CN110399968A - System level testing based on utility function designs Multipurpose Optimal Method - Google Patents
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Abstract
The invention discloses a kind of, and the system level testing based on utility function designs Multipurpose Optimal Method, influence factor and optimization object function are determined first, then weight vectors are set, N number of subproblem is decomposed into a multi-objective optimization question using weight vectors, use the G neighbours of subproblem, new offspring individual is generated by intersecting, making a variation, it is updated using the individual in the best population of fitness difference selection improvement, end in population delete by domination solution to get arrive influence factor vector Pareto optimality disaggregation.Using the present invention, can while guaranteeing to obtain the Pareto optimality disaggregation of influence factor vector, improve convergence effect and and influence factor vector Pareto optimal solution uniformity.
Description
Technical field
The invention belongs to electronic system testability design optimization technical fields, more specifically, are related to a kind of based on effect
Multipurpose Optimal Method is designed with the system level testing of function.
Background technique
In order to mitigate the maintenance difficulties of equipment in the future, system should just consider that testability is set in the initial stage of design
Meter.Testability refers to the degree that the state of system can be detected accurately.In the event for large scale electronic equipment system
Hinder in diagnosis problem, how to select testing scheme, make fault detection rate (FDR, fault diagnose rate), false alarm rate
It (FAR, fault alarm rate) and tests every expense (time, economy etc.) index while meeting constraint condition or even becoming
It is the problem of academic and engineering field is constantly explored to more preferable.
In test optimal selection problem, the faulty verification and measurement ratio of test index of interest (FDR, fault diagnose
Rate), isolation rate, false alarm rate (FAR, fault alarm rate), testing time expense (TC, time cost) and test
Economic expense (PC, price cost) etc..Increase system testing, it is meant that additional test hardware, therefore affect and be
System weight, volume research and develop difficulty, function effect and system reliability.
Assuming that influence factor amounts to D, x is useddIt indicates, d=1,2 ..., D.And will affect factor value be normalized to 0~1 it
Between variable, then influence factor vector X=[x1,…,xD].Assuming that the destination number for needing to optimize is M, each optimization aim
Objective function is fm(X), m=1,2 ..., M.
Test selected objective target is to reasonably select and be arranged X (rationally carrying out testability design, reasonable distribution resource etc.), is made
It is minimum to obtain M objective function.In reality, M objective function is not generally possible to be optimal simultaneously, therefore this is one typical
Multi-objective optimization question.
When multiple-objection optimization be minimize optimization problem, can be expressed with following formula, that is, need to find suitable X and to own
M objective function f (X) is minimum:
Minimize F (X)=(f1(X),f2(X),…,fM(X))
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 above-mentioned formulai) and F (Xj), if two vectors are unequal and F (Xi) inner
All elements be all not more than F (Xj) inner corresponding position element, then claim F (Xi) dominate F (Xj), XjReferred to as dominate solution, XiReferred to as
Non-domination solution.Pareto optimality collection is collectively referred to as by the collection that all non-domination solutions are constituted.
And the algorithm that can solve such problem at present has NSGA-III type algorithm, particle swarm algorithm etc..NSGA-III type
Algorithm is more typical, can find than more comprehensive non-domination solution collection, however due to dominance relation calculate time complexity compared with
The problems such as height, convergence effect is poor.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of system level testings based on utility function
Property design Multipurpose Optimal Method, guarantee obtain the Pareto optimality disaggregation of influence factor vector while, improve convergence effect
Fruit and and influence factor vector Pareto optimal solution uniformity.
