CN106650074B - digital microfluidic chip catastrophic failure testing method based on genetic ant colony fusion algorithm - Google Patents

digital microfluidic chip catastrophic failure testing method based on genetic ant colony fusion algorithm Download PDF

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CN106650074B
CN106650074B CN201611150946.1A CN201611150946A CN106650074B CN 106650074 B CN106650074 B CN 106650074B CN 201611150946 A CN201611150946 A CN 201611150946A CN 106650074 B CN106650074 B CN 106650074B
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汪杰君
刘江宽
许川佩
胡聪
叶松
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Guilin University of Electronic Technology
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Abstract

The invention discloses a digital microfluidic chip catastrophic failure testing method based on a genetic ant colony fusion algorithm, which is characterized by comprising the following steps of: s1, establishing a catastrophic failure test model of the digital microfluidic chip; s2, obtaining a preliminary test path and setting an initial pheromone upper and lower bounds and an initial pheromone value of the maximum and minimum ant colony algorithm; and S3, searching the final test path and outputting a result. The test method can not only improve the problem of poor convergence of a single ant colony algorithm, but also improve the execution efficiency of the test algorithm, and can quickly obtain a test path.

Description

Digital microfluidic chip catastrophic failure testing method based on genetic ant colony fusion algorithm
Technical Field
The invention relates to a digital microfluidic chip testing technology, in particular to a digital microfluidic chip catastrophic failure testing method based on a genetic ant colony fusion algorithm.
Background
the digital microfluidic chip is commonly used in the fields of clinical detection, medical engineering and the like with high requirements on reliability, so that the digital microfluidic chip needs to be tested comprehensively and efficiently to ensure the reliability. The failures of the digital microfluidic chip can be divided into catastrophic failures and parametric failures, and the catastrophic failures can be subdivided into failures such as insulator breakdown, short circuit of adjacent electrodes, open circuit of electrode plates and the like. The destructive nature of the catastrophic failure on the chip is fatal, which can lead to complete stagnation of the experimental droplets on the chip, and the chip can not work normally. Therefore, testing for catastrophic failures is a particularly important step in the testing of digital microfluidic chips.
The catastrophic failure test principle of the digital microfluidic chip is as follows: the test liquid drop is used for traversing the array unit of the digital microfluidic chip, if no fault exists, the test liquid drop can reach a waste liquid pool on the digital microfluidic chip after traversing, if a fault exists, the test liquid drop can be stopped on the digital microfluidic chip, and the test liquid drop cannot reach the waste liquid pool on the digital microfluidic chip. And a detection circuit for detecting whether the liquid drops arrive or not is arranged at the waste liquid pool, if the detection circuit detects that the test liquid drops arrive, the digital microfluidic chip is free from fault, and if not, the digital microfluidic chip is faulty. Different routing orders of the test liquid drops traversing the array units of the digital microfluidic chip form different test paths, the shorter the test path, the less time is spent in the test, and the higher the test efficiency is. In addition, the lower the complexity of the test algorithm is and the better the convergence is, the higher the execution efficiency of the test algorithm is, and the more favorable the execution of the algorithm in the actual work is.
At present, various testing methods such as a hamilton loop testing method, an euler loop testing method, a parallel scanning testing method, a built-in self-testing method, a partition subarray combined scheduling testing method, a testing path searching method based on an ant colony algorithm and the like are available for catastrophic failures of a digital microfluidic chip. Among the methods, a Hamilton loop test method and a partition subarray combined scheduling test method cannot detect short-circuit faults of adjacent electrodes; the parallel scanning test method and the built-in self test method are only suitable for testing the digital microfluidic chip of the regular rectangular array, and the online test efficiency is low; the Euler loop test method has higher algorithm complexity and lower on-line test efficiency when large-scale chip test is applied; the method for searching the test path based on the ant colony algorithm has the advantages that the test model is established in a complicated step, the single ant colony algorithm is poor in convergence, and the efficiency is low when the large-scale chip test is applied.
Disclosure of Invention
The invention aims to provide a digital microfluidic chip catastrophic failure testing method based on a genetic ant colony fusion algorithm aiming at the defects in the technology. The test method can not only improve the problem of poor convergence of a single ant colony algorithm, but also improve the execution efficiency of the test algorithm, and can quickly obtain a test path.
