Hierarchical Approach for Survivable Network Design

A central design challenge facing network planners is how to select a cost-effective network configuration that can provide uninterrupted service despite edge failures. In this paper, we study the Survivable Network Design (SND) problem, a core model underlying the design of such resilient networks that incorporates complex cost and connectivity trade-offs. Given an undirected graph with specified edge costs and (integer) connectivity requirements between pairs of nodes, the SND problem seeks the minimum cost set of edges that interconnects each node pair with at least as many edge-disjoint paths as the connectivity requirement of the nodes. We develop a hierarchical approach for solving the problem that integrates ideas from decomposition, tabu search, randomization, and optimization. The approach decomposes the SND problem into two subproblems, Backbone design and Access design, and uses an iterative multi-stage method for solving the SND problem in a hierarchical fashion. Since both subproblems are NP-hard, we develop effective optimization-based tabu search strategies that balance intensification and diversification to identify near-optimal solutions. To initiate this method, we develop two heuristic procedures that can yield good starting points. We test the combined approach on large-scale SND instances, and empirically assess the quality of the solutions vis-à-vis optimal values or lower bounds. On average, our hierarchical solution approach generates solutions within 2.7% of optimality even for very large problems (that cannot be solved using exact methods), and our results demonstrate that the performance of the method is robust for a variety of problems with different size and connectivity characteristics.

Efficient Liquid Liquid Extraction By Emulsion Formation and Separation in Robust Milli-Fluidic Devices

Conventional liquid liquid extraction (LLE) methods require large volumes of fluids to achieve the desired mass transfer of a solute, which is unsuitable for systems dealing with a low volume or high value product. An alternative to these methods is to scale down the process. Millifluidic devices share many of the benefits of microfluidic systems, including low fluid volumes, increased interfacial area-to-volume ratio, and predictability. A robust millifluidic device was created from acrylic, glass, and aluminum. The channel is lined with a hydrogel cured in the bottom half of the device channel. This hydrogel stabilizes co-current laminar flow of immiscible organic and aqueous phases. Mass transfer of the solute occurs across the interface of these contacting phases. Using a y-junction, an aqueous emulsion is created in an organic phase. The emulsion travels through a length of tubing and then enters the co-current laminar flow device, where the emulsion is broken and each phase can be collected separately. The inclusion of this emulsion formation and separation increases the contact area between the organic and aqueous phases, therefore increasing the area over which mass transfer can occur. Using this design, 95% extraction efficiency was obtained, where 100% is represented by equilibrium. By continuing to explore this LLE process, the process can be optimized and with better understanding may be more accurately modeled. This system has the potential to scale up to the industrial level and provide the efficient extraction required with low fluid volumes and a well-behaved system.