An automated method has been developed to fully characterize the three-dimensional structure of zeolite porous networks. The proposed optimization-based approach starts with the crystallographic coordinates of a structure and identifies all portals, channels, and cages in a unit cell, as well as their connectivity. We apply our algorithms to known zeolites, hypothetical zeolites, and zeolite-like structures and use the characterizations to calculate important quantities such as pore size distribution, accessible volume, surface area, and largest cavity and pore limiting diameters. We aggregate this data over many framework types to gain insights about zeolite selectivity. Finally, we develop a continuous-time Markov chain model to estimate the probability of occupancy of adsorption sites throughout the porous network. ZEOMICS, an online database of structure characterizations and web tool for the automated approach is freely available to the scientific community (http://helios.princeton.edu/zeomics/).

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This work discusses alternative relaxation schemes for the pooling problem, a theoretically and practically interesting optimization problem. The problem nonconvexities appear in the form of bilinear terms and can be addressed with the relaxation technique based on the bilinear convex and concave envelopes. We explore ways to improve the relaxation tightness, and thus the efficiency of a global optimization algorithm, by employing a piecewise linearization scheme that partitions the original domain of the variables involved and applies the principles of bilinear relaxation for each one of the resulting subdomains. We employ 15 different piecewise relaxation schemes with mixed-integer representations and conduct a comprehensive computational comparison study over a collection of benchmark pooling problems. For each case, various partitioning variants can be envisioned, cumulatively accounting for a total of 56 700 relaxations. The results demonstrate that some of the schemes are clearly superior to their counterparts and should, therefore, be preferred in the optimization of pooling processes.

We study the robust capacitated vehicle routing problem (CVRP) under demand uncertainty, which determines a minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random variables, and it determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. We derive and compare the robust optimization counterparts of several deterministic CVRP formulations. We also develop robust rounded capacity inequalities and show how they can be separated efficiently for two classes of demand supports. RTG 1855

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