A water project multi-objective scheduling dynamic collaborative optimization method and system

Abstract

The application discloses a kind of water engineering multi-objective scheduling dynamic collaborative optimization method and system, the method of the present application includes the following steps: S1, the multi-objective collaborative optimization scheduling model with the maximum of water supply benefit, power generation benefit, ecological benefit, sand transport benefit and the like generated by water engineering is established as scheduling target, and constraint condition is added to the optimization scheduling model;S2, dynamic collaborative search algorithm initialization;S3 dynamic collaborative search algorithm iterative operation;S4, individual updating strategy of dynamic collaborative search algorithm is called;S5, non-inferior scheduling scheme set output and optimization are carried out.The water engineering multi-objective scheduling dynamic collaborative optimization method and system proposed in the application have the advantages of strong global optimization ability, low model calculation cost, uniform distribution of non-inferior scheduling scheme, and significant improvement of comprehensive benefit, providing more efficient technology for complex water engineering multi-objective scheduling problem.

Description

Technical Field

[0001] This invention belongs to the field of efficient water resource utilization and water project scheduling, specifically involving a dynamic collaborative optimization method and system for multi-objective scheduling of water projects. Background Technology

[0002] To alleviate the severe water situation in my country, characterized by summer floods and winter droughts, abundant harvests in the south and scarce water in the north, and extremely uneven spatial and temporal distribution of water resources, the construction of the national water network has been continuously advancing. The scale of joint scheduling of cascade water transfer projects in river basins has expanded significantly, and multiple comprehensive benefit objectives have become increasingly intertwined. Existing water resource scheduling and management schemes are unable to fully leverage the collaborative and adaptive regulation and storage functions of water projects, resulting in persistent problems such as severe water resource depletion, significant waste of regulating reservoir capacity, difficulty in guaranteeing water supply and demand, and questionable power supply quality. Scheduling models focused solely on a single objective are no longer sufficient to meet practical application needs, and water project scheduling is gradually evolving towards multi-objective optimization scheduling models.

[0003] Multi-objective optimization scheduling models are mainly divided into two research approaches: (1) transforming multi-objective optimization problems into single-objective optimization problems through operations such as linear weighting and penalty function constraints, and then solving them using traditional classical optimization algorithms, such as linear programming, dynamic programming, and large system decomposition and coordination; (2) applying multi-objective evolutionary algorithms based on Pareto theory to directly solve multi-objective optimization scheduling models, such as MOPSO, NSGA-II, and MOCSA. Among them, the objective transformation strategies such as weighting and constraint methods in approach (1) are subject to certain human experience interference, making it difficult to grasp the optimization progress of each scheduling objective, resulting in low computational efficiency and poor simulation accuracy of the scheduling model; the effectiveness of the scheme in approach (2) mainly depends on the optimization mechanism of the evolutionary algorithm. The optimization mechanisms of different algorithms are varied and the optimization paths are random, making it difficult to guarantee that a uniformly distributed, wide-ranging, continuous, and real Pareto front non-dominated solution set can be obtained. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention conducts research based on the following two optimization approaches: (1) Based on the optimization approach of transforming multi-objective problems into single-objective problems, the MOEA / D algorithm framework aims to decompose multi-objective optimization problems into N single-objective optimization sub-problems and simultaneously optimize and solve the N sub-problems. The neighbor relationship between sub-problems depends on the aggregation coefficient vector distance between individuals in the population. When optimizing and solving each sub-problem, the neighbor information of the sub-problem needs to be considered. After iteration, the population consists of the current optimal solution of each sub-problem. This algorithm framework introduces the decomposition approach into multi-objective optimization problems, effectively reducing the computational complexity and diversity control of the algorithm, and significantly improving the quality and distribution of non-dominated solutions. (2) Based on the optimization approach of multi-objective evolutionary algorithms, the collaborative search algorithm analogizes the optimization problem to the collaborative behavior of modern corporate teams. The optimization process is mainly divided into the following four stages: the team building stage, which focuses on the initialization of individuals in the population; the team communication stage, which focuses on individuals learning new knowledge from the chairman, board of directors, and supervisory board; the reflective learning stage, which focuses on individuals summarizing new knowledge from historical experience; and the internal competition stage, which focuses on selecting team communication knowledge or reflective learning knowledge. This algorithm has the advantages of strong optimization ability, fast convergence speed, and high search accuracy, providing an efficient solution tool for solving complex global optimization problems.

[0005] In summary, this invention combines two optimization approaches for multi-objective scheduling models, and innovatively optimizes based on the MOEA / D algorithm framework and collaborative search algorithm. It proposes a dynamic collaborative optimization method and system for multi-objective scheduling of water projects to meet the needs of flexible adjustment and benefit optimization of actual scheduling schemes at different stages under the comprehensive benefit objective.

[0006] To address the above technical problems, this invention provides the following technical solution: a dynamic collaborative optimization method for multi-objective scheduling of water engineering projects, comprising the following steps:

[0007] S1. Establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply benefits, power generation benefits, ecological benefits, and sediment transport benefits generated by water projects, and add constraints to the optimization scheduling model.

[0008] S2. Initialization of the Dynamic Cooperative Search Algorithm: Initialize the relevant parameters of the scheduling optimization model; initialize the initial search population; initialize the relevant parameters of the MOEA / D algorithm framework; initialize the elite population Arc;

[0009] S3, the dynamic collaborative search algorithm iteratively runs, including team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies, dynamically optimizing to obtain updated offspring Offspring. t ;

[0010] S4. Individual update strategy invocation of dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy;

[0011] S5. Output and optimize the set of non-dominated scheduling schemes. Specifically, return to steps S3 to S4 until the maximum number of iterations is reached, and output the solution space of the elite population Arc variable.

[0012] Furthermore, in step S1 above, the objective function of the multi-objective cooperative optimization scheduling model specifically includes, but is not limited to, the following:

[0013] Maximum total power generation:

[0014]

[0015] in, P represents the total power generation during the dispatch period T, in billions of kWh; t Let be the average power output in the t-th time period, in kW; A is the overall power output coefficient of the power plant. Let m be the power generation flow rate during the t-th time period. 3 / s;H t Let m be the hydropower head generated in the t-th time period, and T be the total number of time periods in the scheduling period.

