CN109190259B - Digital microfluidic chip fault repairing method based on combination of improved Dijkstra algorithm and IPSO - Google Patents

Digital microfluidic chip fault repairing method based on combination of improved Dijkstra algorithm and IPSO Download PDF

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CN109190259B
CN109190259B CN201811044287.2A CN201811044287A CN109190259B CN 109190259 B CN109190259 B CN 109190259B CN 201811044287 A CN201811044287 A CN 201811044287A CN 109190259 B CN109190259 B CN 109190259B
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郑文斌
付平
石金龙
尹洪涛
王安琪
叶俊涛
孙媛媛
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Harbin Institute of Technology
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Abstract

A digital microfluidic chip fault repairing method based on combination of an improved Dijkstra algorithm and IPSO relates to the field of digital microfluidic chip fault repairing, and aims to solve the problems of long time and low efficiency of the conventional digital microfluidic chip fault repairing method. The method comprises the following steps: step one, calculating the shortest path between two drops to be mixed based on an improved Dijkstra algorithm; the improved Dijkstra algorithm is characterized in that a cost function is introduced into the existing Dijkstra algorithm, and the cost function guides the existing Dijkstra algorithm to search in the direction with the shortest distance to a starting point, the shortest distance to a terminal point and the longest distance to a fault point; and step two, calculating a moving path based on IPSO, and realizing the shortest moving distance of the liquid drop under the condition of ensuring the completion of mixing to finish fault repair. The method is suitable for repairing the fault of the digital microfluidic chip.

Description

Digital microfluidic chip fault repairing method based on combination of improved Dijkstra algorithm and IPSO
Technical Field
The invention relates to the field of fault repair of digital microfluidic chips.
Background
With the development of technology, the field of automatic testing has expanded from testing of analog or digital circuits to testing of Micro-Electromechanical Systems (MEMS). Microfluidic chips, also known as Lab-on-a-chips, can perform various functions of biological laboratories and routine chemical testing on a few square centimeters of chip. Has the characteristics of miniaturization, high sensitivity, low cost, integration and the like. The first generation of microfluidic biochips have permanently etched microvalves, micropumps and microchannels, all based on continuous fluid flow for specific operations. The development of microfluidic technology and manufacturing processes has driven the production of digital microfluidic chips that manipulate discrete droplets on a two-dimensional microfluidic array, with a system architecture that can be greatly expanded.
Compared with continuous fluid control, the digital microfluidic chip emphasizes that liquid is dispersed into trace droplets to be operated, each droplet is independently controlled, the energy consumption is low, and the digital microfluidic chip is particularly suitable for biochemical analysis which needs high performance and is relatively complex to operate. Compared with the traditional biochemical analyzer, the digital microfluidic chip has the advantages of reusability, small size, high automation degree, high integration level and the like. The device has the capability of accurately driving trace liquid (liquid with the level of micro-liter or even nano-liter), completing the operations of transporting, storing, separating, mixing and the like of the fluid on a chip, completing the ultrasensitive biochemical detection with low cost, remarkably reducing the testing time and the laboratory space, and increasing the stability and the accuracy of the result due to the reduction of manual operation processes. Therefore, the method has wide application prospects in the aspects of clinical diagnosis, biomedical treatment, health examination, drug diagnosis, air quality detection and the like, and has important significance.
At present, the application of the digital microfluidic chip is mainly focused in the fields of biology and medicine, various body fluids can be analyzed in the digital microfluidic chip, and more complex biochemical experiments including extraction, replication and amplification of DNA, cell analysis, immunoassay and the like can be realized. With the continuous expansion of the application field of the microfluidic chip, people face a great demand for realizing multiple processes and multiple reactions on the same chip. However, due to the fragile links of the micro-scale processing technology, the chips are easy to be at fault risk with the continuous introduction of new materials. The potential failure risk causes the uncertainty of the service life of the chip, thereby limiting the further development of the chip, and the improvement of the stability and the reliability of the DMFB can greatly expand the application field of the digital microfluidic chip. Therefore, in order to ensure the validity of the chip, the chip needs to repair the fault after fault detection and fault diagnosis, and the smooth proceeding of the experiment is ensured.
The fault repairing method of the digital microfluidic chip is to redesign the chip with the fault and ensure that a biochemical experiment can be completed on the chip with the fault. However, the conventional fault repairing method is long in time and low in efficiency.
Disclosure of Invention
The invention aims to solve the problems of long time consumption and low efficiency of the conventional digital microfluidic chip fault repairing method, so that the digital microfluidic chip fault repairing method based on the combination of the improved Dijkstra algorithm and IPSO is provided.
The invention relates to a digital microfluidic chip fault repairing method based on combination of an improved Dijkstra algorithm and IPSO, which comprises the following steps:
step one, calculating a shortest path between two liquid drops to be mixed based on an improved Dijkstra algorithm, and enabling the two liquid drops to be mixed to move to the same position according to the shortest path;
the improved Dijkstra algorithm is characterized in that a cost function is introduced into the existing Dijkstra algorithm, and the cost function guides the existing Dijkstra algorithm to search in the direction with the shortest distance to a starting point, the shortest distance to a terminal point and the longest distance to a fault point;
and step two, calculating a moving path based on IPSO, so that the shortest moving distance of the liquid drops is realized under the condition of ensuring the completion of mixing, and the fault recovery is completed, wherein the moving path is a path required by mixing two liquid drops to be mixed from the same position in the step one.
