CN113590191A - Software reliability model parameter estimation method based on genetic algorithm - Google Patents

Software reliability model parameter estimation method based on genetic algorithm Download PDF

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CN113590191A
CN113590191A CN202110721899.6A CN202110721899A CN113590191A CN 113590191 A CN113590191 A CN 113590191A CN 202110721899 A CN202110721899 A CN 202110721899A CN 113590191 A CN113590191 A CN 113590191A
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徐如远
张生鹏
王刚
李晋鹏
蒲泽良
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Abstract

The present disclosure provides a software reliability model parameter estimation method based on genetic algorithm, comprising the following steps: acquiring a nonlinear function of a software reliability model; generating a population for the nonlinear function; calculating the fitness value of each individual in the population according to the selected fitness function; selecting individuals from the population for entry into a next generation using a roulette algorithm based on the fitness value; performing cross operation and gene mutation on the selected individuals to obtain offspring individuals; and replacing all the individuals in the population with the filial generation individuals, and iterating until a search result meeting a preset requirement is obtained. The method accurately and effectively realizes parameter estimation of the software reliability model by using optimization algorithms such as a genetic algorithm and the like, has good local optimization capability, and is not limited by the existence and continuity of the derivative of the model function.

Description

Software reliability model parameter estimation method based on genetic algorithm
Technical Field
The disclosure relates to software reliability modeling, and in particular, to a method for estimating software reliability model parameters based on a genetic algorithm.
Background
Software plays an important role in many key applications such as air traffic control systems, national security defense systems, embedded systems, etc. The functionality and correctness of software are greatly concerned, the reliability of the software becomes the most important aspect of the quality of the software, and the quantitative evaluation of the reliability of the software through an effective method is very important.
In the past 40 years, a large number of NHPP (non-homogeneous Poisson Process) software reliability growth models with time dependence are proposed to evaluate the reliability of a software system, most faults are subject to linear introduction, and the method has certain limitations in many cases. The existing common methods are maximum likelihood estimation or least square estimation algorithms, but the methods have certain limitations and require partial derivatives of model functions to exist and be continuous, and if the model is nonlinear or has numerous parameters, the conventional method is difficult to solve the problems.
Disclosure of Invention
In view of this, the present disclosure aims to provide a software reliability model parameter estimation method based on a genetic algorithm.
Based on the above purposes, the present disclosure provides a software reliability model parameter estimation method based on a genetic algorithm, comprising the following steps:
a. acquiring a nonlinear function of a software reliability model;
b. generating a population for the nonlinear function based on random numbers generated within a predetermined range;
c. calculating the fitness value of each individual in the population according to the selected fitness function;
d. selecting individuals from the population for entry into a next generation using a roulette algorithm based on the fitness value;
e. performing cross operation and gene mutation on the selected individuals to obtain offspring individuals;
f. replacing all individuals in the population with the offspring individuals, and iteratively executing the steps c-e until a search result meeting a predetermined requirement is obtained;
g. and outputting the search result as a parameter estimation value of the software reliability model.
Optionally, in the step c, the fitness value is subjected to stretch improvement based on a simulated annealing algorithm, so as to improve the probability that the dominant individuals in the population enter the next generation.
Wherein stretch-modifying the fitness value based on the simulated annealing algorithm comprises:
stretching the fitness value based on the size, genetic algebra, and initial temperature of the population.
Optionally, the interleaving operation comprises a heuristic interleaving operation.
Wherein the probability of the crossover operation is adaptively changed according to the distribution of the fitness value.
Wherein, the distribution situation of the fitness value comprises the average value of the fitness value of each individual in the population, the maximum value and the minimum value in the fitness value.
Optionally, the probability of the gene mutation is adaptively changed according to the distribution of the fitness value.
Wherein, the distribution situation of the fitness value comprises the average value of the fitness value of each individual in the population, the maximum value and the minimum value in the fitness value.
From the above, the present disclosure provides a software reliability model parameter estimation method based on genetic algorithm, which accurately and effectively implements parameter estimation of a software reliability model by using optimization algorithms such as genetic algorithm, etc., and has good local optimization capability, and is not limited by existence and continuity of model function derivatives; the results generated by gene mutation and cross operation are limited, infinite special values cannot be generated, encoding and decoding are not needed, and the operation rate is greatly improved; the offspring generated by using the roulette selection is in direct proportion to the fitness, so that a good effect can be obtained; and a nonlinear software reliability model is obtained, so that the method has good goodness of fit and more accurate prediction capability on software.