The technical scheme for realizing the purpose of the invention is as follows:
A digital microfluidic chip catastrophic failure testing method based on a genetic ant colony fusion algorithm is different from the prior art and comprises the following steps:
S1, establishing a catastrophic failure test model of the digital microfluidic chip: according to the array unit structure of the digital microfluidic chip, a catastrophic failure test model of the digital microfluidic chip is established, wherein the model is as follows:
(1) abstracting array units of the digital microfluidic chip into vertexes V of undirected graphs G (V, E), abstracting the connection relation between adjacent array units into edges E of the undirected graphs G (V, E), obtaining undirected graph models G (V, E), and establishing corresponding adjacency matrixes A;
(2) Numbering all vertexes V in the undirected graph model G (V, E), enabling the number of each vertex to correspond to the row number of the vertex in the adjacency matrix A, sequentially searching the edges associated with the current vertex from the vertex with the minimum number, and numbering the searched edges from small to large;
(3) Abstracting an edge E in the undirected graph model G (V, E) into a vertex V 'of an undirected graph model G' (V ', E'), enabling the number of the vertex V 'to correspond to the number of the edge E in the G (V, E) one by one, abstracting the adjacent relation between the edges E in the undirected graph model G (V, E) into an edge E' of the undirected graph model G '(V', E '), and establishing the undirected graph model G' (V ', E') and a corresponding adjacent matrix B;
(4) Calculating the shortest path between any two vertexes in the undirected graph model G ' (V ', E ') by adopting an improved Floyd method, and constructing a completely communicated graph model G ' (V ', E ') by taking the shortest path between the two vertexes as the weight of the edge between the two vertexes, wherein the completely communicated graph model G ' (V ', E ') is taken as a model for testing catastrophic faults of the digital microfluidic chip;
s2, obtaining a primary test path and setting an initial pheromone upper and lower bounds and an initial pheromone value of the maximum and minimum ant colony algorithm: according to a digital microfluidic chip catastrophic failure test model G ' (V ', E '), obtaining a preliminary test path by adopting a genetic algorithm, and setting an initial pheromone upper and lower bounds and an initial pheromone value of a maximum minimum ant colony algorithm according to the preliminary test path, wherein the initial pheromone upper and lower bounds and the initial pheromone value are specifically set according to the following formula:
Wherein, taumax(0)、τmin(0) Respectively an initial pheromone upper bound and a lower bound,is the length, P, of the shortest of the preliminary test paths found by the genetic algorithmbestRepresenting the probability of constructing the optimal solution when the ant colony algorithm converges, avg is equal to m/2, m is the number of ants set in the maximum and minimum ant colony algorithm, rho is the pheromone residual coefficient, tauij(0) Is composed ofInitial values of pheromones on arbitrary paths (i, j), u represents the shortest u test paths selected from the preliminary test paths obtained by the genetic algorithm,The length of one test path k in the preliminary test paths obtained by the genetic algorithm;
S3, searching a final test path and outputting a result: according to the digital microfluidic chip catastrophic failure test model G ' (V ', E ') and the initial pheromone upper and lower bounds and the initial pheromone values obtained in the step S2, searching a final test path by adopting a maximum and minimum ant colony algorithm, and outputting the final test path after the ant colony algorithm is iterated, wherein the target function of the maximum and minimum ant colony algorithm is as follows:
Wherein the content of the first and second substances,For finally testing two adjacent routing nodes v ″' in the pathiand v ″)i+1Distance weight between them, n is total number of nodes, route node v ″)iAnd v ″)i+1Namely two vertexes in a digital microfluidic chip catastrophic failure test model G ' (V ', E ').
the modified Floyd method in step S1 is:
Any two vertices V 'in the computed undirected graph G' (V ', E'iAnd v'jWhen the shortest path exists between the nodes, the inserted node v 'is treated first'rmaking a road length comparison if dir≥dijor drj≥dij，dijRepresenting the distance between two vertices, then insert node v 'is declared'rAfter, v'iV 'through'rto v'jIs not shorter than the original path between two vertices, so d is not calculated any longerir+drjThe next node is searched directly, and vertex V ' in the undirected graph G ' (V ', E ') is searched 'iTo v'jV 'to'jTo v'iAre symmetrically equal if v 'is calculated'ito v'jV 'does not need to be calculated any more'jTo v'iIn doing so, reduces the amount of computation.
the chromosome coding scheme of the genetic algorithm in the step S2 adopts decimal integer coding, a routing node sequence of the preliminary test path is taken as a chromosome, the start bit of the chromosome coding represents the position of the droplet source on the digital microfluidic chip, and the end bit of the coding represents the position of the waste liquid pool on the digital microfluidic chip.
the selection operator of the genetic algorithm in the step S2 adopts a fitness proportion method, the crossover operator adopts a sequential crossover method, the mutation operator adopts an inverse mutation method, and the start and end positions of the chromosome do not participate in crossover operation and mutation operation.
When searching for the final test path, the maximum and minimum ant colony algorithm in step S3 searches for the node of the final test path according to the pseudorandom proportion rule, specifically, the ants search for the node of the final test path according to the following formula:
Wherein q is0E (0,1) is a constant, q e (0,1) is a random number, τij(t) denotes a node v' at time tiAnd v ″)jMeta pheromone, tauil(t) denotes a node v' at time tiand v ″)lMeta pheromone, etaij(t)、ηil(t) all represent heuristic information, ηij(t)＝1/dij，ηil(t)＝1/dilWherein d isij、dilRespectively is a node V 'in a digital micro-fluidic chip catastrophic failure test model G' (V ', E')iAnd v ″)jV ″', betweeniand v ″)lThe distance between, α and β, represent two parameters that affect the relative strengths of the pheromone and heuristic information, respectively.
