the dimensionality of the decision variables can be reduced. Based on the number of time periods to be optimized in the multi-objective flood control optimization model, assuming the initial transformation parameter k = 3, a total of k + 1 = 4 optimization iterations are performed. After each optimization, k decreases by 1. Through this dynamic transformation process, the transformation decision variables with lower dimensionality are optimized first in the initial optimization process, and then this dimension of transformation decision variables is used as the initial solution for the next iteration dimension. Iterative optimization is then performed, finally obtaining γ = n. i The solution is taken as the final solution.

[0112] 2) Collaborative optimization mechanism.

[0113] To address the increased dimensionality of optimization decision variables resulting from the growing number of reservoirs in large-scale reservoir groups, a collaborative optimization mechanism can be introduced. This mechanism isolates the decision variables for each reservoir, constructing multiple co-evolving subpopulations. The competition or cooperation relationships between these subpopulations (i.e., upstream and downstream relationships between reservoirs) are then utilized to optimize the population.

[0114] In the collaborative optimization process, the optimization sequence from upstream to downstream is first determined according to the topological relationship of the cascade reservoir group. The number of evaluations of the optimization objective for each reservoir (i.e., the number of calculations of the objective) and the overall optimization number of the reservoir group are set, and the number of collaborative optimization iterations K is set. x Then, following the optimization order from upstream to downstream, for each reservoir, offspring individuals are produced through crossover and mutation operators, optimizing the decision variables for the i-th reservoir. At this time, the decision variables of other reservoirs can be used as the optimal decision variables (i.e., fixed values) obtained from the current optimization. and x i and all corresponding x j Substituting the values ​​into a multi-objective flood control optimization model, the target value is calculated, and the decision variables of the i-th reservoir are optimized according to the magnitude of the target value. After the optimization of a single reservoir is completed, the optimization results of the decision variables of all reservoirs in the reservoir group are combined to form the overall decision variable x = (x1,...,x...). n ) T The process involves iterative optimization until the number of iterations reaches the total number of iterations required for the overall optimization of the reservoir group, thus completing one round of collaborative optimization. This process is repeated for each individual reservoir and the overall reservoir group optimization until the number of collaborative optimizations reaches K. x The event will end at that time.

[0115] 3) Regional evolution mechanism.

[0116] The key idea behind the above collaborative optimization mechanism is to decompose the overall decision variables of a large-scale optimization problem into multiple co-evolving subpopulations. When optimizing the i-th subpopulation, the other subpopulations maintain their current optimal state. This mechanism is only applicable to single-objective optimization problems; when dealing with multi-objective problems, it cannot provide a globally optimal solution as the optimal state for other subpopulations. To address this, the regional evolution mechanism assigns each individual in the population to a corresponding region based on the spatial dimension of the objective, and then updates and replaces the population through domain parent selection, regional co-evolution, and regional population updates.

[0117] Parent selection: When producing offspring in the r-th region, the parent population pool MP can be determined from the 10 regions adjacent to the r-th region. Then, the binary crossover operator and polynomial mutation operation are used as the core operators of the regeneration process to generate offspring x.

[0118] Regional Co-evolution: During the co-evolution process, when optimizing the i-th reservoir, the decision variables for other reservoirs are the currently optimized parent generation p obtained in the r-th region. r The corresponding decision variables (i.e., fixed values).

[0119] Regional population update: This involves updating the parent population pool by comparing parent and child generations. Specifically, when comparing parent generations p... r When dealing with a child generation x, first determine the region to which they belong. A child generation x can replace a parent generation p only if the following two conditions are met. r a) Child x belongs to region r; b) Child x and parent p r Neither belongs to region r, but d(x,λ) r )≤d(p r ,λ r ).

[0120] For ease of understanding, a dynamic cooperative region evolution algorithm based on dynamic temporal transformation mechanism, cooperative optimization mechanism, and region evolution mechanism is proposed here. See [link to relevant documentation]. Figure 2 As shown, the operation flow of this algorithm mainly includes:

[0121] Step 1.1, Population initialization and region vector initialization; set the number of reservoirs K. s Collaborative optimization iteration count K x and the initial transformation parameter k.

[0122] Step 1.2, let i = 1.

[0123] Step 1.3, let γ = ceil(n) i / 2 k ).

[0124] Step 1.4, Timing Transformation. This involves converting the original n... iDimensional decision variable x i The transformation decision variables are divided into γ groups.

[0125] Step 1.5, let i = i + 1.

[0126] Step 1.6, determine whether i>K is satisfied. s If the condition is met, proceed to step 1.7; otherwise, return to step 1.3.