[0016] Maximum total water supply:

[0017]

[0018] in, The total water supply during the scheduling period T is expressed in m. 3 ; Let m be the water supply flow rate during the t-th time period. 3 / s; Δt is the duration of the time interval, in seconds;

[0019] Minimum water shortage rate due to ecological flow:

[0020] β t =Min(1-Q) t / Q t,x )*100% (3)

[0021] Where, β t Q represents the ecological flow water shortage rate in time period t. t Let m be the discharge flow rate in the t-th time period. 3 / s;Q t,x Let m be the required ecological flow for the t-th time period. 3 / s;

[0022] Minimum total water shortage in the basin:

[0023]

[0024] Among them, W q q represents the total water shortage in the basin; n is the user ID; N is the total number of users; n,t This represents the water shortage for the nth user in time period t.

[0025] The downstream channel carries the largest amount of sediment:

[0026]

[0027] Where Ws is the downstream sediment transport volume (in ten thousand tons); m is the cross-section number; M is the total number of cross-sections; w m (t) represents the sediment transport rate of the m-th cross section in time period t, in kg / s; K, a, and b are the sediment transport rate parameters of the n-th cross section in time period t, respectively. The sediment transport flow rate at section m during time period t, m 3 / s; Let m be the sediment concentration at section m during time period t, in kg / m³. 3 .

[0028] Furthermore, in step S1 above, the constraints specifically include, but are not limited to, the following:

[0029] Water balance constraints:

[0030]

[0031] Among them, V t Let m be the reservoir's water storage capacity at the beginning of the t-th time period. 3 ; The inbound flow rate during the t-th time period is expressed in meters (m). 3 / s; The outbound flow rate during the t-th time period is expressed in meters (m). 3 / s;

[0032] Storage capacity constraints:

[0033]

[0034] V t min Let m be the minimum allowable water storage capacity during time period t. 3 V t max Let m be the maximum allowable water storage capacity of the reservoir during time period t. 3 V t Let m be the reservoir's water storage capacity during the t-th time period. 3 ;

[0035] Downflow constraint:

[0036]

[0037] Let m be the minimum allowable discharge flow rate during time period t. 3 / s; Let m be the maximum allowable discharge flow rate during time period t. 3 / s;

[0038] Output constraints:

[0039]

[0040] P t min The minimum allowable output power during time period t is kW; P t max The maximum allowable output power during time period t is kW; P t The output power during the t-th time period is kW;

[0041] Ecological baseflow constraints:

[0042] Ql t ≥Ql max (10)

[0043] Ql t Let m be the remaining flow rate of the river channel after water intake at the water intake section in time period t. 3 / s;Ql max Let m be the ecological base flow rate at the water intake section during time period t. 3 / s;

[0044] Discharge amplitude constraint:

[0045] H i (t+1)-H i (t)≤ΔH i,xie (11)

[0046] H i (t) represents the water level at the i-th discharge section during time period t, in meters; ΔH i,xie Let be the maximum allowable discharge water level variation at the i-th discharge section;

[0047] Non-negativity constraint: All parameters satisfy the non-negativity constraint condition.

[0048] Furthermore, the aforementioned step S2 includes the following sub-steps:

[0049] S2.1 Initialize the relevant parameters of the scheduling optimization model, including: maximum number of iterations T, population size I, and adjustment parameters α and β;

[0050] S2.2 Initialize the first generation of the optimization population: Randomly generate an initial population based on the preset limit range of the individuals in the population, store the individuals in the initial population as the individual's optimal position pbest, and calculate the fitness of the individuals in the population at the same time.

[0051]

[0052] in, It is the value of the j-th decision variable for the i-th individual at the t-th iteration; Indicates the interval Generate uniformly distributed random numbers internally. x j This represents the lower bound of the range of the j-th decision variable. Let I be the upper limit of the restricted position range of the j-th decision variable; I is the number of individuals in the population; and J is the number of decision variables.

[0053] S2.3, Parameters for initializing the MOEA / D algorithm framework: Initializing the number of neighboring individuals N based on the MOEA / D algorithm framework. b And a weight vector W, and determine the maximum number N of replacements for each offspring individual. r The default number of updates for the weight vector is N. w ;

[0054] S2.4 Initialize the elite population Arc: Select individuals of the first Pareto frontier level among the neighbors to form the globally optimal individual solution set gbest, and further complete the initialization of the elite population Arc;

[0055] gbest=X nh (Pareto=1) (13)

[0056] Where gbest represents the globally optimal set of individual solutions; X nh This represents an individual in the population determined based on its neighbor index in the reference vector; (Pareto=n) represents an individual at the nth front level of Pareto.

[0057] Furthermore, the aforementioned step S3 includes the following sub-steps:

[0058] S3.1 Execution Team Random Communication Strategy: Individuals acquire new knowledge and update their skills through communication with three entities: the Chairman, the Board of Directors, and the Supervisory Board. The Chairman candidate (gbest1), the Board of Directors candidate (gbest2), and the Supervisory Board candidate (pbest) are generated based on the elite population (Arc) using a random selection strategy. The specific team random selection strategy is as follows:

[0059] (a) The chairman candidate, gbest1, is randomly selected from the elite population Arc:

[0060] gbest1 = Arc[randi(N g (14)

[0061] Among them, randi(N) g ) represents the number of individuals N existing from Arc. g The individual serial number randomly determined in the process;

[0062] (b) The board of directors takes the average value of all individuals in the elite population Arc as gbest2:

[0063] gbest2 = Arc(gbest) (15)

[0064] Where: mean(·) represents taking the mean of each dimension for all individuals;

[0065] (c) The supervisory board pbest is the individual in the population whose product of the smallest M distances from an individual to all other individuals is the largest:

[0066] pbest = max[dis(X) nh (16)

[0067] Where max[dis(·)] represents the individual with the largest product of the minimum M distances from the population to all other individuals;

[0068] (d) New knowledge acquired during random team communication mainly includes three parts: Chairman's knowledge A, Board of Directors knowledge B, and Supervisory Board knowledge C.