Preferably, the cost function fcost(Dk,i) Comprises the following steps:
Figure BDA0001792887240000021
wherein, dis (D)k,i,Dk,i,start) Is the distance of the current point to the starting point, dis (D)k,i,Dk,i,end) Min dis (D) is the distance from the current point to the end pointk,i,Ef)]Alpha, beta and gamma are weight coefficients which are the distances between the current point and the nearest fault point.
Preferably, the first step comprises:
step one by one, set S is set, and the set S is the shortest pathIn order, the initial value within set S includes only the starting position of the drop, i.e., S ═ pos1}；
Step two, generating set S ', S' including position pos to which a droplet at the latest element in S may move at the next moment when the constraint is satisfiedt+1S' contains at most five elements, assuming that the current electrode unit position of the droplet is Ei(mi+1,ni)，post+1Comprises the following steps: post+1＝Ei(mi+1,ni)，post+1＝Ei(mi+2,ni)，post+1＝Ei(mi,ni)，post+1＝Ei(mi+1,ni-1)，post+1＝Ei(mi+1,ni+1)，miIs the number of columns, niIs the number of rows;
step three, calculating the cost function of each element in S',
step four, selecting the position with the minimum cost function from the S' as pos2The shortest path access sequence S, S ═ pos is updated1,pos2}；
Repeating the first step and the second step to the first step and the fourth step until the liquid drop moves to the end point, and obtaining S ═ pos1,pos2,pos3……}。
Preferably, the second step is specifically:
step two, setting IPSO parameters including maximum iteration times Gen and acceleration constant c1、c2And c3Speed dependent random number r1、r2And r3；
Step two, calculating the speed direction of the ith particle at the moment t
Figure BDA0001792887240000031
Figure BDA0001792887240000032
Figure BDA0001792887240000033
mk、mu、md、mlAnd mrCorresponding to the respective holding, upward, downward, leftward and rightward speed directions, Ui tThe set of the moving directions of the liquid drops corresponding to the ith particle at the t moment when the constraint condition is met is shown;
step two and step three, updating the speed direction of the ith particle at the moment t
Figure BDA0001792887240000034
Figure BDA0001792887240000035
xgb tPosition of the globally optimal particle for time t, xlb tFor the position of the locally optimal particle at time t, r7Is a randomly generated random number;
step two, updating the position vector X of the ith particle at the t +1 momenti t+1：
Figure BDA0001792887240000036
Repeating the second step to the fourth step until the mixing degree reaches 100%, and switching to the second step and the fifth step;
step two and five, determining the position vector X of the locally optimal particleslb T
Xlb T＝(xlb 1,xlb 2,...,xlb T)
T is experiment completion time;
step two and six, determining the position vector X of the globally optimal particlesgb T；
Xgb T＝(xgb 1,xgb 2,...,xgb T)；
And repeating the second step to the second sixth step until the iteration times reach Gen times, and outputting the globally optimal position vector of the particles meeting the conditions to obtain the moving path.
Preferably, the constraints include fault constraints, static constraints and dynamic constraints;
the fault constraint condition is that the fault electrode unit is not used within the experiment completion time;
the static constraint condition is that two droplets cannot be in the positions of electrode units which are directly adjacent or adjacent along a diagonal line;
the dynamic constraint condition is that when two liquid drops are separated from one electrode unit, the two liquid drops can not move in the same direction along the straight line where the two liquid drops are located simultaneously.
Preferably, the mathematical model of the fault constraint is:
Figure BDA0001792887240000041
wherein E isa f(ma,na) As a faulty electrode unit, EfFor a set of faulty electrode units, TrealIn order to complete the time of the experiment,
Batis binary variable and represents the condition that the electrode unit is used in each time slice, if at time t, the a-th electrode unit Ea(ma,na) Is used, then BatIs 1, otherwise BatIs 0; m isaIs the number of rows in which the a-th electrode unit is located, naThe number of rows of the a-th electrode unit.
Preferably, at time t, the kthaAnd kjThe positions of the droplets are respectively
Figure BDA0001792887240000042
And
Figure BDA0001792887240000043
the mathematical model of the static constraints is:
Figure BDA0001792887240000044
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njRespectively the row number of the a-th and j-th electrode units, DtIs a collection of drop positions.
Preferably, at time t, the positions of the two droplets are
Figure BDA0001792887240000045
And
Figure BDA0001792887240000046
the two drops will make a movement at time t of
Figure BDA0001792887240000047
And
Figure BDA0001792887240000048
the electrode units of the two liquid drops are respectively Ea(ma,na) And Ej(mj,nj) The vector formed by the positions of the two electrode units is expressed as
Figure BDA0001792887240000049
Figure BDA00017928872400000410
Representing the angle between the two vectors, the mathematical model of the dynamic constraint is:
Figure BDA0001792887240000051
Figure BDA0001792887240000052
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njThe number of rows of the a-th electrode unit and the j-th electrode unit are respectively.
