Hydraulic transition process optimization method based on constraint sensitive variable dominant two stages

Abstract

The invention discloses a hydraulic transition process optimization method based on constraint sensitive variable dominant two stages. According to the method, a hydraulic transition process calculation model is constructed, a constraint sensitive variable dominant two-stage cooperative multi-objective evolutionary algorithm is accessed, and dominant constraint variables are determined by utilizing Monte Carlo sampling. After the algorithm parameters and the archive set are initialized, the iterative optimization strategies of the first stage and the second stage are executed in sequence; in the first stage, global search is emphasized, and a population is guided to approach a constrained Pareto frontier; in the second stage, oriented optimization based on constraint sensitive variable recognition results is focused, a cooperative individual updating strategy guided by variable types is adopted, and the sensitive variable optimization precision is improved. According to the method, influence differences of different decision variables are fully mined, resource processing key constraints are concentrated, the search direction is dynamically adjusted, accurate and efficient optimization is achieved, a powerful guarantee is provided for safe and stable operation of hydraulic engineering facilities, the service life of the hydraulic engineering facilities is effectively prolonged, and the maintenance cost is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic transition process calculation research, and in particular to a hydraulic transition process optimization method based on two stages dominated by constrained sensitive variables. Background Art

[0002] Water hammer can cause dramatic pressure fluctuations within a piping system, potentially leading to pipe ruptures, equipment damage, or even system failure. Therefore, optimizing and adjusting water hammer protection parameters to effectively suppress and mitigate the effect is crucial for ensuring the safe and reliable operation of hydraulic engineering facilities and extending their service life.

[0003] Currently, water hammer protection parameter optimization primarily focuses on multi-objective optimization algorithms, including multi-stage algorithms, multi-population algorithms, and multi-task algorithms. Compared to traditional single-objective optimization methods, multi-stage algorithms divide the optimization process into multiple stages, gradually guiding the population to converge toward the constrained Pareto front; multi-population algorithms utilize multiple populations for parallel search, enhancing diversity and global search capabilities; and multi-task algorithms leverage multi-task learning mechanisms to collaboratively perform multiple related optimization tasks, share information, and enrich the diversity of the solution set. Through improved approaches such as multi-stage step-by-step guidance, multi-population parallel exploration, and multi-task collaborative optimization, these algorithms enhance the adaptability and solution diversity of high-dimensional objective spaces. They can more effectively address the complexity and multiple constraints involved in water hammer protection parameter optimization, providing superior solutions.

[0004] However, existing multi-objective optimization methods still have several limitations. For one thing, they ignore the heterogeneity between constraints. Within the same optimization problem, different constraints can have varying degrees of difficulty. Certain difficult-to-satisfy constraints often dominate or significantly impact the algorithm's search capabilities, necessitating the allocation of additional computing resources to address these dominant constraints. Furthermore, they ignore the differences in how different decision variables influence the degree of constraint violation and lack effective mechanisms for handling constraint-sensitive variables. Summary of the Invention

[0005] The purpose of the present invention is to provide a two-stage hydraulic transition process optimization method based on constraint sensitive variables, thereby solving the above-mentioned problems existing in the prior art.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A two-stage hydraulic transition process optimization method based on constraint-sensitive variable dominance includes the following steps:

[0008] S1. Construct a hydraulic transition process calculation model and integrate it into a two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables;

[0009] S2. Perform constraint-dominant analysis based on Monte Carlo sampling to determine the dominant constraint variables;

[0010] S3, initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by the constraint sensitive variables, the feasible solution archive set A and the general archive set B, and randomly generate the initialization population P;

[0011] S4, the population performs iterative optimization of the first-stage strategy until the stage transition conditions are met;

[0012] S5. Enter the second stage optimization strategy: Based on the constraint sensitive variable identification results, the population is iteratively optimized using the variable type guided cooperative individual update strategy;

[0013] S6. After the termination condition is met, a set of optimal feasible and non-dominated solutions is selected from the feasible solution archive set A as the hydraulic transition process optimization solution.

[0014] Preferably, step S2 specifically includes:

[0015] S21. Use the Monte Carlo sampling method to randomly generate a certain number of sample points in the variable space;

[0016] S22. Calculate the proportion of sample points that meet each constraint, denoted as r k , k = 1, 2, ..., q, and all r k The average value of is denoted as ave(r);

[0017]

[0018] In the formula, q is the total number of constraints;

[0019] S23. Determine the dominant constraint variable: For each constraint k, if it satisfies the ratio r k is less than ave(r)-τ1, then the constraint is identified as the dominant constraint;

[0020]

[0021] Preferably, the specific contents of step S3 include:

[0022] S31. Initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables, including: population size N, current iteration number t, total iteration number T, external archive set size N / 2, polynomial mutation probability 1 / D; crossover and mutation distribution index R, crossover probability C r , scaling factor F and expansion factor σ, whose values ​​are dynamically adjusted with the number of iterations to control the update step size of sensitive variables and balance the exploration and development capabilities of the algorithm;

[0023] S32, initializing the feasible solution archive set A and the general archive set B to empty sets;

[0024] A=[]

[0025] B=[]

[0026] S33, randomly generate an initialization population P of size N;

[0027] Objective function: F(x) = [f1(x), f2(x), f3(x), f4(x)] T

[0028] Constraint: x∈Ω

[0029] Decision variable constraints:

[0030] Target value constraint:

[0031] In the formula, Ω is the decision space; F(x) is the objective function, where f1(x) is the minimum system maximum pressure value, f2(x) is the minimum system negative pressure value, f3(x) is the lowest relative reverse speed of the pump station unit, and f4(x) is the shortest total valve closing time; x = [x1, x2, x3] is a solution in Ω, x1 is the quick closing time of the valve after the pump, x2 is the quick closing angle of the valve after the pump, and x3 is the total closing time of the valve after the pump; t min The shortest time the valve after the pump can be operated; t max The maximum time the valve after the pump can be operated; H 额 is the rated pressure value of the pump unit outlet; n r is the rated speed of the water pump unit;

[0032] S34. Initialize the solution of the population to ensure that the solution is in the feasible region or close to the feasible region;

[0033] Preferably, step S4 specifically includes:

[0034] S41, judging whether the stage transition condition is met: whether the solution set has converged to the Pareto front of the dominant constraint or the Pareto front of the non-dominant constraint for solving the problem; if so, executing S5; otherwise, executing S42;

[0035] S42, using differential evolution (DE) operator and polynomial mutation to generate offspring population O1;

[0036] O1=DE(P)+polynomial mutation

[0037] S43, use SPEA2 method to perform environmental selection on P, O1, A and B, and update population P;

[0038] P = environmental selection (P + O1 + A + B)

[0039] S44. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening, and update the archive set A;

[0040] S45, ignoring the constraints from the new population P, performing non-dominated sorting and crowding distance screening, and updating the archive set B;

[0041] S46. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the archive set A as the optimization scheme for the hydraulic transition process; otherwise, add 1 to the number of iterations t and return to step S41.

