Engineering problem optimization method based on differential particle swarm optimization algorithm

Abstract

The invention provides an engineering problem optimization method based on a differential particle swarm optimization algorithm. An engineering optimization model is established according to an engineering problem based on the differential evolution algorithm and the particle swarm optimization algorithm; performing population initialization on the engineering optimization model; particles in the particle swarm optimization population randomly select individuals in the differential evolution population to carry out crossover operation processing; and performing variation processing on the individuals in the differential evolution population according to the optimal positions of the individuals in the particle swarm optimization population to realize optimization of the engineering problem. Compared with the prior art, information is exchanged between the differential evolution population and the particle swarm optimization population to improve the population quality, the differential evolution population is varied through the position vector of the particle swarm optimization population to accelerate the response speed of the differential evolution population, and the learning sample is generated through the differential evolution population. The performance of a particle swarm optimization algorithm is improved, so that the engineering optimization problem is solved more quickly and reliably.

Description

Technical Field

[0001] The present invention is applicable to the field of data processing, and in particular relates to an engineering problem optimization method based on a differential particle swarm optimization algorithm. Background Art

[0002] Particle swarm optimization (PSO) uses only basic mathematical operations and can achieve a high convergence speed. Due to its fast convergence speed and high performance, the PSO algorithm is widely used in function optimization and engineering problems. Since the advent of the PSO algorithm in 1995, many PSO algorithm variants have been reported, and the performance of the PSO algorithm has been significantly improved. However, most of the current PSO algorithm variants can only perform well on some specific optimization problems, and fewer PSO algorithms can achieve high performance on various types of optimization problems.

[0003] However, the existing PSO algorithm uses a relatively small population and converges quickly, but it may easily fall into local optimality when optimizing complex multimodal problems. In addition, the PSO algorithm does not have rotation invariance, so it performs poorly when dealing with problems involving rotation transformations.

[0004] Therefore, the present invention proposes a new engineering problem optimization method based on differential particle swarm optimization algorithm to solve the above technical problems. Summary of the invention

[0005] The present invention proposes an engineering problem optimization method based on differential particle swarm optimization algorithm, which aims to optimize the existing PSO algorithm through differential evolution algorithm to improve the performance of particle swarm optimization algorithm, so as to solve engineering optimization problems more quickly and reliably.

[0006] The present invention proposes an engineering problem optimization method based on differential particle swarm optimization algorithm, comprising the following steps:

[0007] S1. Establish engineering optimization model based on differential evolution algorithm and particle swarm optimization algorithm according to engineering problems;

[0008] S2. Initializing the population of the engineering optimization model to obtain a differential evolution population and a particle swarm optimization population;

[0009] S3, the particles in the particle swarm optimization population randomly select individuals in the differential evolution population to perform crossover processing to obtain experimental learning samples;

[0010] S4, performing mutation processing on individuals in the differential evolution population according to the optimal positions of individuals in the particle swarm optimization population to obtain a test vector;

[0011] S5. The particle swarm optimization population is iteratively optimized according to the experimental learning samples, and the differential evolution population is iteratively optimized according to the experimental vectors to obtain optimization results, thereby achieving optimization of the engineering problem.

[0012] Preferably, in step S2, the parameters for population initialization of the engineering optimization model include the number of individuals, inertia weight and acceleration factor.

[0013] Preferably, in step S3, particles in the particle swarm optimization population randomly select individuals in the differential evolution population to perform crossover processing to satisfy the following relationship:

[0014]

[0015] Among them, i represents the particle number, d represents the dimension number, Exemp i represents the experimental learning sample of particle i, Exemplar i Represents learning samples, Exemplar_val i The fitness of the learning sample, r represents the individual with sequence number r in the differential evolution population, P cr represents the crossover probability, Val(r) represents the fitness value of individual r, Pbestval(i) represents the fitness value of particle i, rand represents a uniformly distributed random number in the range [0,1], ω represents the inertia weight, c1 and c2 both represent the acceleration factor, represents the d-dimensional position vector of particle i, Gbest d represents the global optimum of the particle swarm optimization population, A d-dimensional variable representing the velocity vector of particle i.

[0016] Preferably, in step S4, the individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to satisfy the following relationship:

[0017]

[0018] in, represents the trial vector of individual i, represents the target vector randomly selected from the subset of excellent individuals, F i represents the scaling factor, represents the random selection of the target vector with serial number r2, G is the number of iterations, represents a target vector randomly selected from the differential evolution population and the particle swarm optimization population.

[0019] Preferably, the The following relationship is satisfied:

[0020] Nelite =round(NP-(NP-N end )*iter / iter m );

[0021] Among them, N elite represents the size of the excellent individual subset, round represents rounding, NP represents the size of the individuals in the differential evolution population, N end It indicates the size of the excellent individual subset at the end of optimization, iter indicates the current number of iterations, and iter m Indicates the maximum number of iterations.