[0069]

[0070]

[0071]

[0072]

[0073] in, Let j be the value of the solution i communicated by the team at the t-th iteration; The knowledge obtained from the chairman, board of directors, and supervisory board is selected randomly, in that order; κ(J) and ψ(J) are random numbers in the range [0,1] generated randomly from the variable set J; α and β are adjustment parameters.

[0074] S3.2 Executing a self-perturbation and reflection strategy: Individuals balance existing optimal solutions with innovative mutation solutions by summarizing existing experiences and simulating mutation behaviors, exploring multi-dimensional optimization directions for knowledge updating, as detailed below:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] in: For variable j, reflect on and learn the value of solution i during the t-th iteration; Let i be the value of the solution i obtained by the polynomial mutation and simulated binary crossover operator in the genetic algorithm at the t-th iteration.

[0081] S3.3 Implementation of an internal dynamic competition strategy: Individuals improve population diversity and adaptability by dynamically and randomly selecting solutions through team communication and reflective learning, continuously retaining superior individuals to generate offspring. t To gradually enhance the team's competitiveness, the specific internal dynamic competition strategies are as follows:

[0082]

[0083] I1=floor(I·(1-t / T)) (27)

[0084] in: It is the updated individual selected in the t-th iteration; N u and N v , respectively, represent the number of individuals engaged in communicative learning and reflective learning; floor is the base function; i∈randperm(I,I1) represents the function to randomly select an integer from {1,2,…,I}.

[0085] Furthermore, the aforementioned step S4 includes the following sub-steps S4.1 to S4.2:

[0086] S4.1, Perform population replacement operation of dynamic cooperative search algorithm: using offspring Offspring t The update yielded a new population X. t+1 ;

[0087] S4.2 Execution of the vector density association and population incentive update strategy of the dynamic cooperative search algorithm: First, for the reference vector, delete the inferior reference vector with the most associated solutions and add an equal number of superior reference vectors with the fewest associated solutions to update the reference vector, effectively improving the distribution of non-dominated solutions; then, for the population individuals, delete the inferior population individuals associated with the inferior parameter vectors and with the highest non-dominant ranking, and add an equal number of superior population individuals, significantly enhancing the global search capability of the optimization process.

[0088] Furthermore, the aforementioned step S4.2 includes the following sub-steps S4.2.1 to S4.2.4:

[0089] S4.2.1 Execute the reference vector deletion strategy, specifically as follows:

[0090] (I) Elite Population Merge Update: Merge elite populations Arc t and population individual X t Select individuals from the first frontier level of Pareto to form Arc t+1 Arc t and X t The number of individuals stored remains constant; if the number exceeds this limit, the excess individuals are randomly deleted.

[0091] Combine = Merge(X) t Arc t (28)

[0092] Where: Combine represents the result of merging individuals in the population with the elite population, and Merge(·) represents the merge function;

[0093] (II) Individual and reference vector association: Calculate the cosine distance between the individual and the reference vector, and associate each individual with the nearest reference vector to obtain the corresponding index number pi. At the same time, calculate the number of individuals associated with each reference vector ρ.

[0094]

[0095] ρ=hist(pi,NZ) (30)

[0096] (III) Determination of reference vectors to be deleted: The index of the reference vector with the most associated individuals, nus, is determined as the reference vector s1 to be deleted. del ;

[0097] s1 del =sort descend (ρ,ceil(nus)) (31)

[0098] Where: nus is the preset number of reference vectors to be updated; ceil(·) is the floor function; sort descend (·) is the descending order sorting function; s1 del The index of the reference vector to be deleted;

[0099] S4.2.2 Execute the population individual deletion strategy, specifically as follows:

[0100] (i) Determine the reference vector s1 to be deleted delFor each element in the merge solution set, the individual index Del that is equal to its index pi and falls within the individual population range is the individual index Del. n :

[0101] Del n ={i|pi[i]=s1 del ,i≤N1} (32)

[0102] Where: N1 is the population size of individuals;

[0103] (ii) Determine Del n The highest-ranking individual in the Pareto frontier is added to the set of individuals to be deleted, Sum. Del In the serial number:

[0104] Sum Del =Sum Del ∪{i∣FrontNo[i]=max(FrontNo[Del n ])} (33)

[0105] (iii) After processing all reference vectors to be deleted, ensure that the set of individuals to be deleted, Sum, is complete. Del Uniqueness of elements in the middle:

[0106] Sum Del =unique(Sum Del (34)

[0107] S4.2.3 Execute the reference vector supplementation strategy: Following the minimization principle, select the reference vector with the fewest associated individuals as the reference vector to be supplemented, and find the corresponding associated individual Add from the reference vector with a reference vector having 1 associated number. n The number of associated vectors is incremented sequentially to maintain the same number of added vectors as the number of deleted vectors:

[0108] Add n ={i|pi[i]=find(ρ=i)i=1,2...max(pi) (35)

[0109] length(Add n ) = length(s1 del )} (36)

[0110] newObjs = CombineObj(Add) n (37)

[0111] w new =1 / (newObjs-Z) / sum(1 / (newObjs-Z)) (38)

[0112] Where: Add n The index of the individual found as a reference vector in the merged population; newObjs represents the objective function value of the newly added individual, taken from the merged population; Z represents the ideal point; w new For the new reference vector;

[0113] S4.2.4 Execute the population individual replenishment strategy: Select individuals in the merge solution set that are not in the current population X as newly added population individuals:

[0114]

[0115] Where: N1 is the current population size X, and Nc is the number of merged individuals.

[0116] This invention also proposes a dynamic collaborative optimization system for multi-objective scheduling of water projects, comprising:

[0117] The multi-objective collaborative optimization scheduling model construction module is used to establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply benefits, power generation benefits, ecological benefits, and sediment transport benefits generated by water projects, and to add constraints to the optimization scheduling model.

