A Method and System for Optimal Scheduling of Cascade Reservoirs Based on Physically Embedded Deep Learning and Evolutionary Computation

Abstract

This invention belongs to the field of reservoir group scheduling technology, specifically providing a method and system for optimizing the scheduling of cascade reservoirs based on the synergy of physical embedded deep learning and evolutionary computation. This invention hard-codes physical rules into a temporal convolutional network, constructing a physical embedded temporal convolutional network surrogate model. Through survival analysis, the discrete water discharge objective is transformed into a differentiable loss. PeTCN is used to perform gradient inverse optimization, generating a high-quality initial solution for outflow that satisfies the constraints. This initial solution is injected into the NSGA-III algorithm population for hot start, overcoming the feasibility obstacles caused by random initialization, accelerating the Pareto front search, and ultimately obtaining a non-dominated solution set that balances power generation benefits, water discharge control, and delayed water discharge. This invention structurally ensures the satisfaction of physical constraints, significantly improves the efficiency of feasible solution generation and optimization convergence speed, and the obtained solution set is uniformly distributed and highly applicable to engineering, effectively supporting the efficient and safe operation and scheduling of cascade hydropower stations.

Description

Technical Field

[0001] This invention belongs to the field of reservoir group scheduling technology, specifically, it relates to a method and system for solving the optimal scheduling of cascade reservoirs based on the collaboration of physical embedded deep learning and evolutionary computation. Background Technology

[0002] In practical engineering, the operation and scheduling of cascade hydropower stations, consisting of multiple stages, involves upstream and downstream hydraulic connections and power coupling, characterized by strong coupling, multiple constraints, and cross-timescale decision-making. The operation of cascade reservoirs must adhere to operational constraints such as water balance, water level boundaries, and output and amplitude limits, while simultaneously considering multiple competing objectives such as power generation revenue, water wastage control, power supply security, and water storage targets. This results in a multi-objective optimization problem with a vast decision space, tight constraints, and mutually restraining objectives, making it highly challenging to solve.

[0003] In current research and engineering practice, multi-objective evolutionary algorithms (MOEAs) are widely used for joint scheduling of cascade reservoirs and solving multi-objective optimization problems. Typical methods include NSGA-II, NSGA-III based on the reference point mechanism, and related improved algorithms oriented towards constraint handling. These algorithms typically maintain a diverse population and utilize evolutionary operators such as non-dominated sorting and reference point allocation to achieve trade-offs among multiple objectives, thereby searching for the Pareto front solution set. However, in high-dimensional decision-making and tightly constrained cascade scheduling scenarios, candidate solutions generated by random initialization often have a high probability of violating complex constraints such as water balance equations, water level constraints, and amplitude constraints, leading to significant "feasibility barriers" in the algorithms. That is, a large amount of computational resources are consumed in the repair and elimination of constraint violations, making it difficult to effectively advance the optimization of the actual objectives. In some practical application scenarios, even after a large number of iterative searches, classic MOEAs still struggle to obtain feasible solutions, thus hindering their effectiveness in engineering applications.

[0004] To alleviate the aforementioned computational challenges, surrogate-assisted evolutionary optimization methods propose using machine learning models to approximate expensive objective function evaluations, thereby reducing computational burden and accelerating the optimization process to some extent. However, traditional surrogate models often lack consistency guarantees regarding physical laws, easily leading to predictions that violate physical constraints in reservoir scheduling systems governed by physical laws, thus affecting feasible solution generation and decision reliability. In recent years, Physical Information Neural Networks (PINNs) have enhanced physical consistency by introducing physical equation residuals into the loss function, but their implementation of physical rules through "soft constraint penalties" makes it difficult to guarantee strict satisfaction of key physical constraints such as water balance at each time step. Furthermore, for high-dimensional constrained optimization problems, strict time-by-time feasibility is often the basis for generating feasible scheduling schemes; therefore, the above methods still have limitations in cascade scheduling scenarios. In contrast, physical embedding methods, by directly hard-coding physical rules into the network structure, structurally guarantee that the predicted state satisfies physical laws, making them more suitable for engineering optimization problems requiring strict constraint satisfaction.

[0005] Furthermore, cascade reservoir scheduling exhibits significant temporal dynamics, with reservoir capacity and water levels evolving over time. Operational decisions must consider long-term cumulative effects and intertemporal constraints. Traditional sequence models such as LSTM possess some long-range dependency modeling capabilities, but their sequential computational nature limits parallelization efficiency, and deep structures may suffer from gradient decay, hindering stable training and efficient inference for long-term scheduling problems. Temporal Convolutional Networks (TCNs), employing structures such as dilated causal convolutions and residual connections, achieve parallel computation while maintaining controllable expansion of the receptive field. They offer advantages in stable gradients and efficient modeling, thus demonstrating application potential in long-sequence dynamic modeling.