For achieving the above object, the present invention is based on the system level testings of utility function to design Multipurpose Optimal Method
The following steps are included:
S1: influence factor is determined according to the actual conditions of electronic system, remembers influence factor vector X=[x1,x2,…,xD],
Wherein xdIndicate that the normalized value of d-th of influence factor, d=1,2 ..., D, D indicate the quantity of influence factor；Note needs to optimize
Destination number be M, determine the objective function f of each optimization aimm(X), m=1,2 ..., M, target function value is smaller, influences
The combination of factor is more excellent；
S2: N number of weight vectors are set as neededWherein,Indicate weight vectors Wi's
M-th of element value, i=1,2 ..., N；The Euclidean distance between weight vectors is calculated two-by-two, for i-th of weight vectors, is obtained
Neighbor weight vector with the smallest preceding G weight vectors of its Euclidean distance as i-th of weight vectors, to obtain i-th
The neighborhood B (i) of weight vectors={ i1,i2,…,iG, igIndicate the sequence of i-th of weight vectors, g-th of neighbor weight vector
Number, g=1,2 ..., G；
S3: each weight vectors W is initializediCorresponding utility function πi=1；
S4: it will affect factor vector X=[x1,…,xD] it is used as population at individual, population is initialized, remembers Population Size
For N；Enable the number of iterations S=1；
S5: the corresponding M objective function f of each individual in initial population is calculatedm(Xi) value, XiIt indicates in initial population
I-th of individual, i=1,2 ..., N determine the ideal reference z of each objective functionm=min { fm(X1),fm(X2),…,fm
(XN), obtain initial desired reference point Z=(z1,z2,…,zM)T, T expression transposition；
S6: according to utility function πiIndividual in current population is ranked up from small to large, K individual, remembers this K before selection
A group of individuals is φ, and wherein the size of K is determine according to actual needs；
S7: individual serial number i=1 is initialized；
S8: judge whether XiOtherwise ∈ φ enters step S11 if so, entering step S9:
S9: generating a random number rand in [0,1] range, if rand < δ, δ indicate preset selection pond probability,
Individual choice pond E=B (i) is then enabled, E={ 1,2 ..., N } is otherwise enabled；
S10: individual X is based on using following methodsiCarry out Evolution of Population:
S10.1: a serial number r is randomly choosed from individual choice pond E, by individual XiAnd XrIntersected as parent individuality
And mutation operation, generate two offspring individual y1And y2, calculate the fitness value g of two offspring individuals according to the following formula respectively
(yv|Wi, Z):
Wherein, v=1,2；
If g (y1|Wi,Z)≤g(y2|Wi, Z), then enable evolution target individual Y=y1, otherwise enable evolution target individual Y=
y2；
S10.2: the corresponding M objective function f of evolution target individual Y is calculatedm(Y) value constitutes objective function vector F
(Y)=(f1(Y),f2(Y),…,fM(Y))；
S10.3: for current desired reference point Z=(z1,z2,…,zM)TIn each ideal reference, if zm>
fm(Y), then z is enabledm=fm(Y), any operation is not otherwise made；
S10.4: each individual X in evolution target individual Y and current population is calculated according to the following formulajFitness difference
Uj:
Uj=g (Xj|Wj,Z)-g(Y|Wj,Z)
Select fitness difference UjMaximum individual Xj, it is updated using evolution target individual Y；
S11: judge whether otherwise i < N enters step S13 if so, entering step S12；
S12: individual serial number i=i+1, return step S8 are enabled；
S13: judge whether the number of iterations S < Smax, SmaxDefault maximum number of iterations is indicated, if it is, entering step
Otherwise S14 enters step S17；
S14: the number of iterations S=S+1 is enabled；
S15: judge whether the number of iterations S%Sπ=0, % indicate complementation, SπIndicate the update week of preset utility function value
Otherwise phase does not make any operation, return step S6 if so, entering step S16；
S16: using following formula to each utility function πiIt is updated:
Wherein, ΔiIndicate i-th of individual X in current populationiThe relative reduction number of fitness value, is carried out using following formula
It calculates:
Wherein, g (Xi|Wi, Z) and indicate i-th of individual X in current populationiFitness value,Q before indicating
For i-th of individual in populationFitness value；
Return step S6；
S17: deleting from current population and dominated individual, and remaining individual collections are to be used as the pa of influence factor vector tired
Hold in the palm optimal solution set, each corresponding influence factor vector of individual.
The present invention is based on the system level testing of utility function design Multipurpose Optimal Method, it is first determined influence factor and
Then weight vectors are arranged in optimization object function, be decomposed into N number of son to a multi-objective optimization question using weight vectors and ask
Topic, using the G neighbours of subproblem, generates new offspring individual by intersecting, making a variation, and selects to improve effect using fitness difference
Individual in the best population of fruit is updated, end in population delete by domination solution to get arrive influence factor vector pa
Tired support optimal solution set.Using the present invention, can be improved while guaranteeing to obtain the Pareto optimality disaggregation of influence factor vector
Restrain effect and and influence factor vector Pareto optimal solution uniformity.
Detailed description of the invention
Fig. 1 is that the present invention is based on the specific embodiments of the system level testing of utility function design Multipurpose Optimal Method
Flow chart；
Fig. 2 is the flow chart of Evolution of Population in the present invention；
Fig. 3 is the corresponding objective function vector schematic diagram of Pareto optimal solution obtained in the present embodiment using the present invention；
Fig. 4 is to be shown in the present embodiment using the corresponding objective function vector of Pareto optimal solution that NSGAIII algorithm obtains
It is intended to；
Fig. 5 is the convergence effect contrast figure of the present invention and NSGA-III in the present embodiment.
