CN102694800A - Gaussian process regression method for predicting network security situation - Google Patents
Gaussian process regression method for predicting network security situation Download PDFInfo
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Abstract
The invention discloses a gaussian process regression method for predicting a network security situation in the technical field of network information security. According to the invnetion, a hierarchical network security situation evaluation index system is structured by using an analytic hierarchy process; the damage degree of various network security threats to the network security situation is analyzed by the system so as to calculate a network security situation value of each time monitoring point and structure a time sequence and then structure into a training sample set; the training sample set is subjected to iterative training by utilizing gaussian process regression so as to obtain a prediction model meeting an error requirement; an optimal training parameter of the gaussian process regression is dynamically searched by utilizing an particle swarm optimization in the training process so as to reduce a prediction error, and finally the prediction of the network security situation value of the time monitoring point in the future is finished by utilizing the prediction mode. The gaussian process regression method provided by the invnetion has the beneficial effects of better adaptability and lower prediction error in the respect of reducing the prediction error of the network security situation.
Description
Technical Field
The invention belongs to the technical field of network information security, and particularly relates to a Gaussian process regression method for network security situation prediction.
Background
The popularity and technological innovation of the Internet has profoundly changed human lives and also brought about serious network security problems. Various network security problems emerge endlessly at present, various network attacks gradually show development trends of distribution, scale, complication, indirection and the like, and current network security equipment has no relatively perfect security alarm mechanism, so that the network security equipment has very important theoretical significance and practical significance for accurate alarm of future network security trends. At present, the mainstream method is to predict the network security situation value of a target network node in the future time so as to realize network security early warning. The prediction means of the network security situation value mainly abstracts a target problem into a regression problem by using an artificial intelligence algorithm, and solves the network security situation value of a future time node by constructing a regression model.
The construction of the network security situation evaluation index system requires the calculation of the influence factors, namely the weights, of various network attacks on the network security situation values. The construction method of the evaluation index system directly determines whether the network security situation value can accurately reflect the actual situation of the current network.
The calculation of the network security situation value requires that the times of various network attacks occurring at a certain time node are multiplied by the weights of the various network attacks, and then the sum is obtained, so that the network security situation value of the time node is obtained.
The current prediction method of the network security situation value is mainly based on methods such as an artificial neural network, a support vector machine and a Bayesian network, but the problems of large prediction errors are generally found in practical application.
Disclosure of Invention
The invention discloses a Gaussian process regression method for predicting network security situation aiming at the defects. The invention introduces an Analytic Hierarchy Process (AHP) so as to obtain an evaluation index system capable of accurately reflecting the current network security condition.
The Gaussian process regression method for predicting the network security situation comprises the following steps:
1) constructing a hierarchical network security situation evaluation index system T by using an analytic hierarchy process, and calculating to obtain a total sequencing weight matrix omega of the network security situation evaluation index system T;
2) sequentially inputting historical intrusion detection results of the network security equipment into a network security situation evaluation index system T according to the time sequence to obtain a network security situation value V at the 1 st moment1Network security situation value V to the m-th momentm；
3) Using sliding window method to convert V1~VmIs configured to time-series S, S ═ V1…Vm}；
Then, the time sequence S is randomly divided according to a fixed proportion to obtain GaussReadable training sample set S in program regression methodtrainAnd a test sample set Stest(ii) a Guarantee training sample set StrainAnd a test sample set StestThe data format required by the Gaussian process regression method is met;
4) training sample set S by using Gaussian process regression methodtrainPerforming iterative training to obtain a temporary prediction model H, and performing error correction on the temporary prediction model H by using a particle swarm algorithm to obtain a prediction model H meeting error expectation;
5) and (4) completing the prediction of the network security situation value at the future moment by using the prediction model H.
The structure of the network security situation evaluation index system T is as follows: the network security situation evaluation index system T is divided into three layers, wherein the upper layer is a target layer, and the content of the target layer is a network security situation value; the middle layer is a criterion layer, the contents of which are strong hazard degree, medium hazard degree and weak hazard degree, and the strong hazard degree, the medium hazard degree and the weak hazard degree are divided according to the hazard degree of the network security threat; the lower layer is an index layer with the content of the 1 st network security threat x1To nth network security threat xn。
The calculation process of the total ranking weight matrix ω is as follows: first, threat x to type 1 network security1To nth network security threat xnThen, according to the analytic hierarchy process, respectively calculating the network security threat x in the ithiFor the influence coefficients of the strong hazard degree, the medium hazard degree and the weak hazard degree, i is 1 to n; and calculating final influence coefficients of the strong hazard degree, the medium hazard degree and the weak hazard degree on the network security situation value respectively, and finally obtaining a total sequencing weight matrix omega of the network security situation evaluation index system T.