[0006] Against this background, in the constrained multi-objective optimization of cascade reservoirs, how to efficiently generate feasible and high-quality initial solutions while strictly adhering to physical constraints, in order to overcome the feasibility obstacles brought about by the random initialization of traditional evolutionary algorithms, and further to carry out effective exploration of Pareto fronts on this basis, is a key technical problem that urgently needs to be solved. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a method and system for solving the optimal scheduling of cascade reservoirs based on physical embedded deep learning and evolutionary computation, thereby solving the problem of difficulty in converging constraint violation degrees when solving the optimal scheduling of cascade reservoirs.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a method for solving the optimal scheduling of cascade reservoirs based on the synergy of physical embedded deep learning and evolutionary computation, comprising the following steps: S1. Set the physical relationships and scheduling constraints of cascade hydropower stations, and construct a physical embedded temporal convolutional network proxy model to predict the actual impact of decision variables on the physical system of multi-level reservoirs; S2. Initialize the decision variables, namely the outflow from each hydropower station. The discrete water discharge time objective function is transformed into a differentiable loss function using survival analysis. A physically embedded temporal convolutional network model is then used for gradient inverse optimization. The loss value is calculated using the loss function, and optimization is performed using the gradient descent formula. Finally, the result is projected onto the feasible region of the hydropower station to obtain the outflow rate. As the initial solution; S3. Inject the initial solution into the initial population of the NSGA-III algorithm for a hot start, which accelerates the search process of the Pareto front and finally obtains the Pareto front and the non-dominated solution.

[0009] In the preferred embodiment, in step S1, the physical relationships of the cascade hydropower stations include the water balance equation, reservoir capacity-water level relationship, water level-water consumption rate relationship, gate opening flow calculation, power generation calculation, total power generation, and energy storage calculation at the end of the period. The scheduling constraints include: water level constraints for each reservoir, water level fluctuation constraints, and outflow boundary constraints.

[0010] In a preferred embodiment, the method for constructing the physically embedded temporal convolutional network PeTCN in step S1 is as follows: S1.1 Based on the Temporal Convolutional Network (TCN) backbone structure, three residual blocks are designed, with the dilation factor and kernel size as the parameters. Stacking generates corresponding receptive fields, and each residual block consists of two dilated causal convolutional layers; S1.2, The physically embedded temporal convolutional network architecture combines TCN with a hard-coded physical layer. The TCN uses one-dimensional dilated causal convolution to achieve parallel processing; the TCN component learns to predict changes in library capacity from the input sequence. , probability of opening the gate and gate opening flow The physical layer uses water balance equations and characteristic curves to explicitly calculate water levels. Water consumption rate and efforts Subscript , They represent the first The power station and the first Each time period; S1.3. During training, a composite training loss function is used, the expression of which is: ; in, physical state The mean squared error loss, of which For storage capacity, For water level, Water consumption rate, To contribute one's strength; Probability of opening the gate Binary cross-entropy loss; For the opening flow rate The mean squared error loss; For the product of the overflow With overflow flow The mean squared error loss; For the predicted total energy target The predicted total discharge target And the predicted delayed opening target The sum of the mean squared error losses between its corresponding true value; to These are the weighting coefficients for the corresponding components.

[0011] In a preferred embodiment, step S1, the training configuration of the physically embedded temporal convolutional network model includes: employing a preset type of optimizer, setting a preset initial learning rate, a preset batch size, and a preset weight decay coefficient; setting a learning rate scheduler, which adjusts the training rate when the validation loss reaches a preset threshold. If there is no improvement within consecutive training cycles, the learning rate is reduced by a preset percentage; an early stopping mechanism is adopted, whereby the learning rate is reduced when the validation loss reaches a preset threshold. The training process is terminated if no improvement is observed within a continuous training cycle; the weight coefficients to The settings are configured according to preset values ​​during the training process.

[0012] In the preferred embodiment, the survival analysis method in step S2 is performed as follows: Define power station The first time water was released The expression is: ; Where T represents the length of the entire scheduling cycle. To represent the zero-to-one variable indicating whether water wastage has occurred, when the first... The power station in the first When water is abandoned during a certain period If the first The power station in the first If no water is discarded during a certain period, then If the power station If no water is wasted during the entire scheduling period, then set ; Building power plants At any moment The survival probability function represents the power plant At any moment The probability of no water wastage occurring before is expressed as: ; The discrete delayed water abandonment target is transformed into a differentiable survival analysis loss function, expressed as: ; minimize This is equivalent to maximizing the expected first water discharge time of all power plants.

