Multi-dimensional search algorithm based on multi-dimensional optimization strategy
By introducing multi-dimensional optimization strategy and position variation strategy into the high-dimensional search algorithm, the problem that the swarm particle algorithm is prone to fall into local optimality in high-dimensional optimization, achieving higher optimization accuracy and effect.
Patent Information
- Application Number
- CN202411388574.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-08
- Publication Date
- 2025-01-10
AI Technical Summary
Existing particle algorithms have poor performance on high-dimensional optimization problems, which are prone to local optimality and are difficult to effectively access every possible solution position in the high-dimensional space, resulting in different output optimal solution and theoretical optimal solution. .
A multi-dimensional search algorithm (MDA) based on a multi-dimensional optimization strategy is proposed. By setting multiple anchor points through initial parameters, randomly selecting a certain dimension of the particle position to perform multi-dimensional optimization until each dimension is searched, and When the position remains unchanged, the position mutation strategy is performed, and the iteration is repeated until the end condition is met.
When dealing with high-dimensional optimization problem, MDA significantly improves optimization accuracy, exhibits higher optimization effects than other metaheuristic algorithms, and can find the theoretical optimal solution more accurately.
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Figure CN119294435A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of intelligent algorithms, and specifically relates to a multi-dimensional search algorithm based on a multi-dimensional optimization strategy. Background Art
[0002] In the real world, the optimization problems we face often present the characteristics of high nonlinearity, multi-objective and non-convex constraints, which makes the solution of the problem extremely complicated. Conventional mathematical optimization methods are difficult to implement effective methods to solve these problems. Metaheuristic algorithms rely on their own unique calculation methods to avoid the troubles brought by gradient calculation to a certain extent, and show certain performance for complex optimization problems with simpler mathematical structures.
[0003] In the original heuristic algorithm, the conventional swarm particle algorithm shows poor performance in high-dimensional optimization problems. High-dimensional optimization problems mean that the swarm particles are sparsely distributed in the dimensional space and cannot effectively access every possible solution position in the high-dimensional space, which makes the swarm particle algorithm easy to fall into the local optimum. It is possible that the output optimal solution is different from the theoretical optimal solution. Therefore, for high-dimensional optimization problems, it is necessary to analyze the impact of each dimension on the optimal solution, so as to get rid of the disadvantage that the swarm particle algorithm may fail when dealing with high-dimensional optimization problems, thereby solving practical applications in life. Summary of the invention
[0004] In order to solve the above problems, the present invention proposes a multi-dimensional search algorithm (MDA) based on a multi-dimensional optimization strategy, comprising the following steps:
[0005] S1. Initial parameter setting: setting multiple anchor points within the allowed number of iterations.
[0006] S2. The best starting position is determined inside the anchor point according to the objective function as the initial position of the particle.
[0007] S3. Randomly select a dimension of the particle's position to perform a multi-dimensional optimization operation until all dimensions are exhausted.
[0008] S4, judging whether the position of the particle changes, if not, implementing a position variation strategy for the position of the particle, if changed, proceeding to step S5.
[0009] S5. Repeat steps S1-S4 until the algorithm meets the end condition.
[0010] The beneficial effects of the present invention are as follows: compared with the prior art, the intelligent optimization algorithm proposes MDA based on the multi-dimensional optimization process, wherein MDA has good effects in optimizing problems, and has higher optimization accuracy than other metaheuristic algorithms when dealing with optimization problems of higher dimensions. BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Figure 1 Schematic diagram of the multi-dimensional search algorithm flow of the present invention.
[0012] Figure 2 This is a diagram of the F1-F6 test function used in the present invention.
[0013] Figure 3 The present invention is tested on the test objective function F1, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0014] Figure 4 The present invention is tested on the test objective function F2, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0015] Figure 5 The present invention is tested on the test objective function F3, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0016] Figure 6 The present invention is tested on the test objective function F4, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0017] Figure 7 The present invention is tested on the test objective function F5, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0018] Figure 8 The present invention is tested on the test objective function F6, and compared with the Wheat Whey Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime and Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO).
[0019] Fig. 9 Schematic diagram of the structure of the MDA optimized extreme learning machine (ELM) model for fault diagnosis.