The step 2) comprises the following steps:
21) counting the intrusion detection result r of the network security equipment at the j momentjJ is 1 to m; r isjIs a matrix of 1 x n, and the matrix is,wherein,
toRespectively indicate that: at time j, 1 st cyber-security threat x1To nth network security threat xnThe number of occurrences;
22) will r isjMultiplying the total sorting weight matrix omega of the network security situation evaluation index system T to obtain the network security situation value V at the j momentj。
The fixed ratio is 3: 2.
The step 4) specifically comprises the following steps:
41) in the particle swarm algorithm, the following parameters are set: maximum iteration number of 100, population size of 10, initial inertial weight omega1=0.8, terminating the inertial weight ωT=0.1, 2 for both learning factors 1 and 2, and a particle velocity interval of [0, 0.5%]；
42) Setting a kernel function type of a Gaussian process regression method;
43) normalized training sample set StrainAnd a test sample set Stest；
44) The particle swarm algorithm transfers the initial training parameters to a Gaussian process regression method which is implemented by carrying out regression on a training sample set StrainObtaining a temporary prediction model h by training; the initial training parameters refer to random training parameters initially generated by a particle swarm algorithm;
45) by testing the sample set StestCalculating a training error epsilon of the temporary prediction model h;
46) if the training error epsilon of the temporary prediction model h meets the preset periodThe final prediction model H is obtained when the value theta is observed, otherwise, new training parameters are iteratively generated by a Gaussian process regression method according to the particle swarm optimization, and the new training parameters are obtained by carrying out the iteration on a training sample set StrainThereby updating the temporary prediction model h;
47) when one of the following two conditions is satisfied, executing step 48), otherwise, returning to execute step 45); the first condition is: the iteration times of the Gaussian process regression method reach the maximum iteration times of 100; the second condition is: the temporary prediction model h meets a preset expected value;
48) and outputting the final prediction model H.
The preset desired value θ is 85%.
In the new training parameters iteratively generated by the Gaussian process regression method according to the particle swarm algorithm, the iterative process of the particle swarm algorithm is as follows:
the Particle Swarm Optimization (PSO) is initialized, an initial population consisting of 10 particles is randomly constructed, and the b-th particle in the initial population is assigned with an initial position
And initial velocityb, taking 1 to 10; calculating a fitness function F (b) of each particle in the initial population, if the minimum value min (F (b)) of the fitness functions F (b) of all the particles in the initial population is less than or equal to theta, taking the particle corresponding to min (F (b)) as the optimal solution of the problem to be solved, otherwise, updating the speed and the position of the particle according to the following three formulas, namely performing population iteration;
wherein; pbestRefers to the individual optimal positions through which all particles pass; gbestbThe optimal position through which the population passes; k is the number of iterations, r1And r2Is [0,1 ]]A random number in between; c1And C21 st learning factor and 2 nd learning factor respectively;
and
respectively indicate that: the iteration times are k-1 times and the position of the b-th particle when k times;and
respectively indicate that: the speed of the b-th particle when the iteration times are k-1 times and k times; omega0And ω1Is the initial inertial weight, ω2To omegabThe (b) th inertia weight is the 2 nd inertia weight value; omega0=ω1=0.8。
The invention has the beneficial effects that: the method and the device for predicting the network security situation not only overcome the defects of the prior situation prediction technology, but also improve the accuracy of prediction.
Drawings
FIG. 1 is a flow chart of a method for predicting network security posture;
FIG. 2 is a flow chart of a process for generating an evaluation index system of network security situation based on an analytic hierarchy process;
FIG. 3 is a schematic diagram of a sliding window method;
FIG. 4 is a flow chart of Gaussian process regression algorithm training;
Detailed Description
The preferred embodiments will be described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.