[0022] Compared with the prior art, the present invention establishes an engineering optimization model according to the engineering problem based on the differential evolution algorithm and the particle swarm optimization algorithm; initializes the population of the engineering optimization model to obtain the differential evolution population and the particle swarm optimization population; the particles in the particle swarm optimization population randomly select individuals in the differential evolution population for crossover operation processing to obtain experimental learning samples; the individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to obtain the experimental vector; the particle swarm optimization population is iteratively optimized according to the experimental learning samples, and the differential evolution population is iteratively optimized according to the experimental vector to obtain the optimization result, thereby realizing the optimization of the engineering problem. The present invention improves the population quality by exchanging information between the differential evolution population and the particle swarm optimization population, mutates the differential evolution population through the position vector of the particle swarm optimization population to speed up the response speed of the differential evolution population, and generates learning samples through the differential evolution population to improve the performance of the particle swarm optimization algorithm, thereby solving the engineering optimization problem more quickly and reliably. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The present invention will be described in detail below in conjunction with the accompanying drawings. The above and other aspects of the present invention will become clearer and easier to understand through the detailed description made in conjunction with the following drawings. In the accompanying drawings:

[0024] Figure 1 It is a flowchart of an engineering problem optimization method based on a differential particle swarm optimization algorithm provided by an embodiment of the present invention;

[0025] Figure 2 It is a pseudo code schematic diagram of crossover operation processing of the engineering problem optimization method based on differential particle swarm optimization algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0027] Please refer to Figure 1-Figure 2 The present invention proposes an engineering problem optimization method based on differential particle swarm optimization algorithm, comprising the following steps:

[0028] S1. Establish an engineering optimization model based on engineering problems based on differential evolution algorithm and particle swarm optimization algorithm.

[0029] S2. Initializing the population of the engineering optimization model to obtain a differential evolution population and a particle swarm optimization population.

[0030] In the embodiment of the present invention, in step S2, the parameters for population initialization of the engineering optimization model include the number of individuals, inertia weight, and acceleration factor.

[0031] S3. The particles in the particle swarm optimization population randomly select individuals in the differential evolution population to perform crossover processing to obtain experimental learning samples.

[0032] In the embodiments of the present invention, please refer to Figure 2 , Figure 2 is a pseudo code schematic diagram of the crossover operation processing of the engineering problem optimization method based on the differential particle swarm optimization algorithm provided by an embodiment of the present invention, where fit(·) represents the fitness function. In step S3, the particles in the particle swarm optimization population randomly select individuals in the differential evolution population for crossover operation processing to satisfy the following relationship:

[0033]

[0034] Where i represents the i-th particle, d represents the dimension, and Exemp i represents the experimental learning sample of particle i, Exemplar i Represents learning samples, Exemplar_val i The fitness of the learning sample, r represents the individual in the rth differential evolution population, P cr represents the crossover probability, Val(r) represents the fitness value of individual r, Pbestval(i) represents the fitness value of particle i, rand represents a uniformly distributed random number in the range [0,1], ω represents the inertia weight, c1 and c2 both represent the acceleration factor, represents the d-dimensional variable of particle i, Gbest d represents the global optimal d-dimensional variable of the particle swarm optimization population, A d-dimensional variable representing the velocity vector of particle i.

[0035] Specifically, for any particle i, a random individual r from the differential evolution population is selected, and a test learning sample is generated through a crossover operation. The crossover probability of the differential evolution population is 0.9, which can accelerate convergence. Therefore, when Pbestval(i) (the fitness value of particle i) is not inferior to Val(r) (the fitness value of individual r), the crossover probability P cr =0.9, otherwise P cr =0.1. Based on the crossover operation, most dimensions of the learning samples are copied from the better solutions between the particles in the PSO population and the individuals in the differential evolution population, thereby enhancing the diversity of the PSO population. In the subsequent selection operation, if the fitness value of the latter is better, the original learning sample is replaced by the experimental learning sample. Through the selection operation, the quality of the learning samples of the PSO population is guaranteed. Since the differential evolution population has rotation invariance, using the individuals of the differential evolution population to generate the PSO population learning samples can provide partial rotation invariance for the PSO population.

[0036] S4. The individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to obtain a test vector.

[0037] In the embodiment of the present invention, in order to further enhance the information exchange between the differential evolution population and the particle swarm optimization population, the elite individuals of the differential evolution population and the best position of the particle swarm optimization population (denoted as E-DEx) are used to generate the test vector of the differential evolution population.

[0038] In step S4, the individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to satisfy the following relationship:

[0039]

[0040] in, represents the trial vector of individual i, represents the target vector randomly selected from the subset of excellent individuals, F i represents the scaling factor, represents the random selection of the target vector with serial number r2, G is the number of iterations, represents a target vector randomly selected from the union of the differential evolution population and the particle swarm optimization population. is derived from the differential evolution population and Pos ibest (Pos ibest represents the current position of the best particle in the particle swarm optimization population) and a randomly selected individual. ibest t is updated in each iteration, so use Pos ibestPerforming differential evolution population mutation can speed up the response of the differential evolution population to optimization problems.

[0041] is randomly selected from a subset of excellent individuals,

[0042] Said The following relationship is satisfied:

[0043] N elite =round(NP-(NP-N end )*iter / iter m );

[0044] Among them, N elite represents the size of the excellent individual subset, round represents rounding, NP represents the size of the individuals in the differential evolution population, N end It indicates the size of the excellent individual subset at the end of optimization, iter indicates the number of iterations, and iter m Indicates the maximum number of iterations.

