Generalized Hose uncertainty in single-commodity robust network design

Single-commodity network design considers an edge-weighted, undirected graph with a supply/demand value at each node. It asks for minimum weight capacities such that each node can exactly send (or receive) its supply (or demand). In the robust variant, the supply or demand values may assume any realization in a given uncertainty set. One popular set is the well-known Hose polytope, which specifies an interval for the supply/demand at each node, while ensuring that the total supply and demand are balanced across the whole network. While previous work has established the Hose uncertainty set as a tractable choice, it can yield unnecessarily expensive solutions because it admits many unlikely supply and demand scenarios. In this paper, we propose a generalization of the Hose polytope that more realistically captures existing interdependencies among nodes in real life networks, and we show how to extend the state-of-the-art cutting plane algorithm for solving the single-commodity robust network design problem in view of this new uncertainty set. Our computational studies across multiple robust network design instances illustrate that the new set can provide significant cost savings without sacrificing numerical tractability

Designing networks: A mixed‐integer linear optimization approach

Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes, and the analysis of network evolution. Despite the importance of the task, there currently exists a gap in our ability to systematically generate networks that adhere to theoretical guarantees for the given property specifications. In this paper, we propose the use of Mixed-Integer Linear Optimization modeling and solution methodologies to address this Network Generation Problem. We present a number of useful modeling techniques and apply them to mathematically express and constrain network properties in the context of an optimization formulation. We then develop complete formulations for the generation of networks that attain specified levels of connectivity, spread, assortativity and robustness, and we illustrate these via a number of computational case studies

Predictive Framework for Shape-Selective Separations in Three-Dimensional Zeolites and Metal–Organic Frameworks

With the growing number of zeolites and metal–organic frameworks (MOFs) available, computational methods are needed to screen databases of structures to identify those most suitable for applications of interest. We have developed novel methods based on mathematical optimization to predict the shape selectivity of zeolites and MOFs in three dimensions by considering the energy costs of transport through possible pathways. Our approach is applied to databases of over 1800 microporous materials including zeolites, MOFs, zeolitic imidazolate frameworks, and hypothetical MOFs. New materials are identified for applications in gas separations (CO₂/N₂, CO₂/CH₄, and CO₂/H₂), air separation (O₂/N₂), and chemicals (propane/propylene, ethane/ethylene, styrene/ethylbenzene, and xylenes)