CN107657311B - Test preferred method based on multi-objective particle swarm algorithm - Google Patents
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Abstract
The invention discloses a kind of test preferred method based on multi-objective particle swarm algorithm, determine that electronic system tests several preferred optimization aims and constraint condition as needed, in particle swarm algorithm operational process, whenever there is a new population, i.e. search obtains Pareto optimality collection, calculate the distributed density values that Pareto optimality concentrates each particle, one particle is obtained as global optimum's particle using roulette selection algorithms selection, after particle update, whether its optimal location is dominated according to current location to determine whether being updated to particle position；The position for each particle that Pareto optimality after population end of run is concentrated is as a test preferred embodiment.The present invention improves on the basis of existing particle swarm algorithm and obtains multi-objective particle swarm algorithm, to obtain a variety of test preferred embodiments for meeting multiple targets.
Description
Technical field
The invention belongs to Fault Diagnosis for Electronic System technical fields, more specifically, are related to a kind of based on multiple target grain
The test preferred method of swarm optimization.
Background technique
In the troubleshooting issue for large scale electronic equipment system, how testing scheme is selected, make fault detection rate
(FDR, fault diagnose rate), false alarm rate (FAR, fault alarm rate) and test every expense (time,
Economy etc.) etc. testabilities index meet constraint condition simultaneously and even tend to more preferable, be that academic or engineering field is constantly explored
The problem of.
For the above test optimal selection problem for considering multiple testability indexes simultaneously, multi-objective optimization question can be considered as.
Multi-objective optimization question is to discuss how under certain constraints to find to meet multiple targets and be attained by optimal solution.One
As in the case of, be between each sub-goal of multi-objective optimization question it is contradictory, the improvement of a sub-goal is possible to cause
The reduced performance of another or another several sub-goals, that is, to make simultaneously multiple sub-goals be optimal together value be can not
Can, and can only carry out coordinating among them and compromise processing, make each sub-goal all being optimal as much as possible.
It is assumed that multiple-objection optimization is to minimize optimization problem, can be expressed with formula (1), that is, needing to find suitable x makes
It is minimum to obtain all N number of objective function f (x):
Minimize F (x)=(f1(x),f2(x),…,fN(x)) (1)
Essential distinction with single-object problem is that the solution of multi-objective optimization question is simultaneously not exclusive, but there are one
The optimal solution set that group is made of numerous Pareto (Pareto) optimal solution, each element in set are known as Pareto optimal solution
Or Pareto optimal.For the vector F (x determined by formula (1)i) and F (xj), if two vectors are unequal and F (xi) inner
All elements are all not more than F (xj) inner corresponding position element, then claim F (xi) dominate F (xj), xjReferred to as dominate solution, xiIt is referred to as non-
Solution is dominated, Pareto optimality collection is collectively referred to as by the collection that all non-domination solutions are constituted, is indicated with PS.
For multi-objective optimization question, presently the most universal method is that summation is weighted to multiple target, such as formula (2) institute
Show, and function g (x) regard single-object problem as.
Wherein, n=1,2 ..., N.
There are two the problem of this processing method: (1) weight factor subjectivity is strong, and designer is often less susceptible to select；
(2) optimum results are single, cannot provide multiple selections.For Fault Diagnosis for Electronic System field, sometimes require to be isolated as early as possible
The importance of failure, testing cost is relatively secondary, and sometimes requires strict control cost, of less demanding to the time.It needs at this time
It wants optimization algorithm to be capable of providing multiple choices alternative to policymaker, solution can be provided under different occasions.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of tests based on multi-objective particle swarm algorithm
Preferred method obtains a variety of test preferred embodiments for meeting multiple targets.