Preferably, before the step one, the method further comprises: establishing a mathematical model of the digital microfluidic chip, and determining an operation sequence chart of the digital microfluidic chip according to the sequence between operations;
and after the first step to the second step are executed, repeating the first step to the second step according to the operation sequence until all the operations are finished.
The invention utilizes the improved Dijkstra algorithm and IPSO to solve the path planning problem and the mixed path design problem of the fault repairing method, introduces a cost function in the existing Dijkstra algorithm to carry out heuristic improvement on the method, and preferentially searches the direction in which the optimal solution is more likely to exist in all nodes so as to hopefully and quickly find the shortest distance between two points and avoid the algorithm from falling into the local optimal solution. The method has the advantages of short repair time and high repair efficiency.
Drawings
FIG. 1 is a schematic diagram of a structure in which a defective electrode unit exists in a chip;
(a) no faulty electrode is used, (b) faulty electrode is used;
FIG. 2 is a schematic illustration of static fluid restriction;
(a) before the two liquid drops are fused, (b) after the two liquid drops are fused;
FIG. 3 is a schematic illustration of dynamic fluid restriction;
(a) before the two liquid drops move, (b) during the two liquid drops move, and (c) after the two liquid drops move;
FIG. 4 is a block diagram of a module-based failover method;
FIG. 5 is a schematic diagram of dynamic barrier path planning;
FIG. 6 is a mathematical model of an electrode array;
fig. 7 is a flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
The principle involved in the invention is as follows:
1. digital micro-fluidic chip liquid drop driving mode and fault type
The mode of driving the microfluid by the digital microfluidic chip is dielectric wetting driving. The liquid drop is driven by the liquid-solid surface tension change on the hydrophobic polymer surface by applying an electric field to the liquid drop through the electrode array to change the surface tension of the liquid drop. In order to make the liquid drop move, a driving voltage is applied to the adjacent electrode units, the surface of the liquid drop is enabled to accumulate electric quantity by utilizing the dielectric wetting principle, so that a surface tension gradient covering the adjacent electrodes is generated on the surface of the liquid drop, and when the tension is larger than the resistance between the upper surface and the lower surface and the liquid drop, the driving of the liquid drop movement can be completed, and the driving is the most basic method for controlling the liquid drop movement. The basic operations in the implementation of biochemical assays on a chip can be achieved by applying a sequence of voltages across the corresponding array of electrodes, such as: droplet dispensing, transporting, storing, mixing and separating, and the like.
The fault types of the digital microfluidic chip are divided into two types: parametric faults and permanent faults. The parameter faults are mainly generated in the manufacturing process and are caused by size parameter errors, when the electrode array is not horizontal, the two layers of surfaces are not parallel or the electrode thickness is not uniform, the driving of the digital liquid drops is influenced, and the influence of the faults on the experimental result is represented as large deviation, so that the performance of the chip is seriously influenced.
Permanent failures are caused by open and short circuits between the electrode elements of the chip, which may originate from the manufacturing process or from electrode degradation due to improper control voltage. The permanent fault can cause the liquid drop to stay in the fault unit, can not advance according to the designed route, can not finish the experiment and move to the waste liquid pond, leads to biochemical detection's failure, and the application in the field that the security requirement is high can produce great harmful effects. The present invention is directed to online fault repair of permanent faults.
2. Fault repairing method for digital microfluidic chip
The fault repairing method is that the moving path of the liquid drop is designed directly according to the biochemical experiment process under the condition of meeting the constraint, in order to realize the fault repairing function, the liquid drop can not pass through the fault electrode in the moving process, otherwise, the liquid drop can not move continuously and stops at the fault electrode. As shown in fig. 1, the droplets in fig. 1(a) do not pass through the faulty electrode, and can move along the designed path without hindrance, thereby realizing operations such as mixing and separation. In fig. 1(b), the droplet moves to the faulty electrode, stopping at the faulty electrode, thereby rendering subsequent operations impossible.
3. Mathematical model of constraint condition of fault repairing method
The DMFB fault repairing of the digital microfluidic chip is to reconstruct the design of the chip according to the biochemical experiment requirement under the condition of fault, and aims to ensure the shortest experiment completion time and realize fault repairing on the chip under fault constraint and time constraint. The actual experiment completion time cannot exceed the maximum completion time required for biochemical experiments, which is denoted as TupperlimitThe total number of operations is K, and the time required for completing operation l is TlThen the experiment completion time TrealExpressed as formula (1) and satisfies Tupperlimit≥Treal。
Figure BDA0001792887240000071
The fault constraint is to ensure that all fault points are not used, ensure that all operations do not utilize fault electrodes, and define a binary variable as the formula (2) Shows the situation that the electrode is used in each time slice, if the electrode a is used in t time, BatIs 1, otherwise BatIs 0, where M is the total number of columns of electrodes and N is the total number of rows of electrodes, and the formula is as follows:
Figure BDA0001792887240000072
then electrode Ea(ma,na) The number of times used in the experimental procedure was
Figure BDA0001792887240000073
The failed electrode is at the experiment completion time TrealThe internal unused state needs to meet the following requirements:
Figure BDA0001792887240000074
the objective function is that the experiment completion time after repair is shortest, and is expressed as:
Tmin＝min{Treal} (4)
when there is a multiple droplet movement on the DMFB, the droplet walking follows a certain rule, i.e., a fluid constraint. Fluid constraints are divided into static constraints and dynamic constraints. When the test droplet is close to the test droplet, the two droplets are likely to mix. Therefore, a static fluid constraint condition is adopted, and a certain distance is required to be kept between two liquid drops so as to prevent the two liquid drops from being fused accidentally.