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.
Fig. 1 is that the present invention is based on the specific embodiments of the system level testing of utility function design Multipurpose Optimal Method
Flow chart.As shown in Figure 1, the present invention is based on the specific steps of the system level testing of utility function design Multipurpose Optimal Method
Include:
S101: influence factor and optimization object function are determined:
Influence factor is determined according to the actual conditions of electronic system, remembers influence factor vector X=[x1,…,xD], wherein xd
Indicate that the normalized value of d-th of influence factor, d=1,2 ..., D, D indicate the quantity of influence factor；Note needs the target optimized
Quantity is M, determines the objective function f of each optimization aimm(X), m=1,2 ..., M, target function value is smaller, influence factor
It combines more excellent.
S102: weight vectors are generated:
N number of weight vectors are set as neededWherein,Indicate weight vectors WiM
A element value, i=1,2 ..., N.Calculate the Euclidean distance between weight vectors two-by-two, for i-th of weight vectors, obtain with
Neighbor weight vector of the smallest preceding G weight vectors of its Euclidean distance as i-th of weight vectors, to obtain i-th of power
Neighborhood B (i)={ i of weight vector1,i2,…,iG, igIndicate the sequence of i-th of weight vectors, g-th of neighbor weight vector
Number, g=1,2 ..., G.
The calculation formula of Euclidean distance is as follows between two weight vectors:
Wherein, j=1,2 ..., N.
In the present embodiment, weight vectors are generated using simplex method, and N number of weight vectors WiIt is uniformly distributed.
The quantity N of weight vectors can be calculated using the following equation:
Wherein, H indicates preset constant parameter.
One multi-objective problem can be decomposed into N number of subproblem using N number of weight vectors, a weight vectors correspond to
One subproblem, by the optimization (optimization on each weight vectors direction) to each subproblem, and then it is excellent to complete multiple target
The optimization of change problem.
S103: initialization utility function:
Initialize i-th of weight vectors WiCorresponding utility function πi=1.
S104: initialization population:
It will affect factor vector X=[x1,…,xD] as Population in Genetic Algorithms individual, population is initialized, note kind
Group's size is N, i-th of individual XiWith weight vectors WiWith utility function πiIt is corresponding, i=1,2 ..., N.Enable the number of iterations S=
1。
S105: initialization desired reference point:
Calculate the corresponding M objective function f of each individual in initial populationm(Xi) value, XiIt indicates i-th in initial population
Individual, i=1,2 ..., N determine the ideal reference z of each objective functionm=min { fm(X1),fm(X2),…,fm
(XN), obtain initial desired reference point Z=(z1,z2,…,zM)T, T expression transposition.
S106: screening individual:
According to utility function πiIndividual in current population is ranked up from small to large, K individual before selection remembers this K
Group of individuals is φ, and wherein the size of K is determine according to actual needs.In general, efficiency and effect of optimization in order to balance, K
Value range be [N/4]≤K≤[N/3].
S107: individual serial number i=1 is initialized.
S108: judge whether XiOtherwise ∈ φ enters step S111 if so, entering step S109.
S109: individual choice pond is determined:
A random number rand is generated in [0,1] range, if rand < δ, δ indicate preset selection pond probability, this
δ=0.9 in embodiment, then enable individual choice pond E=B (i), otherwise enables E={ 1,2 ..., N }, as entire population.
S110: Evolution of Population:
Based on individual XiCarry out Evolution of Population.Fig. 2 is the flow chart of Evolution of Population in the present invention.As shown in Fig. 2, of the invention
The specific steps of middle Evolution of Population include:
S201: evolution target individual is generated:
A serial number r is randomly choosed from individual choice pond E, by individual XiAnd XrIntersected as parent individuality and is made a variation
Operation, generates two offspring individual y1And y2, calculate the fitness value g (y of two offspring individuals according to the following formula respectivelyv|Wi,
Z):
Wherein, v=1,2.
If g (y1|Wi,Z)≤g(y2|Wi, Z), then select offspring individual y1Even evolution target individual Y=y1, otherwise
Enable evolution target individual Y=y2。
Intersect in the present embodiment and intersected using simulation binary system, variation is made a variation using multinomial.
S202: evolution target individual objective function vector is calculated:
Calculate the corresponding M objective function f of evolution target individual Ym(Y) value constitutes objective function vector F (Y)=(f1
(Y),f2(Y),…,fM(Y))。
S203: desired reference point is updated:
For current desired reference point Z=(z1,z2,…,zM)TIn each ideal reference, if zm> fm(Y),
Then enable zm=fm(Y), any operation is not otherwise made.