It for achieving the above object, include following step the present invention is based on the test preferred method of multi-objective particle swarm algorithm
It is rapid:
S1: it determines that electronic system tests several preferred optimization aims and constraint condition as needed, remembers optimization aim
Quantity be N, and the optimization object function f of testing scheme is setn(x), n=1,2 ..., N, optimization object function value is smaller, surveys
Examination scheme is more excellent；
S2: initialization the number of iterations q=1, and in initialization population each particle speedWith
PositionY indicates number of particles in population；The position vector table of each particle
Show a kind of testing scheme, when m-th of element in particle position vectorWhen being 0, indicate unselected in testing scheme corresponding to particle
In m-th test, when m-th of element in particle position vectorWhen being 1, indicate to choose m in testing scheme corresponding to particle
A test, m=1,2 ..., M, M indicate the test quantity of electronic system；When initialization population, each particle in initial population
The corresponding testing scheme in position, which needs to meet, tests preferred constraint condition；Enable the optimal location of each particle
The non-domination solution in current population is searched for, set is Pareto optimality collection PS；
S3: the distributed density values of each particle in Pareto optimality collection PS are calculated, using roulette selection algorithms selection
A particle is obtained as global optimum particle Gbest, distributed density values are smaller, particle distribution density bigger by select probability
The calculation method of value is as follows:
Calculate the corresponding N number of optimization object function value f of each particle in Pareto optimality collection PSn(xk), k=1,2 ..., K,
K indicates the number of particles in Pareto optimality collection PS；N number of optimization object function value f of each particlen(xk) constitute a row to
Amount, according to f1(xk) K row vector is arranged from small to large, obtain optimization object function matrix F:
Wherein, f1(x1)≤f1(x2)≤…≤f1(xK)；
The data of each column in optimization object function matrix F are normalized respectively:
Wherein,Indicate fn(xk) corresponding normalized value,Respectively
Indicate the minimum value and maximum value in optimization object function matrix F in n-component column vector；
Enable the 1st row vector and k-th row vector in optimization object function matrix F correspond to the density value Dis (1) of particle=
Dis (K)=1 calculates the density value that remaining each row vector corresponds to particle according to following formula:
Dis (k ')=| | Z (k '+1)-Z (k ' -1) | |
Wherein, 1 < k ' < K, Z (k '+1), Z (k ' -1) respectively indicate kth '+1, k ' -1 in optimization object function matrix Z
Row vector, | | | | indicate norm.
The density value Dis (k) of K particle is normalized in the following ways:
Wherein, Dis* (k) indicates the normalized value of Dis (k),Respectively indicate K
The density value of a particleIn minimum value and maximum value；
Density value Dis* (k) after normalization is the distributed density values of k-th of particle in Pareto optimality collection PS；
S4: each particle is respectively updated its speed and position using following formula:
Wherein,For speed of m-th of element in the q times, the q+1 times iteration in particle i, m=1,2 ...,
M；Vmin_mAnd Vmax_mIt is the minimum and maximum limit to particle rapidity；ω indicates inertial factor；
c1、c2For aceleration pulse；r1、r2It is the random number between 0 to 1；It is m-th of element in particle i in the q times, q
The position of+1 iteration；Rand () indicates random number；
S5: the corresponding each optimization object function value of each particle in current population is calculated；
S6: if testing scheme corresponding to updated i-th of particle is unsatisfactory for testing preferred constraint condition, do not make
Any operation judges whether its current location dominates its optimal location Pbest if meeting constraint conditioni, if it is,
Update optimal location PbestiFor current location, otherwise do not update；
S7: finding out all non-domination solutions in current population, Pareto optimality collection PS is added, if current Pareto optimality
Collect number of particles in PS and be less than or equal to population number of particles Y, does not make any operation, otherwise need to delete extra particle, method
Are as follows: the distributed density values for calculating each particle in Pareto optimality collection PS, using roulette algorithm from current Pareto optimality collection
Y particle is selected in PS, distributed density values are bigger, bigger by select probability；
S8: judging whether to reach preset iteration termination condition, if reached, test preferably terminates, Pareto optimality
The position for collecting each particle in PS is a test preferred embodiment, otherwise enters step S9；
S9: q=q+1, return step S3 are enabled.