When two droplets are close together, as shown in fig. 2(a), the two droplets merge into the droplet in fig. 2 (b).
Mathematical modeling for fluid confinement is performed such that two droplets cannot be placed at directly or diagonally adjacent electrode positions, which would otherwise result in unintended merging of droplets. At time t, kthaAnd kjThe positions of the droplets are respectively
Figure BDA0001792887240000075
And
Figure BDA0001792887240000076
the mathematical model of the static constraints is:
Figure BDA0001792887240000077
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njRespectively the row number of the a-th and j-th electrode units, DtIs a collection of drop positions.
The static constraint conditions indicate the position constraint to be satisfied between the droplets on the electrode array, and the dynamic constraint conditions indicate the constraint conditions to be satisfied when two droplets move, as shown in fig. 3, and when the distance between two droplets is one electrode, as shown in fig. 3(a), if two droplets move to the right side at the same time, a voltage needs to be applied to the shaded electrode in fig. 3(a), so that the right-side droplet is split into two droplets, and a part of the two droplets and the left-side droplet are mixed unexpectedly, which becomes the case in fig. 3 (c).
The dynamic constraint condition is that when two liquid drops are separated from one electrode unit, the two liquid drops can not move in the same direction along the straight line where the two liquid drops are located simultaneously. At time t, the positions of the two droplets are
Figure BDA0001792887240000081
And
Figure BDA0001792887240000082
the two drops will make a movement at time t of
Figure BDA0001792887240000083
And
Figure BDA0001792887240000084
the electrode units of the two liquid drops are respectively Ea(ma,na) And Ej(mj,nj) Two electrode unit position structureIs represented as a vector
Figure BDA0001792887240000085
Figure BDA0001792887240000086
Representing the angle between the two vectors, the mathematical model of the dynamic constraint is:
Figure BDA0001792887240000087
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njThe number of rows of the a-th electrode unit and the j-th electrode unit are respectively.
4. Module-based fault repairing method
The pathized fault repair method eliminates the concept of resource blocks, allowing the operation to complete the operation of biochemical experiments by any one electrode sequence on the array. The operations requiring path design are mixing operation, diluting operation and separating operation, and in the reconfigurable operation, only mixing and diluting operation is required to be designed for the droplet path, and the diluting operation is composed of mixing operation and separating operation, so the present invention requires the droplet path design for the mixing operation to complete biochemical experiments. Fig. 4 is a flow chart of a fault repairing method of a module.
The mixing operation needs to complete two steps, firstly, a path is designed to enable two liquid drops to be mixed to move to the same position, and then the mixed liquid drops move according to any path to complete the mixing operation. In the first step, the shortest path between two droplets needs to be found, and the faulty electrode and other droplets existing on the chip can be regarded as obstacles, so the problem can be equivalent to a dynamic obstacle path planning problem. This problem is an NP-hard problem because the position of the obstacle on the chip varies from time to time, and although the position of the faulty electrode does not vary, the positions of other droplets vary from time to time. The invention adopts an improved Dijkstra algorithm (Dijkstra algorithm) to calculate the shortest path existing between two liquid drops, and completes the first step of mixing.
In the second step, the moving path of the liquid drop is designed to complete the mixing operation, the invention utilizes an Improved Particle Swarm Optimization (IPSO) to carry out path design, the PSO belongs to one of evolutionary algorithms, the PSO algorithm starts from random solution, the optimal solution is searched by iteration, the solution quality is evaluated by utilizing a fitness function, the evolutionary rule is simple, and the global optimal solution is determined by following the currently searched global and local optimal values. The PSO algorithm has the characteristics of easy realization, fast convergence and the like due to high parallelism, and is suitable for solving the problem of large-scale path planning.
By combining the improved Dijkstra algorithm with IPSO, the heuristic path fault repairing method is realized, a body fluid detection experiment is used as a verification experiment, and various experiments for carrying out different detections on different body fluids are applied to the path-based and modular-based digital microfluidic chip DMFB fault repairing method.
(1) Path planning method based on improved Dijkstra algorithm
And (3) performing mathematical simulation on obstacles of the digital microfluidic chip by using a grid method, representing the electrodes of the digital microfluidic chip by using grids, and marking the grids containing the obstacles as obstacle grids, otherwise, the grids are free grids. A mathematical model is established for a chip with a fault by using a grid method, a fault electrode is a barrier grid in a map, and when a moving path is designed for a certain liquid drop according to a fluid constraint condition, electrodes where other liquid drops except for the liquid drop to be operated are located and adjacent electrodes are all barrier grids. The liquid drops need to avoid the barrier grids to complete corresponding operation functions.