The pheromone update strategy of the maximum and minimum ant colony algorithm in the step S3 is as follows: only the shortest test path after each iteration is allowed to add pheromones, specifically, the pheromones are updated according to the following formula:
τij(t+1)＝ρτij(t)+∑Δτij(t)
Wherein, tauij(t) denotes a node v' at time tiAnd v ″)jMeta pheromone, tauij(t +1) represents a node v' at time t +1iAnd v ″)jIn the case of a pheromone of (1, 0), ρ ∈ is the pheromone residual coefficient, Δ τij(t) denotes the pheromone increment on path (i, j), f (S)best) The length L of the shortest test path in the iteration of the maximum and minimum ant colony algorithmlsOr the length L of the current global shortest test pathgs。
The upper and lower pheromone bounds of the maximum and minimum ant colony algorithm in step S3 adopt a dynamic update strategy, and specifically, the upper and lower pheromone bounds update formula is as follows:
Wherein, taumax(t)、τmin(t) is the upper and lower bounds of the pheromone at time t, LlsThe length of the shortest test path after the iteration of the maximum and minimum ant colony algorithm is m, which is the number of ants set in the ant colony algorithm.
When the maximum and minimum ant colony algorithm is used to search the final test path in step S3, the test droplets need to satisfy the static constraint condition and the dynamic constraint condition in order to prevent accidental fusion between droplets.
the test method not only improves the problem of poor convergence of a single ant colony algorithm, but also improves the execution efficiency of the test algorithm and can quickly obtain the test path. The testing method can detect the short circuit fault of the adjacent electrodes, is compatible with the regular array and the irregular array digital microfluidic chips, and is more beneficial to the application of the testing method to the catastrophic fault testing of the large-scale digital microfluidic chips.
Drawings
FIG. 1 is a schematic structural diagram of a digital microfluidic chip for performing a multiplex biochemical experiment;
FIG. 2 is a schematic diagram of a 3 × 3 regular array digital microfluidic chip with a catastrophic failure test model conversion;
FIG. 3 is a schematic diagram of constraints between droplets on a digital microfluidic chip;
FIG. 4 is a schematic diagram illustrating the convergence of the method for catastrophic failure testing of a digital microfluidic chip for multiplex biochemical experiments according to an exemplary embodiment;
FIG. 5 is a schematic diagram showing the comparison of the testing time spent by the embodiment method and the Euler loop method and the ant colony test algorithm respectively applied to the catastrophic failure test of the digital microfluidic chip for the multivariate biochemical experiment;
FIG. 6 is a flow chart of an embodiment method.
Detailed Description
The invention will be further illustrated with reference to the following figures and examples, but is not limited thereto.
Example (b):
Referring to fig. 6, a method for testing catastrophic failures of a digital microfluidic chip based on a genetic ant colony fusion algorithm includes the following steps:
S1, establishing a catastrophic failure test model of the digital microfluidic chip: according to the array unit structure of the digital microfluidic chip, a catastrophic failure test model of the digital microfluidic chip is established, wherein the model is as follows:
(1) abstracting array units of the digital microfluidic chip into vertexes V of undirected graphs G (V, E), abstracting the connection relation between adjacent array units into edges E of the undirected graphs G (V, E), obtaining undirected graph models G (V, E), and establishing corresponding adjacency matrixes A;
(2) Numbering all vertexes V in the undirected graph model G (V, E), enabling the number of each vertex to correspond to the row number of the vertex in the adjacency matrix A, sequentially searching the edges associated with the current vertex from the vertex with the minimum number, and numbering the searched edges from small to large;
(3) abstracting an edge E in the undirected graph model G (V, E) into a vertex V 'of an undirected graph model G' (V ', E'), enabling the number of the vertex V 'to correspond to the number of the edge E in the G (V, E) one by one, abstracting the adjacent relation between the edges E in the undirected graph model G (V, E) into an edge E' of the undirected graph model G '(V', E '), and establishing the undirected graph model G' (V ', E') and a corresponding adjacent matrix B;
(4) calculating the shortest path between any two vertexes in the undirected graph model G ' (V ', E ') by adopting an improved Floyd method, and constructing a completely communicated graph model G ' (V ', E ') by taking the shortest path between the two vertexes as the weight of the edge between the two vertexes, wherein the completely communicated graph model G ' (V ', E ') is taken as a model for testing catastrophic faults of the digital microfluidic chip;
The digital microfluidic chip for a multi-biochemical experiment shown in fig. 1 has a test droplet source and a waste liquid pool, the direction of the arrow in the figure is the moving path of the experiment droplet, the detection positions 1 and 2 are positions for detecting the reaction result of the experiment droplet, in order to perform a catastrophic failure test on the digital microfluidic chip, the test droplet needs to traverse the whole digital microfluidic chip from the droplet source and then reaches the waste liquid pool, in order to prevent accidental fusion between droplets, a static constraint condition and a dynamic constraint condition need to be satisfied between the test droplets, the number of units of the digital microfluidic chip array is 225, and the number of the units is larger, so that in order to intuitively explain the process of converting a test model, the digital microfluidic chip with a 3 × 3 regular array in fig. 2 is specifically:
