Urban drainage system design optimization method and device, electronic equipment and storage medium

Abstract

This application relates to the field of artificial intelligence and provides a method, apparatus, electronic device, and storage medium for optimizing the design of urban drainage systems. The method includes: constructing an objective function based on multiple decision variables and optimization objectives of the urban drainage system design; generating an initial population based on constraints and dividing the initial population into multiple subpopulations; iteratively executing the following steps until the iteration termination condition is met, and outputting the optimal solution: if in the convergent evolution stage, selecting the first parent individual from the subpopulation with the smallest convergence value, selecting the second parent individual from the current subpopulation, and generating the first new individual based on the first and second parent individuals; if in the diversity evolution stage, selecting the third parent individual from the diversity archive, selecting the fourth parent individual from the current subpopulation, and generating the second new individual based on the third and fourth parent individuals; and updating the current subpopulation. This application achieves a balance between convergence and diversity, improving optimization efficiency and quality.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a method, apparatus, electronic device, and storage medium for optimizing the design of urban drainage systems. Background Technology

[0002] Currently, most urban drainage systems implement separate treatment for sewage and rainwater. Designing a reasonable drainage system requires considering multiple factors to optimize high-dimensional multi-objective problems. Balancing these factors is a crucial issue for water resource recycling. Traditional multi-objective evolutionary algorithms, such as Many-objective Optimization Evolutionary Algorithms (MaOEAs) based on objective dimensionality reduction and those based on dominance relationships, struggle to balance convergence and diversity when solving high-dimensional optimization problems, leading to slow convergence and uneven solution distribution. Summary of the Invention

[0003] This application provides a method, apparatus, electronic device, and storage medium for optimizing the design of urban drainage systems, in order to solve the technical problem that existing urban drainage system design optimization methods are difficult to balance convergence and diversity.

[0004] In a first aspect, embodiments of this application provide a method for optimizing the design of an urban drainage system, comprising: Based on multiple decision variables and multiple optimization objectives in urban drainage system design, an objective function is constructed, and the constraints of the decision variables are determined. The multiple optimization objectives include cost minimization and flood economic loss minimization. Based on the constraints of the decision variables, an initial population containing multiple initial design schemes is generated, the initial population is divided into multiple subpopulations, a diversity profile is initialized, and the multiple decision variables are divided into convergence-related variables and diversity-related variables. Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: If it is determined that the current subpopulation is in the first evolutionary stage with convergence as the goal, the first parent individual is selected from the subpopulation with the smallest convergence value, and the second parent individual is selected from the current subpopulation. The convergence-related variables of the first parent individual are assigned to the second parent individual to generate the first new individual. If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, a fourth parent individual is selected from the current subpopulation, and the diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual; the diversity archive records multiple individuals containing diversity design schemes. Based on the first new individual or the second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0005] In some embodiments, dividing the initial population into multiple subpopulations includes: Generate a set of reference vectors that are uniformly distributed and cover the target space, wherein the target space is composed of the plurality of optimization objectives; Calculate the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set, wherein the target vector is calculated based on the objective function; The reference vector that has the smallest angle with the target vector is determined as the reference vector associated with each individual. Based on the associated reference vector, each individual is assigned to a corresponding subpopulation.

[0006] In some embodiments, calculating the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set includes: The target vector corresponding to each individual is normalized to obtain the normalized target vector; Calculate the angle between the normalized target vector and each of the reference vectors.

[0007] In some embodiments, classifying the plurality of decision variables into convergent-related variables and diversity-related variables includes: Multiple candidate solutions are selected from the initial population. For each decision variable of each candidate solution, multiple random perturbations are performed to obtain multiple new solutions. The objective vector of each new solution is calculated based on the objective function. For each of the decision variables, the objective vector corresponding to multiple new solutions is fitted to generate a fitted straight line representing the trend of the objective function value. Calculate the angle between the fitted line and the normal vector of the unit hyperplane in the target space, and calculate the average angle of each decision variable under all candidate solutions; the target space is composed of the plurality of optimization objectives, and the unit hyperplane is defined as the plane where the sum of the function values ​​of all optimization objectives is 1; Clustering is performed on all decision variables based on the average angle to obtain the convergent correlation variables and the diversity correlation variables, wherein the average angle corresponding to the convergent correlation variables is smaller than the average angle corresponding to the diversity correlation variables.

[0008] In some embodiments, selecting the first parent individual from the subpopulation with the smallest convergence value includes: Calculate the convergence of each individual in each subpopulation, where the convergence is the sum of the objective function values ​​of each individual on all the optimization objectives; From all individuals in each subpopulation, determine the target individual with the smallest convergence value, and use the convergence of the target individual as the representative convergence of each subpopulation. The subpopulation with the smallest value corresponding to the representative convergence is determined as the subpopulation with the smallest convergence value. Randomly select an individual from the subpopulation with the smallest convergence value as the first parent individual.

[0009] In some embodiments, updating the current subpopulation based on the first new individual or the second new individual to obtain the next generation subpopulation includes: If the current subpopulation is determined to be in the first evolutionary stage with convergence as the objective, the convergence of the original individuals and the first new individual in the current subpopulation is calculated. The convergence is the sum of the objective function values ​​of the individuals on all the optimization objectives. The individual with the smallest convergence value is retained to update the current subpopulation.

[0010] In some embodiments, updating the current subpopulation based on the first new individual or the second new individual to obtain the next generation subpopulation includes: If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, calculate the comprehensive evaluation value of the original individuals and the second new individuals in the current subpopulation, and retain the individual with the smallest comprehensive evaluation value to update the current subpopulation; The comprehensive evaluation value is calculated by weighting the projection distance of the individual's target vector onto the direction of the associated reference vector and the perpendicular distance between the individual's target vector and the associated reference vector.

[0011] In some embodiments, the decision variables include: maximum overflow rate, maximum treatment rate, and local retention; the maximum overflow rate refers to the maximum rate at which water can overflow after the water storage device is full; the maximum treatment rate refers to the maximum rate at which the treatment device can treat sewage or rainwater; and the local retention refers to the amount of water in the storage facility.

[0012] In some embodiments, the constraints include: The number of floods occurring each year is less than or equal to a preset frequency threshold; The probability that the flood depth exceeds a preset depth threshold is less than or equal to a preset probability threshold. The average weight of suspended solids in water each year is less than or equal to a preset suspended solids weight threshold. The average weight of solids deposited in water each year is less than or equal to a preset sediment weight threshold. The average annual biochemical oxygen demand in water is less than or equal to the preset oxygen demand threshold. The average annual nitrogen content in the water is less than or equal to the preset nitrogen content threshold; The average annual phosphate content in the water is less than or equal to the preset phosphate content threshold.

[0013] In some embodiments, after updating the current subpopulation based on the first new individual or the second new individual, the method further includes: The diversity profile is updated based on the first new individual or the second new individual.