The present invention is based on the test preferred method of multi-objective particle swarm algorithm, determine that electronic system test is preferred as needed
Several optimization aims and constraint condition whenever there is a new population, that is, searched in particle swarm algorithm operational process
To Pareto optimality collection, the distributed density values that Pareto optimality concentrates each particle are calculated, are selected using roulette selection algorithm
Select to obtain a particle as global optimum's particle, after particle update, according to current location whether dominate its optimal location come
Judge whether to be updated particle position；Make the position for each particle that Pareto optimality after population end of run is concentrated
For a test preferred embodiment.The present invention improves on the basis of existing particle swarm algorithm and obtains multi-objective particle swarm algorithm, from
And obtain a variety of test preferred embodiments for meeting multiple targets.
Detailed description of the invention
Fig. 1 is the specific embodiment flow chart of the test preferred method the present invention is based on multi-objective particle swarm algorithm.
Specific embodiment
A specific embodiment of the invention is described with reference to the accompanying drawing, preferably so as to those skilled in the art
Understand the present invention.Requiring particular attention is that in the following description, when known function and the detailed description of design perhaps
When can desalinate main contents of the invention, these descriptions will be ignored herein.
Technical solution in order to better illustrate the present invention first carries out the particle swarm algorithm that the present invention is based on brief
Explanation.
Particle swarm algorithm (Particle Swarm Optimization, PSO) is Kennedy and Eberhart by flock of birds
A kind of optimization algorithm based on population that the inspiration of foraging behavior is proposed in nineteen ninety-five.Based on individual (such as particle) row in group
For and mathematical abstractions developed PSO algorithm, algorithm uses Speed-position model, i.e. PSO algorithm is initialized as within the allowable range
A group random particles (potential solution), each particle have a speed to determine their heading and distance, change each time
Oneself is updated by two extreme values of tracking in generation: the individual extreme value Pbest that particle itself is found so faridWith entire kind
The global extremum Gbest that group is found so farid.The superiority and inferiority of all particles is weighed by the adaptive value that optimised object is determined
Amount.
It is located at the search space of M dimension, a population is formed by Y particle, i-th of particle in PSO optimization algorithm
Position and speed may be expressed as: xi=(xi1,xi2,...,xiM) and vi=(vi1,vi2,...,viM), wherein i=1,2 ..., Y；
Correspondingly, the optimal location that i-th of particle searches so far is recorded as Pbesti=(pbesti1,pbesti2,…,
pbestiM), the optimal location that entire population searches so far, i.e. global optimum are Gbest=(gbest1,
gbest2,…,gbestM).Using these information, PSO algorithm using formula (3) (4) to the speed of i-th particle and position into
Row updates.
In formula,For m-th of element in particle i the q times, the q+1 times iteration speed；M=1,2 ...,
M；Vmin_mAnd Vmax_mIt is the minimum and maximum limit to particle rapidity, particle rapidity is too high, is easy
Far from target area, particle rapidity is too low to be easily trapped into local optimum, cannot select optimal particle；ω indicates inertial factor；c1、
c2For aceleration pulse；r1、r2It is the random number between 0 to 1；It is m-th of element in particle i in the q times, q+1
The position of secondary iteration.
The present invention is based on particle swarm algorithms, when judging particle optimality, introduce the definition that Pareto dominates to determine one
Whether the superiority and inferiority of a particle, non-domination solution improves better than solution is dominated and obtains more mesh suitable for Fault Diagnosis for Electronic System field
Particle swarm algorithm is marked, realizes that test is preferred.
Fig. 1 is the specific embodiment flow chart of the test preferred method the present invention is based on multi-objective particle swarm algorithm.Such as
Shown in Fig. 1, the specific steps the present invention is based on the test preferred method of multi-objective particle swarm algorithm include:
S101: it determines and tests preferred target and constraint condition:
It determines that electronic system tests several preferred optimization aims and constraint condition as needed, remembers the number of optimization aim
Amount is N, and the optimization object function f of testing scheme is arrangedn(x), n=1,2 ..., N, optimization object function value is smaller, test side
Case is more excellent.
In Fault Diagnosis for Electronic System field, testing preferred optimization aim includes test funds minimum, testing time
Minimizing overhead, Fault Isolation degree maximize, fault detection rate maximizes etc., it is clear that when optimization aim is to be the bigger the better, example
Such as Fault Isolation degree and fault detection rate, optimization object function can be set to falling for Fault Isolation degree or fault detection rate
Number.Constraint condition generally comprises Fault Isolation degree, fault detection rate, false alarm rate etc., needs to meet preset threshold.Test is preferred
Target and constraint condition all determine according to actual needs.