[0042] Preferably, step S5 specifically includes:

[0043] S51. Randomly select a relatively optimal individual X from the population P = (x1, x2, ..., x D );

[0044] S52, update each decision variable of individual X in turn, and generate a new solution X′=(x1,…,x′ i …, x D );

[0045]

[0046] In the formula, i=1:D; j=1:NA / D; rand∈[0,1]; D is the decision variable dimension; NA is the total number of sampling times; is the upper bound of the i-th decision variable; is the lower bound of the i-th decision variable;

[0047] S53. Calculate the average constraint violation degree ICV of the new solution X′ i ;

[0048] cv i (X′)=max(0, g i (X′)), i=1,...,p

[0049]

[0050] In the formula, cv i (X′) is the degree of violation of the i-th constraint in the solution; g i (X′) is the inequality constraint; p is the total number of constraints; cv k (X′) is the normalized value to ensure that the weights of each constraint are consistent;

[0051] S54, when ICV i>(1+τ2)AICV, the decision variable is identified as a constraint-sensitive variable, where τ2 is the threshold for distinguishing constraint-sensitive variables from constraint-insensitive variables and is set to τ2=1 / (10D);

[0052]

[0053] S55. Evaluate all individuals in the current population and find a feasible non-dominated solution set (FNDS);

[0054] S56. Select a guide individual: Generate a random number rand∈[0,1]. When rand<θ and FNDS is a non-empty set, randomly select an individual from FNDS as the guide individual. When rand<θ and FNDS is an empty set, randomly select an individual from the feasible solution archive set A as the guide individual. Otherwise, randomly select an individual from the general archive set B as the guide individual.

[0055] θ=0.5×e 0.5-fr

[0056] In the formula, fr is the proportion of feasible solutions in the population, that is, the number of feasible solutions divided by the population size:

[0057] S57, update the position of sensitive variables using the optimal learning strategy;

[0058] x i，k (t+1)=x i，k (t)+σ×rand×(x o，k (t)-x i，k (t))

[0059]

[0060] In the formula, x i，k (t) is the value of the kth variable of the i-th individual in the t-th generation; x o，k (t) is the guiding individual X o (t) is the value of the kth variable; σ is the expansion factor; rand∈[0,1] is a random number; t is the current iteration number; T is the total iteration number; T c is the number of iterations at the end of the first phase;

[0061] S58. Use the DE operator to update the position of the insensitive variable. During the iteration, you can choose the DE / rand / 1 or DE / current-to-best / 1 strategy update, with a probability of 50% for each;

[0062] x i，k (t+1)=x i，k (t)+F×(x r1，k (t)-x r2，k(t))

[0063] x i，k (t+1)=x i，k (t)+rand×(x best，k (t)-x r1，k (t))+F×(x r2，k (t)-x r3，k (t))

[0064] In the formula, x best，k (t) is the k variable of a non-dominated individual randomly selected from the population; r1, r2, r1 are three individuals randomly selected from the population with r1≠r2≠r3≠i; rand∈[0,1] is a random number; F is a scaling factor;

[0065] S59, conduct local search for relevant sensitive variables and adjust their positions to improve the feasibility and diversity of the population;

[0066] x i，k1 (t+1)=x i，k1 (t)+rand×(x o，k1 (t)-x i，k1 (t))

[0067] x i，k2 (t+1)=x i，k2 (t)+(1-rand)×(x o，k2 (t)-x i，k2 (t))

[0068] Among them, k1 and k2 represent a pair of correlated sensitive variables;

[0069] S510, comparing the solutions before and after the update through the constraint dominance principle, retaining the superior solution, that is, generating the offspring population 0;

[0070] S511, use SPEA2 method to select P, O2, A and B, and update population P;

[0071] P = environmental selection (P + O1 + A + B)

[0072] S512. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening, and update the feasible solution archive set A;

[0073] S513, ignoring the constraints from the new population P, performing non-dominated sorting and crowding distance screening, and updating the general archive set B;

[0074] S514. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the feasible solution archive set A as the optimization scheme for the hydraulic transition process; otherwise, add 1 to the number of iterations t and return to step S41.

[0075] Preferably, in step S1, when constructing the hydraulic transition process calculation model, the water hammer control equation of the pipeline system is established by the characteristic line method, and the model construction is completed in combination with the pump and valve boundary conditions. The model serves as an external program, and the coupling between the two is achieved by constraining sensitive variables to dominate the two-stage collaborative multi-objective evolutionary algorithm main program to call the external program.

[0076] Preferably, in step S5, when performing a local search on the relevant sensitive variables, specifically, the positions of a pair of sensitive variables that have an associated relationship are adjusted, so as to improve the feasibility and diversity of the population.

[0077] Preferably, in step S6, when selecting the optimal solution from the feasible solution archive set A, the non-dominated level and the congestion distance of the solution are comprehensively considered, and the solution with a high non-dominated level and a large congestion distance is preferentially selected as the final hydraulic transition process optimization solution.

[0078] The beneficial effects of the present invention are:

[0079] (1) The present invention establishes a two-stage hydraulic transition process optimization method based on the dominance of constraint-sensitive variables. Compared with other methods, this method makes full use of the differences in the degree of constraint violation affected by different decision variables, and improves the algorithm's ability to solve constrained multi-objective optimization problems.

[0080] (2) The present invention introduces a dominant constraint analysis method, which enables the algorithm to concentrate resources on processing key constraints, avoid wasting computing resources, and thus improve optimization efficiency and quality.

[0081] (3) The present invention utilizes an individual selection mechanism based on population status to dynamically adjust the search direction, avoid premature convergence problems, and enhance the diversity of the population and the adaptability of the algorithm.

[0082] (4) The present invention introduces constraint-sensitive variable identification technology and a collaborative individual update strategy based on variable types to achieve directional optimization of key variables, thereby improving the convergence speed of the algorithm and the diversity of solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 Flowchart of the hydraulic transition process calculation optimization method in an embodiment of the present invention;

[0084] Figure 2 A constraint sensitive variable identification strategy diagram in an embodiment of the present invention;

[0085] Figure 3 Schematic diagram of an individual selection mechanism based on population status in an embodiment of the present invention;

[0086] Figure 4 This is a graph of collaborative individual update strategies guided by variable types in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0088] Reference Figure 1 、 Figure 2 、 Figure 3 and Figure 4 The hydraulic transition process optimization method based on the two-stage constraint-sensitive variable-dominated method shown in FIG1 includes the following steps:

[0089] S1. Construct a hydraulic transition process calculation model and integrate it into a two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables.