(1) Abstracting array units of the digital microfluidic chip of the 3 multiplied by 3 regular array into vertexes V in an undirected graph model G (V, E), abstracting the adjacent relation of the array units into edges E to obtain the undirected graph model G (V, E) shown in FIG. 2, and establishing an adjacent matrix A corresponding to the undirected graph model G (V, E);
(2) Numbering the vertexes V in the undirected graph model G (V, E) shown in FIG. 2, wherein the vertex numbers correspond to the line numbers of the vertexes in the adjacency matrix A, searching the edges associated with the current vertex in sequence from the vertex with the smallest number, and numbering the searched edges from small to large, wherein the edges E in the undirected graph model G (V, E) shown in FIG. 2 are numbered from '1' to '12';
(3) Abstracting an edge E in the undirected graph model G (V, E) into a vertex V ' of the undirected graph model G ' (V ', E '), abstracting the adjacency relation between the edges E in the undirected graph model G (V, E) into an edge E ' of the undirected graph model G ' (V ', E '), obtaining the undirected graph model G ' (V ', E '), wherein the adjacency relation between the edges E in the undirected graph model G (V, E) is as follows: if two edges in the undirected graph model G (V, E) have a common vertex, which indicates that the two edges are adjacent, an edge exists between the vertices in the corresponding undirected graph model G ' (V ', E '), as shown in fig. 2, the edges numbered "11" and "12" in the undirected graph G (V, E) are abstracted as the vertices of the undirected graph G ' (V ', E '), and the edges numbered "11" and "12" have a common vertex, which is abstracted as the edge exists between the two vertices in the graph G ' (V ', E ');
(4) And finally, calculating the shortest path between any two vertexes in the G '(V', E ') by using an improved Floyd method according to the undirected graph model G' (V ', E'), and constructing a completely communicated graph model G '(V', E ') by taking the shortest path between the two vertexes as the weight of the edge between the two vertexes, wherein the completely communicated graph model G' (V ', E') is used as a model for testing the catastrophic failure of the digital microfluidic chip. The complete connection graph G ' (V ', E ') converted from the 3X 3 regular array digital microfluidic chip shown in FIG. 2 has 12 vertexes, which correspond to the vertexes G ' (V ', E '), so that the vertexes G ' (V ', E ') correspond to the vertexesThe number of edges is too large to draw intuitively, so that the specific graph of the completely connected graph G ' (V ', E ') is not given in the test model conversion。
The method for converting the catastrophic failure test model of the digital microfluidic chip in the step S1 is applicable to all the digital microfluidic chips with regular and irregular arrays.
S2, obtaining a primary test path and setting an initial pheromone upper and lower bounds and an initial pheromone value of the maximum and minimum ant colony algorithm: according to a digital microfluidic chip catastrophic failure test model G ' (V ', E '), obtaining a preliminary test path by adopting a genetic algorithm, and setting an initial pheromone upper and lower bounds and an initial pheromone value of a maximum minimum ant colony algorithm according to the preliminary test path, wherein the initial pheromone upper and lower bounds and the initial pheromone value are specifically set according to the following formula:
Wherein, taumax(0)、τmin(0) Respectively an initial pheromone upper bound and a lower bound,Is the length, P, of the shortest of the preliminary test paths found by the genetic algorithmbestRepresenting the probability of constructing an optimal solution when the ant colony algorithm converges,avg is equal to m/2, m is the number of ants set in the maximum minimum ant colony algorithm, rho is the pheromone residual coefficient, tauij(0) u represents the shortest u test paths selected from the preliminary test paths obtained by the genetic algorithm as initial values of pheromones on the arbitrary paths (i, j),The length of one test path k in the preliminary test paths obtained by the genetic algorithm;
the method specifically comprises the following steps:
After the genetic algorithm is iterated and finished, a shorter preliminary test path is selected from preliminary test paths obtained by the genetic algorithm to calculate the initial pheromone upper and lower bounds and the initial pheromone value of the maximum and minimum ant colony algorithm, the embodiment is applied to the catastrophic failure test of the digital microfluidic chip of the multivariate biochemical experiment, and the optimal scheme of relevant parameters is as follows: the iteration number of the genetic algorithm is set as 150, the chromosome number N of the population is set as 50, the front u of 50 shortest preliminary test paths are taken from the 50 preliminary test paths after the iteration is finished to form an initial pheromone upper and lower boundary and an initial pheromone value, and the rho is taken to be 0.92, P is takenbest0.05, and 30 of ants;
S3, searching a final test path and outputting a result: according to the digital microfluidic chip catastrophic failure test model G ' (V ', E ') and the initial pheromone upper and lower bounds and the initial pheromone values obtained in the step S2, searching a final test path by adopting a maximum and minimum ant colony algorithm, and outputting the final test path after the ant colony algorithm is iterated, wherein the target function of the maximum and minimum ant colony algorithm is as follows:
Wherein the content of the first and second substances,for finally testing two adjacent routing nodes v ″' in the pathiand v ″)i+1distance weight between them, n is total number of nodes, route node v ″)iAnd v ″)i+1Namely two vertexes in a digital microfluidic chip catastrophic failure test model G ' (V ', E ').
