CN110704259B

CN110704259B - Efficient digital microfluidic biochip test path optimization method

Info

Publication number: CN110704259B
Application number: CN201910846939.2A
Authority: CN
Inventors: 黄喜军; 许川佩; 张龙; 曾莹; 李翔; 胡聪
Original assignee: Guilin University of Electronic Technology
Current assignee: Guilin University of Electronic Technology
Priority date: 2019-09-09
Filing date: 2019-09-09
Publication date: 2023-04-28
Anticipated expiration: 2039-09-09
Also published as: CN110704259A

Abstract

The invention relates to a high-efficient digital microfluidic biochip test path optimization method, which solves the technical problem of high blindness in the random search direction, and comprises the following steps of defining an array unit of a test chip as a vertex, connecting adjacent vertexes by edges, converting the test chip into an undirected connected graph, and completing the construction of a test model; assigning a different decimal to each edge in the undirected communication graph for characterizing the priority level of the edge; defining a priority strategy as a path selection strategy, and generating a path of the traversing edge as a test path by using the priority strategy, wherein the test path is a vertex set which is sequentially traversed by the traversing edge; step three, optimizing the test path of the step two by utilizing a genetic algorithm; the priority strategy comprises an offline test priority strategy and an online test priority strategy, so that the problem is well solved, and the method can be used for testing the digital microfluidic biochip.

Description

Efficient digital microfluidic biochip test path optimization method

Technical Field

The invention relates to the field of off-line and on-line testing of digital microfluidic biochips, in particular to a high-efficiency method for optimizing a testing path of a digital microfluidic biochip.

Background

The digital microfluidic biochip is generally composed of two layers, wherein the top layer is a continuous grounding electrode, the bottom layer is a control electrode which can be independently driven, and the operations of moving, mixing and the like are performed on liquid drops between the two layers by applying different high and low levels to the control electrode. When the chip has catastrophic faults such as short circuit, the liquid drops can be stopped before passing through the faulty array unit, so that the biochemical experiment cannot be normally performed. Since the biochemical experiment has high requirement on the reliability of the digital microfluidic chip, the chip needs to be fully tested, not only offline test needs to be performed after chip production and before experiment development, but also online test needs to be performed on the chip in the experiment development process, so that the chip fault can be found in time, and the reliability of the experimental result is ensured.

Aiming at the testing problem of catastrophic failure of the digital microfluidic biochip, the existing method for traversing all array units of the chip by using test droplets is solved, and whether the test droplets successfully reach a detection area or not is judged by using a capacitance detection circuit, so that whether the chip has failure or not is judged. However, this method cannot detect all short-circuit faults, and cannot detect the short-circuit faults when the droplet advancing direction is inconsistent with the wiring direction of the short-circuit array unit. Therefore, researchers propose not only to traverse all array elements, but also to traverse the boundaries between array elements, i.e. to convert vertex-based detection into edge-based detection, and propose to implement this by using the euler loop method. Firstly, a chip is transformed into an undirected graph model, then edges in the undirected graph can form an Euler loop by adding edges, and all edges in the Euler loop are traversed by using test liquid drops according to a Fleury algorithm. However, the method requires more waiting time during online test and has low detection efficiency. In addition, researchers have proposed a method of performing parallel scanning on a chip by using multiple liquid drops to perform fault detection, and have also proposed a built-in self-test method based on the parallel scanning method, thereby further improving the offline detection efficiency. However, none of the above methods is suitable for online testing, researchers have proposed using ant colony algorithm to perform test path optimization on chips, and although online test efficiency is improved to some extent, since the ant colony algorithm is only used to perform test path searching and optimization, under the condition that heuristic information is not fully utilized, search randomness is high, so that convergence speed is slow, and convergence to an optimal value cannot be achieved.

In order to further reduce the test time and optimize the test path, the invention combines heuristic information with a random search algorithm, reduces the blindness of test path search, adopts a mixed method (PS-GA) combining a Priority Strategy (PS) and a Genetic Algorithm (GA) to search and optimize the test path, and searches for the shortest test path on the basis of traversing the boundary between chip array units and array units, namely on the basis of traversing all sides in an undirected graph.

Disclosure of Invention

The technical problem to be solved by the invention is that the blindness in the random search direction is high in the prior art. The novel high-efficiency digital microfluidic biochip testing path optimizing method has the characteristic of high optimizing efficiency.