[0014] In some embodiments, the method further includes: If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, all individuals recorded in the diversity archive are obtained, and a new set of reference vectors is constructed based on the target vectors of all the individuals. The original reference vector set is replaced with the new reference vector set to obtain the adjusted reference vector set. Based on the adjusted set of reference vectors, the current population is re-divided to obtain multiple updated subpopulations.

[0015] In some embodiments, the method further includes: Based on a preset stage control strategy, the current subpopulation is determined to be in either the first evolutionary stage aimed at convergence or the second evolutionary stage aimed at diversity.

[0016] Secondly, embodiments of this application provide an urban drainage system design optimization device, comprising: The problem construction module is used to construct an objective function based on multiple decision variables and multiple optimization objectives in urban drainage system design, and to determine the constraints of the decision variables. The multiple optimization objectives include cost minimization and flood economic loss minimization. An initialization module is used to generate an initial population containing multiple initial design schemes based on the constraints of the decision variables, divide the initial population into multiple subpopulations, initialize a diversity profile, and divide the multiple decision variables into convergence-related variables and diversity-related variables. The iterative solution module is used to repeatedly execute the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: If it is determined that the current subpopulation is in the first evolutionary stage with convergence as the goal, the first parent individual is selected from the subpopulation with the smallest convergence value, and the second parent individual is selected from the current subpopulation. The convergence-related variables of the first parent individual are assigned to the second parent individual to generate the first new individual. If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, a fourth parent individual is selected from the current subpopulation, and the diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual; the diversity archive records multiple individuals containing diversity design schemes. Based on the first new individual or the second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0017] Thirdly, embodiments of this application provide an electronic device, including a processor and a memory storing a computer program, wherein the processor executes the program to implement the steps of the urban drainage system design optimization method described in the first or second aspect.

[0018] Fourthly, embodiments of this application provide a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the urban drainage system design optimization method described in the first or second aspect.

[0019] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the steps of the urban drainage system design optimization method described in the first or second aspect.

[0020] The urban drainage system design optimization method, apparatus, electronic device, and storage medium provided in this application construct an objective function based on multiple decision variables and optimization objectives of the urban drainage system design; generate an initial population based on constraints, and divide the initial population into multiple sub-populations; iteratively execute the following steps until the iteration termination condition is met, and output the optimal solution: if the current sub-population is in the convergent evolution stage, select the first parent individual from the sub-population with the smallest convergence value, select the second parent individual from the current sub-population, and generate the first new individual based on the first and second parent individuals; if the current sub-population is in the diversity evolution stage, select the third parent individual from the diversity archive, select the fourth parent individual from the current sub-population, and generate the second new individual based on the third and fourth parent individuals; update the current sub-population based on the first or second new individual, achieving a balance between convergence and diversity, and improving optimization efficiency and quality. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is one of the flowcharts illustrating the urban drainage system design optimization method provided in the embodiments of this application; Figure 2 This is the second flowchart illustrating the urban drainage system design optimization method provided in the embodiments of this application; Figure 3 This is a schematic diagram of the actual solution set and the predicted solution set provided in the embodiments of this application; Figure 4 This is a schematic diagram of the urban drainage system design optimization device provided in the embodiments of this application; Figure 5 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0024] As the objective dimension increases, traditional multi-objective evolutionary algorithms encounter varying degrees of difficulties in terms of convergence and diversity when solving high-dimensional multi-objective optimization problems (MaOPs).

[0025] High-dimensional multi-objective evolutionary algorithms based on objective dimensionality reduction: This approach applies data dimensionality reduction methods to multi-objective optimization problems. By analyzing the correlation between objective functions, redundant objectives are identified and removed, thereby simplifying the problem and reducing the optimization difficulty. However, this algorithm cannot solve complex MaOPs.

[0026] High-dimensional multi-objective evolutionary algorithms based on dominance relations: This type of method designs a novel dominance relation to replace the original Pareto dominance relation, thereby solving the problem of insufficient selection pressure. This idea has been widely adopted, and a large number of new dominance relations have been proposed. However, the convergence of this algorithm is not well-suited to the diversity mechanism.

[0027] Decomposition-based high-dimensional multi-objective evolutionary algorithms decompose the objective space using a set of predefined reference vectors. Each reference vector and its controlled subspace constitute a subproblem, thus transforming the high-dimensional multi-objective optimization problem into multiple simpler multi-objective optimization problems. The algorithm utilizes a neighborhood mechanism to achieve interaction between subproblems, simultaneously optimizing multiple subproblems. However, the performance of this algorithm depends on the distribution of the reference vectors, exhibiting certain limitations.

[0028] Indicator-based high-dimensional multi-objective evolutionary algorithms use performance metrics to provide selection pressure during the optimization process, eliminating solutions that contribute the least to the metric at each iteration, and obtaining the final solution set through multiple iterations. However, most performance metrics have high computational costs, and the performance of this algorithm depends on the chosen metric.

[0029] A high-dimensional multi-objective evolutionary algorithm based on diversity improvement: This algorithm ensures a good distribution of the population by improving the diversity maintenance mechanism. However, it focuses only on improving the diversity mechanism and lacks convergence performance.

[0030] Among the methods described above, decomposition-based methods have shown great potential. Compared to other methods, their predefined reference vectors help maintain good diversity, dividing a MaOPs into multiple single-objective optimization problems or multiple multi-objective optimization problems, reducing the difficulty of solving the problem. Furthermore, the use of aggregation functions in solution evaluation, unconstrained by dominance relations, provides strong selection pressure for the population's evolution towards the Pareto front, exhibiting high flexibility. However, some unresolved issues remain in current research.

[0031] First, most decomposition-based multi-objective evolutionary algorithms for high-dimensional problems experience a significant performance degradation when faced with problems having irregular Pareto fronts. Since the reference vectors are not consistent with the distribution of the Pareto front, some reference vectors are far from the region where the Pareto front lies, and thus cannot correctly guide the population to evolve towards the Pareto front. Some studies address this issue by dynamically adjusting the reference vectors during the population evolution process, but there are still some drawbacks: (1) In the early stage of evolution, the population is far from the Pareto front and carries too little information about the Pareto front surface. The adjustment of the reference vectors may be inefficient, and the timing of the reference vector adjustment needs to be carefully considered.

[0032] (2) The reference vector self-adaptive strategy may have an impact on convergence because, during the evolution process, adjusting the reference vectors causes changes in the subproblems, and the frequent changes in the subproblems slow down the overall convergence rate of the population.

[0033] Second, most decomposition-based multi-objective evolutionary algorithms only modify or propose new environmental selection strategies, without considering that the selection of parent individuals used to generate sub-solutions also affects the convergence and diversity of the algorithms.