[0127] Step 1.7: Parent selection and offspring generation. After offspring generation, the γ group of decision variables for the i-th reservoir is transformed into n using a time-series transformation function ψ. i Dimensional decision vector x i and x i Substitute the values ​​into the multi-objective flood control optimization model to obtain the corresponding objective values.

[0128] Step 1.8, determine whether i≤K is satisfied. s If the conditions are met, proceed with steps 1.9 and 1.10 in sequence; otherwise, perform overall evolution and proceed with step 1.10.

[0129] Step 1.9, Regional Co-evolution.

[0130] Step 1.10, Regional population update.

[0131] Step 1.11, let i = i + 1.

[0132] Step 1.12, determine whether i ≤ K is satisfied. s +1, if satisfied, return to step 1.7, otherwise execute step 1.13.

[0133] Step 1.13, let k = k-1.

[0134] Step 1.14: Determine if k < 0. If it is, proceed to step 1.15; otherwise, return to step 1.2.

[0135] Step 1.15: Output the set of non-inferior solutions.

[0136] For ease of understanding, this invention uses the main stream reservoir group of the Xijiang River basin and the tributary reservoir groups of the Liujiang, Yujiang, and Guijiang Rivers as examples. The reservoirs involved in the optimized scheduling include Tianyi, Guangzhao, Longtan, Yantan, Datengxia, Baise, Laokou, Zuojiang Hub, Yangxi, Luojiu, Mudong, Lema, Qingshitan, Fuzikou, Xiaorongjiang, Chuanjiang, and Zhaoping, totaling 17 reservoirs. Taking the typical once-in-a-century flood of 1974 as an example, the scheduling calculation step is 12 hours, with 90 decision variables per reservoir and a total of 1530 decision variables in the model, belonging to a large-scale reservoir group optimization problem. A large-scale reservoir group multi-objective optimization scheduling model is established with the objective functions of minimizing the peak flood discharge at the Wuzhou section of the lower reaches of the Xijiang River and maximizing the flood control capacity reserved by the tributary reservoir groups. To verify the performance of the Dynamic Cooperative Regional Evolutionary Algorithm (DCREA), three commonly used multi-objective solution methods (i.e., multi-objective evolutionary algorithms) – NSGAII, MOPSO, and MOEA / D – are selected for comparison. The evaluation metric used is the Hypervolume (HV) metric, which can simultaneously evaluate the convergence and distribution of a solution set. The larger the HV value, the better the overall performance of the algorithm. To ensure the randomness of the algorithm, each algorithm is run 20 times, and the average value is used as the final result.

[0137] Table 1 lists the average HV index of the four algorithms in the solution set in the examples. As can be seen from Table 1, DCREA has the largest HV index value, indicating that the convergence and distribution of the scheduling solution set obtained by DCREA are the best among the three algorithms.

[0138] Table 1 shows the average HV index of the four algorithms in the solution set in the examples.

[0139]

[0140] Figure 3 The non-dominated front plots of the four algorithms in this case study are shown. The distribution of points in the non-dominated front plots provides a visual indication of the algorithm's distributional nature, while the distance of each point from the origin indicates the algorithm's convergence. Figure 3 It can be seen that DCREA has the widest and most uniform distribution of non-dominated fronts among the four algorithms, and the non-dominated solution set obtained by DCREA has the best convergence, almost dominating the solution sets of other algorithms, which proves the excellent performance of the algorithm.

[0141] Table 2 shows the set of non-dominated solutions obtained from the final iterative solution of DCREA. As can be seen from Table 2, when the flood control capacity of the tributary reservoir group is not utilized (Solution 3, utilizing 0 billion m³ of flood control capacity), the optimal solution is achieved. 3 (This can reduce the peak flow of the flood in Wuzhou from 59,100 m³ / h) 3 / s reduced to 49274m 3 / s; When the flood control capacity of the tributary reservoir group is utilized to the maximum extent (Scheme 5, utilizing 5.311 billion m3 of flood control capacity), the peak flood flow in Wuzhou can be reduced from 59,100 m³ / s. 3 / s reduced to 44364m 3 / s.

