Digital Microfluidic Droplet Path Planning Based on Improved Genetic Algorithm

Abstract

In practical applications of droplet actuation using digital microfluidic (DMF) systems based on electrowetting-on-dielectric (EWOD), various electrode failures can still arise due to diverse operational conditions. To improve droplet transport efficiency, this study proposes a heuristic-elite genetic algorithm (HEGA) for droplet path planning. We introduce a heuristic method and a bidirectional elite fragment recombination method to address the challenge of poor initialization quality in genetic algorithms, particularly in complex environments. These approaches aim to enhance the global search capability and accelerate the algorithm’s convergence. Simulations were performed using MATLAB, and the results indicate that compared to the basic ant colony algorithm, the proposed method reduces the average number of turning points by approximately 17.23% and the average search time by about 92.60%. In multi-droplet transport applications, the algorithm generates optimal paths for test droplets while maintaining fast convergence. Additionally, it effectively prevents droplets from accidentally contacting or merging in non-synthesis areas, ensuring improved testing outcomes for the chip.

1. Introduction

Microfluidic technology [1], also known as microfluidic chips, is a technique primarily used for controlling small volumes of liquids. In contrast to traditional microfluidic chips, digital microfluidic (DMF) systems, which are based on the electrowetting-on-dielectric (EWOD) effect, have emerged in recent years as an innovative method for manipulating discrete microdroplets [2,3]. Due to their simple structure and the ease of developing control systems, EWOD devices are particularly well-suited for applications in fields such as biomedicine, chemical analysis, and chip cooling [4,5].

In the field of digital microfluidics, Dong et al. proposed a comprehensive diagnostic detection method that integrates macro-channels with digital microfluidic platforms [6]. This method is designed for the automated identification of multiple respiratory pathogens, thus improving both the efficiency and accuracy of pathogen detection. Yang et al. highlighted the significant advantages of digital microfluidic technology in emerging applications such as enzyme activity assessment and DNA storage, particularly in enhancing reaction efficiency, precision, and automation [7]. Additionally, the high integration and scalability of digital microfluidic technology present broad potential for biomedical assays. However, further research is required to optimize its performance in practical applications, especially regarding storage stability and scalability for high-throughput applications. Over the past decade, numerous research teams worldwide have actively focused on developing hydrophobic layer materials for EWOD devices and optimizing driving electrode designs [8,9]. Torabinia et al. demonstrated an electrowetting-on-dielectric (EWOD) digital microfluidic device (DMF) as an efficient tool for online organic chemical synthesis reactions [10]. This device controls droplet behavior on the chip surface via a small electrode array, enabling efficient solvent distribution, reaction cleaning, and sample purification at the microscale.

EWOD devices, driven by high voltage, face challenges due to immature manufacturing techniques, which often lead to unavoidable electrode failures in practical applications. As a result, efficient microdroplet path planning [11] has become a major area of interest for researchers. In digital microfluidic systems, droplet path planning involves determining the optimal paths for multiple droplets moving simultaneously from source electrode nodes to target electrode nodes within the 2D electrode array of an EWOD device (which typically has a 2D structure). The goal of path planning is to provide a reference path for droplet movement, enabling the droplets to follow this path while employing dynamic collision strategies to avoid unnecessary fusion and contamination between them.

In research within this field, Xu et al. suggested employing the ant colony algorithm for path planning [12], which can be used to detect electrode damage along the path. To address contamination issues along the droplet path, the team introduced a chaotic particle swarm optimization algorithm [13], which improved the time efficiency for fault elimination, leading to optimized testing paths. Zheng et al. proposed a digital microfluidic biochip repair method based on an improved Dijkstra algorithm and an enhanced particle swarm optimization (ID-IPSO) algorithm [14], achieving efficient path planning and optimization under complex constraints. Bhattacharya et al. (2021) introduced an intelligent path estimation technique [15] to optimize the transport of heterogeneous droplets in digital microfluidic biochips (DMFB). This method uses artificial intelligence to predict droplet trajectories, accounting for the physical differences between droplets. The technique improves the efficiency and accuracy of droplet movement while reducing interference between droplets. Kawakami et al. proposed a droplet routing method based on deep reinforcement learning [16] to address error issues in digital microfluidic biochips. This algorithm enhances the reliability and performance of the chip. Juarez et al. introduced an evolutionary multi-objective optimization algorithm for droplet path planning in digital microfluidic biochips [17] based on the NSGA-II framework, which does not utilize crossover operators. Although the algorithm effectively plans paths, the quality of the initial population remains relatively low in complex environments.