Among many path search algorithms, Dijkstra's algorithm may compute the shortest path from a specified start point to an end point in the graph. The Dijkstra algorithm is run once to obtain the shortest path from the starting point to all nodes in the graph, but in practical application, the shortest path between a certain two specific nodes is concerned instead of the case that the starting point reaches all other points, and the application of the Dijkstra algorithm is limited because the search space is too large. The invention is improved based on the existing Dijkstra algorithm, an intelligent search factor is introduced on the basis of the existing algorithm, a cost function is added in the path search, the path searching strategy is determined by the cost function, and the direction in which the optimal solution is more likely to exist is preferentially searched in all nodes. In the hope of finding the shortest distance between two points quickly and avoiding the algorithm falling into a locally optimal solution.
Each point of the existing Dijkstra algorithm can only be visited once, and based on the idea of a greedy algorithm, a node which ensures the shortest current path is selected in each searching process. A cost function is introduced into a Dijkstra algorithm to perform heuristic improvement on the method, and a map comprises two fault points: the electrode where the faulty electrode and other droplets are located and its adjacent electrodes. The position of a fault electrode does not change with time, but the positions of other liquid drops change with time, in an adjacent time slice, the liquid drop can only move by one electrode at most, the Dijkstra algorithm finds the next position with the shortest path according to the current fault mode in the current time slice, and due to the fact that the fault position of the next time slice changes, the next position possibly falls into a local optimal solution due to being too close to the fault, as shown in figure 5, the liquid drop currently goes to the right, the other liquid drops go downwards in two consecutive time slices, and the liquid drop needs to wait in the original position or bypass the other liquid drops in order to avoid entering the isolation units of the other liquid drops to cause unexpected mixing, so that the planned path is prolonged. Due to dynamic changes of faults, each point is visited only once, and the shortest path cannot be found.
When the next position path calculation is carried out, three parts of contents need to be considered: firstly, selecting a point which ensures the shortest current path; secondly, selecting a point with the shortest distance to a terminal point when no fault exists; finally, the movement position farthest from the failure point is selected. By introducing the cost function, a width-first searching mechanism with equal searching probability in each direction can be improved into a directional depth-first searching mechanism, the influence of various factors is integrated in the selection process, and the situation that partial optimal solution is trapped in the dynamic fault situation is avoided.
The cost function is used to estimate how much of the point-to-endpoint cost is. The larger the value of the cost function is, the longer the path for selecting the path for path planning may be, and the path obtained by continuing searching along the path may deviate from the optimal solution or fall into the local optimal solution. The smaller the value of the cost function, the more likely it is that the shortest path will result from continuing the search in that direction. The cost function is defined as:
Figure BDA0001792887240000101
wherein, dis (D)k,i,Dk,i,start) Is the distance of the current point to the starting point, dis (D)k,i,Dk,i,end) Min dis (D) is the distance from the current point to the end pointk,i,Ef)]Alpha, beta and gamma are weight coefficients which are the distances between the current point and the nearest fault point. The closer to the start point and the end point, the smaller the cost function value of a point farther from the fault point, and the easier it is to select the point with priority.
The flow of calculating the shortest path between two drops to be mixed based on the improved Dijkstra algorithm is as follows:
firstly, a set S is set, the set S is in the shortest path order, the initial value in the set S only comprises the starting point position of the liquid drop, namely S ═ pos1}；
Second, a set S 'is generated, S' including a position pos to which a droplet at the latest element within S may move at the next time when the constraint is satisfiedt+1S' contains at most five elements, and the current motor unit position where the liquid drop is located is assumed to be Ei(mi+1,ni)，post+1Comprises the following steps: post+1＝Ei(mi+1,ni)，post+1＝Ei(mi+2,ni)，post+1＝Ei(mi,ni)，post+1＝Ei(mi+1,ni-1)，post+1＝Ei(mi+1,ni+1)，miIs the number of columns, niIs the number of rows;
thirdly, calculating a cost function of each element in the S',
fourthly, selecting the position with the minimum cost function from S' as pos2The shortest path access sequence S, S ═ po is updateds1,pos2}；
Repeat one to four until the droplet moves to the end point, yielding S ═ pos1,pos2,pos3……}。
The improved Dijkstra algorithm is different from the existing Dijkstra algorithm in that a cost function is introduced, and a better guiding algorithm searches the direction with the shortest distance to a starting point, the shortest distance to a terminal point and the longest distance to a fault position. The existing Dijkstra algorithm stops searching after traversing all positions in a graph, due to the existence of dynamic faults, each position is visited once only and an optimal solution cannot be obtained, and the improved Dijkstra algorithm repeatedly searches until the position moves to an end point.
(2) Path planning method based on IPSO
The design problem of the liquid drop mixing path is to design a liquid drop moving path under the condition of ensuring the completion of mixing and realize the aim of shortest liquid drop moving distance. In the moving process of the liquid drops, the liquid drops need to be prevented from passing through a fault electrode, unnecessary mixing of the liquid drops and other liquid drops is avoided, and the other liquid drops are positioned at different positions in different time slices, so that the problem is the problem of path planning under the condition of dynamic fault.
