Reservoir water-sediment joint optimal scheduling method based on particle swarm optimization algorithm

Abstract

The present invention relates to the field of reservoir sediment scheduling. Disclosed is a reservoir water-sediment joint optimal scheduling method based on a particle swarm optimization (PSO) algorithm. The method comprises: defining a mathematical model of a reservoir water-sediment scheduling problem which comprises decision variables, constraint conditions, and target functions, and defining parameters of the problem; initializing particles, wherein each particle represents one solution of the reservoir water-sediment scheduling problem, and each velocity vector is initialized to zero; designing a fitness function for evaluating the performance of each particle position; using the PSO algorithm to update the velocity and position of each particle; after each position update, ensuring that a new position meets the constraint conditions of the problem, and if the position of a certain particle violates the constraint conditions, using a strategy of adjustment or regeneration to ensure the feasibility of the solution; and iterating the velocities and positions of the particles for continuous update until a termination condition is met. The present invention can effectively cope with the high-dimensional spatial search challenge of the reservoir water-sediment scheduling problem.

Description

A joint optimization scheduling method for reservoir water and sediment based on particle swarm optimization algorithm

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on December 19, 2023, with application number 202311755938.X and invention name “A method for joint optimization scheduling of reservoir water and sediment based on particle swarm optimization algorithm”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention relates to the field of reservoir sediment scheduling, and in particular to a reservoir water and sediment joint optimization scheduling method based on a particle swarm optimization algorithm. Background Art

[0003] Particle Swarm Optimization (PSO) is a heuristic optimization algorithm that can be applied to a variety of problems, including water resource management and reservoir operation. However, reservoir water and sediment scheduling problems typically have multiple decision variables and multiple constraints, which makes the search space very large. The PSO algorithm's search ability in high-dimensional spaces may be limited. Therefore, an effective method is needed to deal with high-dimensional space search for reservoir water and sediment scheduling problems.

[0004] Summary of the Invention

[0005] The present invention proposes a reservoir water and sediment joint optimization scheduling method based on particle swarm optimization algorithm.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A reservoir water and sediment joint optimization scheduling method based on particle swarm optimization algorithm includes the following steps:

[0008] Define the mathematical model of the reservoir water and sediment scheduling problem, including decision variables, constraints, and objective function; define the problem parameters, including reservoir water volume, flood discharge coefficient, and water supply demand;

[0009] Initialize particles. Each particle represents a solution to the reservoir water and sediment scheduling problem. The position vector of each particle represents a set of decision variables, and the velocity vector is initialized to zero.

[0010] Design a fitness function to evaluate the performance of each particle position;

[0011] Use PSO algorithm to update the velocity and position of particles;

[0012] After each position update, ensure that the new position meets the constraints of the problem. If the position of a particle violates the constraints, adjust or regenerate the strategy to ensure the feasibility of the solution;

[0013] Iterate the particle's velocity and position, updating them continuously until a termination condition is reached.

[0014] The proposed method automatically adjusts its search strategy, updating the particle speed and position based on the characteristics of the search space. This adaptability allows the algorithm to better explore the solution space under varying problem conditions, thereby increasing the probability of finding the optimal solution. It can run efficiently on multi-core processors or in distributed computing environments, providing greater computing power and facilitating the handling of large-scale, high-dimensional problems. Due to its iterative nature, the PSO algorithm can gradually improve the solution over multiple iterations, thus finding a more optimal solution through step-by-step optimization. This characteristic is very useful for long-term water resource management decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG1 is a flow chart of the present invention. DETAILED DESCRIPTION

[0016] The present invention will be further described below with reference to the accompanying drawings and specific examples.

[0017] As shown in FIG1 , the present invention discloses a reservoir water and sediment joint optimization scheduling method based on a particle swarm optimization algorithm, comprising the following steps:

[0018] Step 1: Problem modeling and parameter definition.

[0019] Clearly define the mathematical model of the reservoir water and sediment scheduling problem, which includes decision variables, constraints and multiple objective functions, such as water supply quality, flood control and sediment management, and define the various parameters of the problem, including reservoir water storage capacity, flood discharge coefficient, water supply demand, etc.

[0020] Step 2: Particle swarm initialization.

[0021] Initialize a group of particles, each particle represents a solution to the reservoir water and sediment scheduling problem. The position vector of each particle represents a set of decision variables, and the velocity vector is initialized to zero to ensure that the position of the particle is within a reasonable decision space.

[0022] Step 3: Fitness function design.

[0023] A comprehensive fitness function is designed to evaluate the performance of each particle position. The fitness function should take into account objectives such as water supply demand, flood control, sediment management, and ecological needs. It can be expressed as a multi-objective optimization problem, and the weight of each objective function can be adjusted to balance the importance of different objectives.

[0024] Step 4: Particle velocity and position update.

