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

Abstract

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

Optimization method of multi-objective testing based on serial-parallel genetic algorithm

technical field

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.

Background technique

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.

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.

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)＝(f ₁ (x),f ₂ (x),...,f _N (x)) (1)

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.

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.

Among them, n=1,2,...,N.

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.

Contents of the invention

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.

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: 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: Execute the genetic algorithm K times to obtain K optimal solution sets. The specific steps of the genetic algorithm include:

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: Screen individuals who meet the constraint conditions from the current population and join the elite solution set E;

S2.3: 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: Calculate the fitness value F ⁱ of individual x _i :

S2.5: If t<T, go to step S2.6, otherwise go to step S2.8:

S2.6: Perform selection, crossover, and mutation operations on the current population to generate the next generation population;

S2.7: let t=t+1, return to step S2.2;

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: 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.

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.

Description of drawings

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;

Fig. 2 is a flowchart of the genetic algorithm in the present invention.

Detailed ways

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.

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: Determine the preferred objectives and constraints of the test:

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.

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: Execute the genetic algorithm K times:

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: Initialize data:

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: Screen individuals according to constraints:

Screen individuals who meet the constraints from the current population and join the elite solution set E.

S203: Calculate the number of times an individual is dominated:

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, 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: Calculate the fitness value of the individual:

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:

Among them, A ⁱ represents the constraint parameter value of individual x _i .

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: 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: Generate the next generation population:

Perform selection, crossover, and mutation operations on the current population to generate the next generation population.

S207: Let t=t+1, return to step S202.

S208: Obtain the optimal solution set:

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: Comprehensive solution:

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.

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.

Table 1

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.

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%.

Table 2 is the normalized value of the funds and time required for each test.

t ₁ t ₂ t _{3 t4} t ₅ t ₆ t ₇ t ₈ t ₉ t ₁₀ t ₁₁ t ₁₂ t ₁₃ t ₁₄ t ₁₅ t ₁₆ t ₁₇ t ₁₈ t ₁₉ t ₂₀ funding 11 2 10 9 9 5 5 2 5 2 4 5 11 3 8 5 3 1 9 4 time 7 6 3 8 8 6 8 5 8 1 8 2 2 7 2 7 8 2 7 6

Table 2

The expressions of the two optimization objective functions of test cost and test time are as follows:

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.

Constraint conditions, that is, the formula for calculating the fault isolation rate FIR is:

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:

Among them, d _vm , d _v′m represent whether the mth test can test the v fault and the v′ fault respectively.

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:

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.

serial number t ₁ t ₂ t _{3 t4} t ₅ t ₆ t ₇ t ₈ t ₉ t ₁₀ t ₁₁ t ₁₂ t ₁₃ t ₁₄ t ₁₅ t ₁₆ t ₁₇ t ₁₈ t ₁₉ t ₂₀ 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 2 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 3 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 4 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 5 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 6 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 7 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0

Table 4

serial number t ₁ t ₂ t _{3 t4} t ₅ t ₆ t ₇ t ₈ t ₉ t ₁₀ t ₁₁ t ₁₂ t ₁₃ t ₁₄ t ₁₅ t ₁₆ t ₁₇ t ₁₈ t ₁₉ t ₂₀ 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 2 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 3 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 4 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0

table 5

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.

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.

funding time 0.49 0.27 0.33 0.41 0.32 0.42 0.24 0.43 0.36 0.39 0.37 0.34 0.51 0.26

Table 6

funding time 0.26 0.38 0.32 0.33 0.31 0.35 0.47 0.31

Table 7

As can be seen from Tables 6 and 7, each test scenario is not dominated by other test scenarios in its table.

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.

serial number t ₁ t ₂ t _{3 t4} t ₅ t ₆ t ₇ t ₈ t ₉ t ₁₀ t ₁₁ t ₁₂ t ₁₃ t ₁₄ t ₁₅ t ₁₆ t ₁₇ t ₁₈ t ₁₉ t ₂₀ 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 2 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 3 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 4 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 5 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 6 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 7 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0

Table 8

Table 9 is the test funds and time of all test programs in Table 8.

funding time 0.24 0.43 0.26 0.38 0.31 0.35 0.32 0.33 0.38 0.31 0.49 0.27 0.51 0.26

Table 9

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.

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.

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. a multi-objective testing optimal method based on serial-parallel genetic algorithm, is characterized in that, comprises the following steps: 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: Execute the genetic algorithm K times to obtain K optimal solution sets. The specific steps of the genetic algorithm include: 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: Screen individuals who meet the constraint conditions from the current population and join the elite solution set E; S2.3: 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: 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> S2.5: If t<T, go to step S2.6, otherwise go to step S2.8: S2.6: Perform selection, crossover, and mutation operations on the current population to generate the next generation population; S2.7: let t=t+1, return to step S2.2; 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: 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.