NSGA-II algorithm-based sensor layout optimization method

Abstract

The invention discloses a sensor layout optimization method based on an NSGA-II algorithm, and the method comprises the following steps: firstly, dividing a population into different frontier layers through a fast non-dominated sorting NSGA-II algorithm, and determining and calculating the degree of congestion or the degree of congestion distance to maintain the diversity of frontier layer individuals; secondly, the operation of the NSGA-II algorithm is dynamically adjusted by adopting self-adaptive crossover and mutation operation, so that the adaptability and efficiency of the algorithm are improved; and finally, selecting a better Pareto frontier solution set through selection operation, and providing a group of multi-objective optimal solutions. According to the sensor layout optimization method based on the NSGA-II algorithm, the global search capability is high, exploration in a solution space can be wide, and a potential optimal solution can be found.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor layout optimization, and in particular to a sensor layout optimization method based on NSGA-II algorithm. Background Art

[0002] The current development of solving multi-objective optimization problems shows the following main trends and progress: Integrated optimization methods. Integrated optimization methods combine different optimization algorithms and strategies to achieve better performance. For example, combining genetic algorithms with simulated annealing algorithms, combining multi-objective differential evolution with particle swarm optimization, etc. Parallelization and distributed computing. With the improvement of computing power, researchers have begun to use parallel computing and distributed computing methods to speed up the search process and improve the efficiency of algorithms for dealing with large-scale multi-objective optimization problems. Combination with deep learning. In recent years, the application of deep learning technology in multi-objective optimization has received increasing attention. Some researchers have combined deep learning technology with traditional optimization algorithms to improve the performance and generalization ability of optimization algorithms. In general, the research on multi-objective optimization problems continues to develop in a more complex, intelligent and efficient direction, combining a variety of optimization algorithms, adaptability, diversity maintenance, integrated optimization methods and other technical means to cope with ever-changing practical problems and challenges.

[0003] The main defects and deficiencies in solving multi-objective optimization problems are: large-scale problem processing, existing algorithms are difficult to effectively solve complex large-scale problems; lack of interpretability, lack of interpretability affects the credibility of the algorithm; problem specificity, some algorithms perform well on specific problem types, and their versatility needs to be improved. These problems challenge multi-objective optimization research and need further exploration and improvement to improve algorithm performance, efficiency and applicability. Summary of the invention

[0004] The purpose of the present invention is to provide a sensor layout optimization method based on the NSGA-II algorithm, which can solve many shortcomings, balance the selection operation of the frontier layer, effectively promote the diversity of the population, and improve the adaptability and robustness of the algorithm. In addition, efficient calculation is achieved, the computational complexity is reduced, and the overall algorithm is easy to implement, does not require cumbersome parameter adjustment, and is suitable for various multi-objective optimization problems.

[0005] To achieve the above object, the present invention provides a sensor layout optimization method based on NSGA-II algorithm, comprising the following steps:

[0006] S1. Divide the population into different frontier layers by using the fast non-dominated sorting NSGA-II algorithm, determine and calculate the crowding degree or crowding distance;

[0007] S2, using adaptive crossover and mutation operations to dynamically adjust the NSGA-II algorithm;

[0008] S3. After the selection operation, a better Pareto frontier solution set is selected to provide a set of multi-objective optimization solutions.

[0009] Preferably, in step S1, each solution in the fast non-dominated sorting algorithm is assigned two parameters n i and S i , where n i represents the number of solutions that dominate the ith solution, S i Represents the number of solutions dominated by the ith solution, specifically including the following steps:

[0010] S11. Obtain n of each solution by calculating and traversing i and S i The computational complexity of this step is O(MN 2 );

[0011] S12, the solution on the first non-dominated layer satisfies n i = 0, store the solutions on the first non-dominated layer into the set F i For F i Concentration i = 0, and the n of the individuals it dominates i -1; at this time, the newly appeared n i = 0 as the solution on the second non-dominated layer, and the newly appeared n i = 0 are put into another independent set Q;

[0012] S13, repeat step S12 for the individuals in set Q to find the third non-dominated layer;

[0013] S14, repeat the above steps S11 to S14 to find all non-dominated layers;

[0014] S15. When the division of each layer of solutions is completed, a rank is assigned to the solutions of that layer.

[0015] Preferably, in step S1, each individual in the population sets a crowding parameter i distance , if solution i belongs to the non-dominated layer I, the congestion degree or congestion distance of solution i on the non-dominated layer I is calculated as follows:

[0016] For each objective function, find two solutions adjacent to the solution function value and calculate the function difference between the two solutions. The crowding distance of the current solution is the sum of the adjacent solution function differences obtained by all objective functions.