[0045] N elite Represents the top N in the differential evolution population sorted by fitness value elite In the optimization process, N elite Linear reduction aims to focus the search around a small number of promising individuals. In the early stages of optimization, Randomly select from the entire population to achieve enhanced exploration capabilities. As the number of iterations increases, Select from a small number of high-quality individuals to increase the convergence speed in the later stage.

[0046] S5. The particle swarm optimization population is iteratively optimized according to the experimental learning samples, and the differential evolution population is iteratively optimized according to the experimental vectors to obtain optimization results, thereby achieving optimization of the engineering problem.

[0047] In the embodiment of the present invention, the engineering optimization model is divided into a differential evolution population and a particle swarm optimization population. The two populations work alternately and collaboratively according to a mutual learning strategy, and then some potential high-quality information can be fully exchanged, so that the quality of the entire engineering optimization model can be improved, thereby being able to solve engineering optimization problems more quickly and reliably.

[0048] Compared with the prior art, the present invention establishes an engineering optimization model according to the engineering problem based on the differential evolution algorithm and the particle swarm optimization algorithm; initializes the population of the engineering optimization model to obtain the differential evolution population and the particle swarm optimization population; the particles in the particle swarm optimization population randomly select individuals in the differential evolution population for crossover operation processing to obtain experimental learning samples; the individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to obtain the experimental vector; the particle swarm optimization population is iteratively optimized according to the experimental learning samples, and the differential evolution population is iteratively optimized according to the experimental vector to obtain the optimization result, thereby realizing the optimization of the engineering problem. The present invention improves the population quality by exchanging information between the differential evolution population and the particle swarm optimization population, mutates the differential evolution population through the position vector of the particle swarm optimization population to speed up the response speed of the differential evolution population, and generates learning samples through the differential evolution population to improve the performance of the particle swarm optimization algorithm, thereby solving the engineering optimization problem more quickly and reliably.

[0049] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0050] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only the preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation manner. The above-mentioned specific implementation manner is only illustrative rather than restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. An engineering problem optimization method based on differential particle swarm optimization algorithm, characterized in that: The following steps are involved: S1. Establish engineering optimization model based on differential evolution algorithm and particle swarm optimization algorithm according to engineering problems; S2. Initializing the population of the engineering optimization model to obtain a differential evolution population and a particle swarm optimization population; S3, the particles in the particle swarm optimization population randomly select individuals in the differential evolution population to perform crossover processing to obtain experimental learning samples; S4, performing mutation processing on individuals in the differential evolution population according to the optimal positions of individuals in the particle swarm optimization population to obtain a test vector; S5. The particle swarm optimization population is iteratively optimized according to the experimental learning samples, and the differential evolution population is iteratively optimized according to the experimental vectors to obtain optimization results, thereby achieving optimization of the engineering problem.

2. The engineering problem optimization method based on differential particle swarm optimization algorithm according to claim 1, characterized in that: In step S2, the parameters for population initialization of the engineering optimization model include the number of individuals, inertia weight and acceleration factor.

3. The engineering problem optimization method based on differential particle swarm optimization algorithm according to claim 1, characterized in that: In step S3, particles in the particle swarm optimization population randomly select individuals in the differential evolution population to perform crossover processing to satisfy the following relationship: Where i represents the i-th particle, d represents the dimension, and Exemp i represents the experimental learning sample of particle i, Exemplar i Represents learning samples, Exemplar_val i represents the fitness of the learning sample, r represents the random selection of the individual with sequence number r in the differential evolution population, P cr represents the crossover probability, Val(r) represents the fitness value of individual r, Pbestval(i) represents the fitness value of particle i, c1 and c2 both represent acceleration factors, represents the d-dimensional variable of particle i, Gbest d represents the global optimal d-dimensional variable of the particle swarm optimization population, represents the d-dimensional variable of the velocity vector of particle i, rand represents a uniformly distributed random number ranging from 0 to 1, and ω represents the inertia weight.

4. The engineering problem optimization method based on differential particle swarm optimization algorithm according to claim 1, characterized in that: In step S4, the individuals in the differential evolution population are mutated according to the optimal positions of the individuals in the particle swarm optimization population to satisfy the following relationship: in, represents the trial vector of individual i in the differential evolution population, represents the target vector randomly selected from the subset of excellent individuals, F i represents the scaling factor, represents the random selection of the target vector with serial number r2, G is the number of iterations, represents a target vector randomly selected from the union of the differential evolution population and the particle swarm optimization population.

5. The engineering problem optimization method based on differential particle swarm optimization algorithm according to claim 4, characterized in that: Said The following relationship is satisfied: N elite =round(NP-(NP-N end )*iter / iter m ); Among them, N elite represents the size of the excellent individual subset, round represents rounding, N end It indicates the size of the excellent individual subset at the end of optimization, iter indicates the current number of iterations, and iter m represents the maximum number of iterations, and NP represents the size of individuals in the differential evolution population.

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