CN108090566A - Multiple target test preferred method based on connection in series-parallel genetic algorithm - Google Patents

Multiple target test preferred method based on connection in series-parallel genetic algorithm Download PDF

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CN108090566A
CN108090566A CN201711331649.1A CN201711331649A CN108090566A CN 108090566 A CN108090566 A CN 108090566A CN 201711331649 A CN201711331649 A CN 201711331649A CN 108090566 A CN108090566 A CN 108090566A
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杨成林
陈芳
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Abstract

本发明公开了一种基于串并联遗传算法的多目标测试优选方法,根据需要确定若干个电子系统的测试优选的优化目标和约束条件,首先分别执行若干次遗传算法,遗传算法过程中每次得到新的种群,称筛选出满足约束条件的个体加入精英解集合,得到精英解集合中个体的被支配次数,根据种群中的个体是否属于精英解集合采用不同方式来计算适应度值;然后将这若干次遗传算法的最优解集合并,作为初始种群中的个体,再执行一次遗传算法得到最优解集,其每个个体即为一个测试优选方案。本发明基于帕累托最优,设计一种串并联遗传算法,获得满足多个目标的多种测试优选方案,从而为决策者提供多种测试优选方案备选,在不同场合下都可以给出解决方案。

The invention discloses a multi-objective test optimization method based on a series-parallel genetic algorithm. According to the needs, the optimization objectives and constraint conditions of several electronic systems are determined. The new population means that the individuals who meet the constraints are screened out and added to the elite solution set, and the number of individuals in the elite solution set is obtained, and the fitness value is calculated in different ways according to whether the individual in the population belongs to the elite solution set; and then the The optimal solution sets of several genetic algorithms are merged as individuals in the initial population, and the genetic algorithm is executed again to obtain the optimal solution set, and each individual is a test optimal solution. Based on Pareto optimality, the present invention designs a series-parallel genetic algorithm to obtain multiple test optimization schemes that meet multiple objectives, thereby providing decision makers with multiple test optimization scheme alternatives, which can be given in different occasions solution.

Description

基于串并联遗传算法的多目标测试优选方法Optimization method of multi-objective testing based on serial-parallel genetic algorithm

技术领域technical field

本发明属于电子系统故障诊断技术领域,更为具体地讲,涉及一种基于串并联遗传算法的多目标测试优选方法。The invention belongs to the technical field of electronic system fault diagnosis, and more specifically relates to a multi-objective test optimization method based on a series-parallel genetic algorithm.

背景技术Background technique

在针对大型电子设备系统的故障诊断问题中,如何选择测试方案,使故障检测率(FDR,fault diagnose rate)、虚警率(FAR,fault alarm rate)以及测试各项开销(时间、经济等)等可测试性指标同时满足约束条件甚至趋向更好,是学术或者工程领域不断探索的问题。In the problem of fault diagnosis for large-scale electronic equipment systems, how to choose a test plan so that the fault detection rate (FDR, fault diagnosis rate), false alarm rate (FAR, fault alarm rate) and test costs (time, economy, etc.) It is a problem that is constantly being explored in the academic or engineering fields, such as testability indicators that satisfy the constraints at the same time or even tend to be better.

对于以上同时考虑多个测试性指标的测试优选问题,可以视为多目标优化问题。多目标优化问题是讨论如何在一定约束条件下,找到满足多个目标都能达到最优的解。一般情况下,多目标优化问题的各个子目标之间是矛盾的,一个子目标的改善有可能会引起另一个或者另几个子目标的性能降低,也就是要同时使多个子目标一起达到最优值是不可能的,而只能在它们中间进行协调和折中处理,使各个子目标都尽可能地达到最优化。For the above test optimization problem that considers multiple testability indicators at the same time, it can be regarded as a multi-objective optimization problem. The multi-objective optimization problem is to discuss how to find the optimal solution that satisfies multiple objectives under certain constraints. In general, the various sub-objectives of multi-objective optimization problems are contradictory, and the improvement of one sub-objective may cause the performance of another or several other sub-objectives to degrade, that is, to achieve the optimal performance of multiple sub-objectives at the same time. Values are impossible, but can only be coordinated and compromised among them, so that each sub-goal can be optimized as much as possible.

多目标优化可以用公式(1)表达,即需要找到合适的x使得所有N个目标函数f(x)最小:Multi-objective optimization can be expressed by formula (1), that is, it is necessary to find a suitable x to minimize all N objective functions f(x):

minimize F(x)=(f1(x),f2(x),…,fN(x)) (1)minimize F(x)=(f 1 (x),f 2 (x),...,f N (x)) (1)

与单目标优化问题的本质区别在于,多目标优化问题的解并非唯一,而是存在一组由众多Pareto(帕累托)最优解组成的最优解集合,集合中的各个元素称为Pareto最优解或非劣最优解。对于由公式(1)确定的向量F(xi)和F(xj),如果两个相量不相等且F(xi)里的所有元素都不大于F(xj)里的对应位置元素,则称F(xi)支配F(xj),xj称为支配解,xi称为非支配解。由所有非支配解构成的集合称为帕累托最优集。The essential difference from the single-objective optimization problem is that the solution of the multi-objective optimization problem is not unique, but there is a set of optimal solutions composed of many Pareto (Pareto) optimal solutions, and each element in the set is called Pareto optimal solution or non-inferior optimal solution. For the vectors F(x i ) and F(x j ) determined by formula (1), if the two phasors are not equal and all elements in F(x i ) are not greater than the corresponding position in F(x j ) elements, it is said that F( xi ) dominates F(x j ), x j is called the dominant solution, and x i is called the non-dominated solution. The set of all non-dominated solutions is called the Pareto optimal set.