In order to solve the technical problems, the technical scheme adopted is as follows:

an efficient digital microfluidic biochip test path optimization method, comprising:

firstly, defining array units of a test chip as vertexes, connecting adjacent vertexes by edges, converting the test chip into an undirected connected graph, and completing test model construction; assigning a different decimal to each edge in the undirected communication graph for characterizing the priority level of the edge;

defining a priority strategy as a path selection strategy, and generating a path of the traversing edge as a test path by using the priority strategy, wherein the test path is a vertex set which is sequentially traversed by the traversing edge;

and step three, optimizing the test path of the step two by using a genetic algorithm.

The priority policies include an offline test priority policy and an online test priority policy.

In the above scheme, in order to implement test path optimization, further, the offline test priority policy is:

step A, if the vertex where the test liquid drop is located has an adjacent edge which is not traversed, selecting the vertex corresponding to the edge with the highest priority level as the next searching vertex;

and B, if the adjacent edges are traversed, determining the shortest path from the test liquid drop to the non-tested edge in the test model according to the Floyd algorithm, guiding the test liquid drop to move along the shortest path, and finishing the selection of the vertex closest to the non-traversed edge as the next search point.

Further, the online test priority policy is:

step a, defining constraint conditions, judging the number of effective adjacent points when the adjacent vertexes of the test liquid drops meet the constraint conditions as effective adjacent points, and executing the step d if the number of the effective adjacent points is 0; otherwise, the test liquid drops do not fall back, and the step b is executed;

step b, if the number of the effective adjacent points is 1, selecting the vertex as the vertex to be passed at the next moment; if the number of the effective adjacent points is more than 2, judging the number of the adjacent edges which are not traversed;

step c, if the number of the non-traversed adjacent edges is 0, selecting the nearest effective adjacent point from the non-traversed edges as the vertex to be traversed at the next moment according to the Floyd algorithm; if the number of the adjacent edges which are not traversed is 1, selecting the vertexes corresponding to the adjacent edges; if the number of the non-traversed adjacent edges is greater than 1, selecting the vertex corresponding to the edge with the highest priority level as the vertex to be passed next;

step d, if the number of the effective neighboring points is 0, a rollback flag back_flag=1 is needed, and step e is executed;

step e, deleting the current vertex in the effective adjacent points of the vertex before the current vertex, namely deleting the adjacent points which do not meet the constraint condition; deleting the mark of the edge corresponding to the current vertex, and subtracting 1 from the mark edge_flag of the edge where the current vertex is positioned; and the time pointer is retracted from the time t to the time t-1 and points to the vertex before the current vertex.

Further, constraint conditions are static constraint and dynamic constraint;

static constraints are that the droplets cannot be directly adjacent or diagonally adjacent:

the dynamic constraint is that the drop is located at a point in time and the drop is located at a point in time which is not adjacent to the drop.

Further, the test model construction further comprises adding additional virtual edges, converting vertexes with odd degrees into vertexes with even degrees, and converting the undirected communication graph into an Euler circuit graph.

Further, the second step includes:

generating an offline test path based on the offline test priority policy:

step 2.1, designating a vertex in the undirected communication graph as a searching starting point;

step 2.2, judging whether all adjacent edges of the vertex have been traversed according to an offline test priority strategy, and determining the next adjacent vertex to be passed;

step 2.3, repeating the step 2.2 until all edges are traversed, recording vertexes which pass through in sequence as a feasible solution of traversing the edges of the undirected connected graph, and obtaining a test path of offline test;

generating an online test path based on the online test priority policy:

step 2.4, designating a vertex meeting the constraint condition as a searching starting point, and marking the adjacent vertex meeting the constraint condition at the next moment as an effective adjacent point;

step 2.5, judging whether the adjacent vertex of the current vertex meets the constraint condition of the next moment according to the online test priority strategy, and selecting the vertex to be passed at the next moment or executing the rollback operation;

and 2.6, continuously repeating the step 2.5 until all edges are traversed, and recording the vertexes which pass through in sequence as a test path of the online test.