The modified Floyd method in step S1 is:
Any two vertices V 'in the computed undirected graph G' (V ', E'iand v'jWhen the shortest path exists between the nodes, the inserted node v 'is treated first'rmaking a road length comparison if dir≥dijOr drj≥dij，dijRepresenting the distance between two vertices, then insert node v 'is declared'rAfter, v'iV 'through'rto v'jIs not shorter than the original path between two vertices, so d is not calculated any longerir+drjThe next node is searched directly, and vertex V ' in the undirected graph G ' (V ', E ') is searched 'ito v'jV 'to'jTo v'iAre symmetrically equal if v 'is calculated'ito v'jV 'does not need to be calculated any more'jTo v'iIn doing so, reduces the amount of computation.
Specifically, the flow of the improved Floyd method is as follows:
S2-1) searching any pair of vertexes V 'from the vertex with the smallest number in the undirected graph model G' (V ', E').iand v'jIn between, whether there is another vertex v'rV 'is prepared'iV 'through'rTo v'jis more than the current v'iTo v'jis short, if yes, v 'is updated'iAnd v'jIf not, continuing to search the next node; when comparing distances, the node v 'to be inserted can be treated'rFirst, compare the path length, if dir≥dijOr drj≥dij(dijRepresenting the distance between two vertices), then insert node v 'is declared'rAfter, v'iv 'through'rto v'jIf the path is not shorter than the original path between two points, the next node is directly searched;
S2-2) updating the distance weight between any two vertexes, and obtaining an adjacency matrix C of a complete connection graph G ' (V ', E '). In the iterative process of the algorithm, v'iTo v'jV 'to'jTo v'iAre equal, if v 'is updated'iTo v'jV 'does not need to be calculated any more'jto v'iCan improve the efficiency of the Floyd method.
The chromosome coding scheme of the genetic algorithm in the step S2 adopts decimal integer coding, a routing node sequence of the test path is taken as a chromosome, the start bit of the chromosome coding represents the position of the droplet source on the digital microfluidic chip, the last bit of the coding represents the position of the waste liquid pool on the digital microfluidic chip, and the chromosome decimal integer coding scheme is as follows:
The decimal numbers of the vertices in the test model G '(V', E ') are used as codes for genes of chromosomes, and the vertices in G' (V ', E') shown in FIG. 2 are numbered from "1" to "12", and thus, a permutation and combination of the vertex numbers of chromosomes of (1-2-3-4-5-6-7-8-9-10-11-12) or any other cases can be encoded.
The selection operator of the genetic algorithm in the step S2 adopts a fitness proportion method, the crossover operator adopts a sequential crossover method, the mutation operator adopts an inverse mutation method, and the start and end positions of the chromosome do not participate in crossover operation and mutation operation, and the crossover operation and mutation operation flow is as follows:
S2-3) when the genetic algorithm is used for solving the test path, each iteration needs to adopt a fitness proportion method to select M/2(M is larger than or equal to N) from the population N to carry out cross operation on the chromosome. Specifically, the probability that the individual k is selected is:
fk＝1/Lk
Wherein f iskin order to be a function of the fitness measure,is chromosome XkTwo adjacent nodes x in the represented test pathiAnd xi+1The distance between the two chromosomes, N is the number of chromosomes of the population; in this embodiment, a preferred value of M is 80 and N is set to 50.
s2-4) after the chromosome selection is finished, the sequence crossing method is adopted to carry out the crossing operation on the selected M/2 pair chromosome, and the starting point and the end point of the test path represent a liquid drop source and a waste liquid pool and do not participate in the crossing operation. In this embodiment, the number of the connecting edges between the digital microfluidic chip array units shown in fig. 1 is 420, which is large, and it is not convenient to intuitively explain the specific operation of intersection. Without loss of generality, taking chromosome of 10 genes as an example, the crossover process of the sequential crossover method is intuitively explained as follows:
Selecting a cross region randomly from the father strings, wherein the two father strings and the cross region are as follows:
X1＝x0x1x2|x3x4x5x6|x7x8x9
X2＝x0x8x4|x7x6x2x1|x3x5x9
② mixing X2is added to X1Middle starting point x0Thereafter, X is also introduced1is added to X2Middle starting point x0Later, one can obtain:
X′1＝x0|x7x6x2x1|x1x2x3x4x5x6x7x8x9
X′2＝x0|x3x4x5x6|x8x4x7x6x2x1x3x5x9
③ deleting X 'in sequence'1And X'2The same gene as the cross region, the final substring is obtained:
X″1＝x0x7x6x2x1x3x4x5x8x9
X″2＝x0x3x4x5x6x8x7x2x1x9
s2-5), performing mutation operation on the chromosome by adopting an inverse mutation method after the cross operation is finished; similarly, a chromosome of 10 genes is exemplified: such as chromosomes (x)0x1x2x3x4x5x6x7x8x9) In the interval x2x3And interval x6x7The fragment is broken and the broken fragments are inserted in reverse order, so that the reversed chromosome becomes (x)0x1x2x6x5x4x3x7x8x9)。
S2-6), after the mutation operation is finished, sorting the individuals in the population from big to small according to the fitness, and selecting N individuals with high fitness from big to small as the population of the next iteration; and adding 1 to the iteration times, judging whether the set iteration times are reached, if so, terminating the genetic algorithm, otherwise, entering the next loop of the genetic algorithm until the iteration is finished.