[0090] 1. Constructing a hydraulic transition process calculation model and integrating it into the algorithm framework

[0091] (1) Model construction

[0092] 1. Choose the appropriate hydraulic calculation method

[0093] The characteristic line method is used to establish the water hammer control equations for piping systems. This is primarily due to its high accuracy and stability in handling complex problems such as pressure fluctuations during hydraulic transitions. It can transform complex partial differential equations into ordinary differential equations along the characteristic line, making numerical solutions more convenient.

[0094] 2. Consider boundary conditions:

[0095] Incorporate boundary conditions for pumps and valves. For key equipment like pumps and valves, their boundary conditions should be determined based on the actual equipment characteristics in the project. For example, the boundary conditions for pumps should consider the pump's head-flow characteristic curve, while the boundary conditions for valves should consider the relationship between valve opening and flow. These boundary conditions ensure that the calculation model accurately reflects the actual operation of the hydraulic system.

[0096] (2) Model access algorithm

[0097] 1. Overview of the algorithm framework

[0098] The constructed hydraulic transition process calculation model was integrated into the Constraint-Sensitive Variable-Dominated Two-Stage Collaborative Multi-Objective Evolutionary Algorithm (CV-TCMOEA). CV-TCMOEA is an algorithm specifically designed for multi-objective optimization problems. It can comprehensively consider multiple objective functions and various constraints during the optimization process.

[0099] 2. Interaction Mechanism between Model and Algorithm

[0100] The hydraulic transition process calculation model serves as an external program, and the CV-TCMOEA main program calls the external program to achieve coupling between the two. During the optimization process, the CV-TCMOEA main program sends decision variables (such as the pump valve fast closing time, the pump valve fast closing angle, and the total pump valve closing time) to the hydraulic transition process calculation model. The hydraulic transition process calculation model performs hydraulic calculations based on these decision variables, obtains the corresponding objective function values ​​(such as the maximum system pressure, the system negative pressure, the relative reverse speed of the pump station units, the total valve closing time, etc.), and the satisfaction of the constraint conditions, and feeds these results back to the CV-TCMOEA main program.

[0101] S2. Perform constraint dominance analysis based on Monte Carlo sampling to determine the dominant constraint variables.

[0102] Monte Carlo Sampling Principle: Monte Carlo sampling is used to randomly generate a certain number of sample points in the variable space. Monte Carlo sampling is a sampling method based on random number generation. It can cover the variable space relatively evenly, providing a sufficient sample base for subsequent constraint-driven analysis.

[0103] Determining the sample size requires a trade-off between computational accuracy and cost. Generally speaking, a larger sample size results in more accurate constraint-dominant analysis, but the computational cost also increases accordingly. The appropriate sample size can be determined based on the complexity of the problem and the limitations of computing resources.

[0104] S3, initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by the constraint sensitive variables, the feasible solution archive set A and the general archive set B, and randomly generate the initialization population P;

[0105] S4, the population performs iterative optimization of the first-stage strategy until the stage transition conditions are met;

[0106] S5. Enter the second stage optimization strategy: Based on the constraint sensitive variable identification results, the population is iteratively optimized using the variable type guided cooperative individual update strategy;

[0107] S6. After the termination condition is met, a set of optimal feasible and non-dominated solutions is selected from the feasible solution archive set A as the hydraulic transition process optimization solution.

[0108] Preferably, step S2 specifically includes:

[0109] S21. Use the Monte Carlo sampling method to randomly generate a certain number of sample points in the variable space;

[0110] S22. Calculate the proportion of sample points that meet each constraint, denoted as r k , k = 1, 2, ..., q, and all r k The average value of is denoted as ave(r);

[0111]

[0112] In the formula, q is the total number of constraints;

[0113] S23. Determine the dominant constraint variable: For each constraint k, if it satisfies the ratio r k is less than ave(r)-τ1, then the constraint is identified as the dominant constraint;

[0114]

[0115] 1. Determine the criteria for determining the dominant constraint variables:

[0116] For each constraint, if it satisfies the ratio r k If the constraint is less than the average value ave(r), the constraint is identified as the dominant constraint. This is because constraints with a lower satisfaction ratio are usually more difficult to satisfy, have a greater restriction on the feasible region of the optimization problem, and have a more significant impact on the algorithm's search direction and the quality of the solution.

[0117] 2. The role of dominant constraints

[0118] Determining the dominant constraint variables helps the algorithm concentrate computing resources to process these key constraints in the subsequent optimization process, thereby improving optimization efficiency and solution quality. By prioritizing the dominant constraint, the population can be guided to converge faster towards the constrained Pareto front.

[0119] Preferably, the specific contents of step S3 include:

[0120] S31. Initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables, including: population size N, current iteration number t, total iteration number T, external archive set size N / 2, polynomial mutation probability 1 / D; crossover and mutation distribution index R, crossover probability C r , scaling factor F and expansion factor σ, whose values ​​are dynamically adjusted with the number of iterations to control the update step size of sensitive variables and balance the exploration and development capabilities of the algorithm;

[0121] S32, initializing the feasible solution archive set A and the general archive set B to empty sets;

[0122] A=[]

[0123] B=[]

[0124] The archive set is used to store solutions that meet certain conditions during the optimization process. The initial empty set is used to gradually fill the archive set according to the evolution of the population after the optimization starts.

[0125] S33. Randomly generate an initial population P of size N. Initialization of the population must ensure that the solution is within or close to the feasible region. This can be achieved by randomly sampling the decision variables and applying certain constraints. For example, Latin hypercube sampling can be used to generate the initial population to ensure uniform distribution and diversity.

[0126] Objective function: F(x) = [f1(x), f2(x), f3(x), f4(x)] T

[0127] Constraint: x∈Ω

[0128] Decision variable constraints:

[0129] Target value constraint:

[0130] In the formula, Ω is the decision space; F(x) is the objective function, where f1(x) is the minimum system maximum pressure value, f2(x) is the minimum system negative pressure value, f3(x) is the lowest relative reverse speed of the pump station unit, and f4(x) is the shortest total valve closing time; x = [x1, x2, x3] is a solution in Ω, x1 is the quick closing time of the valve after the pump, x2 is the quick closing angle of the valve after the pump, and x3 is the total closing time of the valve after the pump; t min The shortest time the valve after the pump can be operated; t max The maximum time the valve after the pump can be operated; H 额 is the rated pressure value of the pump unit outlet; n r is the rated speed of the pump unit; the setting of these objective functions is intended to comprehensively consider the key performance indicators in the hydraulic transition process. By optimizing these objective functions, the safety and operating efficiency of the hydraulic system can be improved. These constraints can include pressure limitations, flow limitations, equipment operating conditions, etc. of the pipeline system to ensure that the optimized solution is feasible in actual engineering. The definition range of the decision variables limits the search space in the optimization process, ensuring that the optimized valve operating parameters are within the controllable range of the actual equipment. The setting of the target value constraint is to ensure that the operating parameters of the optimized hydraulic system do not exceed the rated value of the equipment, avoiding the occurrence of equipment overload operation and other situations.