[0013] In the preferred embodiment, the method for constructing the loss function for gradient inverse optimization in step S2 is as follows: Freeze the parameters of the trained physical embedded temporal convolutional network model , outbound flow sequence As a trainable variable, construct the loss function: ; Among them, the energy maximization objective , Energy storage for the final period is directly calculated from the water level at the end of the period; the goal is to minimize the discharge flow when the gate is opened. Constraints and penalties for losses , For the first The lower limit of the water level of each power station For the first The upper limit of the water level of each power station Indicates the first Each power station The change in water level between the previous time period and the current time period; , , The target weight coefficient.

[0014] In the preferred embodiment, the optimization process using the gradient descent formula in step S2 is as follows: Initialize outbound flow sequence ; Use a preset type of optimizer and set a preset learning rate and a preset maximum number of iterations; Each iteration performs the following steps: Calculate the predicted value using a physically embedded temporal convolutional network model through forward propagation. , representing the predicted probability of sluice gate opening, the predicted gate discharge, the predicted water level, and the predicted output, respectively; calculate the survival probability. Calculate the loss function Calculate the gradient Update decision variables The updated version Project onto a feasible region with upper and lower bounds; set a preset convergence criterion, and terminate the iteration when the gradient norm is less than a first preset threshold, or the change in the decision variable is less than a second preset threshold, or the maximum number of iterations is reached.

[0015] In a preferred embodiment, step S3, configuring the NSGA-III algorithm parameters, includes: Set the population size to a preset size; The reference points are generated using a preset generation method, ensuring that the reference points are uniformly distributed on the target space hyperplane. Genetic operator configuration: Uses a preset type of crossover operator and sets the preset crossover probability and distribution index. A preset mutation operator is used, and a preset mutation probability and a second preset distribution index are set. The preset mutation probability is determined by the total number of decision variables. The preset function is determined; Objective function evaluation uses physical simulation: Total energy objective ,in Indicates the amount of electricity generated. Indicates energy storage at the end of the period; target total discharge flow rate. Delayed gate opening target The algorithm terminates when the preset running time limit is reached or the convergence criterion is met.

[0016] In the preferred embodiment, the hot start strategy in step S3 is specifically implemented as follows: using the initial solution obtained in step S2... Constructing the initial population: ; in, This is the initial solution obtained through gradient optimization; This is a variant solution obtained by adding a Gaussian perturbation to the original solution. Follows a normal distribution Disturbance scale Set to the preset scaling factor; This is a solution generated by random initialization within the feasible region.

[0017] This invention also provides a cascade reservoir optimization scheduling solution system based on physical embedded deep learning and evolutionary computation, used to execute the above method, including: The model building module is used to set the physical relationships and scheduling constraints of cascade hydropower stations and build a physical embedded temporal convolutional network proxy model to predict the actual impact of decision variables on the physical system of multi-level reservoirs. The gradient optimization module is used to initialize the decision variables, namely the outflow of each hydropower station. It transforms the discrete water abandonment time objective function into a differentiable loss function through survival analysis. It then uses a physically embedded temporal convolutional network model to perform gradient inverse optimization and project it onto the feasible region to obtain the initial solution of the outflow. The evolutionary solution module is used to inject the initial solution into the initial population of the evolutionary algorithm for hot start-up, accelerate the Pareto front search, and finally obtain the Pareto front and non-dominated solutions.

[0018] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-described method for solving the optimal scheduling of cascade reservoirs based on the collaboration of physical embedded deep learning and evolutionary computation.

[0019] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for solving the optimal scheduling of cascade reservoirs based on the collaboration of physical embedded deep learning and evolutionary computation.

[0020] This invention provides a method and system for solving the optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation, which has the following beneficial effects: 1. This invention can embed specific physical models and use them to modify the structure of Temporal Convolutional Networks (TCNs), so that the network output satisfies physical constraints and forms a physically consistent differentiable surrogate model. This enables the rapid generation of high-quality initial solutions that satisfy the constraints. The initial solutions can be used as hot-start seed individuals for genetic algorithms / multi-objective evolutionary algorithms, significantly reducing the feasibility obstacles caused by random initialization, reducing the computational overhead of constraint violation repair, and accelerating the convergence process of genetic algorithms in specific engineering application scenarios, thereby improving optimization efficiency and solution stability.

[0021] 2. This invention uses multiple forecast inflow scenarios and different initial reservoir states as input variables during the PeTCN training process, enabling the surrogate model to learn the complex mapping relationship between inflow forecast information and optimal scheduling decisions. In practical applications, this allows the scheduling scheme to be dynamically generated based on different inflow forecasts, enhancing the adaptability of the scheduling strategy to time-varying hydrological conditions and operational requirements, and improving the feasibility and engineering practical value of the scheme. Attached Figure Description

[0022] The accompanying drawings, which are provided to further illustrate the invention and constitute a part of this invention, do not constitute an undue limitation thereof. In the drawings: Figure 1 Presentation of Pareto front results obtained by the C-TAEA algorithm; Figure 2Presentation of Pareto front results obtained by the NSGA-III algorithm; Figure 3 This is a demonstration of the Pareto front results obtained by the method algorithm provided in this invention; Figure 4 A comparison of the Pareto front obtained by the method (hot start NSGA-III) provided by this invention with the Pareto front obtained by the NSGA-III algorithm (baseline NSGA-III). Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0024] Example 1: A method for solving the optimal scheduling of cascade reservoirs based on the synergy of physical embedded deep learning and evolutionary computation includes the following steps: S1. Set the physical relationships and scheduling constraints of cascade hydropower stations, and construct a Physical Embedded Temporal Convolutional Network (PeTCN) surrogate model to predict the actual impact of decision variables on the physical system of multi-stage reservoirs.