The establishment of a network security situation evaluation index system and the calculation of situation values are the premise of network security situation prediction. Therefore, the method introduces an analytic hierarchy process to analyze original various network security threats so as to obtain a hierarchical evaluation index system; after a hierarchical evaluation index system is obtained, a network security situation value can be calculated, and a discrete time sequence is constructed into a training sample set and a test sample set according to a sliding window method; inputting the training sample set into a Gaussian process regression algorithm, training the training sample set by the Gaussian process regression algorithm to obtain a temporary prediction model, and performing error detection on the temporary prediction model by using the test sample set to obtain a final prediction model meeting error requirements; and finally, the final prediction model is used for completing the prediction of the network security situation value. Therefore, from local to overall, the Gaussian process regression algorithm can be suitable for the more general network security situation prediction problem.
Fig. 1 is a flowchart of a network security situation prediction method based on gaussian process regression according to the present invention.
The Gaussian process regression method for predicting the network security situation comprises the following steps of:
1) constructing a hierarchical network security situation evaluation index system T by using an analytic hierarchy process, and calculating to obtain a total sequencing weight matrix omega of the network security situation evaluation index system T; to analyze the 1 st cyber-security threat x1To nth network security threat xnThe degree of harm to the network security situation; n is a network security threat speciesThe sum of classes;
AHP (analytic hierarchy process) is to quantify the qualitative problem which is difficult to quantify through strict mathematical operation, and to integrate the complex decision problem which originally mixes the quantification and the qualitative into a unified whole, and then to make comprehensive analysis and evaluation. The AHP solving process is as follows: firstly, decomposing the problem to be decided into different layers according to the sequence of a target layer, a criterion layer and a specific scheme, and establishing a hierarchical structure and pairwise judgment matrixes; then solving the characteristic vector of the judgment matrix to obtain the priority weight of each element of each layer relative to the element of the previous layer; and finally, carrying out hierarchical merging on the final weight of each scheme to the target layer by using a weighted summation method, wherein the scheme with the maximum final weight value is the optimal scheme. The AHP solving process can be summarized as "decomposition- > judgment- > synthesis". AHP is applicable to evaluation and decision problems that have hierarchical structures and are difficult to describe quantitatively.
As shown in fig. 2, the structure of the network security situation evaluation index system T is as follows: the network security situation evaluation index system T is divided into three layers, wherein the upper layer is a target layer, and the content of the target layer is a network security situation value; the middle layer is a criterion layer, the contents of which are strong hazard degree, medium hazard degree and weak hazard degree, and the strong hazard degree, the medium hazard degree and the weak hazard degree are divided according to the hazard degree of the network security threat; the lower layer is an index layer with the content of the 1 st network security threat x1To nth network security threat xn。
The calculation process of the total ranking weight matrix ω is as follows: first, threat x to type 1 network security1To nth network security threat xnThen, according to the analytic hierarchy process, respectively calculating the network security threat x in the ithiFor the influence coefficients of the strong hazard degree, the medium hazard degree and the weak hazard degree, i is 1 to n; and calculating final influence coefficients of the strong hazard degree, the medium hazard degree and the weak hazard degree on the network security situation value respectively, and finally obtaining a total sequencing weight matrix omega of the network security situation evaluation index system T.
The step 1) is specifically described as follows:
firstly, the network attack weight is assigned
And (3) giving 1-5 measures by experts in the related field according to the hazard degrees of various network attacks, namely giving weights to the network attacks, wherein the hazard degree of 5 is the highest, the hazard degree of 1 is the lowest, and finally, the average weights of various network threats are calculated by combining a Delphi method.
The second step is that: and determining final weight distribution of an evaluation system by using AHP, wherein the detailed process is as follows:
(1) two-by-two comparison matrix a is calculated, for the element i and the element j under the same criterion, which is more important than the criterion, the two elements need to be quantized, using the scales of tables 1-5 below,
TABLE 1 judge matrix Scale and its meanings
(2) Calculating the relative weight of each element under a certain criterion, and passing AX = lambdamaxX calculates the eigenvector X, lambda of the matrix AmaxThe characteristic value with the maximum index value is obtained, and ω X is unitized and used as the weight of each element under the criterion;
(3) obtaining a total sorting weight matrix of a calculation index system through matrix multiplication;
(4) and (5) matrix consistency checking. Let the consistency index of the matrix be CI, CI = (lambda)max-n)/(n-1), where n is the judgment matrix dimension; RI is an average consistency index, and specific values are shown in Table 2; CR is the random consistency ratio of the judgment matrix, CR = CI/RI, and when CR is less than or equal to 0.1, the matrix satisfies consistency.