[0118] The initialization module is used for the initialization of the dynamic cooperative search algorithm: initializing the relevant parameters of the scheduling optimization model; initializing the initial search population; initializing the relevant parameters of the MOEA / D algorithm framework; and initializing the elite population Arc.

[0119] The algorithm dynamic optimization module is used for iterative execution of the dynamic collaborative search algorithm, including implementing team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies. Dynamic optimization yields updated offspring. t ;

[0120] The strategy update invocation module is used for invoking individual update strategies in the dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy.

[0121] The scheduling scheme output module is used to output and optimize a set of non-dominated scheduling schemes. Specifically, it returns to the dynamic optimization module for executing the algorithm and the strategy update call module until the maximum number of iterations is reached, and outputs the solution space of the elite population Arc variable.

[0122] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0123] (1) The present invention performs iterative search operation of dynamic collaborative search algorithm: the Pareto first frontier level is selected as the global optimal solution set through team communication strategy, the individual distribution position is good and the optimization ability is strong, and better information is provided to guide individual updates; through reflective learning strategy and internal competition strategy, the global optimization, path diversity and individual competition of population optimization are improved, and the local optimum is avoided.

[0124] (2) The vector density association update strategy of the dynamic cooperative search algorithm of this invention is to update the reference vector by deleting the inferior reference vector with the most associated solutions and adding an equal number of superior reference vectors with the fewest associated solutions, thereby improving the distribution of non-inferior solutions and performing better in terms of population competitiveness.

[0125] (3) The population incentive update strategy of the dynamic collaborative search algorithm of the present invention is to delete the inferior population individuals with the highest non-dominant ranking associated with the inferior parameter vector and add an equal number of superior population individuals to achieve the "survival of the fittest" update effect of the population individuals, improve the global search capability of the optimization process, and better explore the diversity of solutions.

[0126] (4) This invention proposes a dynamic collaborative optimization system for multi-objective scheduling of water projects. Based on the multi-objective collaborative optimization scheduling model, the Pareto front non-dominated solution set has a wider distribution range, significantly improving the optimization effect and diversifying the selection of scheduling schemes, effectively improving the scheme selection efficiency and non-dominated solution quality of multi-objective dynamic collaborative scheduling of water projects. Attached Figure Description

[0127] Figure 1 This is a flowchart of the method of the present invention.

[0128] Figure 2 This is a schematic diagram comparing the Pareto front in the multi-objective dynamic collaborative scheduling model for reservoir water supply and power generation according to the present invention. Detailed Implementation

[0129] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0130] In this invention, various aspects of the invention are described with reference to the accompanying drawings, in which numerous illustrative embodiments are shown. Embodiments of the invention are not limited to those depicted in the drawings. It should be understood that the invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0131] refer to Figure 1This invention provides a dynamic collaborative optimization method for multi-objective scheduling of water projects, comprising the following steps:

[0132] S1. Establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply and power generation benefits generated by the reservoir, and add constraints to the optimization scheduling model.

[0133] S2. Initialization of the Dynamic Cooperative Search Algorithm: Initialize the relevant parameters of the scheduling optimization model; initialize the initial search population; initialize the relevant parameters of the MOEA / D algorithm framework; initialize the elite population Arc;

[0134] S3, the dynamic collaborative search algorithm iteratively runs, including team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies, dynamically optimizing to obtain updated offspring Offspring. t ;

[0135] S4. Individual update strategy invocation of dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy;

[0136] S5. Output and optimize the set of non-dominated scheduling schemes. Specifically, return to steps S3 to S4 until the maximum number of iterations is reached, and output the solution space of the elite population Arc variable.

[0137] As a preferred embodiment of the multi-objective scheduling dynamic collaborative optimization method for water engineering according to the present invention, in step S1, the objective function of the multi-objective collaborative optimization scheduling model specifically includes the following:

[0138] Maximum total power generation:

[0139]

[0140] in, P represents the total power generation during the dispatch period T, in billions of kWh; t Let be the average power output in the t-th time period, in kW; A is the overall power output coefficient of the power plant. Let m be the power generation flow rate during the t-th time period. 3 / s;H t Let m be the hydropower head generated in the t-th time period, and T be the total number of time periods in the scheduling period.

[0141] Maximum total water supply:

[0142]

[0143] in, The total water supply during the scheduling period T is expressed in m. 3 ; Let m be the water supply flow rate during the t-th time period. 3 / s; Δt is the duration of the time interval, in seconds.

[0144] Minimum water shortage rate due to ecological flow:

[0145] β t =Min(1-Q) t / Q t,x )*100% (3)

[0146] Where, β t Q represents the ecological flow water shortage rate in time period t. t Let m be the discharge flow rate in the t-th time period. 3 / s;Q t,x Let m be the required ecological flow for the t-th time period. 3 / s;

[0147] Minimum total water shortage in the basin:

[0148]

[0149] Among them, W q q represents the total water shortage in the basin; n is the user ID; N is the total number of users; n,t This represents the water shortage for the nth user in time period t.

[0150] The downstream channel carries the largest amount of sediment:

[0151]

[0152] Among them, W s The downstream sediment load is expressed in ten thousand tons; m is the cross-section number; M is the total number of cross-sections; w m (t) represents the sediment transport rate of the m-th cross section in time period t, in kg / s; K, a, and b are the sediment transport rate parameters of the n-th cross section in time period t, respectively. The sediment transport flow rate at section m during time period t, m 3 / s; Let m be the sediment concentration at section m during time period t, in kg / m³. 3 .