[0142] Table 2. Set of non-dominated solutions obtained from the final iteration of DCREA

[0143]

[0144] Figures 4 to 7 The data shows the water level and flow processes of Longtan Reservoir, Datengxia Reservoir, and Baise Reservoir, which experienced the smallest peak flood flow in Wuzhou during non-inferior flood control operations, as well as the flow process in Wuzhou itself. From... Figures 4 to 7 As can be seen from the data, the Wuzhou section in the typical year of 1974 was a mid-to-upper reaches multi-peak process. Under the design rules, the Longtan Reservoir had already exhausted its flood control capacity during the first two floods, and had no capacity left for flood control and peak reduction during the third flood peak. The optimized Longtan, Datengxia, and Baise Reservoirs accurately predicted the peak reduction opportunity based on the Wuzhou flood peak time, making full use of their flood control capacity. As a result, the flood peak flow at the Wuzhou section was reduced to 44,364 m³ after the scheduling. 3 / s, ensuring the flood control safety of the downstream flood control section while guaranteeing the flood control safety of the reservoir itself.

[0145] Based on the above-mentioned multi-objective flood control optimization method for large-scale reservoir groups, this invention also provides a multi-objective flood control optimization device for large-scale reservoir groups. (See attached document.) Figure 8 As shown, the device may include the following modules:

[0146] The model building module 802 is used to construct a multi-objective flood control optimization model with water level and / or downstream discharge as decision variables, and with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity for tributary utilization. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation scheduling rules of the reservoir group.

[0147] The first initialization module 804 is used to initialize multiple sets of decision variables according to the upper limit value of water level fluctuation, the lower limit value of water level fluctuation and the initial operation scheduling rules of each reservoir in the reservoir group, so as to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables.

[0148] The second initialization module 806 is used to initialize a corresponding target vector and weight vector for each individual in the initial population according to the target number and population size; wherein the dimension of the target vector and the weight vector are equal to the target number.

[0149] The model solving module 808 is used to iteratively solve the multi-objective flood control optimization model based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector; when the number of evolutions meets the preset number, the iteration ends, otherwise the iteration continues.

[0150] The non-dominated scheduling scheme set module 810 is used to take the solution result at the end of the iteration as the non-dominated scheduling scheme set of the reservoir group.

[0151] This invention provides a large-scale reservoir group multi-objective flood control optimization device. Using water level and / or downstream discharge as decision variables, a multi-objective flood control optimization model is constructed with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity used by tributaries. Multiple sets of decision variables are initialized based on the upper and lower limits of water level fluctuations and initial operation scheduling rules for each reservoir in the reservoir group, resulting in an initial population containing multiple individuals. Based on the number of objectives and the population size, corresponding objective vectors and weight vectors are initialized for each individual in the initial population. Based on the initial population and the objective and weight vectors corresponding to each individual, a preset dynamic cooperative regional evolution algorithm is used to iteratively solve the multi-objective flood control optimization model. The iterative solution ends when the number of evolutions meets a preset number; otherwise, iterative solution continues. The solution result at the end of the iterative solution is used as the set of non-dominated scheduling schemes for the reservoir group. The above-mentioned technology provides an efficient solution for multi-objective optimization scheduling of large-scale reservoir groups, which can obtain a set of non-inferior scheduling schemes for large-scale reservoir groups in watersheds and regions, and can provide strong technical support and decision support for actual flood control scheduling operations.

[0152] The aforementioned model building module 802 can also be used for:

[0153] Based on the flow rate of the downstream flood control section after upstream reservoir scheduling at each time period, a first objective function is constructed with the objective of minimizing the maximum flow rate of the downstream flood control section:

[0154]

[0155] Among them, F1 is the maximum flow rate at the downstream flood control section. Let T be the flow rate at the downstream flood control section after the upstream reservoir's operation during the t-th time period, and T be the total operation duration.

[0156] Based on the flood control capacity utilized by each reservoir in each time period, a second objective function is constructed with the goal of minimizing the maximum capacity utilized by tributaries:

[0157]

[0158] Where F2 is the maximum storage capacity used by the branch, ΔV i, Let n be the flood control capacity used by the i-th reservoir in the t-th time period, n be the number of tributary reservoirs, and T be the total scheduling duration.

[0159] The first objective function and the second objective function are combined to form the multi-objective flood control optimization model.

[0160] The aforementioned first initialization module 804 can also be used to: calculate the water level value of each reservoir in the next time period based on the upper limit of water level fluctuation of each reservoir in the reservoir group, the initial water level of the current time period, water level constraints, and flow constraints, and initialize the calculated water level value of each reservoir in each time period as a first set of decision variables; calculate the water level value of each reservoir in the next time period based on the lower limit of water level fluctuation of each reservoir in the reservoir group, the initial water level of the current time period, water level constraints, and flow constraints, and initialize the calculated water level value of each reservoir in each time period as a second set of decision variables; simulate the operation of each reservoir according to the initial operation scheduling rules of each reservoir in the reservoir group, and initialize the water level value of each reservoir in each time period obtained during the simulation operation as a third set of decision variables; and generate other sets of decision variables besides the first set, the second set, and the third set of decision variables by randomly sampling within the preset upper and lower limit ranges of decision variables.