[0025] 1. The physical relationships of cascade hydropower stations include water balance equations, reservoir capacity-water level relationship, water level-water consumption rate relationship, gate opening flow calculation, power generation calculation, total power generation, and energy storage calculation at the end of the period.

[0026] Specifically, the expression is as follows: (1) The water balance equation is: ; Among them, for the first station , For external inflow For downstream power plants , This represents the sum of upstream outflow and inflow within the region.

[0027] (2) The reservoir capacity-water level relationship is as follows: ; The capacity can be determined based on the reservoir capacity curves of each reservoir, and can be expressed as a quadratic function. or linear function form ,in, The function parameters are known.

[0028] (3) The relationship between water level and water consumption rate is as follows: ; in, The average water level over a period of time is the relationship, which can be a linear, quadratic, or constant function, depending on the characteristics of the power station.

[0029] (4) The formula for calculating the gate opening flow rate is: ; Among them, maximum output Constrained by both water head and installed capacity, For the first The maximum output capacity of a power station The function parameters are known.

[0030] (5) The formula for calculating power generation is: .

[0031] (6) Total power generation .

[0032] (7) End-of-period energy storage . 2. Scheduling constraints include: water level constraints for each reservoir, water level fluctuation constraints, and outflow boundary constraints.

[0033] (1) Water level constraints of each reservoir ; in, Indicates the first The lower limit of the water level of each power station Indicates the first The upper limit of water level for each power station; Reservoir water level constraints ensure that the water levels of each reservoir are within the safe operating range.

[0034] (2) Water level fluctuation constraints ; in, This indicates the maximum permissible water level fluctuation, limiting the range of water level changes between adjacent time periods to prevent structural damage or ecological destruction caused by rapid water level fluctuations.

[0035] (3) Boundary constraints on outbound flow ; in, Indicates the first The lower limit of the outflow from the power station Indicates the first The upper limit of outflow from each power station is set to ensure that the outflow meets physical and operational constraints.

[0036] 3. The method for constructing the physically embedded temporal convolutional network PeTCN is as follows: S1.1 Based on the Temporal Convolutional Network (TCN) backbone structure, three residual blocks are designed, with the dilation factor and kernel size as the parameters. Stacking generates corresponding receptive fields, and each residual block consists of two dilated causal convolutional layers.

[0037] In this embodiment, three residual blocks are designed with an expansion factor. and kernel size Stacking, producing The receptive field is expanded. Each residual block consists of two dilated causal convolutional layers, where dilated convolution expands the receptive field without increasing the number of parameters, and causal convolution ensures... t Predicting a time depends solely on past and current observations.

[0038] S1.2, the Physically Embedded Temporal Convolutional Network (PeTCN) architecture combines the Temporal Convolutional Network (TCN) backbone with a hard-coded physical layer to ensure physical consistency. TCN employs one-dimensional dilated causal convolutions to achieve parallel processing and efficiently capture long-range dependencies. TCN components learn to predict changes in storage capacity from the input sequence. , probability of opening the gate and gate opening flow The physical layer uses water balance equations and characteristic curves to explicitly calculate water levels. Water consumption rate and efforts Subscript , They represent the first The power station and the first Each time period.

[0039] S1.3. During training, a composite training loss function is used, the expression of which is: ; in, physical state The mean squared error loss, of which For storage capacity, For water level, Water consumption rate, To contribute one's strength; Probability of opening the gate Binary cross-entropy loss; For the opening flow rate The mean squared error loss; For the product of the overflow With overflow flow The mean squared error loss; For the predicted total energy target The predicted total discharge target And the predicted delayed opening target The sum of the mean squared error losses between its corresponding true value; to These are the weighting coefficients for the corresponding components.

[0040] 4. The training configuration of the physically embedded temporal convolutional network model includes: using a preset type of optimizer, setting a preset initial learning rate, preset batch size, and preset weight decay coefficient; setting a learning rate scheduler, and setting the learning rate scheduler when the validation loss reaches a preset number of... If there is no improvement within consecutive training cycles, the learning rate is reduced by a preset percentage; an early stopping mechanism is adopted, whereby the learning rate is reduced when the validation loss reaches a preset threshold. The training process is terminated if no improvement is observed within a continuous training cycle; the weight coefficients to The settings are configured according to preset values ​​during the training process.