In most cases, when genetic algorithms are applied to more complex environments (such as those involving a higher number of faulty electrodes or numerous dynamic droplet obstacles), generating the initial population becomes more constrained. As a result, the quality of the generated initial population, measured by factors such as individual fitness, overall diversity, and execution time, is often lower. However, the quality of the initial population in genetic algorithms [18] is a crucial factor influencing the algorithm’s convergence speed [19]. To address this issue, this study proposes a heuristic-elite genetic algorithm (HEGA), which offers broader applicability and faster search speed. The algorithm incorporates a heuristic function that directs individuals toward the target node, where the reciprocal of the straight-line distance from the current node to the target node serves as the heuristic function. It also integrates a bidirectional elite segment recombination method, which enhances the quality of the genes in the genetic algorithm’s population by replacing and recombining elite segments from both forward and backward directions. Simulation results show that when HEGA is applied to droplet path planning in digital microfluidic systems, it improves path planning efficiency and accelerates the completion of applications such as chemical detection. This is of great theoretical importance for enhancing the stability and commercialization of DMF chips.

2. Droplet Driving Principles in Digital Microfluidic Systems

Digital microfluidic chips are classified into open and closed types, with most mainstream EWOD devices using a closed device structure, as shown in the droplet driving model in Figure 1.

In a closed digital microfluidic chip, the top electrode serves as the ground electrode, while the bottom electrode applies the external driving voltage. When the driving electrode is inactive, and assuming the droplet’s initial contact angles are equal, the droplet remains symmetrical. Upon activation of the adjacent driving electrode, the droplet transitions from a symmetrical to an asymmetrical shape as the contact angle decreases, which occurs due to the reduction in surface free energy at the solid–liquid interface. This creates a pressure difference inside the droplet, causing it to move toward the activated electrode. This is the driving principle of droplets in electrowetting-based digital microfluidic systems [20,21,22,23].

3. Problem Description and Spatial Modelling

Currently, in practical droplet-driven experiments, various electrode failures continue to occur in EWOD devices due to the influence of diverse operating conditions. Therefore, when planning the droplet’s path, it is essential to avoid known faulty electrodes and dynamic droplets to minimize the risk of experimental errors and improve the efficiency of applications such as droplet synthesis reactions.

In path planning research, grid-based models are commonly used to represent the environment. Most EWOD devices employ rectangular-shaped driving electrodes on the bottom substrate, which aligns with the structure of grid maps. Accordingly, this study uses a grid map to model the two-dimensional internal space of EWOD devices [14], as shown in Figure 2.

In this study, when performing droplet path planning for the EWOD device, each grid in (a) corresponds to an electrode on the chip, which is equivalent to each vertex in (b). In the grid model, the black grids represent faulty electrodes, through which droplets cannot pass, while the white grids represent normal electrodes, through which droplets can pass. Based on the droplet movement characteristics in EWOD devices with rectangular-shaped driving electrodes, droplets are best suited for movement in the four cardinal directions: north, south, east, and west. Therefore, in the simulation experiments of EWOD devices conducted in this study, the droplets move along these four cardinal directions.