TABLE 2 average consistency index values
2) Sequentially inputting historical intrusion detection results of the network security equipment into a network security situation evaluation index system T according to the time sequence to obtain a network security situation value V at the 1 st moment1Network security situation value V to m-th timem(ii) a The 1 st time to the mth time are arranged according to the time sequence;
the step 2) comprises the following steps:
21) counting the intrusion detection result r of the network security equipment at the j momentjJ is 1 to m; r isjIs a matrix of 1 x n, and the matrix is,wherein,
to
Respectively indicate that: at time j, 1 st cyber-security threat x1To nth network security threat xnThe number of occurrences;
22) will r isjMultiplying the total ordering weight matrix omega of the network security situation evaluation index system T, wherein omega is an n multiplied by 1 matrix, thereby obtaining the network security situation value V at the j momentj。
3) Using sliding window method to convert V1~VmIs configured to time-series S, S ═ V1…Vm}; if the sliding window size is set to be 4 and the sliding step length is set to be 1, S1={V1,V2,V3,V4}；S2={V2,V3,V4,V5}，S3={V3,V4,V5,V6And so on, as shown in FIG. 3, as at S1In the middle, the network security situation value V at the 1 st moment1And the network security situation value V at the 2 nd moment2And the network security situation value V at the 3 rd moment3And a network security situation value V at the 4 th moment4To predict the network security situation value V at the 5 th moment5Then, by analogy, a time series S is obtained.
Then, the time sequence S is randomly divided according to a fixed proportion to obtain a training sample set S readable in a Gaussian Process Regression (GPR) methodtrainAnd a test sample set Stest(ii) a Guarantee training sample set StrainAnd a test sample set StestThe data format required by the Gaussian process regression method is met; the fixed ratio is 3: 2.
4) Training sample set S by using Gaussian process regression methodtrainPerforming iterative training to obtain a temporary prediction model H, and performing error correction on the temporary prediction model H by using a Particle Swarm Optimization (PSO) to obtain a prediction model H meeting error expectation;
the step 4) specifically comprises the following steps:
41) in the particle swarm algorithm, the following parameters are set: maximum iteration number of 100, population size of 10, initial inertial weight omega1=0.8, terminating the inertial weight ωT=0.1, 2 for both learning factors 1 and 2, and a particle velocity interval of [0, 0.5%]；
42) Setting a kernel function type of a Gaussian process regression method;
43) normalized training sample set StrainAnd a test sample set Stest；
44) The particle swarm algorithm transfers the initial training parameters to a Gaussian process regression method which is implemented by carrying out regression on a training sample set StrainObtaining a temporary prediction model h by training; the initial training parameters refer to random training parameters initially generated by a particle swarm algorithm; when the kernel function is Gaussian kernel function, the initial training parameter is kernel wide parameterThe number "and the" penalty factor ".
45) By testing the sample set StestCalculating a training error epsilon of the temporary prediction model h;
46) if the training error epsilon of the temporary prediction model H meets the preset expected value theta, the temporary prediction model H is the final prediction model H, otherwise, the Gaussian process regression method iteratively generates new training parameters according to the particle swarm algorithm by aiming at the training sample set StrainThereby updating the temporary prediction model h;
47) when one of the following two conditions is satisfied, executing step 48), otherwise, returning to execute step 45); the first condition is: the iteration times of the Gaussian process regression method reach the maximum iteration times of 100; the second condition is: the temporary prediction model h meets a preset expected value;
48) and outputting the final prediction model H.
The gaussian process regression method is one of the most common stochastic process models in engineering problems. In the field of machine learning, a Gaussian process regression method is a machine learning method developed on the basis of a Gaussian random process and a Bayesian learning theory, has a strict statistical learning theory basis, and has good adaptability to processing complex problems such as high dimension, small samples, nonlinearity and the like. Under the condition of not sacrificing performance, compared with an artificial neural network, the Gaussian process has the characteristic of easy realization; the method has flexible nonparametric inference capability, namely, algorithm parameters of a Gaussian process can be obtained in a self-adaptive manner in the model construction process; meanwhile, the Gaussian process is a nuclear learning machine with probability significance, probability explanation can be made on the prediction output, and a modeler can evaluate the uncertainty of the model prediction output through a confidence interval. Therefore, the gaussian process has been the focus of research in the field of machine learning and has been successfully applied in many fields. FIG. 4 is a training process of the Gaussian process regression method.