PSO simulates predation behavior of a flock of birds. In PSO, each feasible solution corresponds to a bird in the search space, and the food corresponds to the optimal solution of the optimization problem. In particle swarm optimization, each individual is called a "particle," and the PSO is initialized as a group of random particles (each particle represents a feasible solution to the problem). Each particle has an adaptation value determined by an optimization function and a velocity vector that determines the direction and distance of their next search. Each generation of particles determines the direction of the velocity vector according to the speed of the particles, extreme points (called individual optimal solutions) searched by the particles and optimal points (called global optimal solutions) found in the population, and the positions of the particles are updated according to the velocity vector in the iteration process to gradually approach the optimal solutions. The speed of the particles expands the searching capability of the particles and improves the performance of global optimization; the extreme point searched by the particles is a local optimal value, the particles have a memory function, and the influence of the local optimal value is considered when the position is updated; the global optimal part reflects the sharing of information among the particles, the global optimal solution of each generation is a feasible solution closest to the optimal solution, the particles determine the updating of the position at the next moment by referring to other information while utilizing the global optimal information, and the algorithm is prevented from rapidly converging to the local optimal solution.
A mathematical model is established for improving the particle swarm optimization, wherein the maximum iteration number Gen is as follows, and the position of n particles is expressed as x when the iteration is carried out to the mth timen mThe velocity vector of the particle is expressed as
Figure BDA0001792887240000111
xlb mRepresents the optimal solution, x, found by the particlegb mRepresenting the global optimal solution particle, in the (m +1) th iteration, the velocity and position vector update velocities are as follows:
Figure BDA0001792887240000112
Figure BDA0001792887240000113
the speed updating comprises three parts:
Figure BDA0001792887240000114
the method has the characteristics of expanding a search area, exploring a new space and randomly searching, ensures the coverage rate of the algorithm on a solution space, guarantees the global search capability and adjusts the balance between the global search and the local search; x is the number oflb m-xn mThe memory part of the particle is represented, the particle updates the speed according to the historical optimal solution searched by the particle, the learning capacity of the particle in the process of searching the particle in the iterative process is reflected, and the local searching capacity of the particle is guaranteed; x is the number ofgb m-xn mIndicating that the sharing of information between the population of particles is a "population portion",is the learning ability of the particle to the whole population optimization process. c. C1And c2Representing the acceleration constant of the particle, typically in the range of [0, 2%]And taking values in the interval to balance the influence degree of the individual optimization and the global optimization on the particle speed. r is1And r2Is at [0,1 ]]Random number in interval, at set c1And c2And the algorithm is continuously changed along with iteration on the basis, so that the randomness and the global search capability of the algorithm are enhanced.
As described above, the fault recovery is to design a droplet moving path in a fault condition. The droplet mixing path design is to design the moving path to complete the mixing operation in the shortest time under the condition of fault point and other dynamic moving droplets, so the output of the algorithm is the electrode serial number of the test droplet at each time. The time for the experimental droplets to pass through each electrode unit is 0.01s, so the problem of completing the mixed path design in the shortest time can be converted into completing the path design in the shortest path. In order to apply the particle swarm algorithm to the current problem, the particle swarm algorithm needs to be improved, and the position and the speed of the particle need to be redefined.
xi tDenotes the electrode serial number, X, of the particle i at time ti T＝(xi 1,xi 2,...,xi T) Representing the path of movement of the ith particle for the droplet, X, for the position vector of the particlegb T＝(xgb 1,xgb 2,...,xgb T) Position vector, X, representing a globally optimal particlelb T＝(xlb 1,xlb 2,...,xlb T) A position vector representing the locally optimal particle.
The invention relates to a digital microfluidic chip fault repairing method based on combination of an improved Dijkstra algorithm and IPSO, which comprises the following steps:
step one, establishing a mathematical model of the digital microfluidic chip, wherein the fault repair of the digital microfluidic chip is to design the chip under the fault condition, and ensure that a biochemical experiment is completed in the specified maximum time on the fault chip. The digital microfluidic chip is an electrode array formed by a series of electrodes according to a certain layout mode, and the DMFB chip with rectangular electrode array only considers the shape rule in the embodiment. A mathematical model is built for the DMFB electrode array, and as shown in FIG. 6, an electrode array consisting of 25 electrodes in 5 rows and 5 columns is equivalent to the form in the figure.
And step two, determining the biochemical experiment to be completed by the chip, and determining a digital microfluidic chip operation sequence diagram, which is represented as G (O, B), according to the sequence between operations. O denotes a set of all nodes, the number of operation nodes is denoted K, and O ═ OlL belongs to N, l is more than or equal to 1 and less than or equal to K, and a node O for operation in the sequence diagramlTo represent。The directed line segment between the nodes represents the sequence of the two operations, which is OlNode pointing to OsThe directed line segment of the node is marked as Bls(Ol,Os) Is represented by OlAfter the operation is completely completed, OsThe operation can begin.
Step three, calculating a shortest path between two liquid drops to be mixed based on an improved Dijkstra algorithm, and enabling the two liquid drops to be mixed to move to the same position according to the shortest path;
the improved Dijkstra algorithm is characterized in that a cost function is introduced into the existing Dijkstra algorithm, and the cost function guides the existing Dijkstra algorithm to search in the direction with the shortest distance to a starting point, the shortest distance to a terminal point and the longest distance to a fault point;
and step four, calculating a moving path based on IPSO, so that the shortest moving distance of the liquid drops is realized under the condition of ensuring the completion of mixing, and the fault recovery is completed, wherein the moving path is a path required by mixing two liquid drops to be mixed from the same position in the step three.