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In order to more clearly illustrate the technical solutions in the present disclosure or related technologies, the drawings needed to be used in the description of the embodiments or related technologies are briefly introduced below, and it is obvious that the drawings in the following description are only embodiments of the present disclosure, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for estimating software reliability model parameters based on genetic algorithm according to an embodiment of the present disclosure;
FIG. 2 is a flow chart of a genetic algorithm of an embodiment of the present disclosure;
FIG. 3 is a graph of fitness value versus iteration number variation for an embodiment of the present disclosure;
FIG. 4 is a graph of maximum fitness value versus initial temperature change for an embodiment of the present disclosure;
Detailed Description
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
It is to be noted that technical terms or scientific terms used in the embodiments of the present disclosure should have a general meaning as understood by those having ordinary skill in the art to which the present disclosure belongs, unless otherwise defined. The use of the terms "comprising" or "including" and the like in the embodiments of the present disclosure is intended to mean that the elements or items listed before the term cover the elements or items listed after the term and their equivalents, without excluding other elements or items. The terms "first," "second," and the like, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another.
As mentioned in the background, software plays an important role in many key applications, such as air traffic control systems, national security defense systems, embedded systems, etc. The functionality and correctness of software are greatly concerned, the reliability of the software becomes the most important aspect of the quality of the software, and the quantitative evaluation of the reliability of the software through an effective method is very important. In the last 40 years, a large number of NHPP software reliability growth models with time dependency are proposed to evaluate the reliability of a software system, and the residual fault number and failure rate are generally estimated under different scenes, but software debugging is not perfect, new fault introduction is possible, and most faults are subjected to linear introduction, so that certain limitations are caused.
The existing common methods are maximum likelihood estimation or least square estimation algorithms, but the methods have certain limitations and require partial derivatives of model functions to exist and be continuous, and if the model is nonlinear or has a plurality of parameters, the conventional method is difficult to solve the problems.
For a software reliability growth model, particularly for the representation of a fault detection rate, a nonlinear NHPP software model should be established, so that the software reliability is more accurately predicted, meanwhile, the random search genetic algorithm can be used for parameter estimation, the operation efficiency and accuracy can be more effectively improved, and better fitting can be obtained for the software reliability.
The detection process of the new model scene aiming at the fault provided by the disclosure obeys the inhomogeneous poisson process; software debugging is imperfect, and new faults are introduced when existing faults are corrected; the fault content function is non-linear and time dependent; software failure rate at any time depends on the failure detection rate and the number of remaining failures at that time.
Hereinafter, the technical means of the present disclosure will be described in detail by specific examples.
Referring to fig. 1 and fig. 2, a method for estimating software reliability model parameters based on a genetic algorithm is disclosed, which comprises the following steps:
a. and acquiring a nonlinear function of the software reliability model.
The general reliability growth model expression following the non-homogeneous Poisson distribution is as follows:
Figure BDA0003137118650000041
in the formula, λ (t) represents a failure strength function, m (t) represents an expected value of the number of faults by time t, b (t) represents a fault detection rate, and a (t) represents the total number of faults in software at time t.
Based on test coverage, imperfect commissioning, the model obeys equation (2),
Figure BDA0003137118650000042
where h (t) represents the percentage of code that has completed testing by time t, i.e., the test coverage function.
Software debugging is imperfect and fault introduction is non-linear, so a (t) can be expressed as:
a(t)＝a(1+αtd) (3)，
where a is the initial number of faults present at the time of software test, α is the fault introduction rate, and d is the shape parameter.
The test coverage function obeys a weibull distribution, so h (t) is expressed as:
Figure BDA0003137118650000043
wherein p and r are Weibull distribution parameters.
The failure detection rate b (t) can therefore be expressed as:
Figure BDA0003137118650000051
substituting the formula (5) and the formula (3) into the formula (2) to obtain a mean function m (t) of the software reliability model, which is expressed as:
Figure BDA0003137118650000052
wherein τ is a time variable.
Equation (6) is the software reliability model, which has good goodness-of-fit and prediction capability, and contains parameters a, α, d, p, and r.
b. Generating a population for the nonlinear function based on random numbers generated within a predetermined range.
Setting an initial value, generating an initial population to perform a genetic algorithm process, wherein the initial value setting in this embodiment includes:
the population size M is 100, the iteration times g is 3000 times, and the initial cross probability pc 0Is 0.6, coefficient factor betacIs 0.3, coefficient factor ncTo 2, initial mutation probability
Figure BDA0003137118650000053
Is 0.2, coefficient factor betamIs 0.2, coefficient factor nmIs 2, initial temperature T09, etc.
c. And calculating the fitness value of each individual in the population according to the selected fitness function.
Referring to fig. 2, wherein the fitness function is:
Figure BDA0003137118650000054
in the formula, miIndicates the cutoff to time tiThe actual number of failures that occur is,
Figure BDA0003137118650000055
indicates the cutoff to time tiThe number of failures estimated by the model, fitness, represents the fitness value of the individual.