Of particular note is the particle swarm optimization algorithm mentioned in step 4, which searches the optimal training parameters of the gaussian process regression, so as to reduce the training error of the gaussian process regression, and the process is as follows:
the Particle Swarm Optimization (PSO) is initialized, an initial population consisting of 10 particles is randomly constructed, and the b-th particle in the initial population is assigned with an initial position
And initial velocity
b, taking 1 to 10; calculating a fitness function F (b) of each particle in the initial population, if the minimum value min (F (b)) of the fitness functions F (b) of all the particles in the initial population is less than or equal to theta, taking the particle corresponding to min (F (b)) as the optimal solution of the problem to be solved, otherwise, updating the speed and the position of the particle according to the following three formulas, namely performing population iteration;
wherein; pbestRefers to the individual optimal positions through which all particles pass; gbestbThe optimal position through which the population passes; k is the number of iterations, r1And r2Is [0,1 ]]A random number in between; c1And C21 st learning factor and 2 nd learning factor respectively;
and
respectively indicate that: the number of iterations is k-1 and kThe position of the next b-th particle;
and
respectively indicate that: the speed of the b-th particle when the iteration times are k-1 times and k times; omega0And ω1Is the initial inertial weight, ω2To omegabThe (b) th inertia weight is the 2 nd inertia weight value; omega0＝ω1＝0.8。
ωbDetermining the optimizing convergence capability of the particle swarm algorithm when the omega isbWhen the total convergence is larger, the total convergence is stronger, when omega is largerbSmaller, stronger local convergence, sobThe updating formula can ensure that the particle swarm algorithm has strong global convergence capability in the early stage and strong local convergence capability in the later stage. When min (F (i) ≦ θ in a certain iteration occurs or the number of iterations reaches T, the algorithm terminates.
5) And (4) completing the prediction of the network security situation value at the future moment by using the prediction model H.
After the training and learning of the 5 steps, a network security situation value prediction model based on Gaussian process regression is formed, and therefore accurate prediction of situation values of future time monitoring points is achieved.
Compared with the traditional method, the method has better prediction precision in the aspect of predicting the network security situation value, and improves the practicability of network security situation prediction.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. The Gaussian process regression method for predicting the network security situation is characterized by comprising the following steps of:
1) constructing a hierarchical network security situation evaluation index system T by using an analytic hierarchy process, and calculating to obtain a total sequencing weight matrix omega of the network security situation evaluation index system T;
2) sequentially inputting historical intrusion detection results of the network security equipment into a network security situation evaluation index system T according to the time sequence to obtain a network security situation value V at the 1 st moment1Network security state by mth momentPotential value Vm；
3) Using sliding window method to convert V1~VmIs configured to time-series S, S ═ V1…Vm}; then, the time sequence S is randomly divided according to a fixed proportion to obtain a readable training sample set S in a Gaussian process regression methodtrainAnd a test sample set Stest(ii) a Guarantee training sample set StrainAnd a test sample set StestThe data format required by the Gaussian process regression method is met;
4) training sample set S by using Gaussian process regression methodtrainPerforming iterative training to obtain a temporary prediction model H, and performing error correction on the temporary prediction model H by using a particle swarm algorithm to obtain a prediction model H meeting error expectation;
5) and (4) completing the prediction of the network security situation value at the future moment by using the prediction model H.
2. The Gaussian process regression method for network security situation prediction according to claim 1, wherein the structure of the network security situation evaluation index system T is as follows: the network security situation evaluation index system T is divided into three layers, wherein the upper layer is a target layer, and the content of the target layer is a network security situation value; the middle layer is a criterion layer, the contents of which are strong hazard degree, medium hazard degree and weak hazard degree, and the strong hazard degree, the medium hazard degree and the weak hazard degree are divided according to the hazard degree of the network security threat; the lower layer is an index layer with the content of the 1 st network security threat x1To nth network security threat xn。
3. The method of claim 1, wherein the total ranking weight matrix ω is calculated as follows: first, threat x to type 1 network security1To nth network security threat xnThen, according to the analytic hierarchy process, respectively calculating the network security threat x in the ithiFor the influence coefficients of strong hazard degree, medium hazard degree and weak hazard degree, i is 1 ton; and calculating final influence coefficients of the strong hazard degree, the medium hazard degree and the weak hazard degree on the network security situation value respectively, and finally obtaining a total sequencing weight matrix omega of the network security situation evaluation index system T.