Step four, setting IPSO parameters including maximum iteration times Gen and acceleration constant c1、c2And c3Speed dependent random number r1、r2And r3；
Step four and step two, calculating the speed direction of the particles
Figure BDA0001792887240000121
The method has the characteristics of expanding a search area, exploring a new space and randomly searching, ensures the coverage rate of the algorithm on a solution space, guarantees the global search capability and adjusts the balance between the global search and the local search;
the direction of movement of the droplets, denoted Vi tWithout a fault, the droplet has five possibilities of movement at each moment: hold, up, down, left and right, corresponding to V, respectivelyi tThe five possible values of (A) are respectively defined as mk、mu、md、mlAnd mr. However, in the presence of faults and other droplets, the direction of movement of the droplets is limited, defining a set Ui tDenotes the set of directions in which a droplet designed for particle i can move at time t, for which the particle is at pos at time tt＝Ei(mi+1,ni) Particle of (1), set Ui tThe establishment method comprises the following steps:
(1) if the electrode Ei(mi+1,ni) At time t and time t +1, the liquid drop can be kept stillkPut into the set Ui t；
(2) If the electrode Ei(mi,ni) At time t and time t +1, the liquid drop can move to left to move mlPut into the set Ui t；
(3) If the electrode Ei(mi+2,ni) At time t and time t +1, the liquid drop can move to the right, and m is in an unused staterPut into the set Ui t；
(4) If the electrode Ei(mi+1,ni-1) is not in use at time t and at time t +1, the drop can move downwards, mdPut into the set Ui t；
(5) If the electrode Ei(mi+1,ni+1) at time t and at time t +1All are in the state of not being used, the liquid drop can move upwards, and m isuPut into the set Ui t。
Velocity direction at time t of ith particle
Figure BDA0001792887240000131
Figure BDA0001792887240000132
Figure BDA0001792887240000133
mk、mu、md、mlAnd mrCorresponding to the respective holding, upward, downward, leftward and rightward speed directions, Ui tThe set of the moving directions of the liquid drops corresponding to the ith particle at the t moment when the constraint condition is met is shown;
step four and three, updating the speed direction of the ith particle at the moment t
Figure BDA0001792887240000134
Figure BDA0001792887240000135
Then
Figure BDA0001792887240000141
xgb tPosition of the globally optimal particle for time t, xlb tFor the position of the locally optimal particle at time t, r7Is a randomly generated random number;
step four, updating the position vector X of the ith particle at the t +1 momenti t+1：
Figure BDA0001792887240000142
Xi T＝(xi 1,xi 2,...,xi t) Is the position vector of the particle at time t, then Xi t+1＝(xi 1,xi 2,...,xi t,xi t +1)；
Repeating the fourth step, the second step, the fourth step and the fourth step until the mixing degree reaches 100 percent, and turning to the fourth step, the fifth step;
step four and five, determining the position vector X of the locally optimal particleslb T
Xlb T＝(xlb 1,xlb 2,...,xlb T)
T is experiment completion time;
step four and six, determining the position vector X of the globally optimal particlesgb T；
Xgb T＝(xgb 1,xgb 2,...,xgb T)；
And repeating the fourth step, the second step, the fourth step and the sixth step until the iteration times reach Gen times, and outputting the globally optimal position vector of the particles meeting the conditions to obtain the moving path.
And repeating the third step to the fourth step according to the operation sequence until all the operations are finished.

Claims (6)

1. The digital microfluidic chip fault repairing method based on the combination of the improved Dijkstra algorithm and the IPSO is characterized by comprising the following steps of:
step one, calculating a shortest path between two liquid drops to be mixed based on an improved Dijkstra algorithm, and enabling the two liquid drops to be mixed to move to the same position according to the shortest path;
the improved Dijkstra algorithm is characterized in that a cost function is introduced into the existing Dijkstra algorithm, and the cost function guides the existing Dijkstra algorithm to search in the direction with the shortest distance to a starting point, the shortest distance to a terminal point and the longest distance to a fault point;
step two, calculating a moving path based on IPSO, so that the shortest moving distance of the liquid drops is realized under the condition of ensuring the completion of mixing, and the fault repair is completed, wherein the moving path is a path required by mixing two liquid drops to be mixed from the same position in the step one;
the cost function fcost(Dk,i) Comprises the following steps:
Figure FDA0003540808170000011
wherein, dis (D)k,i,Dk,i,start) Is the distance of the current point to the starting point, dis (D)k,i,Dk,i,end) Min dis (D) is the distance from the current point to the end pointk,i,Ef)]Alpha, beta and gamma are weight coefficients which are the distances from the current point to the nearest fault point;
the first step comprises the following steps:
step one, set S is set, the set S is the shortest path order, the initial value in the set S only includes the starting point position of the droplet, i.e., S ═ pos1}；
Step two, generating set S ', S' including position pos to which a droplet at the latest element in S may move at the next moment when the constraint is satisfiedt+1S' contains at most five elements, assuming that the current electrode unit position of the droplet is Ei(mi+1,ni)，post+1Comprises the following steps: post+1＝Ei(mi+1,ni)，post+1＝Ei(mi+2,ni)，post+1＝Ei(mi,ni)，post+1＝Ei(mi+1,ni-1)，post+1＝Ei(mi+1,ni+1)，miIs the number of columns, niIs the number of rows;