[0131] S34. Initialize the solution of the population to ensure that the solution is in the feasible region or close to the feasible region;

[0132] Preferably, step S4 specifically includes:

[0133] S41, judging whether the stage transition condition is met: whether the solution set has converged to the Pareto front of the dominant constraint or the Pareto front of the non-dominant constraint for solving the problem; if so, executing S5; otherwise, executing S42;

[0134] (1) Judgment stage transition conditions

[0135] 1. Judgment basis of stage transition conditions

[0136] Determine whether the solution set has converged to the dominant constraint Pareto front or the non-dominant constraint Pareto front of the problem being solved. This can be achieved by monitoring the population's convergence indicators (such as the population's average distance, the rate of change of the convergence front, etc.). If the population's convergence indicator indicates that the solution set is close to the dominant constraint Pareto front or the non-dominant constraint Pareto front, the stage transition condition is considered met and the second stage optimization strategy can be entered.

[0137] 2. The role of phase transition

[0138] The goal of phase transitions is to employ different strategies at different optimization stages to fully leverage the algorithm's global and local search capabilities. The first phase focuses on global search, rapidly guiding the population toward the constrained Pareto front; the second phase, on the other hand, focuses on local search, fine-tuning key variables to improve the quality and diversity of solutions.

[0139] S42, using differential evolution (DE) operator and polynomial mutation to generate offspring population O1;

[0140] O1=DE(P)+polynomial mutation

[0141] S43. Use the SPEA2 method to perform environmental selection on P, O1, A, and B to update population P. SPEA2 (Strength Pareto Evolutionary Algorithm 2) is a classic multi-objective optimization algorithm that selects the best individuals for the next generation by calculating their fitness. During environmental selection, the fitness of all individuals is first calculated. These individuals are then sorted from high to low, and individuals with higher fitness values ​​are selected to form the new population P. The goal of environmental selection is to gradually guide the population toward a more optimal solution set while maintaining population diversity. By selecting individuals with higher fitness values, solutions that perform well in terms of the objective function and constraints can be retained, thereby improving the overall quality of the population.

[0142] P = environmental selection (P + O1 + A + B)

[0143] S44. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening, and update the archive set A. Filter feasible solutions from the new population P, i.e., solutions that satisfy all constraints. Perform non-dominated sorting and crowding distance screening on these feasible solutions, and update the archive set A. Non-dominated sorting classifies solutions into different levels based on their dominance in the objective function space, with higher-ranked solutions being preferred. Crowding distance screening aims to maintain solution diversity by calculating the distance between each solution and its neighbors in the objective function space. Solutions with larger distances have higher diversity.

[0144] S45. Ignore the constraints from the new population P, perform non-dominated sorting and crowding distance screening, and update the archive set B. Ignore the constraints from the new population P, that is, do not consider whether the solution meets the constraints, perform non-dominated sorting and crowding distance screening on all solutions, and update the archive set B. The purpose of this is to retain some potentially valuable solutions without considering the constraints. These solutions may meet the constraints by adjusting the decision variables in the subsequent optimization process, thereby providing more search directions for the algorithm.

[0145] S46. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the archive set A as the optimization scheme for the hydraulic transition process; otherwise, add 1 to the number of iterations t and return to step S41.

[0146] Determine whether the number of iterations has reached the total number of iterations, T. If the current number of iterations, t ≥ T, the algorithm has completed the predetermined number of iterations and has reached the termination condition. At this point, select the optimal set of feasible and non-dominated solutions from the archive set A as the optimization solution for the hydraulic transition process. Otherwise, increase the number of iterations by 1 and return to the first stage of iterative optimization.

[0147] The purpose of the termination condition is to control the algorithm's runtime and prevent it from running indefinitely. The total number of iterations should be determined based on the complexity of the problem and the limitations of computing resources. A reasonable value can generally be determined through experimentation or experience.

[0148] Preferably, step S5 specifically includes:

[0149] S51. Randomly select a relatively optimal individual X from the population P = (x1, x2, ..., x D );

[0150] Randomly select a relatively optimal individual from the population P. The selection of the relatively optimal individual can be based on indicators such as the individual's fitness value or non-dominated rank in the objective function space. Selecting a relatively optimal individual as a guide individual helps provide a better search direction for other individuals in the subsequent optimization process.

[0151] The role of the guiding individual: The guiding individual serves as a model for the optimization process in the second phase, providing a reference for the updates of other individuals. By following the guiding individual, other individuals can move more quickly towards a more optimal solution set, thereby improving the convergence speed of the algorithm.

[0152] S52, update each decision variable of individual X in turn, and generate a new solution X′=(x1,…,x′ i …, x D );

[0153]

[0154] In the formula, i=1:D; j=1:NA / D; rand∈[0,1]; D is the decision variable dimension; NA is the total number of sampling times; is the upper bound of the i-th decision variable; is the lower bound of the i-th decision variable; a new solution is generated based on the updated decision variables. The generation of the new solution must ensure that it is within the domain of the decision variables and meets certain feasibility conditions (such as constraints). If the new solution does not meet the constraints, it can be made feasible through certain repair mechanisms (such as projection to the boundary of the feasible region).

[0155] S53. Calculate the average constraint violation degree ICV of the new solution X′ i ;

[0156] cv i (X′)=max(0, g i (X′)), i=1,...,p

[0157]

[0158] In the formula, cv i (X′) is the degree of violation of the i-th constraint in the solution; g i (X′) is the inequality constraint; p is the total number of constraints; cv k (X′) is the normalized value to ensure that the weights of each constraint are consistent;

[0159] The constraint violation degree is used to assess the feasibility of the solution. The smaller the constraint violation degree, the closer the solution is to the feasible region. During the optimization process, minimizing the constraint violation degree can guide the population toward the feasible region, thereby improving the feasibility of the solution.

[0160] S54, when ICV i >(1+τ2)AICV, the decision variable is identified as a constraint-sensitive variable, where τ2 is the threshold for distinguishing constraint-sensitive variables from constraint-insensitive variables and is set to τ2=1 / (10D);

[0161]

[0162] Judgment criteria for constraining sensitive variables:

[0163] When the average constraint violation score is greater than 0, the decision variable is identified as a constraint-sensitive variable. This indicates that the solution still contains some constraint violations. In this case, it is important to focus on decision variables that have a significant impact on the degree of constraint violations, known as constraint-sensitive variables. By identifying constraint-sensitive variables, the optimization focus can be placed on these key variables, effectively improving the feasibility of the solution.