When searching for the final test path, the maximum and minimum ant colony algorithm in step S3 searches for the node of the final test path according to the pseudorandom proportion rule, specifically, the ants search for the node of the final test path according to the following formula:
wherein q is0e (0,1) is a constant, q e (0,1) is a random number, τij(t) denotes a node v' at time tiAnd v ″)jMeta pheromone, tauil(t) denotes a node v' at time tiAnd v ″)lMeta pheromone, etaij(t)、ηil(t) all represent heuristic information, ηij(t)＝1/dij，ηil(t)＝1/dilWherein d isij、dilRespectively is a node V 'in a digital micro-fluidic chip catastrophic failure test model G' (V ', E')iAnd v ″)jV ″', betweeniAnd v ″)lthe distance between, α and β, represent two parameters that affect the relative strengths of the pheromone and heuristic information, respectively.
The concrete process of searching the final test path node by the ant is as follows:
when ants select the next node, q is randomly generated firstly, and if q is less than or equal to q0Then select to make [ tauil(t)]α[ηil(t)]βAnd if not, selecting the next routing node according to a probability formula, calculating the probability of each node being selected according to the formula, and then selecting the next testing node according to a roulette mode, wherein the probability value is higher, and the probability of being selected is higher. l is an allowedkIndicating node l in the optional set, and the ant selects this node and then follows allowedkand the node is deleted in the set, so that repeated traversal of the test liquid drop is prevented, and the test efficiency is improved.
In this example, the preferred setting scheme of the relevant parameters of the maximum and minimum ant colony algorithm is as follows:
The number of ants m is 30, q in the pseudo-random proportion rule00.1, pheromone heuristic factor α 1.2, heuristic factor coefficient β 3.0, pheromone residual coefficient ρ 0.92, and probability P of convergence to the optimal solutionbestThe number of ant colony algorithm iterations is set to 1850.05.
The pheromone update strategy of the maximum and minimum ant colony algorithm in step S3 is: only the shortest test path after each iteration is allowed to add pheromones, specifically, the pheromones are updated according to the following formula:
τij(t+1)＝ρτij(t)+∑Δτij(t)
wherein, tauij(t) denotes a node v' at time tiAnd v ″)jmeta pheromone, tauij(t +1) represents a node v' at time t +1iAnd v ″)jIn the case of a pheromone of (1, 0), ρ ∈ is the pheromone residual coefficient, Δ τij(t) denotes the pheromone increment on path (i, j), f (S)best) The length L of the shortest test path in the iteration of the maximum and minimum ant colony algorithmlsOr the length L of the current global shortest test pathgs。
F (S)best) The specific setting scheme is as follows: when the ant colony algorithm searches the test path, the length L of the shortest test path in the iteration is adopted after each iterationlsUpdates the pheromone by selecting the length L of the current global shortest test path to use at a fixed number of iterationsgs. In this embodiment, the length L of the global shortest test path before being used once every 50 iterationsgsThe value of (c).
The pheromone update strategy of the maximum and minimum ant colony algorithm in the step S3 is as follows: only the shortest test path after each iteration is allowed to add pheromones, specifically, the pheromones are updated according to the following formula:
τij(t+1)＝ρτij(t)+∑Δτij(t)
Where ρ is the pheromone residual coefficient, Δ τij(t) represents the pheromone increment on path (i, j). f (S)best) The length L of the shortest test path in the iteration of the maximum and minimum ant colony algorithmlsOr the length L of the current global shortest test pathgs。
The upper and lower pheromone bounds of the maximum and minimum ant colony algorithm in step S3 adopt a dynamic update strategy, and specifically, the upper and lower pheromone bounds update formula is as follows:
Wherein, taumax(t)、τmin(t) is the upper and lower bounds of the pheromone at time t, Llsthe length of the shortest test path after the iteration of the maximum and minimum ant colony algorithm is m, which is the number of ants set in the ant colony algorithm.
when the maximum and minimum ant colony algorithm is used to search the final test path in step S3, in order to prevent unexpected fusion between droplets, the test droplets need to satisfy static constraint conditions and dynamic constraint conditions, which are described as follows: as shown in fig. 5, the solid black circle represents a droplet, and the "x" represents that this cell cannot be accessed by the test droplet at this time t, the static constraint condition means that other droplets cannot exist simultaneously at the same time t on the cells adjacent to each other in a straight line and diagonally adjacent to each other around the droplet, i.e. in order to prevent accidental fusion between droplets, a certain distance needs to be kept between droplets, which is expressed by the following formula:
Or | Yi t-Yj t|≥2
The dynamic constraint condition means that the position of the droplet moved at the next moment cannot be adjacent to other droplets, and can be expressed by the following formula:
The random time can be determined according to the moving path and the constraint condition of the experimental liquid dropThe set of cells that cannot be accessed by the test droplet at time t is denoted as tabu table tab (t). When searching for a node in a test path by using a maximum and minimum ant colony algorithm, if a routing node j selected at a certain time t is in a tabu table tab (t), the node is not accessible at present, the forbidden time of the node is inquired, and the forbidden time is set as waiting time twait(ii) a Re-searching a new node x according to a pseudo-random proportion rule, and adding the waiting time t to the distance weight from the current node i to the original selected node jwaitThe weight of the test liquid drop is compared with the distance weight from the current node i to the new node x, if the distance weight of the new node x is smaller, the test liquid drop moves to the new node x, otherwise, the test liquid drop waits for the original selected node j to be activated at the current node i, and the node j is selected.