S204: more new individual:
Each individual X in evolution target individual Y and current population is calculated according to the following formulajFitness difference Uj:
Uj=g (Xj|Wj,Z)-g(Y|Wj,Z)
Wherein, j=1,2 ..., N,
Select fitness difference UjMaximum individual Xj, it is updated using evolution target individual Y, even Xj=Y.
S111: judge whether otherwise i < N enters step S113 if so, entering step S112.
S112: individual serial number i=i+1, return step S108 are enabled.
S113: judge whether the number of iterations S < Smax, SmaxDefault maximum number of iterations is indicated, if it is, entering step
Otherwise S114 enters step S117.
S114: the number of iterations S=S+1 is enabled.
S115: judge whether the number of iterations S%Sπ=0, % indicate complementation, SπIndicate the update of preset utility function value
Otherwise period does not make any operation, return step S106 if so, entering step S116.Update cycle SπValue it is generally unsuitable
It is too small, it can be set to 50≤Sπ≤100。
S116: utility function is updated:
Using following formula to each utility function πiIt is updated:
Wherein, ΔiIndicate i-th of individual X in current populationiThe relative reduction number of fitness value, is carried out using following formula
It calculates:
Wherein, g (Xi|Wi, Z) and indicate i-th of individual X in current populationiFitness value,Q before indicating
For i-th of individual in populationFitness value.The value range of Q is 20≤Q≤Sπ。
Then return step S106.
S117: Pareto optimal solution set is obtained:
It is deleted from current population and is dominated individual, remaining individual collections are used as the Pareto of influence factor vector most
Excellent disaggregation, each corresponding influence factor vector of individual, can accordingly configure influence factor.
Embodiment
Technical solution in order to better illustrate the present invention, below by taking three objective optimizations as an example, to specific reality of the invention
The process of applying is illustrated.It is assumed that the optimization aim of electronic system testability design is to maximize fault detection rate FDR, expression formula is
f1=maxmize (FDR)；Minimize false alarm rate FAR, expression formula f2=minimize (FAR)；And testing cost C, expression
Formula is f3=minimize (C).Enable f1=1-maxmize (FDR), then be converted to minimization problem.Influence these three targets
Factor is numerous, such as the consideration of design difficulty, volume, function effect, reliability effect, and 7 influence factors are selected in the present embodiment,
That is influence factor vector X=[x1,…,x7]。
Objective function F=[the f constructed in the present embodiment1,f2,f3] and optimization problem it is as follows:
Subject to 0≤xd≤ 1, for d=1,2 ..., 7
Wherein,
Pareto optimality disaggregation is obtained according to flow implementation described previously, then obtains objective function vector.Fig. 3 is this reality
Apply the corresponding objective function vector schematic diagram of Pareto optimal solution obtained in example using the present invention.As shown in figure 3, according to this hair
Bright method, the solution found not still Pareto optimal solution, and also corresponding objective function vector more can be uniformly distributed
In optimal planar.
This corresponding target function value vector of 91 optimal solutions is respectively as follows:
The influence factor vector for obtaining these optimal objective functional vectors is respectively as follows:
Testability designer can be according to three functions (verification and measurement ratio, false alarm rate, fault diagnosis cost) in different occasions
Under demand weight, according to operating above as a result, reasonable disposition influence factor, achievees the purpose that optimal design for testability.
In order to illustrate technical effect of the invention, using NSGAIII algorithm to run this example, (individual amount 92, algebra are
500), its result and result of the invention are compared.Fig. 4 is to be obtained in the present embodiment using NSGAIII algorithm
The corresponding objective function vector schematic diagram of Pareto optimal solution.Comparison diagram 3 and Fig. 4 are it is recognized that while can also using NSGAIII algorithm
To obtain optimal solution, but it is not distributed less uniform close to reference point completely.
Fig. 5 is the convergence effect contrast figure of the present invention and NSGA-III in the present embodiment.As can be seen from Figure 5 of the invention
Convergence is better than traditional NSGA-III type algorithm.