[0034] Therefore, the embodiments of this application provide an urban drainage system design optimization method, device, electronic device, and storage medium. By constructing an objective function based on multiple decision variables and multiple optimization objectives of urban drainage system design; generating an initial population based on the constraint conditions and dividing the initial population into multiple sub-populations; and repeatedly executing the following steps until the iteration termination condition is satisfied and outputting the optimal solution: If the current sub-population is in the convergence evolution stage, select a first parent individual from the sub-population with the smallest convergence degree value, select a second parent individual from the current sub-population, and generate a first new individual based on the first and second parent individuals; if the current sub-population is in the diversity evolution stage, select a third parent individual from the diversity archive, select a fourth parent individual from the current sub-population, and generate a second new individual based on the third and fourth parent individuals; update the current sub-population based on the first new individual or the second new individual. The embodiments of this application can achieve a balance between convergence and diversity and improve the optimization efficiency and quality.

[0035] Figure 1 One of the flow schematic diagrams of the urban drainage system design optimization method provided by the embodiments of this application. Refer to Figure 1 , the embodiments of this application provide an urban drainage system design optimization method, which may include: Step 110: Construct an objective function based on multiple decision variables and multiple optimization objectives of urban drainage system design, determine the constraint conditions of the decision variables, and the multiple optimization objectives include cost minimization and minimum flood economic loss; Optionally, the optimization objectives include, but are not limited to: minimizing drainage network costs, minimizing storage facility costs, minimizing treatment facility costs, minimizing anticipated flood damage costs, and minimizing anticipated flood economic losses. Drainage network costs refer to the cost of constructing drainage network facilities; storage facility costs refer to the cost of water resource storage facilities; treatment facility costs refer to the cost of treating urban sewage and natural precipitation; anticipated flood damage costs refer to the repair costs required if facilities are damaged after a flood; and anticipated flood economic losses refer to other economic losses caused by floods.

[0036] In some embodiments, multiple decision variables include: maximum overflow rate, maximum treatment rate, and local retention; maximum overflow rate refers to the maximum rate at which water can overflow after the water storage device is full; maximum treatment rate refers to the maximum rate at which the treatment device can treat sewage or rainwater; and local retention refers to the amount of water in the storage facility.

[0037] Optionally, the objective function for each optimization objective is calculated using the following formula: ; in, Indicates the cost of the drainage network. Indicates the cost of storage facilities. Indicates the cost of processing facilities. This indicates the expected cost of flood damage. This indicates the expected economic losses from flooding, that is, the anticipated economic losses caused by flooding. Indicates the amount of localized retention. Indicates the maximum processing rate. Indicates the maximum overflow rate. , , .

[0038] In some embodiments, the constraints include: The number of floods occurring each year is less than or equal to a preset frequency threshold; The probability that the flood depth exceeds a preset depth threshold is less than or equal to a preset probability threshold. The average weight of suspended solids in water each year is less than or equal to a preset suspended solids weight threshold. The average weight of solids deposited in the water each year is less than or equal to a preset sediment weight threshold. The average annual biochemical oxygen demand in water is less than or equal to the preset oxygen demand threshold. The average annual nitrogen content in the water is less than or equal to the preset nitrogen content threshold. The average annual phosphate content in the water is less than or equal to the preset phosphate content threshold.

[0039] Alternatively, the expression for the constraint condition is as follows: ; in, Indicates the number of floods that occur each year. This indicates the probability that the flood depth exceeds a preset depth threshold, which can be 1 inch. This represents the average weight of suspended solids in water each year. This represents the average weight of solids deposited in water each year. This represents the average annual biochemical oxygen demand (BOD) in water. This indicates the average nitrogen content in water each year. This indicates the average annual phosphate content in water.

[0040] Optionally, the expression for the above constraints can be processed to obtain the following formula: ; ; Alternatively, the final objective function can be: ; in, This represents the sum of all constraint violations. This indicates the amount of violation related to the constraint on the number of times floods occur each year. This represents the violation quantity associated with the probability constraint that the flood depth exceeds a preset depth threshold. This represents the amount of violation associated with the annual average weight constraint of suspended solids in water. This represents the amount of violation associated with the average weight constraint of solids deposited in water each year. This indicates the amount of violations related to the annual average biochemical oxygen demand (BOD) limit in water. This indicates the amount of violations related to the annual average nitrogen content constraint in water. This indicates the amount of violations associated with the annual average phosphate content constraint in water.

[0041] Step 120: Based on the constraints of the decision variables, generate an initial population containing multiple initial design schemes, divide the initial population into multiple subpopulations, initialize the diversity profile, and divide the multiple decision variables into convergence-related variables and diversity-related variables. Among them, convergence-related variables refer to decision variables that have a direct and significant impact on the objective function value. Changing the value of convergence-related variables will cause the position of the solution in the objective space to move significantly toward or away from the ideal point. Diversity-related variables mainly affect the distribution position of the solution on the Pareto front, while having a relatively small impact on the overall convergence of the solution. Changing the value of diversity-related variables is more likely to cause the solution to move along the Pareto front.

[0042] Optionally, random initialization can be used to generate Individuals as the initial population Specifically, for a problem with n decision variables, the solution... The Decision variables The calculation formula is as follows: ; in, Indicates the first The lower bound of the values ​​of each decision variable. Indicates the first The upper bound of the values ​​of each decision variable. This represents a random number in the interval [0, 1].

[0043] Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: Step 130: If it is determined that the current subpopulation is in the first evolutionary stage with convergence as the goal, select the first parent individual from the subpopulation with the smallest convergence value, select the second parent individual from the current subpopulation, and assign the convergence-related variables of the first parent individual to the second parent individual to generate the first new individual. In some embodiments, the method further includes: Based on the preset stage control strategy, determine whether the current subpopulation is in the first evolutionary stage aimed at convergence or the second evolutionary stage aimed at diversity.

[0044] It should be noted that phase control is divided into two levels: individual phase judgment of subpopulation and overall phase judgment of population.

[0045] Optionally, the standard deviation of the fitness values ​​of the current subpopulation and the previous N generations of subpopulations is calculated. If the standard deviation is greater than or equal to a preset threshold, the current subpopulation is determined to be in the first evolutionary stage with convergence as the goal. If the standard deviation is less than the preset threshold, the current subpopulation is determined to be in the second evolutionary stage with diversity as the goal.

[0046] Optionally, the evolutionary stage of the current population as a whole is determined by the stage status of all current subpopulations. When a sufficient number of current subpopulations enter the second evolutionary stage, the entire population enters the second evolutionary stage. The number of subpopulations entering the second evolutionary stage is counted; if a threshold is reached, the entire population enters the second evolutionary stage, and all subpopulations are forced to enter the second evolutionary stage.

[0047] In some embodiments, selecting the first parent individual from the subpopulation with the smallest convergence value includes: Calculate the convergence of each individual in each subpopulation. The convergence is the sum of the objective function values ​​of each individual across all optimization objectives. From all individuals in each subpopulation, identify the target individual with the smallest convergence value, and use the convergence of the target individual as the representative convergence of each subpopulation. The subpopulation with the smallest value representing the convergence is identified as the subpopulation with the smallest convergence value. Randomly select an individual from the subpopulation with the smallest convergence value to serve as the first parent individual.