In step S3, when the maximum and minimum ant colony algorithm is used to search the final test path, the final test path is output when the number of iterations of the ant colony algorithm reaches a set value. In this embodiment, after the maximum and minimum ant colony algorithm iterates 1850 times, the obtained final test path is output, and the unit time spent on the test is calculated according to the obtained final test path, where the longer the test path is, the more the unit time spent on the test is, and the shorter the test path is, the less the unit time spent on the test is. The less unit time spent in the test indicates the higher the test efficiency. The unit time is the time taken for the test liquid drop to move from one cell to the adjacent cell, and in this embodiment, the unit time of the digital microfluidic chip of the multiplex biochemical experiment shown in fig. 1 is specifically 62.5 ms.
Performing catastrophic failure test simulation on the digital microfluidic chip shown in fig. 1 according to the above steps, wherein a test algorithm is implemented by using C + + programming in a Visual studio 2012 environment, an obtained test method convergence schematic diagram is shown in fig. 4, an abscissa of fig. 4 is iteration times, and an ordinate is unit time; in fig. 5, the ordinate is unit time and the abscissa is different test methods; as can be seen from fig. 5, the test algorithm of the present embodiment is significantly better than the euler loop method in terms of the test time, which is only 1 unit time longer than the test time of the ant colony algorithm. However, the single ant colony algorithm generally converges around 1350 iterations, and as can be seen from fig. 4, the method of the present embodiment converges around 950 iterations, which is 29% higher than the single ant colony algorithm in convergence, and the method has better convergence, and can quickly obtain a better test path under the condition of ensuring that the test takes less time.
Because the Hamilton loop test method and the partition subarray combined scheduling test method cannot detect the short circuit fault of the adjacent electrodes, the parallel test method and the self-built self-test method can only be used for chip test of a regular array, the test methods lack comprehensiveness and compatibility, and the test method of the embodiment is not compared with the test methods.

Claims (8)

1. a digital microfluidic chip catastrophic failure testing method based on a genetic ant colony fusion algorithm is characterized by comprising the following steps:
s1, establishing a catastrophic failure test model of the digital microfluidic chip: according to the array unit structure of the digital microfluidic chip, a catastrophic failure test model of the digital microfluidic chip is established, wherein the model is as follows:
(1) Abstracting array units of the digital microfluidic chip into vertexes V of undirected graphs G (V, E), abstracting the connection relation between adjacent array units into edges E of the undirected graphs G (V, E), obtaining undirected graph models G (V, E), and establishing corresponding adjacency matrixes A;
(2) Numbering all vertexes V in the undirected graph model G (V, E), enabling the number of each vertex to correspond to the row number of the vertex in the adjacency matrix A, sequentially searching the edges associated with the current vertex from the vertex with the minimum number, and numbering the searched edges from small to large;
(3) abstracting an edge E in the undirected graph model G (V, E) into a vertex V 'of an undirected graph model G' (V ', E'), enabling the number of the vertex V 'to correspond to the number of the edge E in the G (V, E) one by one, abstracting the adjacent relation between the edges E in the undirected graph model G (V, E) into an edge E' of the undirected graph model G '(V', E '), and establishing the undirected graph model G' (V ', E') and a corresponding adjacent matrix B;
(4) Calculating the shortest path between any two vertexes in the undirected graph model G ' (V ', E ') by adopting an improved Floyd method, and constructing a completely communicated graph model G ' (V ', E ') by taking the shortest path between the two vertexes as the weight of the edge between the two vertexes, wherein the completely communicated graph model G ' (V ', E ') is taken as a model for testing catastrophic faults of the digital microfluidic chip;
S2, obtaining a primary test path and setting an initial pheromone upper and lower bounds and an initial pheromone value of the maximum and minimum ant colony algorithm: according to a digital microfluidic chip catastrophic failure test model G ' (V ', E '), obtaining a preliminary test path by adopting a genetic algorithm, and setting an initial pheromone upper and lower bounds and an initial pheromone value of a maximum minimum ant colony algorithm according to the preliminary test path, wherein the initial pheromone upper and lower bounds and the initial pheromone value are specifically set according to the following formula:
Wherein, taumax(0)、τmin(0) Respectively an initial pheromone upper bound and a lower bound,is a preliminary measurement derived by a genetic algorithmLength of shortest test path among test paths, PbestRepresenting the probability of constructing the optimal solution when the ant colony algorithm converges, avg is equal to m/2, m is the number of ants set in the maximum and minimum ant colony algorithm, rho is the pheromone residual coefficient, tauij(0) u represents the shortest u test paths selected from the preliminary test paths obtained by the genetic algorithm as initial values of pheromones on the arbitrary paths (i, j),The length of one test path k in the preliminary test paths obtained by the genetic algorithm;
S3, searching a final test path and outputting a result: according to the digital microfluidic chip catastrophic failure test model G ' (V ', E ') and the initial pheromone upper and lower bounds and the initial pheromone values obtained in the step S2, searching a final test path by adopting a maximum and minimum ant colony algorithm, and outputting the final test path after the ant colony algorithm is iterated, wherein the target function of the maximum and minimum ant colony algorithm is as follows:
Wherein the content of the first and second substances,For finally testing two adjacent routing nodes v ″' in the pathiAnd v ″)i+1Distance weight between them, n is total number of nodes, route node v ″)iAnd v ″)i+1Namely two vertexes in a digital microfluidic chip catastrophic failure test model G ' (V ', E ').