[0020] Fig.10 The Western Reserve University bearing fault dataset used for fault classification experiments.
[0021] Fig.11 Confusion matrix plots for the ELM model optimized using MDA and the ELM model without optimization. DETAILED DESCRIPTION
[0022] A multi-dimensional search algorithm (MDA) based on a multi-dimensional optimization strategy, characterized in that it includes the following steps:
[0023] Initial parameter setting, set multiple anchor points within the allowed number of iterations. Set the size to anchor points, each of which is randomly variables, and the anchor point position is created by the following formula
[0024] (1)
[0025] in, for OK The internal elements of the matrix are random numbers between 0 and 1. and Indicates the upper and lower bounds of a variable.
[0026] S2. The anchor point determines the best starting position as the initial position of the particle according to the objective function. Determine the best position as the initial starting position of the particle , when making decisions, the objective function in the anchor point The position corresponding to the optimal value is used as the initial starting position of the particle ; Objective function Taking the minimization problem as an example, the internal elements contained in each anchor point are related to the objective function Comprehensive evaluation is performed. The smaller the evaluation value, the better the effect of the anchor point on the objective function. The calculation formula is as follows:
[0027] (2)
[0028] in, is the minimum value of the function, represents the minimum value function of the internal elements, is an index function that takes equal values.
[0029] Randomly select a dimension of the particle's position to perform multi-dimensional optimization operations until every dimension is exhausted. When the secondary particle moves ( , is the maximum number of MDA S1-S4 runs), the particle position is , randomly select the particle position A certain dimension of the search operation is performed until each dimension is traversed; a complete In the process, the particle's position The particles move in each dimension, and the order of movement is randomly generated. Each dimension of movement has the same probability of being selected for movement, but each dimension will only move once in step S3; before a certain dimension moves, the variable values corresponding to other dimensions remain unchanged, and only the dimension that needs to move moves. No. Dimensions ( ) is as follows:
[0030] P1, particle position Generate temporary particles , The generating formula is: .
[0031] P2. Calculate temporary particles In the The maximum and minimum values of the decision variables corresponding to the dimensions are and , Indicates the number of times the particle repeats in this dimension, , Indicates the number of cycles required for each dimension, initially and They are and , and The calculation formula is as follows:
[0032] (3)
[0033] in, Indicates the step size magnification factor, which is generally between 1 and 2.
[0034] P3, Temporary Particles In the The dimensions will be evenly divided into Equal parts, generate nodes, so the Generated when dimension optimization is performed sub-particles, and the sub-particle collection is expressed as , where the neutron particle The formulas for generating each dimension of are as follows:
[0035] (4).
[0036] in, Indicates the spacing between sub-particles. Represents temporary particles In the The dimension The second cycle produces The position corresponding to each particle, The initial setting is 0. Represents temporary particles In the The value corresponding to the dimension, ,Will middle The sub-particles correspond to the objective function The minimum value of the evaluation is assigned to the temporary particle , The position update formula is as follows:.
[0037] (5)
[0038] P4, repeat steps P2-P3 until , the temporary particles generated Corresponding objective function The evaluation value and particle position Corresponding objective function The evaluation value of the temporary particle is compared. The corresponding The evaluation value is greater than the particle position The corresponding If the evaluation value of is smaller, it will be covered and a new particle position will be generated. , The position update formula is as follows:
[0039] (6)
[0040] S4, determine whether the position of the particle changes. If not, perform a position variation strategy on the particle. If it changes, proceed to step S5. It is possible to get stuck in a local point, where the particle is located In the After the second evolution, the position is updated to , there will be To avoid this situation, it is necessary to perform a particle position Carry out the position mutation strategy to mutate the position of the particle. The method is as follows:
[0041] (7)
[0042] in, Represents the initial anchor particle collection Any anchor point inside .
[0043] S5. Repeat steps S1-S4 until the algorithm meets the end condition.
[0044] like Figure 1 As shown in FIG. 1 , the multi-dimensional search algorithm based on the multi-dimensional optimization strategy includes the following steps:
[0045] S1. Initial parameter setting: setting multiple anchor points within the allowed number of iterations.
[0046] S2. The best starting position is determined inside the anchor point according to the objective function as the initial position of the particle.