[0153] As a preferred embodiment of the dynamic collaborative optimization method for multi-objective scheduling of water engineering according to the present invention, the constraints in step S1 specifically include the following:

[0154] Water balance constraints:

[0155]

[0156] Among them, V t Let m be the reservoir's water storage capacity at the beginning of the t-th time period. 3 ; The inbound flow rate during the t-th time period is expressed in meters (m). 3 / s; The outbound flow rate during the t-th time period is expressed in meters (m). 3 / s;

[0157] Storage capacity constraints:

[0158]

[0159] V t min Let m be the minimum allowable water storage capacity during time period t. 3 V t max Let m be the maximum allowable water storage capacity of the reservoir during time period t. 3 V t Let m be the reservoir's water storage capacity during the t-th time period. 3 ;

[0160] Downflow constraint:

[0161]

[0162] Let m be the minimum allowable discharge flow rate during time period t. 3 / s; Let m be the maximum allowable discharge flow rate during time period t. 3 / s.

[0163] Output constraints:

[0164]

[0165] P t min The minimum allowable output power during time period t is kW; P t max The maximum allowable output power during time period t is kW; P t The output power during the t-th time period is kW;

[0166] Ecological baseflow constraints:

[0167] Ql t ≥Ql max (10)

[0168] Ql t Let m be the remaining flow rate of the river channel after water intake at the water intake section in time period t. 3 / s;Ql max Let m be the ecological base flow rate at the water intake section during time period t. 3 / s;

[0169] Discharge amplitude constraint:

[0170] H i(t+1)-H i (t)≤ΔH i,xie (11)

[0171] H i (t) represents the water level at the i-th discharge section during time period t, in meters; ΔH i,xie Let be the maximum allowable discharge water level variation at the i-th discharge section.

[0172] Non-negativity constraint: All parameters satisfy the non-negativity constraint condition.

[0173] As a preferred embodiment of the dynamic collaborative optimization method for multi-objective scheduling of water engineering according to the present invention, step S2 includes the following sub-steps:

[0174] S2.1 Initialize the relevant parameters of the scheduling optimization model, including: maximum number of iterations T, population size I, and adjustment parameters α and β;

[0175] S2.2 Initialize the first generation of the optimization population: Randomly generate an initial population based on the preset limit range of the individuals in the population, store the individuals in the initial population as the individual's optimal position pbest, and calculate the fitness of the individuals in the population at the same time.

[0176]

[0177] in, It is the value of the j-th decision variable for the i-th individual at the t-th iteration; Indicates the interval Generate uniformly distributed random numbers internally. x j This represents the lower bound of the range of the j-th decision variable. Let I be the upper limit of the restricted position range of the j-th decision variable; I is the number of individuals in the population; and J is the number of decision variables.

[0178] S2.3, Parameters for initializing the MOEA / D algorithm framework: Initializing the number of neighboring individuals N based on the MOEA / D algorithm framework. b And a weight vector W, and determine the maximum number N of replacements for each offspring individual. r The default number of updates for the weight vector is N. w ;

[0179] S2.4 Initialize the elite population Arc: Select individuals of the first Pareto frontier level among the neighbors to form the globally optimal individual solution set gbest, and further complete the initialization of the elite population Arc;

[0180] gbest=X nh (Pareto=1) (13)

[0181] Where gbest represents the globally optimal set of individual solutions; X nh This represents an individual in the population determined based on its neighbor index in the reference vector; (Pareto=n) represents an individual at the nth front level of Pareto.

[0182] As a preferred embodiment of the dynamic collaborative optimization method for multi-objective scheduling of water engineering according to the present invention, step S3 includes the following sub-steps:

[0183] S3.1 Execution Team Random Communication Strategy: Individuals acquire new knowledge and update their skills through communication with three entities: the Chairman, the Board of Directors, and the Supervisory Board. The Chairman candidate (gbest1), the Board of Directors candidate (gbest2), and the Supervisory Board candidate (pbest) are generated based on the elite population (Arc) using a random selection strategy. The specific team random selection strategy is as follows:

[0184] (a) The chairman candidate, gbest1, is randomly selected from the elite population Arc:

[0185] gbest1 = Arc[randi(N g (14)

[0186] Among them, randi(N) g ) represents the number of individuals N existing from Arc. g The individual serial number randomly determined in the process;

[0187] (b) The board of directors takes the average value of all individuals in the elite population Arc as gbest2:

[0188] gbest2 = Arc(gbest) (15)

[0189] Where: mean() means taking the mean of each dimension for all individuals;

[0190] (c) The supervisory board pbest is the individual in the population whose product of the smallest M distances from an individual to all other individuals is the largest:

[0191] pbest = max[dis(X) nh (16)

[0192] Where max[dis(·)] represents the individual with the largest product of the minimum M distances from the population to all other individuals, where M is consistent with the scheduling target number;

[0193] (d) New knowledge acquired during random team communication mainly includes three parts: Chairman's knowledge A, Board of Directors knowledge B, and Supervisory Board knowledge C.

[0194]

[0195]

[0196]

[0197]

[0198] in, Let j be the value of the solution i communicated by the team at the t-th iteration; The knowledge obtained from the chairman, board of directors, and supervisory board is selected randomly, in that order; κ(J) and ψ(J) are random numbers in the range [0,1] generated randomly from the variable set J; α and β are adjustment parameters.

[0199] S3.2 Executing a self-perturbation and reflection strategy: Individuals balance existing optimal solutions with innovative mutation solutions by summarizing existing experiences and simulating mutation behaviors, exploring multi-dimensional optimization directions for knowledge updating, as detailed below:

[0200]

[0201]

[0202]

[0203]

[0204]

[0205] in: For variable j, reflect on and learn the value of solution i during the t-th iteration; Let i be the value of the solution i obtained by the polynomial mutation and simulated binary crossover operator in the genetic algorithm at the t-th iteration.

[0206] S3.3 Implementation of an internal dynamic competition strategy: Individuals improve population diversity and adaptability by dynamically and randomly selecting solutions through team communication and reflective learning, continuously retaining superior individuals to generate offspring. t To gradually enhance the team's competitiveness, the specific internal dynamic competition strategies are as follows:

[0207]

[0208] I1=floor(I·(1-t / T)) (27)

[0209] in: It is the updated individual selected in the t-th iteration; N u and N v, respectively, represent the number of individuals engaged in communicative learning and reflective learning; floor is the base function; i∈randperm(I,I1) represents the function to randomly select an integer from {1,2,…,I}.