对于多目标优化问题,目前最为普遍的方法是对多目标进行加权求和,如式(2)所示,把和函数g(x)看成单目标优化问题。For multi-objective optimization problems, the most common method at present is to carry out weighted summation on multi-objectives, as shown in formula (2), and regard the sum function g(x) as a single-objective optimization problem.

其中,n=1,2,…,N。Among them, n=1,2,...,N.

这种处理方法的问题有两个:(1)权重因子主观性强,设计者往往不太容易选择;(2)优化结果单一,不能提供多个选择。对于电子系统故障诊断领域,有时候要求尽快隔离故障,测试成本的重要性相对次要,而有时候要求严格控制成本,对时间要求不高。此时需要优化算法能够提供多种选择给决策者备选,在不同场合下都可以给出解决方案。There are two problems with this approach: (1) the weight factor is highly subjective, and it is often not easy for the designer to choose; (2) the optimization result is single, and multiple choices cannot be provided. For the field of fault diagnosis of electronic systems, sometimes it is required to isolate the fault as soon as possible, and the importance of test cost is relatively secondary, while sometimes it is required to strictly control the cost, and the time requirement is not high. At this time, the optimization algorithm needs to be able to provide a variety of options for decision makers to choose, and can give solutions in different situations.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足,提供一种基于串并联遗传算法的多目标测试优选方法,基于帕累托最优,设计一种串并联遗传算法,获得满足多个目标的多种测试优选方案。The purpose of the present invention is to overcome the deficiencies of the prior art, to provide a multi-objective test optimization method based on the series-parallel genetic algorithm, based on Pareto optimality, to design a series-parallel genetic algorithm, to obtain a variety of Test options.

为实现上述发明目的,本发明基于串并联遗传算法的多目标测试优选方法包括以下步骤:In order to realize the above-mentioned purpose of the invention, the multi-objective testing optimal method of the present invention based on serial-parallel genetic algorithm comprises the following steps:

S1:根据需要确定若干个电子系统的测试优选的优化目标和约束条件,记优化目标的数量为N,并设置测试方案的优化目标函数fn(x),n=1,2,…,N,优化目标函数值越小,测试方案越优,记约束条件为A≥A*,A表示约束条件参数,A*表示参数阈值;S1: Determine the optimal optimization objectives and constraints for the testing of several electronic systems according to the needs, record the number of optimization objectives as N, and set the optimization objective function f n (x) of the test plan, n=1,2,...,N , the smaller the optimization objective function value is, the better the test plan is, and the constraint condition is A≥A * , where A represents the constraint parameter, and A * represents the parameter threshold;

S2:执行K次遗传算法,得到K个最优解集,遗传算法的具体步骤包括:S2: Execute the genetic algorithm K times to obtain K optimal solution sets. The specific steps of the genetic algorithm include:

S2.1:初始化迭代次数t=1,精英解集合随机生成Y个个体xi,i=1,2,…,Y,每个个体为一个长度为M的二进制码,M表示电子系统的测试数量;每个个体表示一个测试方案,当二进制码中第m个数据为0时,表示个体所对应测试方案中未选中第m个测试,当二进制码中第m个数据为1时,表示个体所对应测试方案中选中第m个测试,m=1,2,…,M;S2.1: Initialize the number of iterations t=1, set elite solutions Randomly generate Y individuals x i , i=1,2,...,Y, each individual is a binary code with a length of M, and M represents the test quantity of the electronic system; each individual represents a test plan, when the binary code When the mth data is 0, it means that the mth test is not selected in the test plan corresponding to the individual; when the mth data in the binary code is 1, it means that the mth test is selected in the test plan corresponding to the individual, m=1 ,2,...,M;

S2.2:从当前种群中筛选中符合约束条件的个体,加入精英解集合E;S2.2: Screen individuals who meet the constraint conditions from the current population and join the elite solution set E;

S2.3:根据N个优化目标函数fn(x),计算当前精英解集合E每个个体xd对应的N个优化目标函数值fn(xd),d=1,2,…,|E|,|E|表示当前精英解集合E中个体数量,两两比较个体的优化目标函数值,获取每个个体被支配的次数zd;搜索当前精英解集合E中被支配次数最多和最少的个体,其被支配次数分别记为zmax和zminS2.3: According to N optimization objective functions f n (x), calculate N optimization objective function values f n (x d ) corresponding to each individual x d in the current elite solution set E, d=1,2,..., |E|, |E| represents the number of individuals in the current elite solution set E, compare the optimization objective function values of individuals pairwise, and obtain the number of times z d of each individual is dominated; search for the most dominated times in the current elite solution set E and The individual with the least amount of domination is recorded as z max and z min respectively;