The fitness function is also called an evaluation function, is a standard for distinguishing the quality of individuals in a group determined according to a target function, is an important step in a genetic algorithm, has good convergence rate and calculation accuracy, and is a basis for natural selection.
In some embodiments, in step c, the fitness value is stretch-refined based on a simulated annealing algorithm to increase the probability of the dominant individual in the population entering the next generation.
The stretch improvement comprises: based on the size, genetic algebra and initial temperature of the population, stretching the fitness value, and calculating as follows:
Figure BDA0003137118650000061
T＝T0(0.99g-1) (9)，
in the formula (f)iThe improved fitness of the ith individual, M is the population size, g is the iteration number, T is the temperature, T is the population size0Is the initial temperature.
The individual difference of the genetic algorithm is large at the initial stage of operation, so that a good effect can be obtained, but in the later stage, the fitness values tend to be consistent, the excellent individual advantages are insufficient, and the selection pressure ratio is large, so that the fitness is improved by using the idea of simulated annealing, the fitness is stretched and improved to a certain extent, and referring to fig. 4, the graph is a relation graph of the maximum fitness value and the initial temperature change of the embodiment of the disclosure, the simulated annealing treatment enables good individuals to have a larger reserved probability, and the accuracy of the model is improved.
d. Selecting individuals from the population for entry into a next generation using a roulette algorithm based on the fitness value.
The roulette algorithm is a random sampling method and is widely applied. Firstly, calculating the fitness value of each individual and the proportion of the fitness value sum of the individuals in the whole population, wherein the probability of each individual entering the next generation is equal to the proportion of the fitness value sum of the individual and the whole population.
e. And carrying out cross operation and gene mutation on the selected individuals to obtain offspring individuals.
In some embodiments, the interleaving operation comprises a heuristic interleaving operation.
Heuristic crossing is one of the most common real-valued crossing methods, determining two offspring chromosomes by calculating fitness of an individual. Assuming that chromosomes a and B exist, the fitness of the two chromosomes is first calculated and compared, and if a is greater than B, chromosome a will be passed on unchanged to the next generation daughter chromosome C, and the other daughter chromosome D is obtained by parent chromosome crossing. Assuming that the fitness value of chromosome a is greater than chromosome B, the crossover method can be expressed as:
offspringC＝parentA
offspringD＝parentA±h*(parentA-parentB) (10)，
wherein h is a random number between 0 and 1.
In some embodiments, as shown in fig. 2, the interleaving operation comprises: generating a first random probability for each selected population individual, if the first random probability is less than the crossover probability pcThen the population individuals are used as cross male parents to carry out the cross operation; otherwise, entering gene mutation operation; the first random probability is a random number between 0 and 1.
In some embodiments, the cross probability is adaptively changed according to a distribution of the fitness value.
Further, the distribution of the fitness value includes an average value of the fitness values of the individuals in the population, and a maximum value and a minimum value of the fitness values.
The calculation formula of the cross probability self-adaptive change is as follows:
Figure BDA0003137118650000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003137118650000072
denotes the initial crossover probability, betacAnd ncIs a coefficient factor, favRepresents the population mean fitness, fmaxRepresenting the maximum fitness of the population, fminRepresenting population minimum fitness.
Because the difference degree of the filial generation individuals is smaller and smaller along with the increment of algebra, the excellent filial generation individuals have insufficient advantages, the excellent filial generation individuals are easy to eliminate, and in order to accelerate the convergence speed and improve the population diversity, the cross probability is subjected to self-adaptive change according to a certain rule, so that the operation efficiency and the genetic expressive force of the reliability model are effectively improved.
In some embodiments, the genetic mutation comprises: generating a second random probability for each selected population individual, if the second random probability is less than the mutation probability pmThen subjecting said population of individuals to said mutation operation; otherwise, entering an iteration operation; the second random probability is a random number between 0 and 1.
In some embodiments, the mutation probability is adaptively changed according to a distribution of the fitness value.
Further, the distribution of the fitness value includes an average value of the fitness values of the individuals in the population, and a maximum value and a minimum value of the fitness values.
The mutation probability self-adaptive change calculation formula is as follows:
Figure BDA0003137118650000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003137118650000082
indicates the probability of initial mutation,. betamAnd nmIs a coefficient factor.
The same purpose as the adaptive improvement of the cross probability, refer to fig. 3, which is a graph of a relationship between the fitness value and the change of the iteration frequency in the embodiment of the present disclosure, where the mutation probability and the cross probability are adaptively changed according to a certain rule, it can be found that the fitness value after adaptive improvement is higher than the fitness value without adaptive improvement, so that the operation efficiency of the reliability model is effectively improved, good individuals are kept entering offspring, and the accuracy of parameter estimation is improved.
f. And replacing all the individuals in the population with the filial generation individuals, and iteratively executing the steps c-e until a search result meeting a preset requirement is obtained.