S102: initialization particle group parameters:
Initialize the number of iterations q=1, and in initialization population each particle speedThe position and
It setsY indicates number of particles in population.The position vector of each particle indicates
A kind of testing scheme, when m-th of element in particle position vectorWhen being 0, indicate unselected in testing scheme corresponding to particle
M-th of test, when m-th of element in particle position vectorWhen being 1, indicate to choose m-th in testing scheme corresponding to particle
Test, m=1,2 ..., M, M indicate the test quantity of electronic system.When initialization population, the position of each particle in initial population
It sets corresponding testing scheme and needs to meet the preferred constraint condition of test.Enable the optimal location of each particleIt searches
Non-domination solution in Suo Dangqian population, set are Pareto optimality collection PS.
S103: selection global optimum's particle:
Global optimum's particle is selected based on particle distribution density, that is, calculates each particle in Pareto optimality collection PS
Distributed density values obtain a particle as global optimum particle G using roulette selection algorithms selectionbest, distributed density values
Smaller, bigger by select probability, the calculation method of particle distribution density is as follows:
Calculate the corresponding N number of optimization object function value f of each particle in Pareto optimality collection PSn(xk), k=1,2 ..., K,
K indicates the number of particles in Pareto optimality collection PS.N number of optimization object function value f of each particlen(xk) constitute a row to
Amount, according to f1(xk) K row vector is arranged from small to large, obtain optimization object function matrix F:
Wherein, f1(x1)≤f1(x2)≤…≤f1(xK)。
The data of each column in optimization object function matrix F are normalized respectively:
Wherein,Indicate fn(xk) corresponding normalized value,Respectively
Indicate the minimum value and maximum value in optimization object function matrix F in n-component column vector.
Enable the 1st row vector and k-th row vector in optimization object function matrix F correspond to the density value Dis (1) of particle=
Dis (K)=1 calculates the density value that remaining each row vector corresponds to particle according to following formula:
Dis (k ')=| | Z (k '+1)-Z (k ' -1) | | (7)
Wherein, 1 < k ' < K, Z (k '+1), Z (k ' -1) respectively indicate kth '+1, k ' -1 in optimization object function matrix Z
Row vector, | | | | indicate norm.
The density value Dis (k) of K particle is normalized in the following ways:
Wherein, Dis* (k) indicates the normalized value of Dis (k),Respectively indicate K
The density value of a particleIn minimum value and maximum value.
Density value Dis* (k) after normalization is the distributed density values of k-th of particle in Pareto optimality collection PS.
Therefore, in Pareto optimality collection PS, the particle of density smaller (spacing is big) is easier to be selected as global optimum's grain
Sub- Gbest, or even repeatedly chosen, this not only guides particle to fly towards Pareto forward position, and is towards sparse non-dominant
Solution flight, so that non-dominant point distribution is more uniform.
S104: particle updates:
Due to being directed to test in the present invention preferably, it is dispersed problem, therefore that the element value in particle position, which is 0 or 1,
It needs to carry out the more new formula of particle position the improvement of adaptability, i.e., uses formula (9), (10) respectively to it on each particle
Speed and position are updated:
Wherein, rand () indicates the random number between 0~1.
S105: particle optimization object function value is calculated:
Calculate the corresponding each optimization object function value of each particle in current population.
S106: local optimum particle is updated:
Next, the corresponding local optimum particle of each particle is updated, method particularly includes: if updated i-th
Testing scheme corresponding to particle is unsatisfactory for testing preferred constraint condition, then does not make any operation, if meeting constraint condition,
Judge whether its current location dominates its optimal location Pbesti, if it is, updating optimal location PbestiFor current location,
Otherwise it does not update.