[0017] Preferably, the smaller the crowding distance is, the more crowded the area around the individual is. The crowding degree comparison operator is defined as <n;

[0018] After the above calculation, each individual in the population has a non-dominated level i rank and crowding distance i distance Two attributes, based on these two attributes, define the following partial order relation:

[0019] i <j

[0020] If two solutions have different ranks, the solution with lower rank is preferred; if two solutions have the same rank, the solution with larger distance is preferred.

[0021] Preferably, in step S2, the NSGA-II algorithm specifically includes the following steps:

[0022] S21, Initialize the population: Randomly generate an initial population, in which each individual is a candidate solution;

[0023] S22, evaluate fitness: for each individual, calculate its fitness value in the objective function space;

[0024] S23, non-dominated sorting: sort the population according to the non-dominated relationship between individuals. Specifically, if an individual is dominated by another individual, if it is at least equal to the other individual in all objective functions and better than the other individual in at least one objective function, the individuals in the population are divided into different levels according to this relationship, forming different Pareto fronts.

[0025] S24, calculate crowding: for each individual in the frontier, calculate its crowding in the objective function space. The crowding is used to evaluate the distribution density of individuals in the solution space.

[0026] S25, selection operation: select the next generation of individuals from the population by combining non-dominated sorting and crowding;

[0027] S26, crossover operation: performing a crossover operation on the selected individuals to generate new individuals;

[0028] S27, mutation operation: mutation operation is performed on individuals after crossover, and certain genes or characteristics of individuals are randomly changed;

[0029] S28, replacement operation: replace part of the individuals in the current population with the newly generated individuals to form the next generation population;

[0030] S29, repeat iteration: Repeat the above steps S21 to S29 until the maximum number of iterations is reached or the objective function value converges, then stop iterating.

[0031] Therefore, the present invention adopts the above-mentioned sensor layout optimization method based on the NSGA-II algorithm, and the beneficial effects are as follows:

[0032] (1) The present invention can effectively handle multi-objective optimization problems, maintain the diversity of the solution space through non-dominated sorting and congestion, and thus generate a set of approximately optimal solutions. Therefore, the best design solution can be found while considering multiple objectives.

[0033] (2) The present invention has strong global search capabilities, can explore extensively in the solution space, and find potential optimal solutions, discover novel and competitive solutions in the design space, and has global search capabilities.

[0034] (3) The present invention can converge to an approximate optimal solution within a relatively small number of iterations, which helps to shorten the development cycle and cost of the patent solution, that is, it has rapid convergence.

[0035] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of an embodiment of a sensor layout optimization method based on NSGA-II algorithm of the present invention;

[0037] Figure 2 This is a schematic diagram before layout optimization of an embodiment of a sensor layout optimization method based on the NSGA-II algorithm of the present invention;.

[0038] Figure 3 It is a schematic diagram after layout optimization of an embodiment of a sensor layout optimization method based on the NSGA-II algorithm of the present invention. DETAILED DESCRIPTION

[0039] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0040] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0041] The present invention provides a sensor layout optimization method based on the NSGA-II algorithm. In the health monitoring of shield tunnels, it is necessary to determine the layout of sensors to ensure monitoring performance while reducing monitoring costs. In order to maximize monitoring performance and minimize monitoring costs, this patent proposes a sensor layout optimization method, which aims to optimize the sensor layout scheme of shield tunnels. This method takes the sensor monitoring cost and the strain reconstruction error of the tunnel section as two objective functions of the optimization problem. Chaotic mapping and decimal coding are used to generate a uniformly distributed initial population, thereby reducing the complexity of the algorithm operation. The optimal layout solution set is solved by the NSGA-II algorithm, and a dynamically updated dual-population mechanism is used for global and local searches, and an elite set is established to guide population updates. After repeated iterative solutions, the optimal sensor layout scheme for the shield tunnel is finally obtained.

[0042] like Figure 1 As shown, a sensor layout optimization method based on NSGA-II algorithm includes the following steps:

[0043] S1. Divide the population into different frontier layers by using the fast non-dominated sorting NSGA-II algorithm, determine and calculate the crowding degree or crowding distance;

[0044] Each solution in the fast non-dominated sort algorithm is assigned two parameters n i and S i , where n i represents the number of solutions that dominate the ith solution, S i Represents the number of solutions dominated by the ith solution, specifically including the following steps:

[0045] S11. Obtain n of each solution by calculating and traversing i and S i The computational complexity of this step is O(MN 2 ), and the first step of ordinary non-dominated sorting can obtain the result of this step;

[0046] S12, it is easy to judge that the solution on the first non-dominated layer satisfies n i = 0, store the solutions on the first non-dominated layer into the set F i For F i Concentration i = 0, the n of the individuals it dominates (individuals in the S set) i -1; at this time, the newly appeared n i = 0 can be used as the solution on the second non-dominated layer, and these newly appeared n i = 0 are put into another independent set Q;

[0047] S13, repeat step S12 for the individuals in set Q, and the third non-dominated layer can be found;

[0048] S14, repeating the above steps S11 to S14, all non-dominated layers can be found;

[0049] S15. When the division of each layer of solutions is completed, a rank is assigned to the solutions of that layer.