[0041] S2. Initialize the decision variables, namely the outflow from each hydropower station. The discrete water discharge time objective function is transformed into a differentiable loss function using survival analysis. A physically embedded temporal convolutional network model is then used for gradient inverse optimization. The loss value is calculated using the loss function, and optimization is performed using the gradient descent formula. Finally, the result is projected onto the feasible region of the hydropower station to obtain the outflow rate. As the initial solution.

[0042] 1. The operation method of survival analysis is as follows: Define power station The first time water was released The expression is: ; Where T represents the length of the entire scheduling cycle. To represent the zero-to-one variable indicating whether water wastage has occurred, when the first... The power station in the first When water is abandoned during a certain period If the first The power station in the first If no water is discarded during a certain period, then If the power station If no water is wasted during the entire scheduling period, then set ; Building power plants At any moment The survival probability function represents the power plant At any moment The probability of no water wastage occurring before is expressed as: ; The discrete delayed water abandonment target is transformed into a differentiable survival analysis loss function, expressed as: ; minimize This is equivalent to maximizing the expected first water discharge time of all power plants, thus aligning with the discrete objective function. Maintain consistency in the direction of optimization.

[0043] 2. The method for constructing the loss function of gradient inverse optimization is as follows: Freeze the parameters of the trained physical embedded temporal convolutional network model , outbound flow sequence As a trainable variable, construct the loss function: ; Among them, the energy maximization objective , Energy storage for the final period is directly calculated from the water level at the end of the period; the goal is to minimize the discharge flow when the gate is opened. Constraints and penalties for losses , For the first The lower limit of the water level of each power station For the first The upper limit of the water level of each power station Indicates the first Each power station The change in water level between the previous time period and the current time period; , , The target weight coefficient.

[0044] 3. The optimization process using the gradient descent formula is as follows: Initialize outbound flow sequence ; Use a preset type of optimizer and set a preset learning rate and a preset maximum number of iterations; Each iteration performs the following steps: Calculate the predicted value using a physically embedded temporal convolutional network model through forward propagation. , representing the predicted probability of sluice gate opening, the predicted gate discharge, the predicted water level, and the predicted output, respectively; calculate the survival probability. Calculate the loss function Calculate the gradient Update decision variables The updated version Project onto a feasible region with upper and lower bounds; set a preset convergence criterion, and terminate the iteration when the gradient norm is less than a first preset threshold, or the change in the decision variable is less than a second preset threshold, or the maximum number of iterations is reached.

[0045] The constraint penalty coefficient is set as follows: the loss function The penalties for violations of the lower water level limit, the upper water level limit, and the amplitude constraint are all calculated using a weighted average of preset constraint penalty coefficients.

[0046] S3. Inject the initial solution into the initial population of the NSGA-III algorithm for a hot start, which accelerates the search process of the Pareto front and finally obtains the Pareto front and the non-dominated solution.

[0047] The evolutionary algorithm uses the NSGA-III algorithm, and the algorithm parameter configuration includes: Set the population size to a preset size; The reference points are generated using a preset generation method. In this embodiment, the Das and Dennis generation method on the unit simplex is used to make the reference points uniformly distributed on the target space hyperplane. Genetic operator configuration: Uses a preset type of crossover operator and sets the preset crossover probability and distribution index. A preset mutation operator is used, and a preset mutation probability and a second preset distribution index are set. The preset mutation probability is determined by the total number of decision variables. The preset function is determined; Objective function evaluation uses physical simulation: Total energy objective ,in Indicates the amount of electricity generated. Indicates energy storage at the end of the period; target total discharge flow rate. Delayed gate opening target The algorithm terminates when the preset running time limit is reached or the convergence criterion is met.

[0048] The specific implementation of the warm start strategy is as follows: using the initial solution obtained in step S2 Constructing the initial population: ; in, This is the initial solution obtained through gradient optimization; This is a variant solution obtained by adding a Gaussian perturbation to the original solution. Follows a normal distribution Disturbance scale Set to the preset scaling factor; This is a solution generated by random initialization within the feasible region.

[0049] A preset hot start ratio is set to determine the proportion of individuals generated based on gradient optimization solutions (including the original solution and its variants) in the initial population. The remaining individuals are filled with randomly initialized individuals to maintain population diversity while preserving high-quality search directions.

[0050] Example 2: The following example uses a cascade hydropower system consisting of six hydropower stations (A, B, C, D, E, and F) to further illustrate the multi-objective optimization method for cascade hydropower scheduling based on physically embedded temporal convolutional networks (PTCs) provided by this invention. The six hydropower stations are arranged sequentially in series along a river basin, from upstream to downstream as follows: Station A, Station B, Station C, Station D, Station E, and Station F. Station A receives the main external inflow, while Station F is located at the downstream end of the system. The inflow into the cascade system includes both external inflow and water from the adjacent sections.