[0210] As a preferred embodiment of the dynamic collaborative optimization method for multi-objective scheduling of water engineering according to the present invention, step S4.2 includes the following sub-steps S4.2.1 to S4.2.4:

[0211] S4.2.1 Execute the reference vector deletion strategy, specifically as follows:

[0212] (I) Elite Population Merge Update: Merge elite populations Arc t and population individual X t Select individuals from the first frontier level of Pareto to form Arc t+1 Arc t and X t The number of individuals stored remains constant; if the number exceeds this limit, the excess individuals are randomly deleted.

[0213] Combine = Merge(X) t Arc t (28)

[0214] Where: Combine represents the result of merging individuals in the population with the elite population, and Merge(·) represents the merge function;

[0215] (II) Individual and reference vector association: Calculate the cosine distance between the individual and the reference vector, and associate each individual with the nearest reference vector to obtain the corresponding index number pi. At the same time, calculate the number of individuals associated with each reference vector ρ.

[0216]

[0217] ρ=hist(pi,NZ) (30)

[0218] (III) Determination of reference vectors to be deleted: The index of the reference vector with the most associated individuals, nus, is determined as the reference vector s1 to be deleted. del ;

[0219] s1 del =sort descend (ρ,ceil(nus)) (31)

[0220] Where: nus is the preset number of reference vectors to be updated; ceil(·) is the floor function; sort descend (·) is the descending order sorting function; s1 del The index of the reference vector to be deleted;

[0221] S4.2.2 Execute the population individual deletion strategy, specifically as follows:

[0222] (i) Determine the reference vector s1 to be deleted del For each element in the merge solution set, the individual index Del that is equal to its index pi and falls within the individual population range is the individual index Del. n :

[0223] Del n ={i|pi[i]=s1 del ,i≤N1} (32)

[0224] Where: N1 is the population size of individuals;

[0225] (ii) Determine Del n The highest-ranking individual in the Pareto frontier is added to the set of individuals to be deleted, Sum. Del In the serial number:

[0226] Sum Del =Sum Del ∪{i∣FrontNo[i]=max(FrontNo[Del n ])} (33)

[0227] (iii) After processing all reference vectors to be deleted, ensure that the set of individuals to be deleted, Sum, is complete. Del Uniqueness of elements in the middle:

[0228] Sum Del =unique(Sum Del (34)

[0229] S4.2.3 Execute the reference vector supplementation strategy: Following the minimization principle, select the reference vector with the fewest associated individuals as the reference vector to be supplemented, and find the corresponding associated individual Add from the reference vector with a reference vector having 1 associated number. n The number of associated vectors is incremented sequentially to maintain the same number of added vectors as the number of deleted vectors:

[0230] Add n ={i|pi[i]=find(ρ=i)i=1,2...max(pi) (35)

[0231] length(Add n ) = length(s1 del )} (36)

[0232] newObjs = CombineObj(Add) n(37)

[0233] w new =1 / (newObjs-Z) / sum(1 / (newObjs-Z)) (38)

[0234] Where: Add n The index of the individual found as a reference vector in the merged population; newObjs represents the objective function value of the newly added individual, taken from the merged population; Z represents the ideal point; w new For the new reference vector;

[0235] S4.2.4 Execute the population individual replenishment strategy: Select individuals in the merge solution set that are not in the current population X as newly added population individuals:

[0236]

[0237] Where: N1 is the current population size X, and Nc is the number of merged individuals.

[0238] Another aspect of the present invention provides a dynamic collaborative optimization system for multi-objective scheduling of water engineering projects, comprising:

[0239] The multi-objective collaborative optimization scheduling model construction module is used to establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply and power generation benefits generated by the reservoir, and to add constraints to the optimization scheduling model.

[0240] The initialization module is used for the initialization of the dynamic cooperative search algorithm: initializing the relevant parameters of the scheduling optimization model; initializing the initial search population; initializing the relevant parameters of the MOEA / D algorithm framework; and initializing the elite population Arc.

[0241] The algorithm dynamic optimization module is used for iterative execution of the dynamic collaborative search algorithm, including implementing team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies. Dynamic optimization yields updated offspring. t ;

[0242] The strategy update invocation module is used for invoking individual update strategies in the dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy.

[0243] The scheduling scheme output module is used to output and optimize a set of non-dominated scheduling schemes. Specifically, it returns to the dynamic optimization module for executing the algorithm and the strategy update call module until the maximum number of iterations is reached, and outputs the solution space of the elite population Arc variable.

[0244] This example establishes a multi-objective collaborative optimization scheduling model for reservoir water supply and power generation under a low-water scheduling scenario. The model is solved using both the present invention and MOEA / D. To compare and analyze the optimization effects of the present invention and MOEA / D on the reservoir multi-objective scheduling problem, the calculation results are analyzed, as shown in Table 1. Pareto front plots are also presented, as detailed in [see Table 1]. Figure 2 .

[0245] Table 1 Comparison of Scheduling Scheme Resolution Results

[0246]

[0247]

[0248] As shown in Table 1, in the reservoir water supply-power generation multi-objective collaborative optimization scheduling model, the optimal solution set, the breadth of solution set distribution, and the water level at the end of the scheduling period are all superior to the MOEA / D algorithm. This indicates that the present invention significantly improves water resource utilization efficiency and increases the water storage potential of the water engineering system while performing better in the scheduling scheme. In the reservoir water supply-power generation collaborative scheduling problem, the feasible scheme of the present invention has better scheduling solution set and optimization breadth, and the global optimization and water resource utilization rate are further improved.

[0249] Figure 2 This diagram illustrates the comparison of Pareto front distribution in the multi-objective scheduling model of reservoir water supply and power generation according to the present invention. It can be seen from the diagram that the feasible range of the Pareto front solution set obtained by the MOEA / D algorithm lags far behind that of the present invention; simultaneously, the positions of the Pareto front solution set of the present invention are superior to those of the MOEA / D algorithm, indicating better solution quality. It can be seen that the present invention can obtain more power generation with relatively less water, demonstrating superior algorithm optimization performance.