To prevent fusion contamination of droplets during transport on EWOD devices, multi-droplet path planning requires droplets to maintain a specific distance from each other throughout the transport process. Therefore, a collision avoidance strategy must be designed to manage the scheduling of multiple droplets. In EWOD devices, certain constraints must be satisfied between droplets, as outlined in Equation (1).

$$\left\{\begin{array}{l}2\le |Ro{w}_2^t-Ro{w}_1^t|\\ 2\le |Colum{n}_2^t-Colum{n}_1^t|\end{array}\right.$$

(1)

In the equation, $Ro{w}_1^t$ and $Colum{n}_1^t$ denote the row and column positions of experimental droplet 1 at time $t$, while $Ro{w}_2^t$ and $Colum{n}_2^t$ denote the row and column positions of experimental droplet 2 at time $t$. A simple example: at a certain moment, if an experimental droplet is located at vertex 22, other droplets that are not involved in biochemical reactions with it should not remain at the vertices of the nine - cell grid adjacent to vertex 22 (that is, the nine vertices 1, 2, 3, 21, 22, 23, 41, 42, 43 in Subfigure (b) of Figure 2), so as to avoid the accidental fusion of the experimental droplet outside the synthesis area, which may affect the results of the biochemical experiment.

4. Heuristic-Elite Genetic Algorithm

Building on the principles of genetic algorithms, we propose a heuristic-elite genetic algorithm (HEGA) that incorporates heuristic strategies and a bidirectional elite segment recombination strategy. The flowchart of HEGA is shown in Figure 3.

4.1. Population Initialization

The individual starts at the initial node $S$, and the probability of moving toward the target node $end$ is enhanced by the heuristic function. $n_{\alpha (i,j)}$ represents the heuristic function, defined as the reciprocal of the straight-line distance from each node to the target node, as expressed in Equation (2):

$$n_{\alpha (i,j)}=\left\{\begin{array}{l}{\displaystyle \frac{1}{\sqrt{{(x_{\alpha (i,j)}-x_{end})}^2+{(y_{\alpha (i,j)}-y_{end})}^2}}},\alpha (i,j)\ne end\\ const,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\alpha (i,j)=end\end{array}\right.$$

(2)

where $P_{\alpha (i,j)}^k$ represents the probability that the $k$-th individual moves to the next grid node, as expressed in Equation (3):

$$P_{\alpha (i,j)}^k=\left\{\begin{array}{l}{\displaystyle \frac{|n_{\alpha (i,j)}{|}^{\beta }}{{\displaystyle \sum n_{\theta (i,j)}{|}^{\beta }}}},{\theta }_{(i,j)}\in allowe{d}_k(\alpha (i,j))\\ 0,\hspace{1em}\hspace{1em}\hspace{1em}else\end{array}\right.$$

(3)

where ${\theta }_{(i,j)}$ represents the set of grid nodes that the $k$-th individual can select for the next step, as expressed in Equation (4).

$${\theta }_{(i,j)}\in allowe{d}_k(\alpha (i,j))=\{1,2,\cdot \cdot \cdot ,m\}-tab{u}_k$$

(4)

In the equations, $\alpha (i,j)$ represents the index of the current node; $tab{u}_k$ is the tabu list, which keeps track of the grid nodes visited by the $k$-th individual; $\beta$ is the expected value heuristic factor; and m denotes the number of individuals in the population.

In this paper, a heuristic function addressing method is used to generate the initial population. The inverse of the straight-line distance between the target node and the current node serves as the heuristic information. During the path search process, individuals use the roulette wheel method to select the next node, with the selection probability being proportional to their fitness values. A tabu list records the nodes that have already been visited by an individual, preventing repeated visits to the same node and avoiding cycles. When an individual encounters a node that cannot be passed, it adds that node to the tabu list and avoids revisiting it in subsequent searches. If an individual encounters a deadlock (i.e., unable to find the next accessible node) during the search, a deadlock rollback strategy is triggered. This strategy moves the individual back to the previous node, adds the current node to the tabu list, and continues the search until the deadlock is resolved. The heuristic function guides the individual toward the target node, effectively reducing the randomness of the path search. The tabu list and deadlock rollback strategy prevent the individual from falling into a cycle, thereby improving the quality of the initial population.