S2.4:计算个体xi的适应度值FiS2.4: Calculate the fitness value F i of individual x i :

S2.5:如果t<T,进入步骤S2.6,否则进入步骤S2.8:S2.5: If t<T, go to step S2.6, otherwise go to step S2.8:

S2.6:对当前种群中进行选择、交叉、变异操作,生成下一代种群;S2.6: Perform selection, crossover, and mutation operations on the current population to generate the next generation population;

S2.7:令t=t+1,返回步骤S2.2;S2.7: let t=t+1, return to step S2.2;

S2.8:计算当前精英解集合E中每个个体对应的N个优化目标函数值,搜索当前精英解集合E中的非支配个体,即构成本次遗传算法的最优解集;S2.8: Calculate the N optimization objective function values corresponding to each individual in the current elite solution set E, and search for non-dominated individuals in the current elite solution set E, which constitute the optimal solution set of the genetic algorithm;

S3:合并步骤S2所获得的K个最优解集,得到集合U,如果集合U中的个体数量|U|等于Y,则将集合U作为种群V;如果|U|小于Y,则随机生成产生Y-|U|个体,与集合U一起构成种群V;如果|U|大于Y,则计算集合U中每个个体对应的N个优化目标函数值,两两比较个体的优化目标函数值,获取每个个体被支配的次数,将个体按被支配次数升序排列,取前Y个个体构成种群V;将种群V作为初始种群,执行一次步骤S2中的遗传算法,得到最优解集,其每个个体即为一个测试优选方案。S3: Merge the K optimal solution sets obtained in step S2 to obtain a set U, if the number of individuals in the set U |U| is equal to Y, then use the set U as the population V; if |U| Generate Y-|U| individuals to form a population V together with the set U; if |U| is greater than Y, calculate the N optimization objective function values corresponding to each individual in the set U, and compare the individual optimization objective function values pairwise. Obtain the number of times each individual is dominated, arrange the individuals in ascending order according to the number of times they are dominated, and take the first Y individuals to form a population V; use the population V as the initial population, execute the genetic algorithm in step S2 once, and obtain the optimal solution set. Each individual is a test preference.

本发明基于串并联遗传算法的多目标测试优选方法,根据需要确定若干个电子系统的测试优选的优化目标和约束条件,首先分别执行若干次遗传算法,遗传算法过程中每次得到新的种群,称筛选出满足约束条件的个体加入精英解集合,得到精英解集合中个体的被支配次数,根据种群中的个体是否属于精英解集合采用不同方式来计算适应度值;然后将这若干次遗传算法的最优解集合并,作为初始种群中的个体,再执行一次遗传算法得到最优解集,其每个个体即为一个测试优选方案。本发明基于帕累托最优,设计一种串并联遗传算法,获得满足多个目标的多种测试优选方案,从而为决策者提供多种测试优选方案备选,在不同场合下都可以给出解决方案。The present invention is based on the multi-objective test optimization method of the serial-parallel genetic algorithm. According to the needs, the optimization objectives and constraint conditions of the test optimization of several electronic systems are determined, and the genetic algorithm is firstly executed several times, and a new population is obtained each time during the genetic algorithm process. It is said that the individuals who meet the constraint conditions are screened out and added to the elite solution set, and the number of individuals in the elite solution set is obtained, and the fitness value is calculated in different ways according to whether the individual in the population belongs to the elite solution set; The optimal solution set of is merged, as an individual in the initial population, and the genetic algorithm is executed again to obtain the optimal solution set, and each individual is a test optimal solution. Based on Pareto optimality, the present invention designs a series-parallel genetic algorithm to obtain multiple test optimization schemes that meet multiple objectives, thereby providing decision makers with multiple test optimization scheme alternatives, which can be given in different occasions solution.

附图说明Description of drawings

图1是本发明基于串并联遗传算法的多目标测试优选方法的具体实施方式流程图;Fig. 1 is the specific embodiment flow chart of the present invention based on the multi-objective testing optimal method of series-parallel genetic algorithm;

图2是本发明中遗传算法的流程图。Fig. 2 is a flowchart of the genetic algorithm in the present invention.