4. The Gaussian process regression method for network security situation prediction according to claim 1, wherein the step 2) comprises the following steps:
21) counting the intrusion detection result r of the network security equipment at the j momentjJ is 1 to m; r isjIs a matrix of 1 x n, and the matrix is,
wherein,
to
Respectively indicate that: at time j, 1 st cyber-security threat x1To nth network security threat xnThe number of occurrences;
22) will r isjMultiplying the total sorting weight matrix omega of the network security situation evaluation index system T to obtain the network security situation value V at the j momentj。
5. The method of Gaussian process regression for network security situation prediction according to claim 1, wherein the fixed ratio is 3: 2.
6. The method for gaussian process regression for network security situation prediction according to claim 1, wherein the step 4) specifically comprises the following steps:
41) in the particle swarm algorithm, the following parameters are set: maximum iteration number of 100, population size of 10, initial inertial weight omega1=0.8, terminating the inertial weight ωT=0.1, 1 st learning factorAnd 2 nd learning factor are both 2, the particle velocity interval is [0, 0.5 ]]；
42) Setting a kernel function type of a Gaussian process regression method;
43) normalized training sample set StrainAnd a test sample set Stest；
44) The particle swarm algorithm transfers the initial training parameters to a Gaussian process regression method which is implemented by carrying out regression on a training sample set StrainObtaining a temporary prediction model h by training; the initial training parameters refer to random training parameters initially generated by a particle swarm algorithm;
45) by testing the sample set StestCalculating a training error epsilon of the temporary prediction model h;
46) if the training error epsilon of the temporary prediction model H meets the preset expected value theta, the temporary prediction model H is the final prediction model H, otherwise, the Gaussian process regression method iteratively generates new training parameters according to the particle swarm algorithm by aiming at the training sample set StrainThereby updating the temporary prediction model h;
47) when one of the following two conditions is satisfied, executing step 48), otherwise, returning to execute step 45); the first condition is: the iteration times of the Gaussian process regression method reach the maximum iteration times of 100; the second condition is: the temporary prediction model h meets a preset expected value;
48) and outputting the final prediction model H.
7. The method of claim 6, wherein the predetermined expected value θ is 85%.
8. The Gaussian process regression method for network security situation prediction according to claim 6, wherein in the new training parameters iteratively generated by the Gaussian process regression method according to the particle swarm optimization, the process of iteration performed by the particle swarm optimization is as follows:
the Particle Swarm Optimization (PSO) is initialized first, and an initial population consisting of 1O particles is randomly constructedAnd assigning an initial position to the b-th particle in the initial populationAnd initial velocity
b, taking 1 to 10; calculating a fitness function F (b) of each particle in the initial population, if the minimum value min (F (b)) of the fitness functions F (b) of all the particles in the initial population is less than or equal to theta, taking the particle corresponding to min (F (b)) as the optimal solution of the problem to be solved, otherwise, updating the speed and the position of the particle according to the following three formulas, namely performing population iteration;
wherein; pbestRefers to the individual optimal positions through which all particles pass; gbestbThe optimal position through which the population passes; k is the number of iterations, r1And r2Is [ O, 1 ]]A random number in between; c1And C21 st learning factor and 2 nd learning factor respectively;
and
respectively indicate that: the iteration times are k-1 times and the position of the b-th particle when k times;and
respectively indicate that: the speed of the b-th particle when the iteration times are k-1 times and k times; omega0And ω1Is the initial inertial weight, ω2To omegabThe (b) th inertia weight is the 2 nd inertia weight value; omega0＝ω1＝0.8。
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| CN103345661A (en) * | 2013-07-10 | 2013-10-09 | 大连海事大学 | Ship grid reconstruction method based on ring topology gauss dynamic particle swarm optimization algorithm |
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