After generating the initial population, we further optimize it using the elite fragment recombination method. Our elite strategy selects the top 10% of individuals with the highest fitness from the current population as elite individuals. Using the roulette wheel method, one elite individual is randomly selected as the template for gene fragment recombination. Starting from the end of the path of the individual to be optimized, we search forward to find the node that corresponds to the same position in the path of the elite individual. Once the same node is found, the path of the individual to be optimized is replaced with the path following that node from the elite individual’s path. A similar operation is then performed in the reverse direction. For the next individual to be optimized, another elite individual is randomly selected using the roulette wheel method, and the optimization process continues. Figure 4 illustrates an example of the optimization strategy using the elite fragment recombination method.

In Figure 4, $Pat{h}_{\min }$ is an elite individual selected randomly from the top 10% of the population’s fitness values using the roulette wheel method, with the probability factor of the elite individual being positively correlated with its fitness value. $Pat{h}_k$ represents the $k$-th individual, and $Pat{h}_k^{″}$ is the new individual obtained by applying elite replacement optimization to $Pat{h}_k$. The detailed steps of the optimization process are as follows:

Step 1: Sort the population based on fitness values, identifying the top 10% as elite individuals. Using the roulette wheel method, randomly select one elite individual, $Pat{h}_{\min }$, with a path length of m.

Step 2: Begin at the m-length path node of the $k$-th individual (e.g., Node 166 in Subfigure (a) of Figure 4). Search for the corresponding path node in elite individual $Pat{h}_{\min }$. If found, move to step 3. If no match is found, decrement by 1 towards the starting node $S$ (i.e., select the previous node) and repeat step 2. If no matching node is found even after decrementing to the second path node, proceed to step 4.

Step 3: Take the matching node identified in step 2 (e.g., Node 41 in Subfigure (a) of Figure 4) as the boundary. Retain the $k$-th individual’s initial path segment and replace the subsequent path with the elite individual’s path beyond the matching node.

Step 4: The optimized individual begins at the path node located at the length value of Node_Len minus m and searches for a matching path node value in the elite individual(e.g., Node 21 in Subfigure (b) of Figure 4). If a match is found, proceed to step 3. If not, decrement by 1 towards the endpoint (i.e., select the next node) and repeat step 2. If no matching node is found, even after decrementing to the second-to-last node, cancel the optimization for this step.

Figure 4 illustrates that the optimized new individual $Pat{h}_k^{″}$, derived from the $k$-th individual, achieves a reduced path length of 35. The elite individuals carry excellent gene fragments, and through bidirectional recombination, these gene fragments are passed on to other individuals, thereby improving the overall quality of the initial population. By introducing the superior gene fragments from the elite individuals, the convergence speed of the population towards the optimal solution can be accelerated. Meanwhile, bidirectional recombination effectively helps escape from local optima, expands the search range, and enhances the global search capability of the algorithm.

4.2. Fitness Function

The fitness function assesses individuals based on their path length and number of turning points. The fitness value $F_k$, of the $k$-th individual is represented by Equation (5):

$$F_k={\displaystyle \frac{1}{a{L}_k+b{T}_k}}$$

(5)

where $L_k$ represents the path length searched by the $k$-th individual, $T_k$ denotes the number of turning points in its path, $a$ and $b$ correspond to the weights of $L_k$ and $T_k$, respectively.

4.3. Genetic Operations

Selection, crossover, and mutation operations mimic natural genetic inheritance, with genetic algorithms exploring optimal solutions through the simulation of biological evolution. In this study, the selection operation uses the roulette wheel method, as represented by Equation (6):

$$\left\{\begin{array}{l}{\mathrm{p}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{F}}_{\mathrm{k}}}{{\displaystyle \sum _{i=1}^N{F}_i}}}\\ q_k={\displaystyle \sum _{i=1}^k{p}_i}\end{array}\right.$$

(6)

where ${\mathrm{p}}_{\mathrm{k}}$ is the probability of the $k$-th individual being selected, $N$ is the size of the population, and $q_k$ is the cumulative probability of the $k$-th individual. Individuals with higher fitness values in the parent generation have a higher likelihood of being selected as offspring.