[0048] For subpopulations in the first evolutionary stage, search resources should be primarily allocated to convergence. Therefore, during the mating selection phase, individuals with better convergence should be given more opportunities to participate in the generation of sub-solutions. The goal is to generate the expected solution for each subpopulation by traversing all subpopulations.

[0049] If a solution exists in a subpopulation, and if some subpopulations in the current population have already converged, then randomly select a solution from those converged subpopulations. As the first parent individual, it then selects the solution with the smallest angle to the reference vector in the current subpopulation. As a second-generation individual, and will The convergence-related variables are assigned to This generates a sub-solution, namely the first new individual. At this point, because the first new individual has obtained... The convergence-related variables, therefore, their performance in convergence is similar to... Similar to, in terms of diversity Similar, this is equivalent to helping The accelerated convergence of the subpopulation speeds up the overall evolution of the population. To preserve the algorithm's ability to explore unknown regions and prevent the population from getting trapped in local optima, this process has a 50% chance of occurring. If no subpopulation converges in the current population, a binary tournament selection algorithm is used to select the first parent individual from the current population based on the convergence degree of each solution. Then, a second parent individual is randomly selected from the current subpopulation. Sub-solutions are generated using the Simulated Binary Crossover (SBX) operator and the Polynomial Mutation (PM) operator. The solution... convergence The formula for calculating is defined as the sum of the objective function values, as shown below: ; in, M It refers to the number of optimization targets.

[0050] If no solution exists in the subpopulation, a convergence-based binary tournament selection algorithm is used to obtain two parent individuals from the current population. Since the offspring generated by SBX have a higher probability of approximating their parents, SBX performs well in local search. When a parent with better convergence is selected, the convergence performance of its generated sub-solutions will also be close to that of its parent. Two solutions are generated using the SBX operator and the PM operator, and one of these two solutions is randomly selected as the sub-solution of the parent.

[0051] Step 140: If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, select the third parent individual from the diversity file and the fourth parent individual from the current subpopulation. Assign the diversity-related variables of the third parent individual to the fourth parent individual to generate the second new individual. The diversity file records multiple individuals containing diversity design schemes. For a subpopulation in the second stage of evolution, if a solution exists in the subpopulation, then any one of those solutions is selected. Otherwise, a solution is randomly selected, and the decision variables for that solution are recorded. If the global evolution of the population is in the first evolutionary stage, a binary tournament selection algorithm based on crowding distance is used to select two solutions from the population, and the SBX and PM operators are applied to them to generate new solutions. Furthermore, during evolution, a diversity archive is maintained to preserve solutions with good diversity performance as candidate individuals. At this point, there is a 50% probability that a solution from the diversity archive will be used to perform the aforementioned operations, thus accelerating the rate of population diversification. Then, the new solution... The diversity-related variables are applied to the parent solution to obtain the final child solution, i.e., the second new individual. In this way, the child solution will simultaneously possess the characteristics of the parent solution. Convergence and new solutions The diversity is significant. Because diversity information was collected in advance in the diversity archive, the population can quickly cover the Pareto frontier.

[0052] Step 150: Based on the first new individual or the second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0053] Optionally, the fitness value of the first new individual or the fitness value of the second new individual is calculated, and the current subpopulation is updated based on the fitness value of the first new individual or the fitness value of the second new individual.

[0054] In some embodiments, after updating the current subpopulation based on the first new individual or the second new individual, the method further includes: Update the diversity profile based on the first or second new individual.

[0055] Optionally, the newly generated individuals, i.e., the first new individual or the second new individual, are merged with the existing individuals in the diversity archive. The crowding distance of all solutions in the merged set is calculated, and the top K solutions with the largest crowding distances are selected from the merged set to form a new diversity archive.

[0056] In this embodiment of the invention, an objective function is constructed based on multiple decision variables and multiple optimization objectives in urban drainage system design; an initial population is generated based on constraints, and the initial population is divided into multiple subpopulations; the following steps are executed iteratively until the iteration termination condition is met, and the optimal solution is output: if the current subpopulation is in the convergent evolution stage, the first parent individual is selected from the subpopulation with the smallest convergence value, and the second parent individual is selected from the current subpopulation; a first new individual is generated based on the first and second parent individuals; if the current subpopulation is in the diversity evolution stage, the third parent individual is selected from the diversity archive, and the fourth parent individual is selected from the current subpopulation; a second new individual is generated based on the third and fourth parent individuals; the current subpopulation is updated based on the first or second new individual, thus achieving a balance between convergence and diversity, and improving optimization efficiency and quality.

[0057] In some embodiments, step 120, dividing the initial population into multiple subpopulations, includes: Step 121: Generate a set of reference vectors that are uniformly distributed and cover the target space, which consists of multiple optimization objectives.

[0058] The objective space refers to the multidimensional space comprised of all objective function values ​​of the problem to be optimized. For example, for a problem with M optimization objectives, its objective space is an M-dimensional space. The ultimate goal of algorithm evolution is to find a solution set such that the set of points corresponding to this solution set in the objective space approximates and uniformly covers the true Pareto front of the problem as closely as possible.

[0059] Here, the reference vectors are a set of predefined direction vectors in the target space. Each reference vector defines a sub-optimization problem, and the algorithm approximates the entire Pareto front by optimizing these sub-problems. The reference vectors provide the algorithm with uniform search directions, guiding the population to find a uniformly distributed set of optimal solutions.

[0060] Step 122: Calculate the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set. The target vector is calculated based on the objective function.

[0061] For population Each solution in The formula for calculating the target value is as follows: ; in, Representing the solution The The objective value of an objective function after being zeroed out. Representing the solution The The objective function value, The first point representing the ideal point The values ​​of each dimension.

[0062] Optionally, the extreme points corresponding to each coordinate axis are calculated, and a hyperplane is constructed using these extreme points. The formula for calculating the extreme points is as follows: ; in, Indicates the first The values ​​of the extreme points corresponding to each coordinate axis Indicates the first Reference vectors along each coordinate axis. ASF This indicates that a scalarization function is achieved, which is used to measure the solution. Given a reference vector A function of performance or cost in the direction. Indicates the first Reference vectors.

[0063] In some embodiments, calculating the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set includes: The target vector corresponding to each individual is normalized to obtain the normalized target vector; Calculate the angle between the normalized target vector and each reference vector.

[0064] Optionally, the intercepts on each coordinate axis are calculated based on the constructed hyperplane. Then the objective value of each solution in the population can be normalized as: ; in, This represents the target value after normalization.

[0065] For the solution in the population , and the reference vector The formula for calculating the cosine of the included angle is: .

[0066] Step 123: Determine the reference vector with the smallest angle to the target vector as the reference vector associated with each individual.

[0067] Step 124: Assign each individual to the corresponding subpopulation based on the associated reference vector.