Further, the third step includes:

step 3.1, initializing and setting a genetic algorithm, and setting the total iteration times N of the genetic algorithm _IT Population size N _PS Chromosome length L _C Crossover probability p _c Probability of variation p _m ；

Step 3.2, generating an initial population according to the population size and the chromosome length;

step 3.3, solving the test paths according to the priority strategy, and calculating the lengths of the paths

And solving a local optimal solution;

step 3.4, calculating the fitness function value

Step 3.5, calculating the selection probability

Step 3.6, selecting a group according to a roulette mode and an elite retention strategy;

step 3.7, performing cross operation on the groups according to the cross probability;

step 3.8, performing mutation operation according to the mutation probability;

and step 3.9, repeating the steps 3.3 to 3.8 until the iteration times are completed.

According to the invention, the test chip is converted into the undirected communication graph, namely the test model, and each side in the graph is assigned with a different decimal, so that the higher the decimal value is, the higher the priority level of the side is. And designing a priority strategy as a path selection strategy according to the test characteristics of the chip, and generating a path of the traversing edge by using the designed priority strategy, wherein the path is a vertex set which is traversed by the traversing edge in sequence.

The offline testing priority strategy is designed as follows: (1) If the vertex where the test liquid drop is located has an adjacent edge which is not traversed, selecting the vertex corresponding to the edge with the highest priority level as the next searching vertex.

(2) If both adjacent sides are traversed, determining the shortest path from the test liquid drop to the non-tested side in the test model according to the Floyd algorithm in the graph theory, and guiding the test liquid drop to move along the shortest path, namely, selecting the vertex closest to the non-traversed side as the next search point by the test liquid drop.

The designed on-line test priority strategy is as follows: (1) If the adjacent vertex of the test liquid drop meets the constraint condition, namely, a valid adjacent point exists, the test liquid drop does not need to be retracted, and the retraction mark back_flag=0. If there are only 1 valid neighbors, then the vertex is selected as the vertex to be passed next. If there are more than 2 valid neighbors, then: a. and if all the adjacent edges are traversed, selecting the effective adjacent point closest to the non-traversed edge as the vertex to be traversed at the next moment according to the Floyd algorithm. b. If the non-traversed adjacent edges exist, when only 1 non-traversed adjacent edge exists, the vertex corresponding to the edge is selected, and if more than 1 non-traversed adjacent edges exist, the next corresponding vertex is selected according to the priority level, namely the priority coefficient.

(2) If the adjacent vertex of the test drop does not satisfy the constraint condition, a rollback flag back_flag=1 is set, and the following rollback operation is performed. First, among the valid neighboring points of the previous vertex, the current vertex is deleted, i.e., the neighboring points that do not satisfy the constraint condition are deleted. Then, the flag of the corresponding edge is deleted, i.e. the flag edge_flag of the current edge is decremented by 1 (the flag edge_flag of the edge will automatically be incremented by 1 after the edge is passed, so the back should be decremented by 1, and the edge is marked as not passed). Finally, the time pointer is retracted from the time t to the time t-1 and points to the previous vertex. So far, the rollback operation ends. Namely, the problem of deadlock generated in the path generation process is solved through the rollback operation of the liquid drops.

And performing crossing and mutation operation on the priority levels of the edges in the selected test paths through a genetic algorithm, generating new priority levels, and gradually obtaining shorter test paths through an iterative mode, thereby realizing the optimization of the test paths.

The invention has the beneficial effects that: the invention can reduce the adverse effect generated in the aspect of random search by only relying on the intelligent algorithm by combining heuristic information with the random search algorithm, namely by combining the priority strategy with the genetic algorithm, improves the optimizing effect of the test path, and enables the test path to approach or be equal to the shortest path. For the 'deadlock' phenomenon of test liquid drops occurring in the online test path searching process, the problem is solved by utilizing a rollback strategy.

Drawings

The invention will be further described with reference to the drawings and examples.

Fig. 1 is a schematic diagram of a test model of a digital microfluidic biochip and its euler model.

FIG. 2 is a schematic diagram of test drop path selection for offline testing.

FIG. 3 is a schematic diagram of deadlock.