The crossover operation uses a single-point crossover method: based on the crossover probability, a common node is randomly selected from the nodes of the two parent individuals, $Pat{h}_i$ and $Pat{h}_j$, and then the nodes after or before this common node are exchanged to generate new offspring individuals, $Pat{h}_i^{\prime }$ and $Pat{h}_j^{\prime }$, as shown in Figure 5.

Mutation operations mimic the genetic and evolutionary processes in biology, where random objective factors cause some genes to mutate. A mutation probability factor is introduced, randomly selecting two different nodes in the path to serve as the start and target nodes, and then a new path is searched to connect these two nodes. Mutation operations enhance the comprehensiveness of genetic algorithm path searches, effectively avoiding local optima and increasing search diversity.

5. Simulation Validation

The simulation platform for this experiment is MATLAB R2021b, with the hardware comprising an Intel(R) CORE(TM) i5-7300HQ and 8GB RAM. The computer is of the Hasee brand from Shenzhen, China.

5.1. Single Droplet Path Planning for EWOD Devices

The single-droplet path planning experiment for EWOD devices was conducted in a 30 × 30 grid environment. Both the HEGA proposed in this paper and the traditional ant colony algorithm had a population size of 80 and a maximum iteration count of 60, with fitness function parameters a and b assigned values of 2 and 5, respectively. The crossover probability of the genetic algorithm was 0.8, and the mutation probability was 0.2. The selection of parameters was based on our experimental validation of the algorithm’s performance, with the aim of effectively maintaining population diversity and assisting the algorithm in conducting extensive searches within complex solution spaces. Figure 6 shows the path planning results comparison between the two algorithms, and Figure 7 shows the convergence results comparison.

As shown in Figure 6, compared to the HEGA algorithm presented in this paper, the basic ant colony algorithm produces a droplet transport path with more twists, more sharp turns, and a longer path length. In contrast, the HEGA algorithm generates a smoother droplet transport path with fewer turns.

Figure 7 illustrates that the proposed algorithm reaches the optimal value at the 11th iteration, while the traditional ant colony algorithm reaches the optimal value at the 26th iteration. Additionally, the proposed algorithm’s average fitness value converges close to the optimal value after about 30 iterations, whereas the traditional ant colony algorithm’s fitness value converges close to the optimal value after approximately 40 iterations.

In summary, the proposed algorithm produces paths with fewer sharp turns, resulting in higher fitness values and a significantly faster convergence speed compared to the traditional ant colony algorithm.

In this comparative study, both algorithms were tested 15 times in identical complex environments using a controlled variable approach. The simulation results are presented in

Table 1. Average data from 15 simulation experiments.

Algorithm	Average Shortest Paths	Mean Turning Points for Shortest Paths	Execution Time/s
Basic ant colony algorithm	58	10.27	13.8533
HEGA of this study	58	8.5	1.0255

.

Table 1 compares the average shortest path length, average number of turns, and search time between the two algorithms. Both algorithms achieve the shortest path length, but the HEGA algorithm presented in this paper shows significant advantages in terms of the number of turns and execution time compared to the traditional ant colony algorithm. Compared to the traditional ant colony algorithm, the HEGA algorithm reduces the average number of turns by approximately 17.23% and the average search time by about 92.60%. Fewer turns can reduce the droplet’s dwell time and the likelihood of drive failures during multiple droplet transport processes, thereby accelerating the completion time of droplet synthesis.

5.2. Collision Avoidance Strategies for Multiple Droplets in EWOD Devices

For multi-droplet fusion reactions on EWOD devices, whether a droplet can proceed is determined by applying collision avoidance strategies relative to other droplets, Multiple droplets must maintain a certain distance from each other at all times to avoid accidental contact. In the two-droplet collision avoidance strategy, Droplet A and Droplet B are assumed, where Droplet A is given higher priority, and Droplet B has lower priority.

In applications such as multi-droplet fusion reactions on EWOD devices, when droplets are about to collide, their movement is determined based on the collision avoidance strategy. Droplets must maintain a certain distance from each other to prevent accidental contact or fusion in non-synthesis areas. In the two-droplet collision avoidance strategy, Droplet A is given higher priority, while Droplet B has lower priority.