Referring to fig. 3, the relationship diagram of the fitness value and the change of the iteration number in the embodiment of the present disclosure is shown, the iteration number in this embodiment is 3000, the fitness value tends to be stable in the later stage of the iteration, and the search results are compared by using a data set of a real software product, so as to improve the accuracy of parameter estimation, where the data set is as shown in table 1:
TABLE 1 software failure data set
Figure BDA0003137118650000083
In table 1, m (t)' represents an actual value of the number of faults until time t, the unit of time t is week, 38 software faults occur in 14 weeks, and a search result meeting a predetermined requirement is obtained through various comparison criteria, in this embodiment, the predetermined requirement is that the mean square error MSE of an expected value and an actual value of the software reliability model is calculated to be less than 0.1, so that the software fault prediction is more accurate.
g. And outputting the search result as a parameter estimation value of the software reliability model.
The final parameter estimates are shown in table 2:
TABLE 2 model parameter estimation
Model parameters a α d p r
Estimated value 12.93 0.127 2.186 1.047 0.281
The method accurately and effectively realizes parameter estimation of the software reliability model by using optimization algorithms such as a genetic algorithm and the like, has good local optimization capability, is not limited by the existence and continuity of a model function derivative, improves the operation efficiency, and cannot generate infinite special values; the adaptability value is stretched and improved by using the idea of simulated annealing, so that the discipline of leading the dominant individual to enter the next generation is improved; the cross probability and the variation probability are subjected to self-adaptive change by using a formula, so that the accuracy of parameter estimation is effectively improved; and a nonlinear software reliability model is established, so that the method has good goodness of fit and more accurate prediction capability on software.
It should be noted that the method of one or more embodiments of the present disclosure may be performed by a single device, such as a computer or server. The method of the embodiment can also be applied to a distributed scene and completed by the mutual cooperation of a plurality of devices. In such a distributed scenario, one of the devices may perform only one or more steps of the method of one or more embodiments of the present disclosure, and the devices may interact with each other to complete the method.
The foregoing description of specific embodiments of the present disclosure has been described. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
It should be noted that the embodiments of the present disclosure can be further described in the following ways:
a software reliability model parameter estimation method based on genetic algorithm comprises the following steps:
a. acquiring a nonlinear function of a software reliability model;
b. generating a population for the nonlinear function based on random numbers generated within a predetermined range;
c. calculating the fitness value of each individual in the population according to the selected fitness function;
d. selecting individuals from the population for entry into a next generation using a roulette algorithm based on the fitness value;
e. performing cross operation and gene mutation on the selected individuals to obtain offspring individuals;
f. replacing all individuals in the population with the offspring individuals, and iteratively executing the steps c-e until a search result meeting a predetermined requirement is obtained;
g. and outputting the search result as a parameter estimation value of the software reliability model.
Optionally, in the step c, the fitness value is subjected to stretch improvement based on a simulated annealing algorithm, so as to improve the probability that the dominant individuals in the population enter the next generation.
Wherein stretch-modifying the fitness value based on the simulated annealing algorithm comprises:
stretching the fitness value based on the size, genetic algebra, and initial temperature of the population.
Optionally, the interleaving operation comprises a heuristic interleaving operation.
Wherein the probability of the crossover operation is adaptively changed according to the distribution of the fitness value.
Wherein, the distribution situation of the fitness value comprises the average value of the fitness value of each individual in the population, the maximum value and the minimum value in the fitness value.
Optionally, the probability of the gene mutation is adaptively changed according to the distribution of the fitness value.
Wherein, the distribution situation of the fitness value comprises the average value of the fitness value of each individual in the population, the maximum value and the minimum value in the fitness value.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the present disclosure, also technical features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present disclosure as described above, which are not provided in detail for the sake of brevity.
In addition, well-known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown in the provided figures for simplicity of illustration and discussion, and so as not to obscure the embodiments of the disclosure. Furthermore, devices may be shown in block diagram form in order to avoid obscuring embodiments of the present disclosure, and this also takes into account the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform within which the embodiments of the present disclosure are to be implemented (i.e., specifics should be well within purview of one skilled in the art). Where specific details are set forth in order to describe example embodiments of the disclosure, it will be apparent to one skilled in the art that the embodiments of the disclosure can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative instead of restrictive.
While the present disclosure has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description.
The disclosed embodiments are intended to embrace all such alternatives, modifications and variances which fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalents, improvements, and the like that may be made within the spirit and principles of the embodiments of the disclosure are intended to be included within the scope of the disclosure.