Detailed Description

The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

Example 1

The embodiment provides a high-efficiency digital microfluidic biochip testing path optimization method, which comprises the following steps:

Fig. 1 is a test model of a digital microfluidic biochip and an euler model thereof, wherein the model comprises 5 rows and 5 columns of array units. In fig. 1, (a) is a physical model of a chip, and each array unit represents one control electrode. According to the graph theory, the chip is regarded as an undirected connected graph G, the array unit is transformed into vertexes V in the undirected connected graph G, and adjacent vertexes are connected by edges E, so that a graph theory model shown in (b) in FIG. 1, namely a test model of the chip, can be obtained.

Preferably, the undirected communication graph G may be euler-converted to obtain a euler graph G1, and as shown in (c) of fig. 1, the undirected communication graph G may be changed into a graph having an euler loop by adding an additional virtual edge to convert the vertex having an odd degree into the vertex having an even degree. Since the start point and the end point of the euler circuit must be the same vertex, and the euler path does not need to satisfy the condition, the euler path may have 1 side or 2 sides less than the euler circuit.

Defining the microfluidic chip as an array of m rows and N columns, the total number of sides is N _E =m× (n-1) + (m-1) ×n. According to the Euler loop theory of the undirected graph, the total number of edges experienced by traversing all edges in the graph once and only once and returning to the starting point is N _EC As shown in equation (1), the total number of edges in the Euler path may be N _EC -1 or N _EC -2。

In online testing, further consideration of fluid constraints between droplets is required in order to avoid collisions between test droplets and experimental droplets. Assume that

Is a droplet l ₁ Row and column at time t (+)>

Is a droplet l ₁ Row and column at time t+1), likewise, let +.>

Is a droplet l ₂ Row and column at time t (+)>

Is a droplet l ₂ Row and column at time t+1), while fluid constraints can be divided into static constraints and dynamic constraints, as follows:

1) Static constraints

Or->

Indicating that two stationary droplets at the same time are at least 2 positions apart in the row or column, i.e. the droplets cannot be directly adjacent or diagonally adjacent, otherwise droplet fusion will occur.

2) Dynamic constraints

Or->

Or alternatively

Or->

It is stated that the two droplets should satisfy the constraint that they cannot be adjacent when they differ by one time, that is, that one droplet is located at a position that is not adjacent to the other droplet at a position that is located at a previous time and at a next time.

The implementation of test path optimization based on the priority policy and the genetic algorithm specifically comprises the following steps:

1. generating test paths based on priority policies

(1) According to the foregoing priority policy, the problem of how to select the next vertex for the test drop is solved, and the design steps for generating the offline test path in this embodiment can be briefly described as follows:

step 1: one vertex in the undirected graph is designated as a search starting point.

Step 2: and judging whether all adjacent edges of the vertex are traversed or not according to an offline test priority strategy, and determining the next adjacent vertex to be passed.

Step 3: and (3) continuously repeating the step (2) until all edges are traversed, and recording vertexes which pass through in sequence as a feasible solution of traversing the edges of the undirected graph, namely obtaining a test path of offline test.

FIG. 2 is a schematic diagram of a test drop selecting a next adjacent vertex according to a priority policy during an offline test. In fig. 2 (a), a situation that an adjacent edge is not traversed is described, after the test droplet reaches the vertex 13, the priority coefficient of the edge from the vertex 13 to the vertex 14 is 0.60, which is greater than the priority coefficient of the other 2 edges, that is, the priority level of the edge is highest, so the test droplet will choose to go to the vertex 14;

in fig. 2 (b), the path of the test droplet is (13,14,19,20,25,24,19,18,23,24), and when the droplet reaches the vertex 24, the adjacent surrounding edges are traversed, so that the next vertex is not selected according to the size of the priority coefficient, but the vertex closest to the non-traversed edge is obtained according to the Floyd algorithm, and when the obtained vertex is 23, the test droplet reaches the vertex 23 from the vertex 24.

(2) The process of generating an online test path according to the defined online test priority policy is as follows:

step 1: and designating a vertex meeting the constraint condition as a searching starting point, and marking the adjacent vertex meeting the constraint condition at the next moment as a valid adjacent point.

Step 2: and judging whether the adjacent vertex of the current vertex meets the constraint condition of the next moment according to the online test priority strategy, and selecting the vertex to be passed at the next moment or executing the rollback operation.

Step 3: and (3) continuously repeating the step 2 until all edges are traversed, and recording the vertexes which pass through in sequence as a test path for online testing.