[0025] The standard PSO algorithm is used to update the velocity and position of the particles.

[0026] Step 5: Constraint processing.

[0027] After each position update, it is necessary to ensure that the new position meets the constraints of the problem, such as minimum release flow, water storage capacity limit, etc. If the position of a particle violates the constraints, an adjustment or regeneration strategy can be adopted to ensure the feasibility of the solution.

[0028] Step 6: Convergence check and termination conditions.

[0029] The speed and position of the particles are iterated and continuously updated until a certain termination condition is reached, such as reaching the maximum number of iterations or the fitness value tends to be stable. Convergence checks can help determine whether the optimal reservoir water and sediment scheduling solution that meets various requirements has been found.

[0030] Step 1 includes: clearly defining the mathematical model of the reservoir water and sediment scheduling problem, including decision variables, constraints and multiple objective functions.

[0031] The decision variables of the reservoir water and sediment scheduling problem include the reservoir water storage, flood discharge, and water supply flow. These variables can be represented by symbols: Reservoir Storage: V i ; Release Flow: Q i ; Water Supply Flow: S i , i represents the time.

[0032] Reservoir water and sediment scheduling problems involve multiple objective functions, such as water supply quality, flood control, and sediment management.

[0033] Water supply quality objective function:

[0034] N represents the number of scheduling periods, S i is the actual water supply flow at time i, D i is the water demand at time i.

[0035] Flood control objective function:

[0036] Q i is the actual flood discharge at time i, F i is the flood control requirement at time i.

[0037] Sediment management objective function:

[0038] M i is the sediment content of the flood outlet at time i, T iis the sediment control standard at time i.

[0039] The reservoir water and sediment scheduling problem includes multiple constraints, such as water storage capacity limit and minimum release flow. These constraints can be expressed by symbols:

[0040] Water storage capacity constraint: V i ≤V max , V max It is the maximum water storage capacity of the reservoir.

[0041] Minimum release flow constraint: Q i ≥Q min , Q min is the minimum allowable flood discharge.

[0042] Sediment control constraint: M i ≤M max , M max It is the maximum allowable value of sediment content.

[0043] The decision variables, objective function and constraints constitute the mathematical model of the reservoir water and sediment scheduling problem, which provides the basis for the subsequent optimization process. In this step, the mathematical structure of the problem is clarified so that the particle swarm optimization algorithm can be used in the subsequent steps to solve the optimal reservoir water and sediment scheduling strategy.

[0044] Step 2 includes: initializing a group of particles, each particle represents a solution to the reservoir water and sediment scheduling problem. The following are the implementation steps:

[0045] Initialize the particle swarm:

[0046] Define the size of the particle swarm, represented by the symbol N.

[0047] For each particle i, its position vector and velocity vector are initialized. The position vector represents a set of decision variables, such as water storage, flood discharge, and water supply flow. The velocity vector is used to guide the movement of the particle in the search space. These initialized vectors can be expressed as:

[0048] Position vector: x i =[V i ,Q i ,S i ],V i Indicates the water storage capacity of the reservoir, Q i represents the flood discharge, S i Indicates the water supply flow rate.

[0049] Velocity vector: v i =[0,0,0], the velocity vector is initialized to zero at the beginning.

[0050] Initialize the fitness value of each particle by substituting its position vector into the fitness function for calculation, such as:

[0051] Water supply quality fitness value:

[0052] Flood control fitness value:

[0053] Sediment management fitness value:

[0054] Ensure that the particle's position vector is within a reasonable decision space, i.e., V i In [0,V max ] interval, Q i In [Q min ,∞] interval, S i In [0,S max ] interval, S max It is the maximum value of water supply flow.

[0055] After the above steps, the initialization of the particle swarm is completed, and each particle has a reasonable initial position and fitness value. They will be updated and searched for the optimal solution through the particle swarm optimization algorithm in subsequent steps.

[0056] Step 3 involves designing a comprehensive fitness function to evaluate the performance of each particle location. The fitness function should consider objectives such as water supply demand, flood control, sediment management, and ecological needs. This can be formulated as a multi-objective optimization problem, where the weight of each objective function can be adjusted to balance the importance of different objectives.

[0057] Define a multi-objective fitness function and combine the fitness of different objectives into a comprehensive fitness value. You can use a weighted summation method, where each objective function has a weight. The multi-objective fitness function is:

[0058] F(x i ) is the comprehensive fitness value, is the fitness value of the jth objective function, ω j is the weight of the j-th objective.

[0059] The definitions of the objective functions have been given in step 1, including the water supply quality objective function f1, the flood control objective function f2, and the sediment management objective function f3.

[0060] The choice of weights can be adjusted according to the specific needs of the problem. For example, if the quality of water supply is more important, the weight associated with the quality of water supply can be increased. In this way, the fitness function can balance the trade-offs between different objectives so that each objective is properly considered.

