Droplet Routing Problem Research Articles

An Evolutionary Multi-objective Optimization algorithm for the routing of droplets in Digital Microfluidic Biochips

Many laboratory scale biochemical processes, including clinical diagnostics are being revolutionized by Digital Microfluidic Biochips (DMFBs). This is owing to their high automation capability, low cost, portability, and efficiency. Central to the efficient operation of these devices is the droplet routing problem that aims to drive a set of droplets, each from its source to its target cells, without violating a given set of fluidic and timing constraints. The efficiency of the routing is measured by the amount of cells used and the arrival time of the latest droplet and both criteria are aimed to be minimized simultaneously. To solve this problem we propose an Evolutionary Multi-objective Optimization algorithm for the Droplet Routing problem (EMO-DR) based on the NSGA-II framework, where the crossover operator is not used. EMO-DR features new mutation operators and a biased random generator of initial solutions. Experimental results show that the proposed approach produces competitive results when compared with those obtained through state-of-the-art methods. The paper also highlights the main challenges that evolutionary approaches need to solve when dealing with this routing problem.

Placement and Routing for Cross-Referencing Digital Microfluidic Biochips

Computer-aided design problems of digital microfluidic biochips are receiving much attention, and most of the previous works focus on direct-addressing biochips. In this paper, we solve the placement and droplet routing problem in cross-referencing biochips. In these biochips, the electrodes are addressed in a row-column manner, which may cause electrode interference that prevents simultaneous movements of multiple droplets. We propose a routing algorithm that solves the droplet routing problem directly. A two-coloring graph-theoretic method is used in our router to detect and prevent the electrode interference. In addition, we propose an integer linear programming based method to solve the placement problem. Our method considers the characteristics of cross-referencing biochips and is aware of droplet routing. Real-life benchmarks are used to evaluate the proposed methods. Compared with previous works, our router improves on average 4% in routing time and 58% in runtime. It can route all the benchmarks within the time limits, while the latest work fails in some cases. Moreover, experimental results show that by running our router on the placement result generated by our method and those generated by the latest work, an average improvement of 11%, 29%, 54%, and 46% in the maximum routing time, average routing time, stalling steps, and cell usage can be achieved.

A Two-Stage Integer Linear Programming-Based Droplet Routing Algorithm for Pin-Constrained Digital Microfluidic Biochips

With the increasing design complexities, the design of pin-constrained digital microfluidic biochips (PDMFBs) is of practical importance for the emerging marketplace. However, solutions of current pin-count reduction are inevitably limited by simply adopting it after the droplet routing stage. In this paper, we propose the first droplet routing algorithm for PDMFBs that can integrate pin-count reduction with droplet routing stage. Furthermore, our algorithm is capable of minimizing the number of control pins, the number of used cells, and the droplet routing time. We first present a basic integer linear programming (ILP) formulation to optimally solve the droplet routing problem for PDMFBs with simultaneous multiobjective optimization. Due to the complexity of this ILP formulation, we also propose a two-stage technique of global routing followed by incremental ILP-based routing to reduce the solution space. To further reduce the runtime, we present a deterministic ILP formulation that casts the original routing optimization problem into a decision problem, and solve it by a binary solution search method that searches in logarithmic time. Extensive experiments demonstrate that in terms of the number of the control pins, the number of the used cells, and the routing time, we obtain much better achievement than all the state-of-the-art algorithms in any aspect.

A Contamination Aware Droplet Routing Algorithm for the Synthesis of Digital Microfluidic Biochips

Recent advances of digital microfluidic biochips (DMFBs) have revolutionized the traditional laboratory procedures. By providing the droplet-based system, DMFB can perform real-time biological analysis and safety-critical biomedical applications. However, different droplets being transported and manipulated on the DMFB may introduce the contamination problem caused by liquid residue between different biomolecules. To overcome this problem, a wash droplet is introduced to clean the contaminations on the surface of the microfluidic array. However, current scheduling of wash droplet does not restrict the extra used cells and execution time of bioassay, thereby degrading the reliability and fault-tolerance significantly. In this paper, we propose a contamination aware droplet routing algorithm for DMFBs. To reduce the routing complexity and the used cells, we first construct preferred routing tracks by analyzing the global moving vector of droplets to guide the droplet routing. To cope with contaminations within one subproblem, we first apply a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -shortest path routing technique to minimize the contaminated spots. Then, to take advantage of multiple wash droplets, we adopt a minimum cost circulation (MCC) algorithm for optimal wash-droplet routing to simultaneously minimize used cells and the cleaning time. Since the droplet routing problem consists of several subproblems, a look-ahead prediction technique is further used to determine the contaminations between successive subproblems. After that, we can simultaneously clean both contaminations within one subproblem and those between successive subproblems by using the MCC-based algorithm to reduce the execution time and the used cells significantly. Based on four widely used bioassays, our algorithm reduces the used cells and the execution time significantly compared with the state-of-the-art algorithm.

A Progressive-ILP-Based Routing Algorithm for the Synthesis of Cross-Referencing Biochips

Due to recent advances in microfluidics technology, digital microfluidic biochips and their associated computer-aided-design problems have gained much attention, most of which has been devoted to direct-addressing biochips. In this paper, we solve the droplet routing problem under the more scalable cross-referencing biochip paradigm. We propose the first droplet routing algorithm that directly solves the problem of routing. We first present an optimal basic integer-linear-programming (ILP) formulation. Due to its complexity, we also propose a progressive-ILP scheme to determine the locations of droplets at each time step. Simulation results demonstrate the efficiency and effectiveness of our algorithm.

BioRoute: A Network-Flow-Based Routing Algorithm for the Synthesis of Digital Microfluidic Biochips

Due to recent advances in microfluidics, digital microfluidic biochips are expected to revolutionize laboratory procedures. One critical problem for biochip synthesis is the droplet routing problem. Unlike traditional very large scale integration routing problems, in addition to routing path selection, the biochip routing problem needs to address the issue of scheduling droplets under practical constraints imposed by the fluidic property and timing restriction of synthesis results. In this paper, we present the first network-flow-based routing algorithm that can concurrently route a set of noninterfering nets for the droplet routing problem on biochips. We adopt a two-stage technique of global routing followed by detailed routing. In global routing, we first identify a set of noninterfering nets and then adopt the network-flow approach to generate optimal global-routing paths for nets. In detailed routing, we present the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> polynomial-time algorithm for simultaneous routing and scheduling using the global-routing paths with a negotiation-based routing scheme. Our algorithm targets at both the minimization of cells used for routing for better fault tolerance and minimization of droplet transportation time for better reliability and faster bioassay execution. Experimental results show the robustness and efficiency of our algorithm.