[0050] Individuals in the second layer and above i The maximum is N-1 (this solution is dominated by other N-1 solutions). Therefore, these individuals are i Before it becomes 0 (that is, before the stratification is completed), it will be visited at most N-1 times. There are at most N-1 such solutions. Therefore, the maximum computational complexity of steps S12, S13, and S14 can reach O(N 2 ). Therefore, the computational complexity of the fast non-dominated algorithm is O(MN 2 ).

[0051] NSGA uses a sharing function to ensure population diversity. The key is to choose a suitable sharing parameter. sh are Determines the degree to which virtual fitness is shared. In actual calculations, this parameter represents the maximum Euclidean distance between any two individuals in the population that share virtual fitness. However, this method has the following two problems:

[0052] 1. The performance of this method is overly dependent on the shared parameter σ sh are , usually set by the user;

[0053] 2. It is necessary to calculate the Euclidean distance between all individuals and compare them, with a complexity of O(N 2 ).

[0054] The biggest advantage of the NSGA-II method is that it does not require any parameters to be set, and the computational complexity is also optimized to a certain extent. Crowding and crowding comparison operator are two key concepts in this part of the algorithm.

[0055] 1. Determination of congestion:

[0056] Each individual in the population sets a crowding parameter i distance , if solution i belongs to a specific non-dominated layer I, the congestion degree or crowding distance of solution i on non-dominated layer I is calculated as follows:

[0057] For each objective function, find two solutions adjacent to the solution function value and calculate the function difference between the two solutions. The crowding distance of the current solution is the sum of the function differences of the adjacent solutions obtained by all objective functions. Note that the individual crowding degree of the boundary of each non-dominated layer is directly set to infinity.

[0058] It can also be understood as follows: the crowding distance of the i-th solution is the perimeter of the rectangular cuboid formed by two adjacent points on its non-dominated front; that is, the rectangle with the nearest neighbor points of the same dominant layer as vertices.

[0059] 2. Crowding comparison operator:

[0060] The smaller the crowding distance is, the more crowded the individual is. In order to ensure the uniformity of solution distribution, a crowding comparison operator is defined: <n;

[0061] After the above calculation, each individual in the population has a non-dominated level i rank and crowding distance i distance Based on these two attributes, the following partial order relationship is defined:

[0062] i <j

[0063] Among them, i represents the solution currently being considered, and j represents the solution to be compared with solution i;

[0064] if(i rank <j rank or i rank =j rank ∧i distance >j distance )

[0065] i rank represents the non-dominated level, j distance Represents the crowding distance; that is, if two solutions have different ranks, the solution with the lower rank is preferred; if two solutions have the same rank, the solution with the larger distance is preferred.

[0066] S2. Adopt adaptive crossover and mutation operations to dynamically adjust the NSGA-II algorithm. The NSGA-II algorithm specifically includes the following steps:

[0067] S21. Initialize the population: Randomly generate an initial population, in which each individual is a candidate solution.

[0068] S22. Evaluate fitness: For each individual, calculate its fitness value in the objective function space; this usually involves inputting the individual's solution into the objective function and then calculating its objective function value.

[0069] S23. Non-dominated sorting: Sort the population according to the non-dominated relationship between individuals. Specifically, an individual can be dominated by another individual if it is at least equal to the other individual in all objective functions and better than the other individual in at least one objective function. According to this relationship, the individuals in the population are divided into different levels to form different pareto fronts.

[0070] S24. Calculate the crowding degree: For each individual in the frontier, calculate its crowding degree in the objective function space. The crowding degree is used to evaluate the distribution density of individuals in the solution space to promote the diversity of the population.

[0071] S25, selection operation: select the next generation of individuals from the population by combining non-dominated sorting and crowding; the selection operation tends to retain individuals in the frontier and select more individuals that are closer to the frontier and have lower crowding.

[0072] S26. Crossover operation: Perform a crossover operation on the selected individuals to generate new individuals. The crossover operation can be performed in different ways, such as single-point crossover or multi-point crossover.

[0073] S27. Mutation operation: Perform mutation operation on individuals after crossover to increase the diversity of the population. Mutation operation usually involves random changes to certain genes or characteristics of individuals.

[0074] S28, replacement operation: replace part of the individuals in the current population with newly generated individuals to form the next generation population.

[0075] S29, repeat iteration: Repeat the above steps S21 to S29 until the stopping condition is met, for example, when the maximum number of iterations is reached or the objective function value converges, the iteration is stopped.