S107: Pareto optimality collection is updated:
All non-domination solutions in current population are found out, Pareto optimality collection PS is added, if current Pareto optimality collection
Number of particles is less than or equal to population number of particles Y in PS, does not make any operation, otherwise needs to delete extra particle, method are as follows:
The distributed density values for calculating each particle in Pareto optimality collection PS, using roulette algorithm from current Pareto optimality collection PS
Y particle is selected, distributed density values are bigger, bigger by select probability.
S108: judging whether to reach preset iteration termination condition, if reached, test preferably terminates, and Pareto is most
The position of each particle in excellent collection PS is a test preferred embodiment, otherwise enters step S109.
Iteration termination condition, which can according to need, to be configured, and maximum number of iterations generally can be set, also may determine that
Whether the particle distribution of Pareto optimality collection PS meets preset requirement, if met, that is, it is preferred to terminate test.
S109: q=q+1, return step S103 are enabled.
Technical solution in order to better illustrate the present invention, using a specific example, the present invention is described in detail.Table 1
It is the test dependence matrix of the present embodiment.
Table 1
As shown in table 1, the electronic system of the present embodiment shares 20 kinds of malfunctions, 10 alternative tests.It indicates to test with D
Matrix is relied on, D [v] indicates that test relies on the v row binary data of matrix, when D [v] ≠ D [v '], v failure
It can be distinguished with v ' failure, the element d in tablevmIt indicates to test whether that v failure can be tested for m-th, if it is possible to it tests,
Then dvm=1, otherwise dvm=0.
In the present embodiment, optimization aim is that test funds and testing time are minimum, and constraint condition uses Percent Isolated, needs
It is greater than preset threshold 0.8.
The vector difference for carrying out funds and time overhead composition that each test needs is as follows:
C=[0.2945,0.3214,0.3008,0.9407,0.8093,0.2939,0.1585,0.3902,0.5592,
0.3525]。
T=[0.7264,0.0638,0.2240,0.3903,0.1005,0.2984,0.7179,0.3959,0.7117,
0.6831]。
According to historical data, the incidence of each malfunction is normalized, the failure after obtained normalization occurs
The vector of rate composition is as follows:
W=[0.0186,0.0144,0.0188,0.0251,0.0826,0.0710,0.0031,0.0040,0.0310,
0.0689,0.0965,0.0649,0.0775,0.0900,0.0475,0.0693,0.0218,0.0942,0.0806,
0.0203]。
The expression formula difference of two optimization object functions of test funds and testing time is as follows:
Wherein, xmIndicate m-th of element in particle position x, cm、τmFunds needed for respectively indicating m-th of test and when
Between.
Constraint condition, the i.e. calculation formula of Percent Isolated FIR are as follows:
Wherein, wvIndicate the incidence of v failure, dvm、dv′mM-th is respectively indicated to test whether that v failure can be tested
With v ' failure.
Using the method for the present invention, 5 non-domination solutions for meeting constraint condition can be found out:
Table 2 is the test funds, testing time and Percent Isolated FIR of 5 non-domination solutions.
| Test funds | Testing time | FIR | |
| x1 | 2.1734 | 2.5116 | 0.8222 |
| x2 | 2.4120 | 2.1152 | 0.8408 |
| x3 | 2.2180 | 2.1500 | 0.8429 |
| x4 | 2.7935 | 1.7938 | 0.8408 |
| x5 | 3.0208 | 1.6622 | 0.8149 |
Table 2
All meet constraint condition, and testing time and survey using 5 non-domination solutions that the present invention obtains as can be seen from Table 2
Examination expense does not all dominate mutually, and tester selects from the corresponding testing scheme of 5 non-domination solutions according to actual needs.
Although the illustrative specific embodiment of the present invention is described above, in order to the technology of the art
Personnel understand the present invention, it should be apparent that the present invention is not limited to the range of specific embodiment, to the common skill of the art
For art personnel, if various change the attached claims limit and determine the spirit and scope of the present invention in, these
Variation is it will be apparent that all utilize the innovation and creation of present inventive concept in the column of protection.