[0047] S3. Randomly select a dimension of the particle's position to perform a multi-dimensional optimization operation until all dimensions are exhausted.
[0048] S4, judging whether the position of the particle changes, if not, implementing a position variation strategy for the position of the particle, if changed, proceeding to step S5.
[0049] S5. Repeat steps S1-S4 until the algorithm meets the end condition.
[0050] like Figure 2 The figure shows some of the test functions used in CEC2005 (Competitive Evolution Stress Test 2005 Function Set). F1, F2, F3, F4, F5, and F6 are used to refer to these selected test functions, which are used for testing.
[0051] like Figure 3-Figure 8 The figure shows the comparison between MDA and the World Wide Web Optimizer (WWPA), Chernobyl Disaster Optimizer (CDO), Gold Rush Optimizer (GRO), Rime Ice Optimizer (RIME), Subtraction Optimizer (SABO) and Snow Melt Optimizer (SAO). Their initial particles are all set to 50 and the number of evolutions is 100.
[0052] Table 1 shows the comparison of the best fitness values of each algorithm, the average fitness corresponding to the optimal solution, and the experimental standard deviation.
[0053] Table 1
[0054] From the data in Table 1, we can see that MDA, CDO, GRO, and SABO can produce the least target value and deviation under the above-mentioned specific test function, but WWPA, RIME, and SAO cannot produce the least target value and deviation in the above-mentioned specific test function. The MDA algorithm is competitively compared with 6 optimization algorithms. The results shown in 30 independent running experiments of F1-F6 show that the two functions of F1 and F3 achieve slightly worse results in the average value evaluation and median evaluation. The average value and median are the smallest in the four test function results of F2, F4, F5, and F6. MDA achieves the smallest variance in the variance ranking of the three function tests of F2, F4, and F5. This shows that MDA has a good handling of optimization problems.
[0055] Fig. 9 Schematic diagram of the structure of using MDA to optimize the extreme learning machine (ELM) model for fault diagnosis.
[0056] Fig.10 The data set used in the fault process. The fault diagnosis analysis was performed using the bearing fault data of Western Reserve University. The fault was divided into four types of faults. In the case of a bearing fault diameter of 0.1778 mm, a motor load of 0, and a motor speed of 1197, there were four types of fault data, namely inner ring fault (105.mat), rolling element fault (118.mat), outer ring fault (130.mat), and normal base data (97.mat). Each type of fault contained 200 fault data, for a total of 800 data, of which 80% were used as training data and 20% as test data. The fault data was processed using wavelet transform to obtain new fault signals, which were then divided into training set and test set for ELM fault classification, and MDA was used to optimize and adjust the ELM internally.
[0057] The wavelet transform process refers to the new signal sequence obtained after the input data is processed by the wavelet soft threshold denoising.
[0058] Among them, the fault diagnosis method based on MDA optimization of ELM model, the model principle of ELM is as follows:
[0059] The extreme learning machine is a feedforward neural network. During the training process, the input layer is set to neurons, and the output layer has neurons, and the hidden layer has neurons. Assume is the connection weight between the input layer and the hidden layer, where each element is a random number between [-1,1]. for A matrix of .
[0060]
[0061] set up is a bias of the hidden layer, corresponding to the hidden layer exist An offset under the product, then the bias vector The size is A column vector where each element is a random number between [0, 1].
[0062] .
[0063] remember is the connection weight between the hidden layer and the output layer, and its size is The matrix of . The initial hidden layer weights can be and bias Find out and get the trained extreme learning model.
[0064]
[0065] Through the activation function By mapping, we can get the output value of the extreme learning machine.
[0066]
[0067] set up is the expected minimum output value, and the minimum difference method can be used to obtain This makes the error function approach 0.
[0068]
[0069] Among them, MDA optimization of ELM parameters refers to the optimization weights and bias , the randomly generated and As the input of MDA, MDA seeks the best and Make the classification success rate of the training set reach the best.
[0070] Fig.11The following are the confusion matrices obtained by using MDA to optimize the ELM model and the confusion matrices obtained by the ELM model without optimization. The results of using MDA to optimize the ELM model training include a classification accuracy of 99.84% for the training set and 96.25% for the test set; the ELM model without optimization algorithm has a classification accuracy of 84.53% for the training set and 73.13% for the test set. Compared with the classification results of the bearing fault data of Western Reserve University, the accuracy of the ELM model optimized by MDA is significantly improved by 15.31% and 23.12% in the training set and test set, respectively, compared with the ELM model without optimization.