In the process of generating a path by using the test liquid drop, the situation that the test liquid drop cannot stay in place to wait or cannot move forward due to the fluid constraint is called a deadlock phenomenon. This phenomenon also occurs when the test path generation is performed using an online test priority policy, which can be solved by a rollback operation.

FIG. 3 is a schematic diagram of deadlock, where droplet 1 is at array unit 39 at time t, going to array unit 38 and array unit 37 in sequence; the experimental droplet 2 was located at the 12 th array unit and would go again to the 20 th and 28 th array units; while the test drop is at array 36, where the test drop meets the fluid constraints. But at the next moment, the test drop will not meet the fluid constraints, will not be stopped in place, nor will it go to 4 adjacent vertices, and a "deadlock" phenomenon occurs. Once this occurs, the test drop must be retracted to the position at the previous time, i.e., at the 35 th array element, and the 36 th array element marked as an inactive contiguous vertex, and the path selection restarted.

2. Genetic algorithm implementation of optimization of test paths

Before optimizing test path by Genetic Algorithm (GA), setting total number of iterative times N of genetic algorithm according to the size of test chip _IT Population size N _PS Chromosome length L _C Crossover probability p _c Probability of variation p _m And the like.

1) Initial population generation

The initial population generated comprises N _PS Individual of length L _C Corresponding to the number of edges in the undirected graph. In the priority strategy, the priority coefficient of each edge in the undirected graph is a random number of 0-1 generated according to a chaos operator, L _C The individual priority data constitute individuals formed by real number codes in the genetic algorithm, i.e. the initial population generated is actually made up of N _PS Length L _C Is comprised of priority coefficients of (a).

2) Fitness function design

Based on the generation of the initial group, a group of test paths traversing all sides in the undirected graph can be solved according to a priority strategy, and the result of decoding by the genetic algorithm is corresponded. The feasible solution, i.e., the obtained test path, can be expressed as

Wherein t=1, 2, [ N ] N _IT Represents the number of iterations, j=1, 2, [ N ] N _PS The individual number is indicated.

The formula for calculating the fitness function value:

wherein,,

for fitness function>

To test the length of the path, L _EulerPath Epsilon is a constant (0.000001) taking a minimum value for the length of the Euler path of the chip, and calculation overflow is prevented.

3) Improvement of selection probability

Firstly, according to the principle that the probability of the selected individual is in direct proportion to the fitness value, the preliminary selection probability is obtained

As shown in formula (5), wherein +.>

To adapt the function, N _PS Is the size of the group.

(5) The preliminary selection probability in the formula is generally smaller, the efficiency is low when the group selection is carried out, more time is needed for the selection operation, the difference of individual fitness values cannot be reflected during the selection, and the method is similar to the random selection, so that the selection probability is expanded according to the formula (6). Wherein the random () random function generates a random number of 0 to 1 so that the individuals with the largest fitness value in the population correspond toThe probability of selection is approximately between 0.6 and 0.93,

probability +.>

Maximum value of>

Probability of selection for the individual. At this time, the individual selection probability is also amplified in the same proportion according to the expression (6), and the efficiency of the selection operation can be improved.

After the selection probability is determined, the local optimum is retained according to elite retention policy, and then N is selected according to roulette mode _PS -1 individual, together forming N _PS And (5) performing solution.

4) Crossover and mutation operation design

The groups are first grouped into 2 individuals each, each individual being a set of priority data of length L _C . Each group of individuals adopts a single-point crossing mode, and whether 5 data after randomly selected crossing points need to be crossed is judged according to the comparison of the crossing probability and the random number. Because of each individual length L _C To further increase the diversity of the population, the priority data of each group is processed

And performing secondary crossover operation.

The mutation operation is similar to the crossover operation in terms of the mutation probability, and it is determined whether each individual needs to mutate 5 data at the selected position. Also, each set of priority data is subjected to

Performing mutation operation. After the priority data is selected, crossed and mutated, new priority data is generated, and then a new feasible solution can be obtained according to a priority strategy.

5) Algorithm design flow

Through the foregoing description of the genetic algorithm, the design steps for realizing path optimization by the genetic algorithm are briefly described as follows:

step 1: firstly, carrying out initialization setting on a genetic algorithm.

Step 2: based on a given population size and chromosome length, an initial population is generated.

Step 3: solving the test path according to the designed priority strategy, and calculating the length of each path

And a local optimal solution is obtained.