[0164] The role of constraint-sensitive variables: Identifying constraint-sensitive variables facilitates targeted adjustments to these variables during subsequent optimization. Because constraint-sensitive variables significantly influence the degree of constraint violations, appropriately updating these variables can more effectively reduce the degree of constraint violations and accelerate solution convergence to the feasible region.

[0165] S55. Evaluate all individuals in the current population and find a feasible non-dominated solution set (FNDS);

[0166] Evaluate individuals in the population: Evaluate all individuals in the current population, including calculating their objective function values ​​and constraint violations. Based on this information, the feasibility and non-domination relationship of each individual can be determined. A feasible individual is one that satisfies all constraints, and a non-domination relationship is one in which one individual is no worse than another in the objective function space and is superior to another on at least one objective function.

[0167] Find the feasible non-dominated solution set (FNDS): Find the feasible non-dominated solution set (FNDS) in the population. The FNDS is the set of all feasible and non-dominated individuals in the population. These individuals represent the best solutions in the current population in terms of the objective function and the constraints. They are the most promising solutions in the optimization process and can provide direction for subsequent optimization.

[0168] S56. Select a guide individual: Generate a random number rand∈[0,1]. When rand<θ and FNDS is a non-empty set, randomly select an individual from FNDS as the guide individual. When rand<θ and FNDS is an empty set, randomly select an individual from the feasible solution archive set A as the guide individual. Otherwise, randomly select an individual from the general archive set B as the guide individual.

[0169] θ=0.5×e 0.5-fr

[0170] In the formula, fr is the fraction of feasible solutions in the population, which is the number of feasible solutions divided by the population size. This strategy for selecting guide individuals comprehensively considers the feasibility and diversity of the population, providing appropriate guidance for individual updates under different circumstances. Guide individuals play a leading role in the second-stage optimization process, providing a reference for the updates of other individuals. By selecting guide individuals from different archives, existing optimization information can be fully utilized, improving the algorithm's search efficiency and solution quality.

[0171] S57, update the position of sensitive variables using the optimal learning strategy;

[0172] x i，k (t+1)=x i，k (t)+σ×rand×(x o，k (t)-x i，k (t))

[0173]

[0174] In the formula, x i，k (t) is the value of the kth variable of the i-th individual in the t-th generation; x o，k (t) is the guiding individual X o (t) is the value of the kth variable; σ is the expansion factor; rand∈[0,1] is a random number; t is the current iteration number; T is the total iteration number; T c is the number of iterations at the end of the first phase. This update method effectively leverages the excellent characteristics of the guiding individuals, guiding the sensitive variables toward more optimal regions. Updating the positions of sensitive variables improves the feasibility of the population and the quality of the solution. By learning from the guiding individuals, sensitive variables can be more quickly adjusted to positions that are more conducive to satisfying constraints and optimizing the objective, thereby accelerating the population's convergence.

[0175] S58. Use the DE operator to update the position of the insensitive variable. During the iteration, you can choose the DE / rand / 1 or DE / current-to-best / 1 strategy update, with a probability of 50% each;

[0176] x i，k (t+1)=x i，k (t)+F×(x r1，k (t)-x r2，k (t))

[0177] x i，k (t+1)=x i，k (t)+rand×(xbest，k (t)-x r1，k (t))+F×(x r2，k (t)-x r3，k (t))

[0178] In the formula, x best，k (t) represents k variables randomly selected from the population as non-dominated individuals; r1, r2, and r1 are three individuals randomly selected from the population with r1 ≠ r2 ≠ r3 ≠ i; rand ∈ [0, 1] is a random number; and F is a scaling factor. This update method fully utilizes information in the population and effectively explores and exploits insensitive variables. Updating the positions of insensitive variables maintains population diversity and prevents premature convergence to local optimal solutions. By appropriately updating insensitive variables, a certain level of exploration capability can be retained during the optimization process, increasing the chances of finding a global optimal solution.

[0179] S59, conduct local search for relevant sensitive variables and adjust their positions to improve the feasibility and diversity of the population;

[0180] x i，k1 (t+1)=x i，k1 (t)+rand×(x o，k1 (t)-x i，k1 (t))

[0181] x i，k2 (t+1)=x i，k2 (t)+(1-rand)×(x o，k2 (t)-x i，k2 (t))

[0182] Here, k1 and k2 represent a pair of interrelated sensitive variables. Local search can further improve the optimization accuracy of sensitive variables, bringing the solution closer to the true constrained Pareto front. At the same time, local search can increase the diversity of the population to a certain extent, preventing the population from being overly concentrated in a certain local area, thereby improving the algorithm's global search capability.

[0183] S510. The solutions before and after the update are compared using the constraint dominance principle. The superior solution is retained, generating offspring population 0. The constraint dominance principle effectively balances the relationship between optimizing the objective function and satisfying the constraints during the optimization process. By retaining the superior solution, the population is ensured to continuously evolve toward a more optimal solution set while satisfying the constraints, thereby improving the feasibility and practicality of the solution.

[0184] S511. Use the SPEA2 method to perform environmental selection on P, O2, A, and B, and update population P. Use the SPEA2 method to perform environmental selection on the current population P, the offspring population O, and the archived sets A and B, and update population P. Similar to the first stage, the SPEA2 method calculates individual fitness values ​​and selects individuals with higher fitness values ​​from all individuals to form the new population P. During the environmental selection process, the fitness calculation fully considers factors such as the individual's objective function value, the degree of constraint violation, and the diversity of the population.

[0185] The role of environmental selection: The purpose of environmental selection is to further improve the quality of the population while maintaining population diversity. By selecting individuals with higher fitness values, we can retain those solutions that perform well in terms of the objective function and constraints, while eliminating some inferior solutions, thereby guiding the population to evolve towards a more optimal solution set.

[0186] P = environmental selection (P + O1 + A + B)

[0187] S512. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening on these feasible solutions, and update the feasible solution archive set A. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening on these feasible solutions, and update the archive set A. The updated archive set A contains the optimal feasible solutions found in the current optimization process. These solutions represent the best approximation to the constrained Pareto front.

[0188] S513. Ignore the constraints from the new population P, perform non-dominated sorting and crowding distance screening on the new population, and update the general archive set B. Ignore the constraints from the new population P, perform non-dominated sorting and crowding distance screening on all solutions, and update the archive set B. The updated archive set B contains the optimal solutions when the constraints are not considered. These solutions can provide more search directions for the algorithm and help discover some potential feasible solutions.