[0068] Understandably, by dividing the initial population into multiple subpopulations, dimensionality reduction of the high-dimensional problem is achieved, which facilitates the subsequent use of differentiated evolutionary strategies to solve the optimization problem, thereby synergistically optimizing the convergence speed and solution set distribution.

[0069] In some embodiments, multiple decision variables are divided into convergent-related variables and diversity-related variables, including: Multiple candidate solutions are selected from the initial population. For each decision variable of each candidate solution, multiple random perturbations are performed to obtain multiple new solutions. The objective vector of each new solution is calculated based on the objective function. For each decision variable, the objective vector corresponding to multiple new solutions is fitted to generate a fitted straight line representing the trend of the objective function value. Calculate the angle between the fitted line and the normal vector of the unit hyperplane in the target space, and calculate the average angle of each decision variable under all candidate solutions; the target space consists of multiple optimization objectives, and the unit hyperplane is defined as the plane where the sum of the function values ​​of all optimization objectives is 1; Clustering all decision variables based on the average angle yields convergent correlation variables and diversity correlation variables. The average angle corresponding to the convergent correlation variables is smaller than the average angle corresponding to the diversity correlation variables.

[0070] Optionally, the k-means clustering method can be used to divide multiple decision variables into two categories: convergent variables and diversity variables.

[0071] First, randomly select from the initial population. There are several candidate solutions, and a decision variable of the selected solution is... The system performs several random perturbations. Then, it calculates the objective value of the solution after each perturbation and fits it to a straight line. This is used to represent the trend of the target value after a change in the decision variable. Then, the straight line is calculated. With the unit hyperplane The angle between the normals. For each decision variable, the co-fit... A straight line, producing The average angle between the fitted line and the normal to the hyperplane represents the convergence direction of the solution. A smaller average angle indicates a stronger correlation between the decision variables and convergence, while a larger angle indicates a stronger correlation between the decision variables and diversity. Finally, the k-means clustering algorithm is used to divide the decision variables into two groups based on their angle values: the group with the larger average angle is considered to have variables related to diversity, and the other group is considered to have variables related to convergence.

[0072] In some embodiments, the current subpopulation is updated based on a first new individual or a second new individual to obtain the next generation subpopulation, including: Given that the current subpopulation is in the first evolutionary stage with convergence as the objective, calculate the convergence of the original individuals and the first new individual in the current subpopulation. The convergence is the sum of the objective function values ​​of the individual on all optimization objectives. The individual with the smallest convergence value is retained to update the current subpopulation.

[0073] For the subpopulation in the first evolutionary stage, if the subpopulation is not empty, calculate the convergence of all solutions within it, select the solution with the best convergence, and record its best convergence as the fitness of the subpopulation. If the convergence ranking of this solution is not among the top N in the population, then the subpopulation is considered a lagging subpopulation. To accelerate the evolution of the population, directly eliminate all solutions from the lagging subpopulation, and record their fitness according to the following formula: ; in, , , A random number uniformly distributed between [0, 1] This is the fitness of the previous generation of the subpopulation. Based on the above formula, the fitness of the subpopulation can fluctuate within a random range, preventing convergence, but preserving the evolutionary progress of the subpopulation. Then, record the number of subpopulations that did not choose a solution. If the solution is ranked high... If a solution is selected, it is included in the next generation of the subpopulation, and the fitness of this subpopulation is recorded as the convergence of the selected solution. When the subpopulation is empty, a random number between [0, 1] is generated as the fitness of the subpopulation. Finally, if the subpopulation updates the solution, the standard deviation of the fitness of the subpopulation over the past 30 generations is calculated. If the standard deviation is less than a preset threshold, it proceeds to the next stage; otherwise, the standard deviation of the previous generation is used as the result for this generation.

[0074] In some embodiments, the current subpopulation is updated based on a first new individual or a second new individual to obtain the next generation subpopulation, including: Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, calculate the comprehensive evaluation value of the original individuals and the second new individuals in the current subpopulation, and retain the individual with the smallest comprehensive evaluation value to update the current subpopulation. The comprehensive evaluation value is calculated by weighting the projection distance of the individual's target vector onto the direction of the associated reference vector, and the perpendicular distance between the individual's target vector and the associated reference vector.

[0075] Optionally, the overall evaluation value can be the fitness value.

[0076] Optionally, for the subpopulation in the second evolutionary stage, when the subpopulation is not empty, calculate the fitness of all solutions in the subpopulation, and select the solution with the best fitness to enter the next generation population. Its fitness is calculated using the modified penalized boundary cross method, and the calculation formula is as follows: ; ; in, Solution fitness value, Solution The projected distance of the target vector in the direction of the associated reference vector. Solution The normalized projected distance of the target vector in the direction of the associated reference vector. Solution The perpendicular distance between the target vector and the associated reference vector. Indicates the penalty factor. This represents the reference vector corresponding to the current subpopulation. Solution The target vector. By adjusting the parameters The size of the [something] can control the proportion of diversity in evolution. The larger the PBI value, the more severe the penalty when the solution deviates from the reference vector, and vice versa. This forces the solution to move closer to the reference vector. Since the reference vector is uniformly distributed, the final solution distribution is also uniform. For minimizing MaOPs, a smaller PBI value indicates better solution performance. If the current subpopulation is empty, the number of empty subpopulations is recorded. Meanwhile, modifications are made to the original PBI method. The methods for calculating distances can be expanded to understand the differences in convergence.

[0077] After the first round of selection, some solutions with better performance have been chosen. The unselected solutions are represented as... In the second round of selection, the remaining solutions need to be chosen based on the needs of the current stage of the population as a whole. If the population as a whole is in the first stage, the calculation... The convergence of the solutions is evaluated, and then the solutions with better convergence are selected from among them. A solution is used to guarantee the convergence of the entire population; if the population is in the second stage, calculate... The solution to the population The distance is calculated, and then the solution with the furthest distance is selected to enter the next generation. This process is repeated until the population size is reached. Among them, the solution arrive The formula for calculating the distance is as follows: ; in, Solution To the next generation of selected populations The minimum Euclidean distance, This indicates that they have been selected for the next generation of the species. One of the solutions, Indicates that a solution has been selected. The The objective function value.

[0078] In some embodiments, the method further includes: Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, all individuals recorded in the diversity archive are obtained, and a new set of reference vectors is constructed based on the target vectors of all individuals. The original reference vector set is replaced with the new reference vector set to obtain the adjusted reference vector set; Based on the adjusted set of reference vectors, the current population is re-divided to obtain multiple updated subpopulations.

[0079] It should be noted that, due to the reference vector being different from the true Pareto front... Inconsistent distribution can lead to poor diversity in the final solution set. To improve the performance of the algorithm in this case, the reference vector is adjusted to make its distribution more suitable. .

[0080] It is understandable that after the population distribution stabilizes, the reference vector is adjusted. At this point, since the population has already converged, the adjustment of the reference vector will not affect the convergence speed of the population, and the population distribution is similar to the Pareto front.