step three, calculating the cost function of each element in S',
step one, selecting from SSelecting the position with the minimum cost function as pos2The shortest path access sequence S, S ═ pos is updated1,pos2}；
Repeating the first step and the second step to the first step and the fourth step until the liquid drop moves to the end point, and obtaining S ═ pos1,pos2,pos3......}；
The second step is specifically as follows:
step two, setting IPSO parameters including maximum iteration times Gen and acceleration constant c1、c2And c3Speed dependent random number r1、r2And r3；
Step two, calculating the speed direction of the ith particle at the moment t
Figure FDA0003540808170000021
Figure FDA0003540808170000022
Figure FDA0003540808170000023
mk、mu、md、mlAnd mrCorresponding to the respective holding, upward, downward, leftward and rightward speed directions, Ui tThe set of the moving directions of the liquid drops corresponding to the ith particle at the t moment when the constraint condition is met is shown;
step two and step three, updating the speed direction of the ith particle at the moment t
Figure FDA0003540808170000024
Figure FDA0003540808170000025
xgb tPosition of the globally optimal particle for time t, xlb tFor the position of the locally optimal particle at time t, r7Is a randomly generated random number;
step two, updating the position vector X of the ith particle at the t +1 momenti t+1：
Figure FDA0003540808170000026
Repeating the second step to the fourth step until the mixing degree reaches 100%, and switching to the second step and the fifth step;
step two and five, determining the position vector X of the locally optimal particleslb T
Xlb T＝(xlb 1,xlb 2,...,xlb T)
T is experiment completion time;
step two and six, determining the position vector X of the globally optimal particlesgb T；
Xgb T＝(xgb 1,xgb 2,...,xgb T)；
And repeating the second step to the second sixth step until the iteration times reach Gen times, and outputting the globally optimal position vector of the particles meeting the conditions to obtain the moving path.
2. The digital microfluidic chip fault repairing method based on the combination of the improved Dijkstra algorithm and the IPSO according to claim 1, wherein the constraint conditions comprise fault constraint conditions, static constraint conditions and dynamic constraint conditions;
the fault constraint condition is that the fault electrode unit is not used within the experiment completion time;
the static constraint condition is that two droplets cannot be in the positions of electrode units which are directly adjacent or adjacent along a diagonal line;
the dynamic constraint condition is that when two liquid drops are separated from one electrode unit, the two liquid drops can not move in the same direction along the straight line where the two liquid drops are located simultaneously.
3. The digital microfluidic chip fault repairing method based on the combination of the improved Dijkstra algorithm and the IPSO as claimed in claim 2, wherein the mathematical model of the fault constraint condition is as follows:
Figure FDA0003540808170000031
wherein E isa f(ma,na) As a faulty electrode unit, EfFor a set of faulty electrode units, TrealIn order to complete the time of the experiment,
Batis binary variable and represents the condition that the electrode unit is used in each time slice, if at time t, the a-th electrode unit Ea(ma,na) Is used, then BatIs 1, otherwise BatIs 0; m isaIs the number of rows in which the a-th electrode unit is located, naThe number of rows of the a-th electrode unit.
4. The method for repairing the fault of the digital microfluidic chip based on the combination of the improved Dijkstra algorithm and the IPSO as claimed in claim 2, wherein the kth time is taAnd kjThe positions of the droplets are respectively
Figure FDA0003540808170000032
And
Figure FDA0003540808170000033
the mathematical model of the static constraints is:
Figure FDA0003540808170000034
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njAre respectively the a-th and the j-thNumber of rows of electrode units, DtIs a collection of drop positions.
5. The method for repairing the fault of the digital microfluidic chip based on the combination of the improved Dijkstra algorithm and the IPSO as claimed in claim 2, wherein the positions of the two liquid drops are respectively at time t
Figure FDA0003540808170000035
And
Figure FDA0003540808170000036
the two drops will make a movement at time t of
Figure FDA0003540808170000037
And
Figure FDA0003540808170000038
the electrode units of the two liquid drops are respectively Ea(ma,na) And Ej(mj,nj) The vector formed by the positions of the two electrode units is expressed as
Figure FDA0003540808170000039
Figure FDA00035408081700000310
Representing the angle between the two vectors, the mathematical model of the dynamic constraint is:
Figure FDA0003540808170000041
Figure FDA0003540808170000042
maand mjThe number of rows, n, in which the a-th and j-th electrode units are respectively locatedaAnd njThe number of rows of the a-th electrode unit and the j-th electrode unit are respectively.
6. The method for repairing the fault of the digital microfluidic chip based on the combination of the improved Dijkstra algorithm and the IPSO as claimed in claim 1, further comprising before the step one: establishing a mathematical model of the digital microfluidic chip, and determining an operation sequence chart of the digital microfluidic chip according to the sequence between operations;
and after the first step to the second step are executed, repeating the first step to the second step according to the operation sequence until all the operations are finished.
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