[0161] The second initialization module 806 described above can also be used to: uniformly initialize a weight vector for each individual in the initial population within a spatial range where the number of dimensions is equal to the number of targets, based on the population size; calculate the corresponding target value for each individual in the initial population, and initialize the target value of each individual into a target vector.

[0162] The aforementioned model solving module 808 can also be used to: determine the region to which each individual in the initial population belongs based on the vertical distance between each individual in the initial population and its corresponding weight vector; separate the decision variables corresponding to the same reservoir contained in each individual in the initial population as a group of decision variables, and form a corresponding subpopulation with all the separated groups of decision variables corresponding to the same reservoir; perform iterative optimization on each subpopulation based on the region to which each individual in each subpopulation belongs; wherein, during each iterative optimization, the corresponding decision variables are substituted into the multi-objective flood control optimization model to obtain the corresponding target value; and perform iterative solution on the multi-objective flood control optimization model based on the iterative optimization results of each subpopulation; wherein, the iterative optimization result of each subpopulation includes the corresponding optimization decision variables and target value.

[0163] The large-scale reservoir group multi-objective flood control optimization device provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned large-scale reservoir group multi-objective flood control optimization method embodiment. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0164] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0165] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0166] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0167] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-objective flood control optimization method for large-scale reservoir groups, characterized in that, The method includes: Step 1: Using water level and / or downstream discharge as decision variables, construct a multi-objective flood control optimization model with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity used by tributaries. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation and scheduling rules of the reservoir group. Step 2: Initialize multiple sets of decision variables based on the upper limit and lower limit of water level fluctuation of each reservoir in the reservoir group and the initial operation scheduling rules to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables; Step 3: Based on the target number and population size, initialize the corresponding target vector and weight vector for each individual in the initial population; wherein the dimension of the target vector and weight vector are equal to the target number. Step 4: Based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, the multi-objective flood control optimization model is iteratively solved using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector; Step 5: When the number of evolutions meets the preset number, the iterative solution ends; otherwise, proceed to step 4 to continue the iterative solution. Step 6: The solution results at the end of the iteration are used as the set of non-inferior scheduling schemes for the reservoir group; Step 4 includes: (41) Determine the region to which each individual in the initial population belongs based on the vertical distance between each individual in the initial population and its corresponding weight vector; (42) Separate the decision variables corresponding to the same reservoir contained in each individual in the initial population as a set of decision variables, and form a subpopulation by combining all the separated sets of decision variables corresponding to the same reservoir. (43) Based on the region to which each individual in each subpopulation belongs, iterative optimization is performed on each subpopulation; wherein, during each iteration of optimization, the corresponding decision variables are substituted into the multi-objective flood control optimization model to obtain the corresponding target value; (44) Based on the iterative optimization results of each subpopulation, the multi-objective flood control optimization model is iteratively solved; wherein, the iterative optimization results of each subpopulation include the corresponding optimization decision variables and objective values; The (43) includes: For each subpopulation, the following steps are performed based on the preset initial time-series transformation parameters and negative time-series transformation parameter step size: (431) Based on the current time series transformation parameters, divide each individual in the current subpopulation into multiple groups of transformation decision variables according to the order of time periods; (432) Determine the parent population pool from the neighborhood of the region corresponding to each individual in the current subpopulation, and generate offspring through crossover mutation. Then update the parent population pool by comparing the parent and offspring. Each offspring and each parent is a set of transformation decision variables. (433) Use a preset time series transformation function to transform all transformation decision variables corresponding to each individual in the current subpopulation into corresponding decision variables; (434) Take the decision variable corresponding to the current subpopulation as the decision variable to be optimized, and take the decision variables corresponding to other subpopulations outside the current subpopulation as fixed values, and substitute them into the multi-objective flood control optimization model to calculate the target value; (435) Iterate through (431) to (434) until the number of iterations reaches the preset number of iterations, then end the iteration and take the iteration result of the decision variable to be optimized at the end of the iteration as the optimization decision variable corresponding to the subpopulation.