[0189] S514. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the feasible solution archive set A as the optimization solution for the hydraulic transition process; otherwise, increase the number of iterations t by 1 and return to step S41. The basis for determining the termination condition: Determine whether the number of iterations has reached the total number of iterations T. If the current number of iterations t≥T, it means that the algorithm has completed the predetermined number of iterations and met the termination condition. At this time, select a set of optimal feasible and non-dominated solutions from the archive set A as the optimization solution for the hydraulic transition process; otherwise, increase the number of iterations by 1 and return to continue executing the optimization step.

[0190] The purpose of the termination condition is to control the algorithm's runtime and ensure that the algorithm completes the optimization task within a limited time. By properly setting the total number of iterations, a balance can be achieved between ensuring the quality of the solution and the computational cost.

[0191] Preferably, in step S1, when constructing the hydraulic transition process calculation model, the water hammer control equation of the pipeline system is established by the characteristic line method, and the model construction is completed in combination with the pump and valve boundary conditions. The model serves as an external program, and the coupling between the two is achieved by constraining sensitive variables to dominate the two-stage collaborative multi-objective evolutionary algorithm main program to call the external program.

[0192] Preferably, in step S5, when performing a local search on the relevant sensitive variables, specifically, the positions of a pair of sensitive variables that have an associated relationship are adjusted, so as to improve the feasibility and diversity of the population.

[0193] Preferably, in step S6, when selecting the optimal solution from the feasible solution archive set A, the non-dominated level and the congestion distance of the solution are comprehensively considered, and the solution with a high non-dominated level and a large congestion distance is preferentially selected as the final hydraulic transition process optimization solution.

[0194] 1. Method for selecting the optimal solution

[0195] After the termination conditions are met, a set of optimal feasible and non-dominated solutions is selected from the feasible solution archive set A as the optimization scheme for the hydraulic transition process. The method for selecting the optimal solution can be based on indicators such as the solution's non-dominated level and congestion distance. First, the solutions in archive set A are non-dominated and sorted to obtain solution sets with different non-dominated levels. Then, the solutions in each non-dominated level are sorted from large to small according to the congestion distance, and the solutions with high non-dominated levels and large congestion distances are selected as the final optimization scheme. This selection method ensures that the selected solutions have good distribution and representativeness in the objective function space, which can meet the diverse needs of actual engineering.

[0196] 2. The significance of choosing the optimal solution

[0197] The resulting hydraulic transition optimization scheme strikes a balance between multiple objectives (such as minimizing maximum system pressure, minimizing system negative pressure, minimizing relative reverse speed of pumping station units, and minimizing total valve closing time), while simultaneously satisfying all constraints (such as pressure limits, flow limits, and equipment operating conditions). These optimization schemes provide a scientific basis for decision-making in the safe and reliable operation of water conservancy project facilities, helping to extend their service life, improve operational efficiency, reduce maintenance costs, and avoid accidents such as pipe ruptures and equipment damage caused by water hammer. These optimization schemes are of great practical significance for ensuring the normal operation and economic benefits of water conservancy projects.

[0198] Example

[0199] 1. Background and Requirements

[0200] At a pump station in a large urban water supply system, fluctuating water demand caused frequent pump starts and stops, leading to frequent water hammer. These dramatic pressure fluctuations in the piping system not only caused leaks at pipe connections but also increased vibration in the pump units, resulting in increasing equipment repair costs year by year. To ensure a safe and stable urban water supply, optimizing and adjusting water hammer protection parameters was urgently necessary to mitigate the adverse effects of water hammer.

[0201] II. Implementation process (I) Construction of hydraulic transition process calculation model

[0202] The characteristic curve method was used to establish the water hammer control equations for the pump station's piping system. Incorporating the actual operating characteristics of equipment such as pumps and valves as boundary conditions, a precise hydraulic transient process calculation model was constructed. This model simulates the temporal evolution of pressure and flow within the pipeline under different operating conditions of the pump unit, providing basic simulation support for subsequent optimization.

[0203] (II) Integration of the Constrained-Sensitive Variable-Dominated Two-Stage Collaborative Multi-Objective Evolutionary Algorithm: The hydraulic transition process calculation model constructed above is seamlessly integrated into the Constrained-Sensitive Variable-Dominated Two-Stage Collaborative Multi-Objective Evolutionary Algorithm (CV-TCMOEA) framework as an external program. The two interact through a data interface. The main algorithm program sends decision variables (such as the quick closing time of the valve after the pump, the quick closing angle, the total valve closing time, etc.) to the model, and the model feedbacks the corresponding objective function values ​​(maximum system pressure value, negative pressure value, relative reverse speed of the pump station unit, total valve closing time) and whether the constraint conditions are satisfied.

[0204] (3) Monte Carlo sampling for constraint-dominated analysis

[0205] Using Monte Carlo sampling techniques within the variable space, 1,000 sample points were randomly generated. The satisfaction ratio for each of the various constraints in the water supply system, such as the maximum pipe pressure limit, minimum operating pressure requirement, and the permissible speed range of the pump units, was calculated. Statistical analysis revealed that the satisfaction ratio for the maximum pipe pressure constraint was far below average, making it accurately identified as the dominant constraint variable.

[0206] (4) Algorithm initialization

[0207] The CV-TCMOEA algorithm parameters were initialized according to the established strategy: the population size was set to 100, the initial value of the current iteration was 1, the total number of iterations was planned to be 200, and the size of the external archive sets A and B was set to 50. The polynomial mutation probability was set to 1 / 3 (the decision variable dimension was 3), the distribution exponents of both crossover and mutation were set to 20, the crossover probability was set to 1, the initial value of the scaling factor was 0.5, and the initial range of the expansion factor was set to [0.1, 0.5]. Furthermore, the feasible solution archive set A and the general archive set B were initialized to empty sets. An initial population P of 100 individuals was randomly generated near the feasible region that met the basic operational requirements of the water supply system.

[0208] (V) First-stage strategy iteration optimization

[0209] The population enters the first phase of the iterative optimization process. In each iteration, the differential evolution (DE) operator and polynomial mutation operation are used to generate an offspring population with exploration capabilities. Subsequently, with the help of the SPEA2 method, the objective function value and constraints are comprehensively considered, and environmental selection is performed on the current population P, the offspring population O, and the archive sets A and B, updating the new generation population P. At the same time, feasible solutions are screened from the updated population and, after screening by non-dominated sorting and crowding distance, archive set A is refreshed. Constraints are ignored, and the population is screened only from the perspective of the objective function, and archive set B is updated. The convergence status of the solution set is continuously monitored during the iteration process. Based on the set stage transition condition (the solution set approaches the dominant constraint Pareto front), after completing 80 iterations, the stage transition condition is determined to be met, and a smooth transition to the second phase of optimization is achieved.