[0051] This embodiment utilizes historical water sequence data from the basin where the cascade hydropower stations are located over many years, including historical inflow sequences, reservoir characteristics, and operational constraints. The physical parameters of each reservoir (storage capacity-water level relationship, water consumption rate curve, and power generation characteristics) are derived from engineering design documents and operational records. The scheduling period covers 60 time periods on a daily scale, corresponding to a two-month operating cycle. Since power station F operates as a runoff reservoir with no significant storage capacity, the delayed opening objective does not include power station F, but focuses on the other five impoundable reservoirs. The optimization problem involves 360 decision variables, 3 objectives, and 1080 constraints; the amplitude limit for each reservoir is uniformly set at 2m / day to ensure operational safety.

[0052] The method of the present invention is performed in the following three stages on this cascade system: (1) PeTCN training phase: PeTCN was trained on a dataset of 40,000 generated samples; the network employed a linear encoder (18 input dimensions mapped to 128 features), 3 stacked TCN blocks (kernel size 3, dilation factor [1, 2, 4]), and independent MLP prediction heads were set for different predictor variables; training used the AdamW optimizer with an initial learning rate of Batch size 2048, weight decay The training employed a learning rate scheduling and early stopping mechanism, with a total training time of approximately 14.79 minutes. The average relative prediction error of PeTCN over 60 time periods is shown in Table 1.

[0053] Table 1. Average relative prediction error of PeTCN over 60 time periods.

[0054] (2) Gradient-based inverse optimization stage: Freeze the trained PeTCN parameters, use the outbound flow sequence as the optimization variable, and iteratively update using the Adam optimizer; initial learning rate. The maximum number of iterations is 800, and a large constraint penalty weight is set (boundary violation coefficient 1000, amplitude violation coefficient 500) to ensure that a high-quality initial solution that meets the running constraints is obtained.

[0055] (3) NSGA-III hot-start evolutionary search phase: The high-quality solutions obtained in the gradient phase are used as seed individuals to perform a warm start for NSGA-III. The algorithm settings parameters of the method of this invention (Boosted NSGA-III), NSGA-III and C-TAEA are shown in Table 2.

[0056] Table 2. Method, NSGA-III, and C-TAEA algorithm setting parameters provided by this invention.

[0057] Through the above configuration, this embodiment completes the multi-objective scheduling optimization of the cascade system and outputs a well-distributed Pareto front solution set, allowing dispatchers to make trade-offs among objectives such as "maximizing power generation, minimizing gate discharge, and delaying gate opening." Table 3 shows a comparison of the effectiveness of the method provided by this invention with NSGA-III and C-TAEA.

[0058] Table 3. Comparison of the performance of the method provided by this invention with NSGA-III and C-TAEA algorithms.

[0059] Example 3: To further illustrate the effects of the present invention, under the same tiered system and the same running time limit (1000s) in Example 2, the Boosted NSGA-III (with gradient hot start) of the present invention was compared with the baseline NSGA-III (random initialization) and the constrained multi-objective algorithm C-TAEA. The parameter settings of each algorithm are shown in Table 1.

[0060] Table 3 shows the comparison results of the proposed method with the baselines NSGA-III and C-TAEA in terms of feasible solution acquisition efficiency and constraint satisfaction capability. As can be seen from Table 3, the proposed method can quickly obtain feasible solutions and significantly improve the proportion of feasible individuals in the early stages of evolutionary search, thus effectively overcoming the "feasibility barrier" caused by random initialization in tightly constrained high-dimensional problems. In contrast, the baseline NSGA-III mainly consumes time in the longer iteration phase for constraint violation repair and elimination, and C-TAEA struggles to form a stable feasible solution set within a given runtime constraint. To further illustrate, in this embodiment, the proposed method obtains the first feasible solution in the 34th generation, while the baseline NSGA-III requires 3606 generations to obtain its first feasible solution; C-TAEA fails to find a feasible solution within the given time constraint. Regarding final feasibility… This invention achieves 136 / 400 feasible solutions with zero final constraint violations, while the baseline NSGA-III achieves 16 / 400 feasible solutions with zero final constraint violations, and C-TAEA has a final feasible solution of 0 / 400 with significant constraint violations.

[0061] Furthermore, the Pareto front results finally obtained by each algorithm are as follows: Figures 1-4 As shown, the method of this invention significantly shortens the time to "enter the feasible region," allowing the computational budget for evolutionary search to be used more for Pareto front exploration rather than constraint satisfaction, thereby obtaining a wider and more fully distributed non-dominated solution set in the target space. Compared to the baseline NSGA-III, the method of this invention can form a more advantageous Pareto front shape in the target trade-off dimensions such as energy-gate discharge, and exhibits better solution set diversity and selectivity; in contrast, the solution set coverage of the baseline NSGA-III is relatively limited, and C-TAEA is difficult to form an effective Pareto front. As a further illustration, the method of this invention demonstrates an additional power generation gain of approximately 1000 MkWh in this embodiment and obtains better solution distribution characteristics.