[0081] Figure 2 This is the second flowchart illustrating the urban drainage system design optimization method provided in this application embodiment. (Refer to...) Figure 2 This application provides a method for optimizing the design of an urban drainage system, which may include: Initialize the population and generate a uniformly distributed set of reference vectors; Enter a main loop and execute the following key steps in sequence: Clustering of decision variables: dividing multiple decision variables into convergent related variables and diversity related variables; Subpopulation partitioning: Based on the angle between the target vector and the reference vector corresponding to the solution, the entire population is divided into multiple subpopulations; Mating selection: Different strategies are used to select parents to produce new individuals based on the evolutionary stage of the subpopulation; Environmental selection: Based on the evolutionary stage of the subpopulation and the population as a whole, a two-round selection strategy is adopted to select the next generation from the population where the parent and offspring generations are merged. Update the diversity archive: collect information on solutions with high diversity; Reference vector adjustment: Based on the evolutionary stage of the population, the reference vector is selectively adjusted to better match the actual Pareto front shape; Termination Check: Check if the termination condition is met, such as reaching the maximum number of iterations. If met, output the final solution set; otherwise, return to the main loop to continue iteration.

[0082] In this embodiment of the invention, by decomposing the initial population into multiple subpopulations and introducing a two-stage evolutionary mechanism, the difficulty of problem optimization is reduced while providing sufficient selection pressure for population evolution, ensuring population convergence. Furthermore, the decomposition method is beneficial for maintaining good population diversity in high-dimensional cases. By adopting different mating selection operators in stages, selecting excellent parent solutions helps generate better-performing sub-solutions, thereby accelerating the convergence speed of the population. By adopting different environmental selection strategies in stages, suitable solutions can be selected for different subpopulations, resulting in better robustness. This not only accelerates the overall population's approach to the Pareto front but also ensures that the final solution set uniformly covers the entire front region.

[0083] Figure 3 This is a schematic diagram illustrating the true solution set and the predicted solution set provided in the embodiments of this application. For example... Figure 3 As shown, the left subgraph displays the true Pareto solution set of the Water Resource Planning (WRP) problem. This subgraph represents the theoretical optimal solution set of this multi-objective optimization problem, which is the set of all possible best trade-off solutions for the decision-maker. The right subgraph displays the final solution set, i.e. the predicted solution set, obtained after running the algorithms of this application, namely the multi-objective optimization evolutionary algorithm MaOEA and the two-stage decomposition TSD algorithm. Figure 3 In the diagram, the horizontal axis Dimension No represents the number of the optimization objective, with values ​​ranging from 1 to 6, and the vertical axis Value represents the objective function value. The predicted solution set is close to the true Pareto front, has good convergence, and can cover various regions of the true solution set, exhibiting good diversity.

[0084] Ultimately, decision-makers can choose the appropriate solution based on their different preferences. They can choose the solution with the lowest drainage network cost, or the solution with the lowest expected flood damage cost. Table 1 shows the decision-making schemes for the WRP problem based on different preferences.

[0085] Table 1. WRP Problem Decision Scheme Based on Different Preferences

[0086] As shown in Table 1, the solution is [0.22, 0.01, 0.01] for drainage network cost priority and [0.01, 0.07, 0.01] for storage facility cost priority.

[0087] The urban drainage system design optimization device provided in the embodiments of this application is described below. The urban drainage system design optimization device described below and the urban drainage system design optimization method described above can be referred to in correspondence.

[0088] Figure 4 A schematic diagram of the urban drainage system design optimization device provided in this application embodiment. Figure 4 As shown, the urban drainage system design optimization device 400 includes: Problem construction module 410 is used to construct the objective function and determine the constraints of the decision variables based on multiple decision variables and multiple optimization objectives in urban drainage system design. The multiple optimization objectives include cost minimization and flood economic loss minimization. The initialization module 420 is used to generate an initial population containing multiple initial design schemes based on the constraints of decision variables, divide the initial population into multiple subpopulations, initialize the diversity profile, and divide multiple decision variables into convergence-related variables and diversity-related variables. The iterative solution module 430 is used to repeatedly execute the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: Given that the current subpopulation is in the first evolutionary stage with convergence as the goal, select the first parent individual from the subpopulation with the smallest convergence value, select the second parent individual from the current subpopulation, and assign the convergence-related variables of the first parent individual to the second parent individual to generate the first new individual. Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, and a fourth parent individual is selected from the current subpopulation. The diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual. The diversity archive contains multiple individuals with diversity design schemes. Based on the first or second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0089] Optionally, the initial population can be divided into multiple subpopulations, including: Generate a set of reference vectors that are uniformly distributed and cover the target space, which consists of multiple optimization objectives; Calculate the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set. The target vector is calculated based on the objective function. The reference vector with the smallest angle to the target vector is determined as the reference vector associated with each individual. Each individual is assigned to a corresponding subpopulation based on the associated reference vector.

[0090] Optionally, the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set is calculated, including: The target vector corresponding to each individual is normalized to obtain the normalized target vector; Calculate the angle between the normalized target vector and each reference vector.

[0091] Optionally, multiple decision variables can be divided into convergence-related variables and diversity-related variables, including: Multiple candidate solutions are selected from the initial population. For each decision variable of each candidate solution, multiple random perturbations are performed to obtain multiple new solutions. The objective vector of each new solution is calculated based on the objective function. For each decision variable, the objective vector corresponding to multiple new solutions is fitted to generate a fitted straight line representing the trend of the objective function value. Calculate the angle between the fitted line and the normal vector of the unit hyperplane in the target space, and calculate the average angle of each decision variable under all candidate solutions; the target space consists of multiple optimization objectives, and the unit hyperplane is defined as the plane where the sum of the function values ​​of all optimization objectives is 1; Clustering all decision variables based on the average angle yields convergent correlation variables and diversity correlation variables. The average angle corresponding to the convergent correlation variables is smaller than the average angle corresponding to the diversity correlation variables.

[0092] Optionally, the first parent individual is selected from the subpopulation with the smallest convergence value, including: Calculate the convergence of each individual in each subpopulation. The convergence is the sum of the objective function values ​​of each individual across all optimization objectives. From all individuals in each subpopulation, identify the target individual with the smallest convergence value, and use the convergence of the target individual as the representative convergence of each subpopulation. The subpopulation with the smallest value representing the convergence is identified as the subpopulation with the smallest convergence value. Randomly select an individual from the subpopulation with the smallest convergence value to serve as the first parent individual.

[0093] Optionally, based on the first new individual or the second new individual, the current subpopulation is updated to obtain the next generation subpopulation, including: Given that the current subpopulation is in the first evolutionary stage with convergence as the objective, calculate the convergence of the original individuals and the first new individual in the current subpopulation. The convergence is the sum of the objective function values ​​of the individual on all optimization objectives. The individual with the smallest convergence value is retained to update the current subpopulation.