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 (6)
1. a kind of system level testing based on utility function designs Multipurpose Optimal Method, which is characterized in that including following step
It is rapid:
S1: influence factor is determined according to the actual conditions of electronic system, remembers influence factor vector X=[x1,x2,…,xD], wherein xd
Indicate that the normalized value of d-th of influence factor, d=1,2 ..., D, D indicate the quantity of influence factor；Note needs the target optimized
Quantity is M, determines the objective function f of each optimization aimm(X), m=1,2 ..., M, target function value is smaller, influence factor
It combines more excellent；
S2: N number of weight vectors are set as neededWherein,Indicate weight vectors WiM-th
Element value, i=1,2 ..., N；Calculate the Euclidean distance between weight vectors two-by-two, for i-th of weight vectors, obtain and its
Neighbor weight vector of the smallest preceding G weight vectors of Euclidean distance as i-th of weight vectors, to obtain i-th of weight
The neighborhood B (i) of vector={ i1,i2,…,iG, igIndicate the serial number of i-th of weight vectors, g-th of neighbor weight vector, g
=1,2 ..., G；
S3: each weight vectors W is initializediCorresponding utility function πi=1；
S4: it will affect factor vector X=[x1,…,xD] it is used as population at individual, population is initialized, note Population Size is N；
Enable the number of iterations S=1；
S5: the corresponding M objective function f of each individual in initial population is calculatedm(Xi) value, determine the reason of each objective function
Think reference value zm=min { fm(X1),fm(X2),…,fm(XN), obtain initial desired reference point Z=(z1,z2,…,zM)T, T table
Show transposition；
S6: according to utility function πiIndividual in current population is ranked up from small to large, K individual before selection remembers this K
The collection of body is combined into φ, and wherein the size of K is determine according to actual needs；
S7: individual serial number i=1 is initialized；
S8: judge whether XiOtherwise ∈ φ enters step S11 if so, entering step S9:
S9: generating a random number rand in [0,1] range, if rand < δ, δ expression preset selection pond probability, then enable
Individual choice pond E=B (i) otherwise enables E={ 1,2 ..., N }；
S10: individual X is based on using following methodsiCarry out Evolution of Population:
S10.1: a serial number r is randomly choosed from individual choice pond E, by individual XiAnd XrIntersected as parent individuality and is become
ETTHER-OR operation generates two offspring individual y1And y2, calculate the fitness value g (y of two offspring individuals according to the following formula respectivelyv|
Wi, Z):
Wherein, v=1,2；
If g (y1|Wi,Z)≤g(y2|Wi, Z), then enable evolution target individual Y=y1, otherwise enable evolution target individual Y=y2；
S10.2: the corresponding M objective function f of evolution target individual Y is calculatedm(Y) value, composition objective function vector F (Y)=
(f1(Y),f2(Y),…,fM(Y))；
S10.3: for current desired reference point Z=(z1,z2,…,zM)TIn each ideal reference, if zm> fm
(Y), then z is enabledm=fm(Y), any operation is not otherwise made；
S10.4: each individual X in evolution target individual Y and current population is calculated according to the following formulajFitness difference Uj:
Uj=g (Xj|Wj,Z)-g(Y|Wj,Z)
Select fitness difference UiMaximum individual Xi, it is updated using evolution target individual Y；
S11: judge whether otherwise i < N enters step S13 if so, entering step S12；
S12: individual serial number i=i+1, return step S8 are enabled；
S13: judge whether the number of iterations S < Smax, SmaxIndicate default maximum number of iterations, if it is, S14 is entered step,
Otherwise S17 is entered step；
S14: the number of iterations S=S+1 is enabled；
S15: judge whether the number of iterations S%Sπ=0, % indicate complementation, SπIndicate the update cycle of preset utility function value,
If so, entering step S16, any operation, return step S6 are not otherwise made；
S16: using following formula to each utility function πiIt is updated:
Wherein, ΔiIndicate i-th of individual X in current populationiThe relative reduction number of fitness value, is counted using following formula
It calculates:
Wherein, g (Xi|Wi, Z) and indicate i-th of individual X in current populationiFitness value,Q generation kind before indicating
I-th of individual in groupFitness value；
Return step S6；
S17: deleting from current population and dominated individual, and remaining individual collections are used as the Pareto of influence factor vector most
Excellent disaggregation, each corresponding influence factor vector of individual.
2. system according to claim 1 grade testability designs Multipurpose Optimal Method, which is characterized in that the step S2
Middle weight vectors are generated using simplex method, and N number of weight vectors WiIt is uniformly distributed.
3. system according to claim 1 grade testability designs Multipurpose Optimal Method, which is characterized in that the step S2
Middle weight vectors quantity N is calculated using the following equation:
Wherein, H indicates preset constant parameter.
4. system according to claim 1 grade testability designs Multipurpose Optimal Method, which is characterized in that the step S6
The value range of middle K is [N/4]≤K≤[N/3].
5. system according to claim 1 grade testability designs Multipurpose Optimal Method, which is characterized in that the step
Update cycle S in S15πValue range be 50≤Sπ≤100。
6. system level testing according to claim 5 designs Multipurpose Optimal Method, which is characterized in that the step
The value range of Q is 20≤Q≤S in S16π。
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