[0062] Example 4: This embodiment provides a cascade reservoir optimization scheduling solution system based on physical embedded deep learning and evolutionary computation, used to execute the method described in Embodiment 1, including: The model building module is used to set the physical relationships and scheduling constraints of cascade hydropower stations and build a physically embedded temporal convolutional network (PeTCN) model to predict the actual impact of decision variables on the physical system of multi-stage reservoirs. The gradient optimization module is used to initialize the decision variables, namely the outflow of each hydropower station. It transforms the discrete water abandonment time objective function into a differentiable loss function through survival analysis. It then uses a physically embedded temporal convolutional network model to perform gradient inverse optimization and project it onto the feasible region to obtain the initial solution of the outflow. The evolutionary solution module is used to inject the initial solution into the initial population of the evolutionary algorithm for hot start-up, accelerate the Pareto front search, and finally obtain the Pareto front and non-dominated solutions.

[0063] Example 5: This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the cascade reservoir optimization scheduling solution method based on physical embedded deep learning and evolutionary computation collaboration described in Embodiment 1.

[0064] Example 6: This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the cascade reservoir optimization scheduling solution method based on physical embedded deep learning and evolutionary computation collaboration described in Embodiment 1.

[0065] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A cascade reservoir optimal scheduling solution method based on physical embedded deep learning and evolutionary calculation cooperation, characterized in that, Includes the following steps: S1. Set the physical relationships and scheduling constraints of cascade hydropower stations, and construct a physical embedded temporal convolutional network proxy model to predict the actual impact of decision variables on the physical system of multi-level reservoirs; S2. Initialize the decision variables, namely the outflow from each hydropower station. The discrete water discharge time objective function is transformed into a differentiable loss function using survival analysis. A physically embedded temporal convolutional network model is then used for gradient inverse optimization. The loss value is calculated using the loss function, and optimization is performed using the gradient descent formula. Finally, the result is projected onto the feasible region of the hydropower station to obtain the outflow rate. As the initial solution; S3. Inject the initial solution into the initial population of the NSGA-III algorithm for a hot start, which accelerates the search process of the Pareto front and finally obtains the Pareto front and the non-dominated solution.

2. The method for optimal scheduling of cascade reservoirs based on physical embedded deep learning and evolutionary computation as described in claim 1, characterized in that, In step S1, the physical relationships of the cascade hydropower stations include the water balance equation, reservoir capacity-water level relationship, water level-water consumption rate relationship, gate opening flow calculation, power generation calculation, total power generation, and energy storage calculation at the end of the period. The scheduling constraints include: water level constraints for each reservoir, water level fluctuation constraints, and outflow boundary constraints.

3. The method for optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 1, characterized in that, In step S1, the method for constructing the physically embedded temporal convolutional network PeTCN is as follows: S1.1 Based on the Temporal Convolutional Network (TCN) backbone structure, three residual blocks are designed, with the dilation factor and kernel size as the parameters. Stacking generates corresponding receptive fields, and each residual block consists of two dilated causal convolutional layers; S1.2, The physically embedded temporal convolutional network architecture combines TCN with a hard-coded physical layer. The TCN uses one-dimensional dilated causal convolution to achieve parallel processing; the TCN component learns to predict changes in library capacity from the input sequence. , probability of opening the gate and gate opening flow The physical layer uses water balance equations and characteristic curves to explicitly calculate water levels. Water consumption rate and contribution Subscript , They represent the first The power station and the first Each time period; S1.

3. During training, a composite training loss function is used, the expression of which is: ； in, physical state The mean squared error loss, of which For storage capacity, For water level, Water consumption rate, To contribute one's strength; Probability of opening the gate Binary cross-entropy loss; For the opening flow rate The mean squared error loss; Product of overflow With overflow flow The mean squared error loss; For the predicted total energy target The predicted total discharge target And the predicted delayed opening target The sum of the mean squared error losses between its corresponding true value; to These are the weighting coefficients for the corresponding components.

4. The method for optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 3, characterized in that, In step S1, the training configuration of the physically embedded temporal convolutional network model includes: using a preset type of optimizer, setting a preset initial learning rate, a preset batch size, and a preset weight decay coefficient; setting a learning rate scheduler, which is used when the validation loss reaches a preset number of... If there is no improvement within consecutive training cycles, the learning rate is reduced by a preset percentage; an early stopping mechanism is adopted, whereby the learning rate is reduced when the validation loss reaches a preset threshold. The training process is terminated if no improvement is observed within a continuous training cycle; the weight coefficients to The settings are configured according to preset values ​​during the training process.