[0210] (6) Second-stage optimization strategy

[0211] The second phase begins, deeply optimizing the population using a variable-type-guided cooperative individual update strategy based on the previously identified constraint-sensitive variables. First, the relatively optimal individual is randomly selected from population P as a guide individual. Next, the individual decision variables are sequentially updated to generate new solutions, and the average constraint violation level of the new solutions is calculated to accurately locate the constraint-sensitive variables. In subsequent iterations, guide individuals are flexibly selected from the feasible non-dominated solution set (FNDS), archive set A, or B, based on the proportion of feasible solutions in the population. An optimal learning strategy is used to optimize the positions of sensitive variables, while the DE operator is used to update the positions of insensitive variables. Local searches are interspersed to enhance the optimization accuracy of sensitive variables. After each iteration, superior solutions are selected using the constraint dominance principle to form the offspring population O. The SPEA2 method is then used again to update population P and archive sets A and B. Finally, after 200 iterations, a set of optimal feasible non-dominated solutions is carefully selected from archive set A using the non-dominated level and congestion distance screening principles to serve as the optimization solution for the pumping station's hydraulic transition process.

[0212] 3. Implementation Results

[0213] (1) Optimize the presentation of results

[0214] The optimized hydraulic transition process of the pump station demonstrated significant advantages: the system's maximum pressure was reduced by 28% compared to the pre-optimization period, effectively mitigating pressure shocks in the pipeline and reducing the risk of leakage. The system's negative pressure dropped by 35%, reducing the likelihood of air pockets in the pipeline and ensuring water supply continuity. The relative reverse speed of the pump station units was reduced by 19%, reducing vibration and wear of the pump units and extending equipment life. The total valve closing time was shortened by 22%, improving the flexibility and responsiveness of the pump station's operational adjustments. The resulting optimization solution achieved a good balance across multiple key performance indicators, comprehensively improving the hydraulic transition performance of the pump station.

[0215] In summary, the beneficial effects of the present invention are:

[0216] 1. Improve optimization efficiency

[0217] By introducing a dominant constraint analysis method, this paper accurately identifies the dominant constraint variables that are critical to solving the problem at the initial optimization stage. This allows the algorithm to focus computing resources on addressing these key constraints, rather than distributing resources evenly across all constraints. This strategy of focusing on key issues significantly improves the efficiency of the optimization process, avoids inefficient computation on non-critical constraints, and shortens the optimization cycle.

[0218] 2. Avoid Waste of Resources

[0219] Given the varying difficulty levels of different constraints in optimization problems, existing methods often neglect these differences, leading to wasted computing resources. This invention addresses this shortcoming by analyzing the dominant constraints and precisely directing resources to the constraints that are most difficult to satisfy and have the greatest impact on the results. This significantly improves resource utilization from algorithm startup to convergence, avoiding wasting excessive computing power on insignificant constraints.

[0220] 3. Enhancing population adaptability and diversity

[0221] Another highlight of this invention is the individual selection mechanism based on population state. This mechanism dynamically and flexibly selects individuals for reproduction based on the population's current evolutionary state. This dynamic selection process overcomes the limitations of traditional fixed selection strategies and effectively avoids the dilemma of premature convergence of the population to a local optimal solution. By continuously introducing diverse individuals, the population remains dynamic during the evolutionary process, enabling extensive exploration of the solution space. This enhances the algorithm's adaptability to various complex optimization problems and broadens the scope of the solution set.

[0222] 4. Accelerate convergence and ensure solution quality

[0223] The present invention integrates the constraint-sensitive variable identification technology and the accompanying collaborative individual update strategy based on variable types. The two work together to achieve precise positioning and directional optimization of constraint-sensitive variables. During the optimization process, sensitive variables are given special attention and refined adjustments, while non-sensitive variables maintain the overall feasibility and diversity of the solution through collaborative update strategies. This optimization method with a clear division of labor accelerates the convergence speed of the population to the constrained Pareto front, ensuring that the final solution set not only performs well in the objective function, but also has high feasibility in terms of the degree of constraint satisfaction, greatly improving the overall quality of the solution set. 5. Comprehensive optimization of water conservancy project facility performance

[0224] Focusing on optimizing the hydraulic transition process, the present invention addresses multiple key performance indicators, including minimizing the system's maximum pressure, minimizing the system's negative pressure, reducing the relative reverse speed of the pump station units, and shortening the total valve closing time. By collaboratively optimizing these objectives, the rapid pressure fluctuations caused by the water hammer effect can be effectively suppressed. This not only reduces the risk of pipeline rupture and equipment damage, but also significantly enhances the safety and stability of the operation of water conservancy project facilities. At the same time, optimized operating parameters such as valve closing time help improve the overall operating efficiency of the facility, extend the service life of the equipment, reduce maintenance costs, and provide a solid guarantee for the long-term and reliable operation of water conservancy project facilities.

Claims

1. A two-stage hydraulic transition process optimization method based on constraint sensitive variables, characterized in that: The following steps are involved: S1. Construct a hydraulic transition process calculation model and integrate it into a two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables; S2. Perform constraint-dominant analysis based on Monte Carlo sampling to determine the dominant constraint variables; S3, initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by the constraint sensitive variables, the feasible solution archive set A and the general archive set B, and randomly generate the initialization population P; S4, the population performs iterative optimization of the first-stage strategy until the stage transition conditions are met; S5. Enter the second stage optimization strategy: Based on the constraint sensitive variable identification results, the population is iteratively optimized using the variable type guided cooperative individual update strategy; S6. After the termination condition is met, a set of optimal feasible and non-dominated solutions is selected from the feasible solution archive set A as the hydraulic transition process optimization solution.

2. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: The step S2 specifically includes: S21. Use the Monte Carlo sampling method to randomly generate a certain number of sample points in the variable space; S22. Calculate the proportion of sample points that meet each constraint, denoted as r k , k=1,2,…,q, and all r k The average value of is denoted as ave(r); In the formula, q is the total number of constraints; S23. Determine the dominant constraint variable: For each constraint k, if it satisfies the ratio r k is less than ave(r)-τ1, then the constraint is identified as the dominant constraint; 3. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: The specific contents of step S3 include: S31. Initialize the parameters of the two-stage collaborative multi-objective evolutionary algorithm dominated by constraint-sensitive variables, including: population size N, current iteration number t, total iteration number T, external archive set size N / 2, polynomial mutation probability 1 / D; crossover and mutation distribution index R, crossover probability C r , scaling factor F and expansion factor σ, whose values ​​are dynamically adjusted with the number of iterations to control the update step size of sensitive variables and balance the exploration and development capabilities of the algorithm; S32, initializing the feasible solution archive set A and the general archive set B to empty sets; A＝[] B＝[] S33, randomly generate an initialization population P of size N; Objective function: F(x) = [f1(x), f2(x), f3(x), f4(x)] T Constraint: x∈Ω Decision variable constraints: Target value constraint: In the formula, Ω is the decision space; F(x) is the objective function, where f1(x) is the minimum system maximum pressure value, f2(x) is the minimum system negative pressure value, f3(x) is the lowest relative reverse speed of the pump station unit, and f4(x) is the shortest total valve closing time; x = [x1, x2, x3] is a solution in Ω, x1 is the quick closing time of the pump valve, x2 is the quick closing angle of the pump valve, and x3 is the total closing time of the pump valve; t min The shortest time the valve after the pump can be operated; t max The maximum time the valve after the pump can be operated; H 额 is the rated pressure value of the pump unit outlet; n r is the rated speed of the water pump unit; S34. Initialize the solution of the population to ensure that the solution is in the feasible region or close to the feasible region.

4. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: The step S4 specifically includes: S41, judging whether the stage transition condition is met: whether the solution set has converged to the Pareto front of the dominant constraint or the Pareto front of the non-dominant constraint for solving the problem; if so, executing S5; otherwise, executing S42; S42, using differential evolution (DE) operator and polynomial mutation to generate offspring population O1; O1=DE(P)+polynomial mutation S43, use SPEA2 method to perform environmental selection on P, O1, A and B, and update population P; P = environmental selection (P + O1 + A + B) S44. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening, and update the archive set A; S45, ignoring the constraints from the new population P, performing non-dominated sorting and crowding distance screening, and updating the archive set B; S46. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the archive set A as the optimization scheme for the hydraulic transition process; otherwise, add 1 to the number of iterations t and return to step S41.

5. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: The step S5 specifically includes: S51. Randomly select a relatively optimal individual X from the population P = (x1, x2, ..., x D ); S52, update each decision variable of individual X in turn, and generate a new solution X′=(x1,…,x′ i …,x D ); In the formula, i=1:D; j=1:NA / D; rand∈[0,1]; D is the decision variable dimension; NA is the total number of sampling times; is the upper bound of the i-th decision variable; is the lower bound of the i-th decision variable; S53. Calculate the average constraint violation degree ICV of the new solution X′ i ; cv i (X′)=max(0,g i (X′)),i=1,…,p In the formula, cv i (X′) is the degree of violation of the i-th constraint in the solution; g i (X′) is the inequality constraint; p is the total number of constraints; cv k (X′) is the normalized value to ensure that the weights of each constraint are consistent; S54, when ICV i >(1+τ2)AICV, the decision variable is identified as a constraint-sensitive variable, where τ2 is the threshold for distinguishing constraint-sensitive variables from constraint-insensitive variables and is set to τ2=1 / (10D); S55. Evaluate all individuals in the current population and find a feasible non-dominated solution set (FNDS); S56. Select a guide individual: Generate a random number rand∈[0,1]. When rand<θ and FNDS is a non-empty set, randomly select an individual from FNDS as the guide individual. When rand<θ and FNDS is an empty set, randomly select an individual from the feasible solution archive set A as the guide individual. Otherwise, randomly select an individual from the general archive set B as the guide individual. θ=0.5×e 0.5-fr In the formula, fr is the proportion of feasible solutions in the population, that is, the number of feasible solutions divided by the population size; S57, update the position of sensitive variables using the optimal learning strategy; x i,k (t+1)=x i,k (t)+σ×rand×(x o,k (t)-x i,k (t)) In the formula, x i,k (t) is the value of the kth variable of the i-th individual in the t-th generation; x o,k (t) is the guiding individual X o (t) is the value of the kth variable; σ is the expansion factor; rand∈[0,1] is a random number; t is the current iteration number; T is the total iteration number; T c is the number of iterations at the end of the first phase; S58. Use the DE operator to update the position of the insensitive variable. During the iteration, you can choose the DE / rand / 1 or DE / current-to-best / 1 strategy update, with a probability of 50% for each; x i,k (t+1)=x i,k (t)+F×(x r1,k (t)-x r2,k (t)) x i,k (t+1)=x i,k (t)+rand×(x best,k (t)-x r1,k (t))+F×(x r2,k (t)-x r3,k (t)) In the formula, x best,k (t) is the k variable of non-dominated individuals randomly selected from the population; r1, r2, r1 are three individuals randomly selected from the population with r1≠r2≠r3≠i; rand∈[0,1] is a random number; F is the scaling factor; S59, conduct local search for relevant sensitive variables and adjust their positions to improve the feasibility and diversity of the population; x i,k1 (t+1)=x i,k1 (t)+rand×(x o,k1 (t)-x i,k1 (t)) x i,k2 (t+1)=x i,k2 (t)+(1-rand)×(x o,k2 (t)-x i,k2 (t)) Among them, k1 and k2 represent a pair of correlated sensitive variables; S510, comparing the solutions before and after the update through the constraint dominance principle, retaining the superior solution, that is, generating the offspring population O; S511, use SPEA2 method to select P, O2, A and B, and update population P; P = environmental selection (P + O1 + A + B) S512. Filter feasible solutions from the new population P, perform non-dominated sorting and crowding distance screening, and update the feasible solution archive set A; S513, ignoring the constraints from the new population P, performing non-dominated sorting and crowding distance screening, and updating the general archive set B; S514. Determine whether the termination condition is met: the number of iterations t>T. If so, select a set of optimal feasible and non-dominated solutions from the feasible solution archive set A as the optimization scheme for the hydraulic transition process; otherwise, add 1 to the number of iterations t and return to step S41.

6. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: In step S1, when constructing the hydraulic transition process calculation model, the water hammer control equation of the pipeline system is established through the characteristic line method, and the model construction is completed in combination with the pump and valve boundary conditions. The model is used as an external program, and the coupling between the two is achieved by constraining sensitive variables to dominate the two-stage collaborative multi-objective evolutionary algorithm main program to call the external program.

7. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: In step S5, when performing a local search on the relevant sensitive variables, specifically, the positions of a pair of sensitive variables that have an associated relationship are adjusted, so as to improve the feasibility and diversity of the population.

8. The hydraulic transition process optimization method based on two-stage constraint-sensitive variable dominance according to claim 1 is characterized in that: In step S6, when selecting the optimal solution from the feasible solution archive set A, the non-dominated level and the congestion distance of the solution are comprehensively considered, and the solution with a high non-dominated level and a large congestion distance is preferentially selected as the final hydraulic transition process optimization solution.

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