[0061] Step 4 involves updating the particle's velocity and position using a standard PSO algorithm.

[0062] Particle velocity and position update: For each particle i, the standard PSO algorithm is used to update its velocity and position. The velocity update formula of the PSO algorithm is as follows: V ij (t+1)=ωV ij (t)+c1r1(p ij (t)-x ij (t))+c2r2g ij (t)-x ij (t)).

[0063] Among them, V ij (t+1) is the velocity of particle i in dimension j at time t+1, x ij (t) is the position of particle i in dimension j at time t, p ij (t) is the best position found by particle i so far, g ij (t) is the best position found so far in the entire swarm, ω is the inertia weight, c1 and c2 are acceleration coefficients, and r1 and r2 are random numbers.

[0064] Update the particle's position: x ij (t+1)=x ij (t)+V ij (t+1).

[0065] Repeat the above update process until the maximum number of iterations or the termination condition is reached.

[0066] This step uses the standard PSO algorithm to guide particles to find the optimal solution in the search space. The speed of the particles is determined by the individual optimal position p. ij (t) and the global optimal position g ij (t) is adjusted to achieve a balance between global search and local search. These updates will help particles gradually move towards a better reservoir water and sediment scheduling strategy to optimize the multi-objective fitness function.

[0067] Step 5 includes: processing constraints to ensure that after each position update, the new position meets the constraints of the problem. If the position of a particle violates the constraints, corresponding adjustment measures need to be taken to ensure the feasibility of the solution.

[0068] Handling constraints: After each position update, check each particle's position vector to ensure that it satisfies the problem's constraints.

[0069] For each constraint, such as water storage capacity constraint, minimum release flow constraint, etc., check whether the corresponding decision variable is within the allowed range.

[0070] If a decision variable exceeds the allowed range, one of the following strategies can be adopted:

[0071] By adjusting the strategy, the decision variables are adjusted to the closest legal value. For example, the water storage capacity under the water storage capacity constraint is limited to the maximum water storage capacity V max .

[0072] Regenerate the particle's position to randomly generate a legal position vector, ensuring it satisfies all constraints.

[0073] According to the constraints of the specific problem, other appropriate constraint processing methods are adopted to ensure the feasibility of the solution.

[0074] The above steps of handling constraints ensure that the solutions generated during the optimization process are feasible and do not violate the constraints of the problem. This is very important for the joint optimization of water and sediment scheduling in reservoirs, as it involves multiple constraints such as reservoir capacity, flood discharge requirements, and water supply demand.

[0075] Step 6 includes: performing convergence checks and determining termination conditions to determine whether the optimal reservoir water and sediment scheduling solution that meets various requirements has been found.

[0076] Convergence checks and termination conditions:

[0077] After each iteration, the fitness value of the particle swarm needs to be calculated to understand the progress of the optimization. The global best fitness value F can be recorded. best and the corresponding global optimal position x best .

[0078] Set the termination condition, for example:

[0079] The maximum number of iterations is reached (for example, the number of iterations reaches a preset maximum value).

[0080] The fitness value tends to be stable, that is, the change in the fitness value after several consecutive iterations is less than a predetermined threshold.

[0081] Achieve convergence criteria to meet specific problem needs, such as meeting water supply needs, flood control requirements, etc.

[0082] After each iteration, the termination condition is checked. If any of the termination conditions is met, the algorithm stops iterating, otherwise it continues to the next round of iteration.

[0083] Once the termination condition is met, the global optimal position x bestFind the final reservoir water and sediment scheduling solution, which will be an optimized strategy that meets the multi-objective optimization goals and constraints.

[0084] This step ensures that the optimization algorithm terminates when a certain number of iterations is reached or a specific fitness value stability condition is met, thereby finding the optimal reservoir water and sediment scheduling solution that meets various requirements. This solution can be used as the final decision-making strategy for actual water resources management.

Claims

1. A reservoir water and sediment joint optimization scheduling method based on particle swarm optimization algorithm, characterized in that: The steps include: Define the mathematical model of the reservoir water and sediment dispatch problem, including decision variables, constraints and objective function; define the parameters of the problem, including reservoir water volume, flood discharge coefficient and water supply demand; Initialize particles. Each particle represents a solution to the reservoir water and sediment scheduling problem. The position vector of each particle represents a set of decision variables, and the velocity vector is initialized to zero. Design a fitness function to evaluate the performance of each particle position; Use PSO algorithm to update the velocity and position of particles; After each position update, ensure that the new position meets the constraints of the problem. If the position of a particle violates the constraints, adjust or regenerate the strategy to ensure the feasibility of the solution; Iterate the particle's velocity and position, updating them continuously until the termination condition is reached.

Images