具体实施方式Detailed ways

下面结合附图对本发明的具体实施方式进行描述,以便本领域的技术人员更好地理解本发明。需要特别提醒注意的是,在以下的描述中,当已知功能和设计的详细描述也许会淡化本发明的主要内容时,这些描述在这里将被忽略。Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

图1是本发明基于串并联遗传算法的多目标测试优选方法的具体实施方式流程图。如图1所示,本发明基于串并联遗传算法的多目标测试优选方法的具体步骤包括:Fig. 1 is a specific implementation flow chart of the multi-objective testing optimization method based on the serial-parallel genetic algorithm of the present invention. As shown in Fig. 1, the specific steps of the multi-objective testing optimization method based on the serial-parallel genetic algorithm of the present invention include:

S101:确定测试优选的目标和约束条件:S101: Determine the preferred objectives and constraints of the test:

根据需要确定若干个电子系统的测试优选的优化目标和约束条件,记优化目标的数量为N,并设置测试方案的优化目标函数fn(x),n=1,2,…,N,优化目标函数值越小,测试方案越优,记约束条件为A≥A*,A表示约束条件参数,A*表示参数阈值。Determine the optimal optimization objectives and constraint conditions for the testing of several electronic systems according to the needs, record the number of optimization objectives as N, and set the optimization objective function f n (x) of the test plan, n=1,2,...,N, optimize The smaller the value of the objective function is, the better the test plan is, and the constraint condition is A≥A * , where A represents the parameter of the constraint condition, and A * represents the parameter threshold.

在电子系统故障诊断领域,测试优选的优化目标包括测试经费最小化、测试时间开销最小化、故障隔离度最大化、故障检测率最大化等,显然,当优化目标为越大越好时,例如故障隔离度和故障检测率,其优化目标函数可以设置为故障隔离度或故障检测率的倒数。约束条件的参数一般可以选择故障隔离度、故障检测率、虚警率等。测试优选的目标和约束条件都是根据实际需要来确定的。In the field of electronic system fault diagnosis, the optimization objectives of test optimization include the minimization of test funds, the minimization of test time overhead, the maximization of fault isolation, and the maximization of fault detection rate. Isolation and fault detection rate, the optimization objective function can be set as the reciprocal of fault isolation or fault detection rate. The parameters of constraint conditions can generally choose fault isolation degree, fault detection rate, false alarm rate and so on. The preferred objectives and constraints of the test are determined according to actual needs.

S102:执行K次遗传算法:S102: Execute the genetic algorithm K times:

执行K次遗传算法,得到K个最优解集。K的大小是根据实际需要来设置的,时间要求紧迫,K可以取较小值,对精度要求高时可以取较大值。用于进行多目标测试优选的遗传算法是本发明的关键算法。图2是本发明中遗传算法的流程图。如图2所示,遗传算法的具体步骤包括:Execute the genetic algorithm K times to obtain K optimal solution sets. The size of K is set according to actual needs, and the time requirement is urgent, K can take a smaller value, and a larger value can be taken when the precision is high. The optimal genetic algorithm for multi-objective testing is the key algorithm of the present invention. Fig. 2 is a flowchart of the genetic algorithm in the present invention. As shown in Figure 2, the specific steps of the genetic algorithm include:

S201:初始化数据:S201: Initialize data:

初始化迭代次数t=1,精英解集合随机生成Y个个体xi,i=1,2,…,Y,每个个体为一个长度为M的二进制码,M表示电子系统的测试数量。每个个体表示一个测试方案,当二进制码中第m个数据为0时,表示个体所对应测试方案中未选中第m个测试,当二进制码中第m个数据为1时,表示个体所对应测试方案中选中第m个测试,m=1,2,…,M。Initialize the number of iterations t=1, the set of elite solutions Randomly generate Y individuals xi , i=1, 2, ..., Y, each individual is a binary code with a length of M, and M represents the number of tests of the electronic system. Each individual represents a test plan. When the mth data in the binary code is 0, it means that the mth test is not selected in the test plan corresponding to the individual. When the mth data in the binary code is 1, it means that the individual corresponds to Select the mth test in the test plan, m=1,2,...,M.

S202:根据约束条件筛选个体:S202: Screen individuals according to constraints:

从当前种群中筛选中符合约束条件的个体,加入精英解集合E。Screen individuals who meet the constraints from the current population and join the elite solution set E.

S203:计算个体被支配次数:S203: Calculate the number of times an individual is dominated:

根据N个优化目标函数fn(x),计算当前精英解集合E每个个体xd对应的N个优化目标函数值fn(xd),d=1,2,…,|E|,|E|表示当前精英解集合E中个体数量,两两比较个体的优化目标函数值,获取每个个体被支配的次数zd。搜索当前精英解集合E中被支配次数最多和最少的个体,其被支配次数分别记为zmax和zminAccording to N optimization objective functions f n (x), calculate N optimization objective function values f n (x d ) corresponding to each individual x d in the current elite solution set E, d=1,2,...,|E|, |E| represents the number of individuals in the current elite solution set E, and compares the optimization objective function values of individuals pairwise to obtain the number z d of times each individual is dominated. Search for the individuals with the most and least dominated times in the current elite solution set E, and their dominated times are recorded as z max and z min respectively.