[0250] While the present invention has been described above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A dynamic collaborative optimization method for multi-objective scheduling of water projects, characterized in that, Includes the following steps: S1. Establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply benefits, power generation benefits, ecological benefits, and sediment transport benefits generated by water projects, and add constraints to the optimization scheduling model. S2. Initialization of the Dynamic Cooperative Search Algorithm: Initialize the relevant parameters of the scheduling optimization model; initialize the initial search population; initialize the relevant parameters of the MOEA / D algorithm framework; initialize the elite population Arc; S3, the dynamic collaborative search algorithm iteratively runs, including team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies, dynamically optimizing to obtain updated offspring. ; S4. Individual update strategy invocation of dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy; This includes the following sub-steps S4.1 to S4.2: S4.1, Perform the population replacement operation of the dynamic cooperative search algorithm: utilize the offspring The update resulted in a new population. ; S4.2 Execution of the vector density association and population incentive update strategy of the dynamic cooperative search algorithm: First, for the reference vector, delete the inferior reference vector with the most associated solutions and add an equal number of superior reference vectors with the fewest associated solutions to update the reference vector, effectively improving the distribution of non-dominated solutions; then, for the population individuals, delete the inferior population individuals associated with the inferior parameter vectors and with the highest non-dominant ranking, and add an equal number of superior population individuals, significantly enhancing the global search capability of the optimization process; Step S4.2 includes the following sub-steps S4.2.1 to S4.2.4: S4.2.1 Execute the reference vector deletion strategy, specifically as follows: (I) Elite Population Merge Update: Merge elite populations and population individuals Select individuals from the first frontier level of Pareto. ,in and The number of individuals stored remains constant; if the number exceeds this limit, the excess individuals are randomly deleted. （28）， Where: Combine represents the result of merging individuals in the population with the elite population. Represents the merge function; (II) Individual and reference vector association: Calculate the cosine distance between an individual and a reference vector, and associate each individual with the nearest reference vector to obtain the corresponding index number pi. At the same time, calculate the number of individuals associated with each reference vector. ; （29）， （30）， (III) Determination of reference vectors to be deleted: The indexes of the reference vectors with the most associated individuals (nus) are determined as the reference vectors to be deleted. ; （31）， Where: nus is the preset number of reference vectors to be updated; It is a rounding function; It is a function for sorting in descending order; The index of the reference vector to be deleted; S4.2.2 Execute the population individual deletion strategy, specifically as follows: (i) Determine the reference vector to be deleted For each element in the merge solution set, the individual index pi that is equal to it and whose index is within the range of the individual population is the individual index. : （32）， in: For individual population size; (ii) Determine The highest-ranking individual in the Pareto frontier is added to the set of individuals to be deleted. In the serial number: (33), (iii) After processing all reference vectors to be deleted, ensure that the set of individuals to be deleted is... Uniqueness of elements in the middle: (33), S4.2.3 Execute the reference vector supplementation strategy: Following the minimization principle, select the reference vector with the fewest associated individuals as the reference vector to be supplemented, and find the corresponding associated individuals from the reference vector with a number of 1 associated individuals. The number of associated vectors is incremented sequentially to maintain the same number of added vectors as the number of deleted vectors: (35), （36）， （37）， （38）， in: The index of the individual found as a reference vector in the merged population is used for calculation; newObjs represents the objective function value of the newly added individual, taken from the merged population; Z represents the ideal point; For the new reference vector; S4.2.4 Execute the population individual replenishment strategy: Select individuals in the merge solution set that are not in the current population X as newly added population individuals: （39）， Where: N1 is the current population size X, and Nc is the number of merged individuals; S5. Output the set of non-dominated scheduling schemes - specifically: return to execute steps S3 to S4 until the maximum number of iterations is reached, and output the solution space of the elite population Arc variable.

2. The dynamic collaborative optimization method for multi-objective scheduling of water projects according to claim 1, characterized in that, In step S1, the objective function of the multi-objective cooperative optimization scheduling model specifically includes the following: Maximum total power generation: (1), in, The total power generation during the dispatch period T is expressed in hundreds of millions of kWh. For the first Average output over a time period, kW; This refers to the overall power output coefficient of the power plant. For the first Power generation flow rate within a time period, m³ / s; For the first The hydropower head for power generation within a given time period, m, and T represent the total number of time periods in the scheduling period; Maximum total water supply: (2), in, The total water supply during the scheduling period T is expressed in m³. For the first Water supply flow rate during a given time period, m³ / s; For a time period of s; Minimum water shortage rate due to ecological flow: （3）， in, For the first Ecological flow water shortage rate for a given period; For the first The discharge flow rate for each time period, m³ / s; For the first The required ecological flow for each time period, m³ / s; Minimum total water shortage in the basin: (4), in, denoted as the total water shortage in the basin; n represents the user ID; N represents the total number of users. Let n be the water shortage amount for the nth user in time period t. The downstream channel carries the largest amount of sediment: （5）， in, The downstream sediment transport volume is expressed in ten thousand tons; m is the cross-section number; M is the total number of cross-sections. Let be the sediment transport rate of the m-th cross section in time period t, in kg / s; K, a, and b are the sediment transport rate parameters of the n-th cross section in time period t, respectively. The sediment transport flow rate at section m during time period t, m³ / s; Let be the sediment concentration at section m during time period t, in kg / m³.

