Optimization Algorithms for Hierarchical Problems with Application to Nanoporous Materials

Abstract

We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas storage and filtration, electrical energy storage in batteries and capacitors, and catalysis. The design of such materials involves modeling of the material over many length scales, leading to a hierarchy of mathematical models. Our algorithms are also hierarchical in structure with the goal of exploiting the model hierarchy to obtain solutions more rapidly. We discuss the choice of optimization models, initialization schemes, the hierarchical optimization algorithm, software design, and computational results.