S204:计算个体的适应度值:S204: Calculate the fitness value of the individual:

很显然,当前种群中的个体有两种:属于精英解集合E或不属于集合E,在计算适应度值需要区别计算。本发明中,个体的适应度值按照以下公式计算:Obviously, there are two types of individuals in the current population: they belong to the elite solution set E or they do not belong to the set E, and they need to be calculated differently when calculating the fitness value. In the present invention, the fitness value of an individual is calculated according to the following formula:

其中,Ai表示个体xi的约束条件参数值。Among them, A i represents the constraint parameter value of individual x i .

显然,属于精英解集合E中的个体,被支配次数越少越优,不属于集合E的个体,约束条件参数越大越优,因此本发明,个体的适应度值越大,个体越优。Obviously, the individuals belonging to the elite solution set E, the less dominated the better, and the individuals not belonging to the set E, the greater the constraint parameter, the better. Therefore, in the present invention, the greater the fitness value of the individual, the better the individual.

S205:判断迭代次数t是否小于预设最大迭代次数T,如果是,进入步骤S206,否则进入步骤S208。S205: Determine whether the number of iterations t is less than the preset maximum number of iterations T, if yes, go to step S206, otherwise go to step S208.

S206:生成下一代种群:S206: Generate the next generation population:

对当前种群中进行选择、交叉、变异操作,生成下一代种群。Perform selection, crossover, and mutation operations on the current population to generate the next generation population.

S207:令t=t+1,返回步骤S202。S207: Let t=t+1, return to step S202.

S208:得到最优解集:S208: Obtain the optimal solution set:

计算当前精英解集合E中每个个体对应的N个优化目标函数值,搜索当前精英解集合E中的非支配个体,即构成本次遗传算法的最优解集。Calculate the N optimization objective function values corresponding to each individual in the current elite solution set E, and search for the non-dominated individuals in the current elite solution set E, which constitute the optimal solution set of the genetic algorithm.

S103:综合求解:S103: Comprehensive solution:

合并步骤S102所获得的K个最优解集,得到集合U,如果集合U中的个体数量|U|等于Y,则将集合U作为种群V;如果|U|小于Y,则随机生成产生Y-|U|个体,与集合U一起构成种群V;如果|U|大于Y,则计算集合U中每个个体对应的N个优化目标函数值,两两比较个体的优化目标函数值,获取每个个体被支配的次数,将个体按被支配次数升序排列,取前Y个个体构成种群V。将种群V作为初始种群,执行一次步骤S102中的遗传算法,得到最优解集,其每个个体即为一个测试优选方案。Combine the K optimal solution sets obtained in step S102 to obtain a set U, if the number of individuals in the set U |U| is equal to Y, then use the set U as the population V; if |U| is less than Y, then randomly generate Y -|U| individuals form a population V together with the set U; if |U| is greater than Y, then calculate the N optimization objective function values corresponding to each individual in the set U, compare the individual optimization objective function values pairwise, and obtain each The number of times an individual is dominated, the individuals are arranged in ascending order of the number of times they are dominated, and the first Y individuals are taken to form a population V. The population V is used as the initial population, and the genetic algorithm in step S102 is executed once to obtain the optimal solution set, and each individual is an optimal solution for testing.

为了更好地说明本发明技术方案,采用一个具体实例对本发明进行详细说明。表1是本实施例的测试依赖矩阵。In order to better illustrate the technical solution of the present invention, a specific example is used to describe the present invention in detail. Table 1 is the test dependency matrix of this embodiment.

表1Table 1

如表1所示,本实施例的电子系统共有50种故障状态,20个备选测试,表1中的第一列数据为各个故障的归一化发生率,其余二进制数据表示相应测试是否能测试对应的故障,1表示能够测试,0则表示不能测试。As shown in Table 1, the electronic system of this embodiment has 50 kinds of fault states and 20 alternative tests. The first column of data in Table 1 is the normalized incidence rate of each fault, and the rest of the binary data represent whether the corresponding test can be performed. Test the corresponding fault, 1 means it can be tested, and 0 means it cannot be tested.

本实施例中,优化目标为测试经费和测试时间最小,约束条件采用故障隔离率,要求故障隔离率达到100%。In this embodiment, the optimization goal is to minimize the test cost and test time, and the constraint condition is the fault isolation rate, which requires the fault isolation rate to reach 100%.

表2是各项测试所需经费与时间的归一化值。Table 2 is the normalized value of the funds and time required for each test.

t1 t 1 t2 t 2 t3 t 3 t4 t4 t5 t 5 t6 t 6 t7 t 7 t8 t 8 t9 t 9 t10 t 10 t11 t 11 t12 t 12 t13 t 13 t14 t 14 t15 t 15 t16 t 16 t17 t 17 t18 t 18 t19 t 19 t20 t 20 经费funding 1111 22 1010 99 99 55 55 22 55 22 44 55 1111 33 88 55 33 11 99 44 时间time 77 66 33 88 88 66 88 55 88 11 88 22 22 77 22 77 88 22 77 66

表2Table 2

测试经费和测试时间两个优化目标函数的表达式分别如下:The expressions of the two optimization objective functions of test cost and test time are as follows:

其中,xm表示个体x中的第m个元素,cm、τm分别表示第m个测试所需的经费和时间。Among them, x m represents the mth element of individual x, and c m and τ m represent the funds and time required for the mth test respectively.