5.2.1. Collision Avoidance Strategy 1: Lower-Priority Droplet Remains Stationary

The simulation results are shown in Figure 8. ${\mathrm{S}}_{\mathrm{A}}$ represents the origin node of Droplet A, ${\mathrm{S}}_{\mathrm{B}}$ represents the origin node of Droplet B, and “end” denotes the destination node. The shaded area indicates the droplet synthesis region. Subfigures a, b, c, d, e, and f correspond to the droplet paths at timestamps 18, 19, 20, 21, 23, and 24, respectively. At timestamp 18, the two droplets are about to collide. Strategy 1 is applied, with Droplet B pausing for one cycle to avoid the collision, while Droplet A continues moving normally. At timestamp 19, the droplets are again, on the verge of colliding, triggering Strategy 1 once more. By timestamp 21, high-priority Droplet A reaches the destination, and by timestamp 24, the lower-priority Droplet B reaches its destination, successfully completing the reaction synthesis.

5.2.2. Collision Avoidance Strategy 2: Retraction of the Secondary Priority Droplet

The simulation results are shown in Figure 9. After the droplets reach timestamp 18, they are about to collide at the next timestamp. If Strategy 1 were applied, the distance between the two droplets would not satisfy the constraint given by Equation (1) (i.e., the distance between the droplets would be less than 2), causing them to fuse in a non-synthesis region. Therefore, Strategy 2 is employed, where Droplet B retreats to the previous grid node, allowing Droplet A to pass through normally. After reaching timestamp 21, Droplet A arrives at its destination. By timestamp 24, Droplet B reaches its destination, and the two droplets successfully complete the reaction synthesis.

5.2.3. Collision Avoidance Strategy 3: Droplet Priority Switching

The simulation results are shown in Figure 10. After reaching timestamp 18, the two droplets are about to collide at the next moment. However, Droplet B will reach its destination first. If either Collision Strategy 1 or Strategy 2 were applied, it would affect the droplet addressing efficiency. Therefore, Collision Strategy 3 is used at this point, where Droplet B is given higher priority and proceeds to its destination, while Droplet A is assigned lower priority and follows afterward. By timestamp 19, the high-priority Droplet B reaches its destination. By timestamp 20, the lower-priority Droplet A reaches its destination, and the two droplets successfully complete the reaction synthesis.

5.3. Test Droplet Path Planning for EWOD Devices

If a structural fault (such as a short circuit or open circuit) occurs during a biochemical experiment, leading to the complete failure of the digital microfluidic chip, it may result in inaccurate or even entirely opposite experimental outcomes compared to a normal experiment. Therefore, by using a test droplet to traverse the electrodes on the chip, structural faults in the digital microfluidic chip can be detected [24]. (In the case of a fault, such as a short circuit or open circuit, the test droplet will be unable to pass through the faulty electrode and cannot reach the target node.) To improve testing efficiency, the test should be completed in the shortest time possible.

Before the experiment begins, the chip can be tested for faults to ensure it is functioning properly. This fault detection is typically performed in a time-segmented manner, separate from the actual experiment, and is referred to as offline testing. In contrast, online detection involves using a test droplet to monitor the chip for faults while the experiment is ongoing, allowing real-time detection of structural faults during the experiment.

In this study, we apply multiplexed biochemical detection examples from references [25,26,27] to perform online detection for a digital microfluidic biochip with a 15 × 15 array unit, as illustrated in the test model in Figure 11.

The experiment involves two samples and two reagents. Sample 1 is glucose, which is to be tested, and Reagent 1 is glucose oxidase. Sample 2 is lactic acid, and Reagent 2 is lactate oxidase, both at specific concentrations. As shown by the arrows in the diagram, Sample 2 and Reagent 2 are transported along the designated path to a mixing zone with a 2 × 3 array, where they undergo a complete enzyme-catalyzed reaction. The resulting mixture is then moved to Detection Zone 2 for optical detection and ultimately transported to the waste pool. Similarly, Sample 1 and Reagent 1 follow the designed route during the experiment. The detailed process of the entire multiplexed biochemical experiment is shown in

Table 2. Schedule of multiplexed biochemical experiment.