[0076] S3, after the selection operation, a better Pareto frontier solution set is selected, providing a set of better multi-objective optimization solutions such as Figure 2 , Figure 3 shown.

[0077] That is, the output result is: when the algorithm converges or reaches the maximum number of iterations, the best individuals are selected from the final population as the final solution set, which represents the approximate optimal solution to the multi-objective optimization problem.

[0078] Therefore, the present invention adopts the above-mentioned sensor layout optimization method based on the NSGA-II algorithm. First, the crowding distance is used to maintain diversity, balance the selection operation of the frontier layer, and effectively promote the diversity of the population. Secondly, the algorithm adopts adaptive crossover and mutation operations to adjust the strategy and probability according to the population situation, thereby improving the adaptability and robustness of the algorithm. It also achieves efficient calculation, adopts a fast non-dominated sorting algorithm and crowding distance calculation, reduces the computational complexity, and improves the efficiency of the algorithm. The overall algorithm is easy to implement, does not require cumbersome parameter adjustment, and is suitable for various multi-objective optimization problems.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A sensor layout optimization method based on NSGA-II algorithm, characterized in that: The following steps are involved: S1. Divide the population into different frontier layers by using the fast non-dominated sorting NSGA-II algorithm, determine and calculate the crowding degree or crowding distance; S2, using adaptive crossover and mutation operations to dynamically adjust the NSGA-II algorithm; S3. After the selection operation, a better Pareto frontier solution set is selected to provide a set of multi-objective optimization solutions.

2. The sensor layout optimization method based on the NSGA-II algorithm according to claim 1, characterized in that: In step S1, each solution in the fast non-dominated sorting algorithm is assigned two parameters n i and S i , where n i represents the number of solutions that dominate the ith solution, S i Represents the number of solutions dominated by the ith solution, specifically including the following steps: S11. Obtain n of each solution by calculating and traversing i and S i The computational complexity of this step is O(MN 2 ); S12, the solution on the first non-dominated layer satisfies n i = 0, store the solutions on the first non-dominated layer into the set F i For F i Concentration i = 0, and the n of the individuals it dominates i -1; at this time, the newly appeared n i = 0 as the solution on the second non-dominated layer, and the newly appeared n i = 0 are put into another independent set Q; S13, repeat step S12 for the individuals in set Q to find the third non-dominated layer; S14, repeat the above steps S11 to S14 to find all non-dominated layers; S15. When the division of each layer of solutions is completed, a rank is assigned to the solutions of that layer.

3. The sensor layout optimization method based on NSGA-II algorithm according to claim 2 is characterized in that: In step S1, each individual in the population sets a crowding parameter i distance , if solution i belongs to the non-dominated layer I, the congestion degree or congestion distance of solution i on the non-dominated layer I is calculated as follows: For each objective function, find two solutions adjacent to the solution function value and calculate the function difference between the two solutions. The crowding distance of the current solution is the sum of the adjacent solution function differences obtained by all objective functions.

4. The sensor layout optimization method based on NSGA-II algorithm according to claim 3 is characterized in that: The smaller the crowding distance is, the more crowded the individual is. The crowding comparison operator is defined as <n; After the above calculation, each individual in the population has a non-dominated level i rank and crowding distance i distance Two attributes, based on these two attributes, define the following partial order relation: i <j Among them, i represents the solution currently being considered, and j represents the solution to be compared with solution i; If two solutions have different ranks, the solution with lower rank is preferred; if two solutions have the same rank, the solution with larger distance is preferred.

5. The sensor layout optimization method based on NSGA-II algorithm according to claim 4 is characterized in that: In step S2, the NSGA-II algorithm specifically includes the following steps: S21, Initialize the population: Randomly generate an initial population, in which each individual is a candidate solution; S22, evaluate fitness: for each individual, calculate its fitness value in the objective function space; S23, non-dominated sorting: sort the population according to the non-dominated relationship between individuals. Specifically, if an individual is dominated by another individual, if it is at least equal to the other individual in all objective functions and better than the other individual in at least one objective function, the individuals in the population are divided into different levels according to this relationship, forming different Pareto fronts. S24, calculate crowding: for each individual in the frontier, calculate its crowding in the objective function space. The crowding is used to evaluate the distribution density of individuals in the solution space. S25, selection operation: select the next generation of individuals from the population by combining non-dominated sorting and crowding; S26, crossover operation: performing a crossover operation on the selected individuals to generate new individuals; S27, mutation operation: mutation operation is performed on individuals after crossover, and certain genes or characteristics of individuals are randomly changed; S28, replacement operation: replace part of the individuals in the current population with the newly generated individuals to form the next generation population; S29, repeat iteration: Repeat the above steps S21 to S29 until the maximum number of iterations is reached or the objective function value converges, then stop iterating.

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