约束条件,即故障隔离率FIR的计算公式为:Constraint conditions, that is, the formula for calculating the fault isolation rate FIR is:

其中,wv表示v号故障的发生率,bv(x)表示个体x所对应的测试方案下v号故障是否被隔离,其计算公式为:Among them, w v represents the occurrence rate of fault v, and b v (x) represents whether fault v is isolated under the test scheme corresponding to individual x, and its calculation formula is:

其中,dvm、dv′m分别表示第m个测试是否能够测试v号故障和v′号故障。Among them, d vm , d v′m represent whether the mth test can test the v fault and the v′ fault respectively.

首先运行两次遗传算法,初始种群个体数量为100。本实施例个体的适应值度按照以下公式计算:First run the genetic algorithm twice, and the initial population number is 100. The fitness value of the individual in this example is calculated according to the following formula:

表4是第一次遗传算法得到的最优解集。表5是第二次遗传算法得到的最优解集。Table 4 is the optimal solution set obtained by the first genetic algorithm. Table 5 is the optimal solution set obtained by the second genetic algorithm.

序号serial number t1 t 1 t2 t 2 t3 t 3 t4 t4 t5 t 5 t6 t 6 t7 t 7 t8 t 8 t9 t 9 t10 t 10 t11 t 11 t12 t 12 t13 t 13 t14 t 14 t15 t 15 t16 t 16 t17 t 17 t18 t 18 t19 t 19 t20 t 20 11 00 00 11 00 11 00 00 00 00 11 00 11 11 11 11 00 00 11 00 00 22 00 11 00 00 00 00 00 00 00 00 11 11 11 11 00 00 11 11 00 11 33 00 11 00 00 00 11 00 11 00 11 11 11 00 11 00 00 00 00 11 00 44 00 11 00 00 00 11 00 11 11 11 11 00 00 11 00 00 00 11 00 00 55 00 11 00 00 11 11 00 00 00 11 00 11 00 11 00 00 00 11 11 00 66 00 11 11 00 00 11 00 00 00 11 00 11 00 11 00 00 00 11 11 00 77 11 00 11 00 00 00 00 00 00 11 00 11 11 11 11 00 00 11 00 00

表4Table 4

序号serial number t1 t 1 t2 t 2 t3 t 3 t4 t4 t5 t 5 t6 t 6 t7 t 7 t8 t 8 t9 t 9 t10 t 10 t11 t 11 t12 t 12 t13 t 13 t14 t 14 t15 t 15 t16 t 16 t17 t 17 t18 t 18 t19 t 19 t20 t 20 11 00 11 00 00 00 11 00 00 00 11 11 11 00 11 00 00 00 11 00 11 22 00 11 11 00 00 11 00 00 00 11 00 11 00 11 00 00 00 11 00 11 33 00 11 11 00 00 11 00 00 00 11 00 11 00 11 00 00 11 11 00 00 44 00 11 11 00 00 11 00 00 00 11 00 11 11 11 11 00 00 11 00 00

表5table 5

如表4和表5所示,表中的各行各对应一种测试方案,每一种测试方案中的每一列取0或1,0表示对应测点未被选中,如表4中,第2行第1列为0,表示第2个测试方案中测试1未被选中。而第一行第三列为1,表示第三个测试在方案一中被选中。不难验证,表4与表5中所有方案的FIR均为1,满足最低指标要求。As shown in Table 4 and Table 5, each row in the table corresponds to a test scheme, and each column in each test scheme takes 0 or 1, and 0 indicates that the corresponding measuring point is not selected, as in Table 4, the second The first column of the row is 0, indicating that test 1 is not selected in the second test plan. And the third column of the first row is 1, indicating that the third test is selected in the first scheme. It is not difficult to verify that the FIR of all the schemes in Table 4 and Table 5 is 1, which meets the minimum index requirements.

表6是表4中所有测试方案的测试经费与时间。表7是表5中所有测试方案的测试经费与时间。Table 6 is the test funds and time of all test programs in Table 4. Table 7 is the test funds and time of all test programs in Table 5.

经费funding 时间time 0.490.49 0.270.27 0.330.33 0.410.41 0.320.32 0.420.42 0.240.24 0.430.43 0.360.36 0.390.39 0.370.37 0.340.34 0.510.51 0.260.26

表6Table 6

经费funding 时间time 0.260.26 0.380.38 0.320.32 0.330.33 0.310.31 0.350.35 0.470.47 0.310.31

表7Table 7

从表6和表7可以看出,每个测试方案在其表中都不被其他测试方案支配。As can be seen from Tables 6 and 7, each test scenario is not dominated by other test scenarios in its table.

将表4和表5中包含的11个测试方案,以及随机生成89个测试方案,构成综合求解的初始种群。表8是综合求解得到的最优解集。The 11 test schemes included in Table 4 and Table 5, as well as 89 test schemes randomly generated, constitute the initial population for the comprehensive solution. Table 8 is the optimal solution set obtained by comprehensive solution.