2. The digital microfluidic chip catastrophic failure testing method based on the genetic ant colony fusion algorithm according to claim 1, wherein the improved Floyd method in the step S1 is as follows:
Any two vertices V 'in the computed undirected graph G' (V ', E'iAnd v'jWhen the shortest path exists between the nodes, the inserted node v 'is treated first'rTo carry outthe path length is compared, if dir≥dijOr drj≥dij，dijRepresenting the distance between two vertices, then insert node v 'is declared'rafter, v'iV 'through'rTo v'jIs not shorter than the original path between two vertices, so d is not calculated any longerir+drjthe next node is searched directly, and vertex V ' in the undirected graph G ' (V ', E ') is searched 'iTo v'jV 'to'jTo v'iAre symmetrically equal if v 'is calculated'iTo v'jV 'does not need to be calculated any more'jTo v'iThe distance of (c).
3. the method for testing the catastrophic failure of the digital microfluidic chip based on the genetic ant colony fusion algorithm according to claim 1, wherein the chromosome coding scheme of the genetic algorithm in the step S2 adopts decimal integer coding, a routing node sequence of the preliminary test path is taken as a chromosome, the start bit of the chromosome coding represents the position of a droplet source on the digital microfluidic chip, and the end bit of the coding represents the position of a waste liquid pool on the digital microfluidic chip.
4. The method for testing the catastrophic failure of the digital microfluidic chip based on the genetic ant colony fusion algorithm according to claim 1, wherein the selection operator of the genetic algorithm in the step S2 adopts a fitness proportion method, the crossover operator adopts a sequential crossover method, the mutation operator adopts an inverse mutation method, and start bits and end bits of chromosomes do not participate in crossover operation and mutation operation.
5. the method for testing catastrophic failure of a digital microfluidic chip based on genetic ant colony fusion algorithm as claimed in claim 1, wherein the maximum and minimum ant colony algorithm in step S3 searches the nodes of the final test path according to the pseudo-random scaling rule when searching the final test path, specifically, ants search the nodes of the final test path according to the following formula:
Wherein q is0E (0,1) is a constant, q e (0,1) is a random number, τij(t) denotes a node v' at time tiand v ″)jMeta pheromone, tauil(t) denotes a node v' at time tiAnd v ″)lMeta pheromone, etaij(t)、ηil(t) all represent heuristic information, ηij(t)＝1/dij，ηil(t)＝1/dilWherein d isij、dilrespectively is a node V 'in a digital micro-fluidic chip catastrophic failure test model G' (V ', E')iAnd v ″)jV ″', betweeniAnd v ″)lthe distance between, α and β, represent two parameters that affect the relative strengths of the pheromone and heuristic information, respectively.
6. The method for testing catastrophic failure of a digital microfluidic chip based on genetic ant colony fusion algorithm according to claim 1, wherein the pheromone updating strategy of the maximum and minimum ant colony algorithm in the step S3 is as follows: only the shortest test path after each iteration is allowed to add pheromones, specifically, the pheromones are updated according to the following formula:
τij(t+1)＝ρτij(t)+∑Δτij(t)
wherein, tauij(t) denotes a node v' at time tiAnd v ″)jMeta pheromone, tauij(t +1) represents a node v' at time t +1iand v ″)jin the case of a pheromone of (1, 0), ρ ∈ is the pheromone residual coefficient, Δ τij(t) denotes the pheromone increment on path (i, j), f (S)best) The length L of the shortest test path in the iteration of the maximum and minimum ant colony algorithmlsOr the length L of the current global shortest test pathgs。
7. The method for testing catastrophic failures of a digital microfluidic chip based on a genetic ant colony fusion algorithm according to claim 1, wherein the upper and lower pheromone bounds of the maximum and minimum ant colony algorithm in step S3 adopt a dynamic update strategy, and specifically, the upper and lower pheromone bounds update formula is as follows:
Wherein, taumax(t)、τmin(t) is the upper and lower bounds of the pheromone at time t, Llsthe length of the shortest test path after the iteration of the maximum and minimum ant colony algorithm is m, which is the number of ants set in the ant colony algorithm.
8. The method for testing the catastrophic failure of the digital microfluidic chip based on the genetic ant colony fusion algorithm according to claim 1, wherein when the maximum and minimum ant colony algorithm is adopted to search the final test path in the step S3, the test droplets need to satisfy static constraint conditions and dynamic constraint conditions.
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