Claims (8)

1. A software reliability model parameter estimation method based on genetic algorithm comprises the following steps:
a. acquiring a nonlinear function of a software reliability model;
b. generating a population for the nonlinear function based on random numbers generated within a predetermined range;
c. calculating the fitness value of each individual in the population according to the selected fitness function;
d. selecting individuals from the population for entry into a next generation using a roulette algorithm based on the fitness value;
e. performing cross operation and gene mutation on the selected individuals to obtain offspring individuals;
f. replacing all individuals in the population with the offspring individuals, and iteratively executing the steps c-e until a search result meeting a predetermined requirement is obtained;
g. and outputting the search result as a parameter estimation value of the software reliability model.
2. The method of claim 1, wherein, in the step c, the fitness value is stretch-refined based on a simulated annealing algorithm to increase the probability of a dominant individual in the population entering the next generation.
3. The method of claim 2, wherein stretch-modifying the fitness value based on the simulated annealing algorithm comprises:
stretching the fitness value based on the size, genetic algebra, and initial temperature of the population.
4. The method of any of claims 1-3, wherein the intersection operation comprises a heuristic intersection operation.
5. The method of claim 4, wherein the probability of the crossover operation is adaptively varied according to the distribution of the fitness value.
6. The method of claim 5, wherein the distribution of fitness values comprises a mean value of the fitness values, a maximum value and a minimum value of the fitness values for each individual of the population.
7. The method according to any one of claims 1 to 3, wherein the probability of the genetic mutation is adaptively varied according to the distribution of the fitness value.
8. The method of claim 7, wherein the distribution of fitness values comprises a mean value of the fitness values, a maximum value and a minimum value of the fitness values for each individual of the population.
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Citations (2)

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Patent Citations (2)

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Publication number Priority date Publication date Assignee Title
WO2002082371A2 (en) * 2001-04-06 2002-10-17 Honeywell International Inc. Genetic algorithm optimization method
CN108509335A (en) * 2018-01-31 2018-09-07 浙江理工大学 Software Test Data Generation Method based on genetic algorithm optimization

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