序号serial number t1 t 1 t2 t 2 t3 t 3 t4 t4 t5 t 5 t6 t 6 t7 t 7 t8 t 8 t9 t 9 t10 t 10 t11 t 11 t12 t 12 t13 t 13 t14 t 14 t15 t 15 t16 t 16 t17 t 17 t18 t 18 t19 t 19 t20 t 20 11 00 00 11 00 11 00 00 00 00 11 00 11 11 11 11 00 00 11 00 00 22 00 11 00 00 00 11 00 00 00 11 11 11 00 11 00 00 00 11 00 11 33 00 11 00 00 00 11 00 11 11 11 11 00 00 11 00 00 00 11 00 00 44 00 11 11 00 00 00 00 00 00 11 11 11 11 11 00 00 00 11 00 00 55 00 11 11 00 00 11 00 00 00 11 00 11 00 11 00 00 00 11 00 11 66 00 11 11 00 00 11 00 00 00 11 00 11 00 11 00 00 11 11 00 00 77 11 00 11 00 00 00 00 00 00 11 00 11 11 11 11 00 00 11 00 00

表8Table 8

表9是表8中所有测试方案的测试经费与时间。Table 9 is the test funds and time of all test programs in Table 8.

经费funding 时间time 0.240.24 0.430.43 0.260.26 0.380.38 0.310.31 0.350.35 0.320.32 0.330.33 0.380.38 0.310.31 0.490.49 0.270.27 0.510.51 0.260.26

表9Table 9

从表9可以看出,相对于其它6种方案,第一行给出的方案其测试经费最少,只有0.24,但是其测试时间最高,为0.43,适用于对成本控制较为严格的场合。反之,最后一行适用于对测试时间要求紧迫的情况。中间几行的方案是折衷的方案,无论那种方案,都是满足指标要求的。It can be seen from Table 9 that, compared with the other 6 schemes, the scheme given in the first row has the least test expenditure, only 0.24, but the highest test time, 0.43, which is suitable for occasions with strict cost control. Conversely, the last line is suitable for cases where the test time is critical. The schemes in the middle rows are compromised schemes, no matter what kind of scheme, they all meet the requirements of the indicators.

分别将综合求解的最优解与之前两次遗传算法的最优解作对比,不难看出,综合求解得到的最优解都支配了前两次遗传算法的最优解,即综合求解得到的测试方案更优。可见,本发明可以为电子系统提供多种测试方案选择,且得到的测试方案比单次遗传算法得到的更优。Comparing the optimal solutions of the comprehensive solution with the optimal solutions of the previous two genetic algorithms, it is not difficult to see that the optimal solutions obtained by the comprehensive solution dominate the optimal solutions of the previous two genetic algorithms, that is, the optimal solutions obtained by the comprehensive solution The test plan is better. It can be seen that the present invention can provide multiple test scheme options for the electronic system, and the obtained test scheme is better than that obtained by a single genetic algorithm.

尽管上面对本发明说明性的具体实施方式进行了描述,以便于本技术领域的技术人员理解本发明,但应该清楚,本发明不限于具体实施方式的范围,对本技术领域的普通技术人员来讲,只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内,这些变化是显而易见的,一切利用本发明构思的发明创造均在保护之列。Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

Claims (1)