[0094] Optionally, based on the first new individual or the second new individual, the current subpopulation is updated to obtain the next generation subpopulation, including: Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, calculate the comprehensive evaluation value of the original individuals and the second new individuals in the current subpopulation, and retain the individual with the smallest comprehensive evaluation value to update the current subpopulation. The comprehensive evaluation value is calculated by weighting the projection distance of the individual's target vector onto the direction of the associated reference vector, and the perpendicular distance between the individual's target vector and the associated reference vector.

[0095] Optionally, multiple decision variables include: maximum overflow rate, maximum treatment rate, and local retention; maximum overflow rate refers to the maximum rate at which water can overflow after the water storage device is full; maximum treatment rate refers to the maximum rate at which the treatment device can treat sewage or rainwater; and local retention refers to the amount of water in the storage facility.

[0096] Optionally, the constraints include: The number of floods occurring each year is less than or equal to a preset frequency threshold; The probability that the flood depth exceeds a preset depth threshold is less than or equal to a preset probability threshold. The average weight of suspended solids in water each year is less than or equal to a preset suspended solids weight threshold. The average weight of solids deposited in water each year is less than or equal to a preset sediment weight threshold. The average annual biochemical oxygen demand in water is less than or equal to the preset oxygen demand threshold. The average annual nitrogen content in the water is less than or equal to the preset nitrogen content threshold; The average annual phosphate content in the water is less than or equal to the preset phosphate content threshold.

[0097] In some embodiments, the apparatus further includes: The update unit is used to update the diversity profile based on the first or second new individual.

[0098] Optionally, the device further includes: The building unit is used to acquire all individuals recorded in the diversity archive and construct a new set of reference vectors based on the target vectors of all individuals, given that the current subpopulation is in the second evolutionary stage with diversity as the goal. The adjustment unit is used to replace the original reference vector set with a new reference vector set to obtain the adjusted reference vector set. The partitioning unit is used to repartition the current population based on the adjusted set of reference vectors, resulting in multiple updated subpopulations.

[0099] Optionally, the device further includes: The determining unit is used to determine whether the current subpopulation is in the first evolutionary stage aimed at convergence or the second evolutionary stage aimed at diversity, according to a preset stage control strategy.

[0100] It should be noted that the urban drainage system design optimization device provided in this application embodiment can realize all the method steps implemented in the above method embodiment and can achieve the same technical effect. Here, the parts that are the same as those in the method embodiment and the beneficial effects will not be described in detail.

[0101] Figure 5 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application, such as... Figure 5 As shown, the electronic device may include: a processor 510, a communication interface 520, a memory 530, and a communication bus 540, wherein the processor 510, the communication interface 520, and the memory 530 communicate with each other via the communication bus 540. The processor 510 can call a computer program in the memory 530 to execute the steps of the urban drainage system design optimization method, such as including: Based on multiple decision variables and multiple optimization objectives in urban drainage system design, an objective function is constructed, the constraints of the decision variables are determined, and the multiple decision variables are divided into convergent related variables and diversity related variables. The multiple optimization objectives include cost minimization and flood economic loss minimization. Based on the constraints of the decision variables, an initial population containing multiple initial design schemes is generated, the initial population is divided into multiple subpopulations, and the diversity profile is initialized. Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: Given that the current subpopulation is in the first evolutionary stage with convergence as the goal, select the first parent individual from the subpopulation with the smallest convergence value, select the second parent individual from the current subpopulation, and assign the convergence-related variables of the first parent individual to the second parent individual to generate the first new individual. Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, and a fourth parent individual is selected from the current subpopulation. The diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual. The diversity archive contains multiple individuals with diversity design schemes. Based on the first or second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0102] Furthermore, the logical instructions in the aforementioned memory 530 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0103] On the other hand, embodiments of this application also provide a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform the steps of the urban drainage system design optimization method provided in the above embodiments, such as including: Based on multiple decision variables and multiple optimization objectives in urban drainage system design, an objective function is constructed, the constraints of the decision variables are determined, and the multiple decision variables are divided into convergent related variables and diversity related variables. The multiple optimization objectives include cost minimization and flood economic loss minimization. Based on the constraints of the decision variables, an initial population containing multiple initial design schemes is generated, the initial population is divided into multiple subpopulations, and the diversity profile is initialized. Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: Given that the current subpopulation is in the first evolutionary stage with convergence as the goal, select the first parent individual from the subpopulation with the smallest convergence value, select the second parent individual from the current subpopulation, and assign the convergence-related variables of the first parent individual to the second parent individual to generate the first new individual. Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, and a fourth parent individual is selected from the current subpopulation. The diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual. The diversity archive contains multiple individuals with diversity design schemes. Based on the first or second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0104] On the other hand, embodiments of this application also provide a processor-readable storage medium storing a computer program for causing a processor to execute the steps of the urban drainage system design optimization method provided in the above embodiments, such as including: Based on multiple decision variables and multiple optimization objectives in urban drainage system design, an objective function is constructed, the constraints of the decision variables are determined, and the multiple decision variables are divided into convergent related variables and diversity related variables. The multiple optimization objectives include cost minimization and flood economic loss minimization. Based on the constraints of the decision variables, an initial population containing multiple initial design schemes is generated, the initial population is divided into multiple subpopulations, and the diversity profile is initialized. Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: Given that the current subpopulation is in the first evolutionary stage with convergence as the goal, select the first parent individual from the subpopulation with the smallest convergence value, select the second parent individual from the current subpopulation, and assign the convergence-related variables of the first parent individual to the second parent individual to generate the first new individual. Given that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, and a fourth parent individual is selected from the current subpopulation. The diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual. The diversity archive contains multiple individuals with diversity design schemes. Based on the first or second new individual, update the current subpopulation to obtain the next generation subpopulation.

[0105] The processor-readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic memory (e.g., floppy disk, hard disk, magnetic tape, magneto-optical disk (MO)), optical memory (e.g., CD, DVD, BD, HVD), and semiconductor memory (e.g., ROM, EPROM, EEPROM, non-volatile memory (NAND FLASH), solid-state drive (SSD)).

[0106] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0107] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for optimizing the design of an urban drainage system, characterized in that, include: Based on multiple decision variables and multiple optimization objectives in urban drainage system design, an objective function is constructed, and the constraints of the decision variables are determined. The multiple optimization objectives include cost minimization and flood economic loss minimization. Based on the constraints of the decision variables, an initial population containing multiple initial design schemes is generated, the initial population is divided into multiple subpopulations, a diversity profile is initialized, and the multiple decision variables are divided into convergence-related variables and diversity-related variables. Repeat the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: If it is determined that the current subpopulation is in the first evolutionary stage with convergence as the goal, the first parent individual is selected from the subpopulation with the smallest convergence value, and the second parent individual is selected from the current subpopulation. The convergence-related variables of the first parent individual are assigned to the second parent individual to generate the first new individual. If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, a fourth parent individual is selected from the current subpopulation, and the diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual; the diversity archive records multiple individuals containing diversity design schemes. Based on the first new individual or the second new individual, update the current subpopulation to obtain the next generation subpopulation.