[0071] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can replace or change the technical solution and concept of the present invention within the technical scope disclosed by the present invention, which should be within the protection scope of the present invention.
Claims
1. A multi-dimensional search algorithm (MDA) based on a multi-dimensional optimization strategy, characterized in that: The steps include: S1, initial parameter setting, setting multiple anchor points within the allowed number of iterations; S2, the anchor point determines the best starting position according to the objective function as the initial position of the particle; S3, randomly select a dimension of the particle's position to perform multi-dimensional optimization operation until all dimensions are searched; S4, judging whether the position of the particle changes, if not, performing a position variation strategy on the position of the particle, if it changes, proceeding to step S5; S5. Repeat steps S1-S4 until the algorithm meets the end condition.
2. A multi-dimensional search algorithm based on a multi-dimensional optimization strategy as claimed in claim 1, characterized in that In the steps S1 and S2, in S1, the size is set to anchor points, each of which is randomly variables, and the anchor position is created using the following formula: (1) in, for OK The internal elements of the matrix are random numbers between 0 and 1. and Indicates the upper and lower bounds of the variable; in S2, the anchor point is internally located according to the objective function Determine the best position as the initial starting position of the particle , when making decisions, the objective function in the anchor point The position corresponding to the optimal value is used as the initial starting position of the particle ; Objective function Taking the minimization problem as an example, the internal elements contained in each anchor point are related to the objective function Comprehensive evaluation is performed. The smaller the evaluation value, the better the effect of the anchor point on the objective function. The calculation formula is as follows: (2) in, is the minimum value of the function, represents the minimum value function of the internal elements, is an index function that takes equal values.
3. A multi-dimensional search algorithm based on a multi-dimensional optimization strategy as claimed in claim 1, characterized in that In step S3, When the secondary particle moves ( , is the maximum number of MDA S1-S4 runs), the particle position is , randomly select the particle position A certain dimension of the search operation is performed until each dimension is traversed; a complete In the process, the particle's position The particles move in each dimension, and the order of movement is randomly generated. Each dimension of movement has the same probability of being selected for movement, but each dimension will only move once in step S3; before a certain dimension moves, the variable values corresponding to other dimensions remain unchanged, and only the dimension that needs to move moves. No. Dimensions ( ) is as follows: P1, particle position Generate temporary particles , The generating formula is: ; P2. Calculate temporary particles In the The maximum and minimum values of the decision variables corresponding to the dimensions are and , Indicates the number of times the particle repeats in this dimension, , Indicates the number of cycles required for each dimension, initially and They are and , and The calculation formula is as follows: (3) in, Indicates the step size magnification factor, which is generally between 1 and 2; P3, Temporary Particles In the The dimensions will be evenly divided into Equal parts, generate nodes, so the Generated when dimension optimization is performed sub-particles, and the sub-particle collection is expressed as , where the neutron particle The formulas for generating each dimension of are as follows: (4) in, Indicates the spacing between sub-particles. Represents temporary particles In the The dimension The second cycle produces The position corresponding to each particle, The initial setting is 0. Represents temporary particles In the The value corresponding to the dimension, ,Will middle The sub-particles correspond to the objective function The minimum value of the evaluation is assigned to the temporary particle , The position update formula is as follows: (5) P4, repeat steps P2-P3 until , the temporary particles generated Corresponding objective function The evaluation value and particle position Corresponding objective function The evaluation value of the temporary particle is compared. The corresponding The evaluation value is greater than the particle position The corresponding If the evaluation value of is smaller, it will be covered and a new particle position will be generated. , The position update formula is as follows: (6)。 4. A multi-dimensional search algorithm based on a multi-dimensional optimization strategy as claimed in claim 1, characterized in that In step S3, the particle is located at It is possible to get stuck in a local point, where the particle is located In the After the second evolution, the position is updated to , there will be To avoid this situation, it is necessary to perform a particle position Carry out the position mutation strategy to mutate the position of the particle. The method is as follows: (7) in, Represents the initial anchor particle collection Any anchor point inside .