Step 4: obtaining fitness function value

Step 5: determining a selection probability

Step 6: the selection of the population is based on the roulette pattern and elite retention strategy.

Step 7: and performing crossover operation on the groups according to the crossover probability.

Step 8: and performing mutation operation according to the mutation probability.

Step 9: repeating the steps 3 to 8 until the iteration times are completed.

3. Algorithm simulation results

(1) Off-line test simulation result

When the chip is tested offline, the size N of the genetic algorithm group is set _PS Number of iterations n=30 _IT =300, cross probability p _c =0.6 and probability of variation p _m =0.2. At the same time, m=n, which are equal for the rows and columns of the digital microfluidic chipThe test was performed in a manner wherein m was taken as 7, 9, 11, 13, 15, respectively. The shortest test path length measured is shown in table 1, wherein the IACA algorithm is an improved ant colony algorithm, the PMF algorithm is an euler loop method, and it can be seen that the algorithm proposed herein can obtain a shorter test path length, and the shortest path of the traversing edge in the graph theory has been reached in the path length.

TABLE 1 shortest test Path Length at offline test

Chip scale	7×7	9×9	11×11	13×13	15×15
						IACA algorithm	100	165	254	350	470
PMF algorithm	96	160	240	336	448
						Algorithm herein	94	158	238	334	446

(2) On-line test simulation results

Compared with the off-line test, the on-line test needs to consider the fluid constraint of the experimental liquid drop to the test liquid drop, so the difficulty of searching the optimized path is further increased. When the algorithm is used for test simulation, the iteration number N of the genetic algorithm corresponding to the 15 multiplied by 15 chip is set _IT =500, the other test parameters are the same as the off-line test. The shortest test path length obtained is shown in table 2, from which it can be seen that the shortest test path length has been close to or equal to the limit value of the euler path.

TABLE 2 shortest test Path Length at Online test

Chip scale	7×7	9×9	11×11	13×13	15×15
						IACA algorithm	105	171	260	361	471
PMF algorithm	110	178	269	380	486
						Algorithm herein	95	158	239	335	446

According to the embodiment, the adverse effect generated in the aspect of random search by only relying on an intelligent algorithm can be reduced by combining heuristic information with a random search algorithm, namely by combining a priority strategy with a genetic algorithm, so that the optimization effect of a test path is improved, and the test path approaches or is equal to the shortest path. For the 'deadlock' phenomenon of test liquid drops occurring in the online test path searching process, the problem is solved by utilizing a rollback strategy.

While the foregoing describes the illustrative embodiments of the present invention so that those skilled in the art may understand the present invention, the present invention is not limited to the specific embodiments, and all inventive innovations utilizing the inventive concepts are herein within the scope of the present invention as defined and defined by the appended claims, as long as the various changes are within the spirit and scope of the present invention.

Claims

1. An efficient digital microfluidic biochip test path optimization method is characterized in that: the digital microfluidic biochip testing path optimization method comprises the following steps:

step three, optimizing the test path of the step two by utilizing a genetic algorithm;

the priority policies include an offline test priority policy and an online test priority policy;

the offline test priority policy is:

step B, if the adjacent edges are traversed, determining the shortest path from the test liquid drop to the non-tested edge in the test model according to the Floyd algorithm, guiding the test liquid drop to move along the shortest path, and finishing the selection of the vertex closest to the non-traversed edge as the next search point;

the online test priority policy is:

2. The efficient digital microfluidic biochip testing path optimization method of claim 1, characterized by: the constraint conditions are static constraint and dynamic constraint;

3. The efficient digital microfluidic biochip testing path optimization method according to claim 1, characterized by: the test model construction further comprises adding additional virtual edges, converting vertexes with odd degrees into vertexes with even degrees, and converting the undirected communication graph into an Euler circuit graph.

4. The efficient digital microfluidic biochip testing path optimization method according to claim 1, characterized by: the second step comprises:

generating an offline test path based on the offline test priority policy:

generating an online test path based on the online test priority policy:

5. The efficient digital microfluidic biochip testing path optimization method according to claim 1, characterized by: the third step comprises:

And solving a local optimal solution;

step 3.4, calculating the fitness function value

Step 3.5, calculating the selection probability

step 3.8, performing mutation operation according to the mutation probability;