2. The urban drainage system design optimization method according to claim 1, characterized in that, The process of dividing the initial population into multiple subpopulations includes: Generate a set of reference vectors that are uniformly distributed and cover the target space, wherein the target space is composed of the plurality of optimization objectives; Calculate the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set, wherein the target vector is calculated based on the objective function; The reference vector that has the smallest angle with the target vector is determined as the reference vector associated with each individual. Based on the associated reference vector, each individual is assigned to a corresponding subpopulation.

3. The urban drainage system design optimization method according to claim 2, characterized in that, The calculation of the angle between the target vector corresponding to each individual in the initial population and each reference vector in the reference vector set includes: The target vector corresponding to each individual is normalized to obtain the normalized target vector; Calculate the angle between the normalized target vector and each of the reference vectors.

4. The urban drainage system design optimization method according to claim 1, characterized in that, The step of classifying the multiple decision variables into convergent-related variables and diversity-related variables includes: Multiple candidate solutions are selected from the initial population. For each decision variable of each candidate solution, multiple random perturbations are performed to obtain multiple new solutions. The objective vector of each new solution is calculated based on the objective function. For each of the decision variables, the objective vector corresponding to multiple new solutions is fitted to generate a fitted straight line representing the trend of the objective function value. Calculate the angle between the fitted line and the normal vector of the unit hyperplane in the target space, and calculate the average angle of each decision variable under all candidate solutions; the target space is composed of the plurality of optimization objectives, and the unit hyperplane is defined as the plane where the sum of the function values ​​of all optimization objectives is 1; Clustering is performed on all decision variables based on the average angle to obtain the convergent correlation variables and the diversity correlation variables, wherein the average angle corresponding to the convergent correlation variables is smaller than the average angle corresponding to the diversity correlation variables.

5. The urban drainage system design optimization method according to claim 1, characterized in that, The selection of the first parent individual from the subpopulation with the smallest convergence value includes: Calculate the convergence of each individual in each subpopulation, where the convergence is the sum of the objective function values ​​of each individual on all the optimization objectives; From all individuals in each subpopulation, determine the target individual with the smallest convergence value, and use the convergence of the target individual as the representative convergence of each subpopulation. The subpopulation with the smallest value corresponding to the representative convergence is determined as the subpopulation with the smallest convergence value. Randomly select an individual from the subpopulation with the smallest convergence value as the first parent individual.

6. The urban drainage system design optimization method according to claim 1, characterized in that, The step of updating the current subpopulation based on the first new individual or the second new individual to obtain the next generation subpopulation includes: If the current subpopulation is determined to be in the first evolutionary stage with convergence as the objective, the convergence of the original individuals and the first new individual in the current subpopulation is calculated. The convergence is the sum of the objective function values ​​of the individuals on all the optimization objectives. The individual with the smallest convergence value is retained to update the current subpopulation.

7. The urban drainage system design optimization method according to claim 2, characterized in that, The step of updating the current subpopulation based on the first new individual or the second new individual to obtain the next generation subpopulation includes: If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, calculate the comprehensive evaluation value of the original individuals and the second new individuals in the current subpopulation, and retain the individual with the smallest comprehensive evaluation value to update the current subpopulation; The comprehensive evaluation value is calculated by weighting the projection distance of the individual's target vector onto the direction of the associated reference vector and the perpendicular distance between the individual's target vector and the associated reference vector.

8. The urban drainage system design optimization method according to claim 1, characterized in that, The decision variables include: maximum overflow rate, maximum treatment rate, and local retention; the maximum overflow rate refers to the maximum rate at which water can overflow after the water storage device is full; the maximum treatment rate refers to the maximum rate at which the treatment device can treat sewage or rainwater; and the local retention refers to the amount of water in the storage facility.

9. The urban drainage system design optimization method according to claim 1, characterized in that, The constraints include: The number of floods occurring each year is less than or equal to a preset frequency threshold; The probability that the flood depth exceeds a preset depth threshold is less than or equal to a preset probability threshold. The average weight of suspended solids in water each year is less than or equal to a preset suspended solids weight threshold. The average weight of solids deposited in the water each year is less than or equal to a preset sediment weight threshold. The average annual biochemical oxygen demand in water is less than or equal to the preset oxygen demand threshold. The average annual nitrogen content in the water is less than or equal to the preset nitrogen content threshold. The average annual phosphate content in the water is less than or equal to the preset phosphate content threshold.

10. The urban drainage system design optimization method according to claim 1, characterized in that, After updating the current subpopulation based on the first new individual or the second new individual, the method further includes: The diversity profile is updated based on the first new individual or the second new individual.

11. The urban drainage system design optimization method according to claim 2, characterized in that, The method further includes: If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, all individuals recorded in the diversity archive are obtained, and a new set of reference vectors is constructed based on the target vectors of all the individuals. The original reference vector set is replaced with the new reference vector set to obtain the adjusted reference vector set. Based on the adjusted set of reference vectors, the current population is re-divided to obtain multiple updated subpopulations.

12. The urban drainage system design optimization method according to claim 1, characterized in that, The method further includes: Based on a preset stage control strategy, the current subpopulation is determined to be in either the first evolutionary stage aimed at convergence or the second evolutionary stage aimed at diversity.

13. A device for optimizing the design of an urban drainage system, characterized in that, include: The problem construction module is used to construct an objective function based on multiple decision variables and multiple optimization objectives in urban drainage system design, and to determine the constraints of the decision variables. The multiple optimization objectives include cost minimization and flood economic loss minimization. An initialization module is used to generate an initial population containing multiple initial design schemes based on the constraints of the decision variables, divide the initial population into multiple subpopulations, initialize a diversity profile, and divide the multiple decision variables into convergence-related variables and diversity-related variables. The iterative solution module is used to repeatedly execute the following steps until the iteration termination condition is met, and output the optimal solution of the objective function: If it is determined that the current subpopulation is in the first evolutionary stage with convergence as the goal, the first parent individual is selected from the subpopulation with the smallest convergence value, and the second parent individual is selected from the current subpopulation. The convergence-related variables of the first parent individual are assigned to the second parent individual to generate the first new individual. If it is determined that the current subpopulation is in the second evolutionary stage with diversity as the goal, a third parent individual is selected from the diversity archive, a fourth parent individual is selected from the current subpopulation, and the diversity-related variables of the third parent individual are assigned to the fourth parent individual to generate a second new individual; the diversity archive records multiple individuals containing diversity design schemes. Based on the first new individual or the second new individual, update the current subpopulation to obtain the next generation subpopulation.

14. An electronic device comprising a processor and a memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the urban drainage system design optimization method according to any one of claims 1 to 12.

15. A non-transitory 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 urban drainage system design optimization method as described in any one of claims 1 to 12.

16. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the urban drainage system design optimization method according to any one of claims 1 to 12.

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