5. The method for solving the optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 3, characterized in that, In step S2, the survival analysis method is operated as follows: Define power station The first time water was released The expression is: ； Where T represents the length of the entire scheduling cycle. To represent the zero-to-one variable indicating whether water wastage has occurred, when the first... The power station in the first When water is released during a certain period If the first The power station in the first If no water is discarded during a certain period, then If the power station If no water is wasted during the entire scheduling period, then set as follows: ; Building power plants At any moment The survival probability function represents the power plant At any moment The probability of no water wastage occurring before is expressed as: ； The discrete delayed water abandonment target is transformed into a differentiable survival analysis loss function, expressed as: ； minimize This is equivalent to maximizing the expected first water discharge time of all power plants.

6. The method for solving the optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 5, characterized in that, In step S2, the method for constructing the loss function for gradient inverse optimization is as follows: Freeze the parameters of the trained physical embedded temporal convolutional network model , outbound flow sequence As a trainable variable, construct the loss function: ； Among them, the energy maximization objective , Energy storage for the final period is directly calculated from the water level at the end of the period; the goal is to minimize the discharge flow when the gate is opened. Constraints and penalties for losses , For the first The lower limit of the water level of each power station For the first The upper limit of the water level of each power station Indicates the first Each power station The change in water level between the previous time period and the current time period; , , The target weight coefficient.

7. The method for optimal scheduling of cascade reservoirs based on physical embedded deep learning and evolutionary computation as described in claim 6, characterized in that, In step S2, the optimization process using the gradient descent formula is as follows: Initialize outbound flow sequence ; Use a preset type of optimizer and set a preset learning rate and a preset maximum number of iterations; Each iteration performs the following steps: Calculate the predicted value using a physically embedded temporal convolutional network model through forward propagation. , representing the predicted probability of sluice gate opening, the predicted gate discharge, the predicted water level, and the predicted output, respectively; calculate the survival probability. Calculate the loss function Calculate the gradient Update decision variables The updated version Project onto a feasible region with upper and lower bounds; set a preset convergence criterion, and terminate the iteration when the gradient norm is less than a first preset threshold, or the change in the decision variable is less than a second preset threshold, or the maximum number of iterations is reached.

8. The method for solving the optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 1, characterized in that, In step S3, the NSGA-III algorithm parameter configuration includes: Set the population size to a preset size; The reference points are generated using a preset generation method, ensuring that the reference points are uniformly distributed on the target space hyperplane. Genetic operator configuration: Uses a preset type of crossover operator and sets the preset crossover probability and distribution index. A preset mutation operator is used, and a preset mutation probability and a second preset distribution index are set. The preset mutation probability is determined by the total number of decision variables. The preset function is determined; Objective function evaluation uses physical simulation: Total energy objective ,in Indicates the amount of electricity generated. Indicates energy storage at the end of the period; target total discharge flow rate. Delayed gate opening target The algorithm terminates when the preset running time limit is reached or the convergence criterion is met.

9. The method for optimal scheduling of cascade reservoirs based on the synergy of physically embedded deep learning and evolutionary computation as described in claim 1, characterized in that, In step S3, the hot start strategy is specifically implemented as follows: using the initial solution obtained in step S2... Constructing the initial population: ； in, This is the initial solution obtained through gradient optimization; This is a variant solution obtained by adding a Gaussian perturbation to the original solution. Follows a normal distribution Disturbance scale Set to the preset scaling factor; This is a solution generated by random initialization within the feasible region.

10. A cascade reservoir optimization scheduling solution system based on physical embedded deep learning and evolutionary computation, characterized in that, For performing the method according to any one of claims 1 to 9, comprising: The model building module is used to set the physical relationships and scheduling constraints of cascade hydropower stations and build a physical embedded temporal convolutional network proxy model to predict the actual impact of decision variables on the physical system of multi-stage reservoirs. The gradient optimization module is used to initialize the decision variables, namely the outflow of each hydropower station. It transforms the discrete water abandonment time objective function into a differentiable loss function through survival analysis. It then uses a physically embedded temporal convolutional network model to perform gradient inverse optimization and project it onto the feasible region to obtain the initial solution of the outflow. The evolutionary solution module is used to inject the initial solution into the initial population of the evolutionary algorithm for hot start-up, accelerate the Pareto front search, and finally obtain the Pareto front and non-dominated solutions.

11. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the cascade reservoir optimization scheduling solution method based on the collaboration of physical embedded deep learning and evolutionary computation as described in any one of claims 1 to 9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for solving the optimal scheduling of cascade reservoirs based on the collaboration of physical embedded deep learning and evolutionary computation as described in any one of claims 1 to 9.

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