Time/s	Operation
0	Sample 2 and reagent 2 move towards the mixing area
0.8	Sample 2 and reagent 2 start mixing in the mixing area
6.0	Sample 1 and reagent 1 move towards the mixing area & Sample 2 and reagent 2 continue to mix
6.8	Sample 2 and reagent 2 are mixed and moved to the testing area 2 & Sample 1 and reagent 1 start mixing in the mixing area
12.8	Sample 1 and reagent 1 are mixed and moved to the testing area 1 & Mixture 2 continues to be tested in the testing area
19.8	Mixture 2 has been tested and is moving to the waste reservoir & Mixture 1 continues to be tested
25.8	Mixture 1 is tested and moved to the waste reservoir, and the experiment is over

.

The time for droplets to move between two adjacent electrodes is 62.5 ms, which is defined as one unit of time. The path length covered by the droplet in this time is designated as 1, representing one unit length in the grid model. The total time for this multiplexed biochemical experiment is 25.8 s, which is approximately equivalent to 413 unitized lengths. Online testing must fully account for the fluid constraints of the experimental droplets on the test droplets. In the anti-collision strategy, we assign a higher priority to the experimental droplets than to the test droplets.

Parameter settings for the genetic algorithm (GA): the population size is set to 30, with 500 iterations, a crossover probability of 0.6, and a mutation probability of 0.2. To demonstrate the effectiveness of the proposed improved algorithm, the results are compared with the PMF [25], IACA [26], and PS-GA [27] methods, as shown in Figure 12.

In offline detection, PMF yields better results than IACA. However, in online detection, IACA outperforms PMF. Both our improved genetic algorithm and PS-GA achieve a result of 446 in both offline and online detection, reaching the optimal Eulerian path value. Compared to IACA, this represents a 5% improvement. Therefore, our improved genetic algorithm demonstrates strong testing performance in both offline and online settings, making it a highly effective testing method.

To demonstrate the convergence performance of our improved genetic algorithm during online testing, we compare it with PS-GA, as shown in Figure 13. PS-GA reaches the optimal value at the 120th iteration, and its average value gradually converges to the optimal value around the 300th iteration. In contrast, our improved genetic algorithm reaches the optimal value at the 80th iteration, and the average value converges to the optimal value around the 200th iteration. These results indicate that our algorithm converges to the optimal value more quickly and exhibits better convergence performance for the average value. Therefore, the proposed improved algorithm not only achieves the theoretical optimum but also demonstrates a faster convergence speed, leading to better overall performance during testing.

6. Conclusions

This paper applies genetic algorithms to droplet path planning within digital microfluidic systems and introduces a heuristic-elite genetic algorithm (HEGA). The proposed HEGA addresses the issue of poor initialization quality in complex environments, improves the search efficiency of the genetic algorithm in intricate grid environments, and enhances both the global search capability and convergence speed of the algorithm.

The simulation results show that the proposed HEGA has a wider range of applicability and higher path planning efficiency. Compared with the basic ant colony algorithm, HEGA demonstrates significant advantages, with the average number of turning points reduced by about 17.23% and the average search time reduced by about 92.60%. This effectively proves that the HEGA proposed in this paper can find better paths for droplets in EWOD devices in a short time.

In multi-droplet transport applications, we combine a multi-droplet collision avoidance strategy to prevent cross-contamination during the droplet addressing process. The algorithm we propose ensures that the path generated for the test droplets reaches the theoretical optimum, while also exhibiting good convergence speed. It effectively prevents accidental contact or fusion of droplets in non-synthesis areas, and the droplets’ movement is efficient, providing better testing results for the chip.

Although the algorithm shows promising potential for multi-droplet addressing in EWOD devices, further research can be done to improve online detection efficiency, particularly by enabling parallel online detection for multiple test droplets. This could lead to even higher performance in chip testing.