3. The dynamic collaborative optimization method for multi-objective scheduling of water projects according to claim 1, characterized in that, In step S1, the constraints specifically include, but are not limited to, the following: Water balance constraints: (6), in, For the first Reservoir storage capacity during a given period, in m³; For the first Inflow rate within a time period, in m³ / s; For the first Outflow rate within a time period, in m³ / s; Storage capacity constraints: (7), For the first Minimum allowable water storage capacity of the reservoir during the specified time period, in m³; For the first Maximum allowable water storage capacity during the time period, in m³; For the first Reservoir storage capacity during a given time period, in m³; Downflow constraint: (8), For the first Minimum allowable discharge flow rate during the time period, m³ / s; For the first Maximum permissible discharge flow rate during the time period, m³ / s; Output constraints: (9), For the first Minimum output limit allowed during the time period, kW; For the first Maximum output limit during the time period, kW; For the first Power output during a given time period, kW; Ecological baseflow constraints: （10）， For the first The remaining flow rate of the river channel after water intake at the water intake section during a given period, in m³ / s; For the first Ecological base flow rate at the water intake section during a given time period, m³ / s; Discharge amplitude constraint: （11）， Let m be the water level at the i-th discharge section during time period t. Let be the maximum allowable discharge water level variation at the i-th discharge section; Non-negativity constraint: All parameters satisfy the non-negativity constraint condition.

4. The dynamic collaborative optimization method for multi-objective scheduling of water projects according to claim 1, characterized in that, Step S2 includes the following sub-steps: S2.1 Initialize the relevant parameters of the scheduling optimization model, including: maximum number of iterations T, population size I, and adjustment parameters α and β; S2.2 Initialize the first generation of the optimization population: Randomly generate an initial population based on the preset limit range of the individuals in the population, store the individuals in the initial population as the individual's optimal position pbest, and calculate the fitness of the individuals in the population at the same time. （12）， in, It is in the The value of the j-th decision variable for the i-th individual in the next iteration; Indicates the interval Generate uniformly distributed random numbers internally. This represents the lower bound of the range of the j-th decision variable. This represents the upper limit of the restricted location range for the j-th decision variable; The number of individuals in the population; The number of decision variables; S2.3, Parameters for initializing the MOEA / D algorithm framework: Initializing the number of neighboring individuals based on the MOEA / D algorithm framework. And the weight vector W, and determine the maximum number of replacements for each offspring individual. and the default number of updates to the weight vector ; S2.4 Initialize the elite population Arc: Select individuals of the first Pareto frontier level among the neighbors to form the globally optimal individual solution set gbest, and further complete the initialization of the elite population Arc; （13） in, Represents the set of globally optimal individual solutions; This represents an individual in the population determined based on its neighbor index in the reference vector; Representing Pareto Advanced level individuals.

5. The dynamic collaborative optimization method for multi-objective scheduling of water projects according to claim 1, characterized in that, Step S3 includes the following sub-steps: S3.1, Execution Team Random Communication Strategy: Individuals acquire new knowledge and update their skills through communication with three parties: the Chairman, the Board of Directors, and the Supervisory Board; among them, the selection of the Chairman... ,Board of Directors and Supervisory Board Generated based on the elite population Arc, using a random selection strategy. The specific team random selection strategy is as follows: (a) Chairman candidate Randomly selected from the elite population Arc: （14） in, Representative from Number of individuals The individual serial number randomly determined in the process; (b) Board of Directors Take the average value of all individuals in the elite population Arc: （15）， in: This means taking the average of each dimension for all individuals; (c) Supervisory Board The individual with the largest product of the M smallest distances from each individual to all other individuals in the population will be selected as the candidate. (16) in, This represents the individual with the largest product of the minimum M distances from the population to all other individuals. (d) New knowledge acquired during random team communication mainly includes three parts: Chairman's knowledge A, Board of Directors knowledge B, and Supervisory Board knowledge C. （17）， （18）， （19）， （20）， in, For variables In the During the next iteration, team communication was resolved. The value; The knowledge was obtained sequentially from the chairman, the board of directors, and the supervisory board through random selection. For variable set Generate random numbers in the range [0,1]. To adjust the parameters; S3.2 Executing a self-perturbation and reflection strategy: Individuals balance existing optimal solutions with innovative mutation solutions by summarizing existing experiences and simulating mutation behaviors, exploring multi-dimensional optimization directions for knowledge updating, as detailed below: （21）， （22）， （23）， （24）， （25）， in: This indicates that the value of the solution is learned through reflection at the (t+1)th iteration; Let i be the value of the solution i obtained by the polynomial mutation and simulated binary crossover operator in the genetic algorithm at the t-th iteration. S3.3 Implementation of internal dynamic competition strategy: Individuals improve the diversity and adaptability of the population by dynamically and randomly selecting solutions through team communication and reflective learning, continuously retaining superior individuals, and generating offspring. To gradually enhance the team's competitiveness, the specific internal dynamic competition strategies are as follows: （26）， （27）， in: It is in the The updated individual selected in the next iteration; and The number of individuals engaged in communicative learning and reflective learning, respectively; It is a base function; Indicates to from A function that randomly selects an integer.

6. A dynamic collaborative optimization system for multi-objective scheduling of water projects, applied to the dynamic collaborative optimization method for multi-objective scheduling of water projects as described in any one of claims 1-5, characterized in that... ,include: The multi-objective collaborative optimization scheduling model construction module is used to establish a multi-objective collaborative optimization scheduling model with the goal of maximizing the water supply benefits, power generation benefits, ecological benefits and sediment transport benefits generated by water projects, and to add constraints to the optimization scheduling model. The initialization module is used for the initialization of the dynamic cooperative search algorithm: initializing the relevant parameters of the scheduling optimization model; initializing the initial search population; initializing the relevant parameters of the MOEA / D algorithm framework; and initializing the elite population Arc. The algorithm dynamic optimization module is used for iterative execution of the dynamic collaborative search algorithm, including implementing team random communication strategies, self-perturbation and reflection strategies, and internal dynamic competition strategies, to dynamically optimize and obtain updated offspring. ; The strategy update invocation module is used for invoking individual update strategies in the dynamic cooperative search algorithm, including population replacement operation, vector density association strategy and population incentive update strategy. The scheduling scheme output module is used to output a set of non-dominated scheduling schemes. Specifically, it returns the execution algorithm dynamic optimization module and the policy update call module until the maximum number of iterations is reached, and outputs the solution space of the elite population Arc variable.

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