1.一种基于串并联遗传算法的多目标测试优选方法,其特征在于,包括以下步骤:1. a multi-objective testing optimal method based on serial-parallel genetic algorithm, is characterized in that, comprises the following steps: S1:根据需要确定若干个电子系统的测试优选的优化目标和约束条件,记优化目标的数量为N,并设置测试方案的优化目标函数fn(x),n=1,2,…,N,优化目标函数值越小,测试方案越优,记约束条件为A≥A*,A表示约束条件参数,A*表示参数阈值;S1: Determine the optimal optimization objectives and constraint conditions for the test of several electronic systems according to the needs, record the number of optimization objectives as N, and set the optimization objective function f n (x) of the test plan, n=1,2,...,N , the smaller the optimization objective function value is, the better the test plan is, and the constraint condition is A≥A * , where A represents the constraint parameter, and A * represents the parameter threshold; S2:执行K次遗传算法,得到K个最优解集,遗传算法的具体步骤包括:S2: Execute the genetic algorithm K times to obtain K optimal solution sets. The specific steps of the genetic algorithm include: S2.1:初始化迭代次数t=1,精英解集合随机生成Y个个体xi,i=1,2,…,Y,每个个体为一个长度为M的二进制码,M表示电子系统的测试数量。每个个体表示一个测试方案,当二进制码中第m个数据为0时,表示个体所对应测试方案中未选中第m个测试,当二进制码中第m个数据为1时,表示个体所对应测试方案中选中第m个测试,m=1,2,…,M;S2.1: Initialize the number of iterations t=1, set elite solutions Randomly generate Y individuals xi , i=1, 2, ..., Y, each individual is a binary code with a length of M, and M represents the number of tests of the electronic system. Each individual represents a test plan. When the mth data in the binary code is 0, it means that the mth test is not selected in the test plan corresponding to the individual. When the mth data in the binary code is 1, it means that the individual corresponds to Select the mth test in the test plan, m=1,2,...,M; S2.2:从当前种群中筛选中符合约束条件的个体,加入精英解集合E;S2.2: Screen individuals who meet the constraint conditions from the current population and join the elite solution set E; S2.3:根据N个优化目标函数fn(x),计算当前精英解集合E每个个体xd对应的N个优化目标函数值fn(xd),d=1,2,…,|E|,|E|表示当前精英解集合E中个体数量,两两比较个体的优化目标函数值,获取每个个体被支配的次数zd;搜索当前精英解集合E中被支配次数最多和最少的个体,其被支配次数分别记为zmax和zminS2.3: According to N optimization objective functions f n (x), calculate N optimization objective function values f n (x d ) corresponding to each individual x d in the current elite solution set E, d=1,2,..., |E|, |E| represents the number of individuals in the current elite solution set E, compare the optimization objective function values of individuals pairwise, and obtain the number of times each individual is dominated z d ; search for the most dominated times and The individual with the least amount of domination is recorded as z max and z min respectively; S2.4:计算个体xi的适应度值FiS2.4: Calculate the fitness value F i of individual x i : <mrow> <msup> <mi>F</mi> <mi>i</mi> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mi>E</mi> <mo>|</mo> </mrow> <mi>Y</mi> </mfrac> <mfrac> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;Element;</mo> <mi>E</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <mi>E</mi> <mo>|</mo> </mrow> <mi>Y</mi> </mfrac> <mo>)</mo> <mfrac> <msup> <mi>A</mi> <mi>i</mi> </msup> <msup> <mi>A</mi> <mo>*</mo> </msup> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>&amp;NotElement;</mo> <mi>E</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mrow><msup><mi>F</mi><mi>i</mi></msup><mo>=</mo><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mo>|</mo><mi>E</mi><mo>|</mo></mrow><mi>Y</mi></mfrac><mfrac><mrow><mo>(</mo><msub><mi>z</mi><mi>i</mi></msub><mo>-</mo><msub><mi>z</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mo>(</mo><msub><mi>z</mi><mi>max</mi></msub><mo>-</mo><msub><mi>z</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>)</mo></mrow></mfrac><mo>,</mo></mrow></mtd><mtd><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>&amp;Element;</mo><mi>E</mi></mrow></mtd></mtr><mtr><mtd><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mo>|</mo><mi>E</mi><mo>|</mo></mrow><mi>Y</mi></mfrac><mo>)</mo><mfrac><msup><mi>A</mi><mi>i</mi></msup><msup><mi>A</mi><mo>*</mo></msup></mfrac><mo>,</mo></mrow></mtd><mtd><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>&amp;NotElement;</mo><mi>E</mi></mrow></mtd></mtr></mtable></mfenced></mrow> S2.5:如果t<T,进入步骤S2.6,否则进入步骤S2.8:S2.5: If t<T, go to step S2.6, otherwise go to step S2.8: S2.6:对当前种群中进行选择、交叉、变异操作,生成下一代种群;S2.6: Perform selection, crossover, and mutation operations on the current population to generate the next generation population; S2.7:令t=t+1,返回步骤S2.2;S2.7: let t=t+1, return to step S2.2; S2.8:计算当前精英解集合E中每个个体对应的N个优化目标函数值,搜索当前精英解集合E中的非支配个体,即构成本次遗传算法的最优解集;S2.8: Calculate the N optimization objective function values corresponding to each individual in the current elite solution set E, and search for non-dominated individuals in the current elite solution set E, which constitute the optimal solution set of the genetic algorithm; S3:合并步骤S2所获得的K个最优解集,得到集合U,如果集合U中的个体数量|U|等于Y,则将集合U作为种群V;如果|U|小于Y,则随机生成产生Y-|U|个体,与集合U一起构成种群V;如果|U|大于Y,则计算集合U中每个个体对应的N个优化目标函数值,两两比较个体的优化目标函数值,获取每个个体被支配的次数,将个体按被支配次数升序排列,取前Y个个体构成种群V;将种群V作为初始种群,执行一次步骤S2中的遗传算法,得到最优解集,其每个个体即为一个测试优选方案。S3: Merge the K optimal solution sets obtained in step S2 to obtain a set U, if the number of individuals in the set U |U| is equal to Y, then use the set U as the population V; if |U| Generate Y-|U| individuals to form a population V together with the set U; if |U| is greater than Y, calculate the N optimization objective function values corresponding to each individual in the set U, and compare the individual optimization objective function values pairwise. Obtain the number of times each individual is dominated, arrange the individuals in ascending order according to the number of times they are dominated, and take the first Y individuals to form a population V; use the population V as the initial population, execute the genetic algorithm in step S2 once, and obtain the optimal solution set. Each individual is a test preference.
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