Claims (1)
1. a kind of test preferred method based on multi-objective particle swarm algorithm, it is characterised in that the following steps are included:
S1: it determines that electronic system tests several preferred optimization aims and constraint condition as needed, remembers the number of optimization aim
Amount is N, and the optimization object function f of testing scheme is arrangedn(x), n=1,2 ..., N, optimization object function value is smaller, test side
Case is more excellent；
S2: initialization the number of iterations q=1, and in initialization population each particle speedThe position andY indicates number of particles in population；The position vector of each particle indicates one
Kind testing scheme, when m-th of element in particle position vectorWhen being 0, indicate corresponding to particle unselected the in testing scheme
M test, when m-th of element in particle position vectorWhen being 1, indicate to choose m-th of survey in testing scheme corresponding to particle
Examination, m=1,2 ..., M, M indicate the test quantity of electronic system；When initialization population, the position of each particle in initial population
Corresponding testing scheme, which needs to meet, tests preferred constraint condition；Enable the optimal location of each particleSearch
Non-domination solution in current population, set are Pareto optimality collection PS；
S3: the distributed density values of each particle in Pareto optimality collection PS are calculated, are obtained using roulette selection algorithms selection
For one particle as global optimum particle Gbest, distributed density values are smaller, bigger by select probability, particle distribution density value
Calculation method is as follows:
Calculate the corresponding N number of optimization object function value f of each particle in Pareto optimality collection PSn(xk), k=1,2 ..., K, K table
Show the number of particles in Pareto optimality collection PS；N number of optimization object function value f of each particlen(xk) row vector is constituted,
According to f1(xk) K row vector is arranged from small to large, obtain optimization object function matrix F:
Wherein, f1(x1)≤f1(x2)≤…≤f1(xK)；
The data of each column in optimization object function matrix F are normalized respectively:
Wherein,Indicate fn(xk) corresponding normalized value,It respectively indicates excellent
Change the minimum value and maximum value in objective function matrix F in n-component column vector；
The 1st row vector and k-th row vector in optimization object function matrix F is enabled to correspond to density value Dis (1)=Dis of particle
(K)=1, the density value that remaining each row vector corresponds to particle is calculated according to following formula:
Dis (k ')=| | Z (k '+1)-Z (k ' -1) | |
Wherein, 1 < k ' < K, Z (k '+1), Z (k ' -1) respectively indicate kth '+1 in optimization object function matrix Z, -1 row of k ' to
Amount, | | | | indicate norm；
The density value Dis (k) of K particle is normalized in the following ways:
Wherein, Dis* (k) indicates the normalized value of Dis (k),Respectively indicate K grain
The density value of sonIn minimum value and maximum value；
Density value Dis* (k) after normalization is the distributed density values of k-th of particle in Pareto optimality collection PS；
S4: each particle is respectively updated its speed and position using following formula:
Wherein,For speed of m-th of element in the q times, the q+1 times iteration, m=1,2 ..., M in particle i；Vmin_mAnd Vmax_mIt is the minimum and maximum limit to particle rapidity；ω indicates inertial factor；c1、
c2For aceleration pulse；r1、r2It is the random number between 0 to 1；It is m-th of element in particle i in the q times, q+1
The position of secondary iteration；Rand () indicates random number；
S5: the corresponding each optimization object function value of each particle in current population is calculated；
S6: if testing scheme corresponding to updated i-th of particle is unsatisfactory for testing preferred constraint condition, do not make any
Operation, if meeting constraint condition, judges whether its current location dominates its optimal location Pbesti, if it is, updating
Optimal location PbestiFor current location, otherwise do not update；
S7: finding out all non-domination solutions in current population, and Pareto optimality collection PS is added, if current Pareto optimality collection PS
Middle number of particles is less than or equal to population number of particles Y, does not make any operation, otherwise needs to delete extra particle, method are as follows: meter
The distributed density values for calculating each particle in Pareto optimality collection PS, are selected from current Pareto optimality collection PS using roulette algorithm
Y particle is selected, distributed density values are bigger, bigger by select probability；
S8: judging whether to reach preset iteration termination condition, if reached, test preferably terminates, Pareto optimality collection PS
In the position of each particle be a test preferred embodiment, otherwise enter step S9；
S9: q=q+1, return step S3 are enabled.
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