2. The method according to claim 1, characterized in that, Step 1 includes: Based on the flow rate of the downstream flood control section after upstream reservoir scheduling at each time period, a first objective function is constructed with the objective of minimizing the maximum flow rate of the downstream flood control section: in, This represents the maximum flow rate at the downstream flood control section. Let T be the flow rate at the downstream flood control section after the upstream reservoir's operation during the t-th time period, and T be the total operation duration. Based on the flood control capacity utilized by each reservoir in each time period, a second objective function is constructed with the goal of minimizing the maximum capacity utilized by tributaries: in, To utilize the maximum storage capacity for branch operations, Let n be the flood control capacity used by the i-th reservoir in the t-th time period, n be the number of tributary reservoirs, and T be the total scheduling duration. The first objective function and the second objective function are combined to form the multi-objective flood control optimization model.

3. The method according to claim 1, characterized in that, Step 2 includes: The water level values ​​of each reservoir in the reservoir group in the next period are calculated based on the upper limit of water level fluctuation, the initial water level of the current period, water level constraints and flow constraints, and the calculated water level values ​​of each reservoir in each period are initialized as the first set of decision variables. The water level values ​​of each reservoir in the next period are calculated based on the lower limit of water level fluctuation of each reservoir in the reservoir group, the initial water level of the current period, water level constraints and flow constraints, and the calculated water level values ​​of each reservoir in each period are initialized as the second set of decision variables. The reservoirs in the reservoir group are simulated according to their initial operation and scheduling rules, and the water level values ​​of each reservoir at each time period obtained during the simulation are initialized as the third set of decision variables. Other groups of decision variables besides the first, second, and third groups are generated by randomly sampling within the preset upper and lower limit ranges of decision variables.

4. The method according to claim 3, characterized in that, Step 3 includes: Based on the population size, a weight vector is uniformly initialized for each individual in the initial population within a space where the number of dimensions is equal to the number of targets. Calculate the target value for each individual in the initial population, and initialize the target value of each individual into a target vector.

5. The method according to claim 1, characterized in that, The (44) includes: The optimization decision variables corresponding to all subpopulations are substituted into the multi-objective flood control optimization model for iterative solution.

6. The method according to claim 1, characterized in that, The vertical distance between an individual and its corresponding weight vector is defined as follows: in, For individual x and its corresponding weight vector The vertical distance between them For n-dimensional decision variables, Let m be the target vector corresponding to individual x, and m be the number of targets. Let be a vector within an m-dimensional space. It is the minimum value of the i-th target in all populations; The region to which an individual belongs is defined as follows: in, The region to which individual x belongs.

7. The method according to claim 1, characterized in that, The steps involved in updating the parent population pool by comparing the parent and offspring generations include: Comparing parent generation p r When dealing with a child generation x, first determine the region to which they belong. A child generation x can replace a parent generation p only if the following two conditions are met. r a) Child x belongs to region r; b) Child x and parent p r Neither of them belong to region r, but .

8. A multi-objective flood control optimization device for a large-scale reservoir group, characterized in that, The apparatus is used to execute the multi-objective flood control optimization method for large-scale reservoir groups as described in claim 1, and the apparatus includes: The model building module is used to construct a multi-objective flood control optimization model with water level and / or downstream discharge as decision variables, and with the objectives of minimizing the maximum discharge at downstream flood control sections and minimizing the maximum reservoir capacity for tributary utilization. The total number of decision variables is determined based on the number of reservoirs in the reservoir group participating in the optimization scheduling, the time step of the scheduling period, and the total scheduling duration. The constraints of the multi-objective flood control optimization model include water level constraints, water balance constraints, river flow evolution, discharge capacity constraints, downstream discharge constraints, flood control point flow constraints, and the initial operation and scheduling rules of the reservoir group. The first initialization module is used to initialize multiple sets of decision variables based on the upper limit and lower limit of water level fluctuation of each reservoir in the reservoir group and the initial operation scheduling rules, to obtain an initial population containing multiple individuals; wherein, each individual in the initial population is a set of decision variables; The second initialization module is used to initialize a corresponding target vector and weight vector for each individual in the initial population according to the target number and population size; wherein the dimension of the target vector and the weight vector are equal to the target number. The model solving module is used to iteratively solve the multi-objective flood control optimization model based on the initial population and the target vector and weight vector corresponding to each individual in the initial population, using a preset dynamic cooperative regional evolution algorithm; wherein, the solution result of each iteration includes the corresponding decision variables and target vector; when the number of evolutions meets the preset number, the iteration ends, otherwise the iteration continues; The non-dominated scheduling scheme set module is used to take the solution result at the end of the iteration as the non-dominated scheduling scheme set of the reservoir group.

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