A Solution Method for Stochastic Multilevel Programming Problems. A Systematic Sampling Evolutionary Approach

Stochastic multilevel programming is a mathematical programming problem with some given number of hierarchical levels of decentralized decision makers and having some kind of randomness properties in the problem definition. The introduction of some randomness property in its hierarchical structure makes stochastic multilevel problems computationally challenging and expensive. In this article, a systematic sampling evolutionary method is adapted to solve the problem. The solution procedure is based on realization of the random variables and systematic partitioning of each hierarchical level's decision space for searching an optimal reaction. The search goes sequentially upwards starting from the bottom up through the top hierarchical level problem. The existence of solution and convergence of the solution procedure is shown. The solution procedure is implemented and tested on some selected deterministic test problems from literature. Moreover, the proposed algorithm can be used to solve stochastic multilevel programming problems with additional complexity in their problem definition. (original abstract

Advances in Data-Driven Modeling and Global Optimization of Constrained Grey-Box Computational Systems

The effort to mimic a chemical plant’s operations or to design and operate a completely new technology in silico is a highly studied research field under process systems engineering. As the rising computation power allows us to simulate and model systems in greater detail through careful consideration of the underlying phenomena, the increasing use of complex simulation software and generation of multi-scale models that spans over multiple length and time scales calls for computationally efficient solution strategies that can handle problems with different complexities and characteristics. This work presents theoretical and algorithmic advancements for a range of challenging classes of mathematical programming problems through introducing new data-driven hybrid modeling and optimization strategies. First, theoretical and algorithmic advances for bi-level programming, multi-objective optimization, problems containing stiff differential algebraic equations, and nonlinear programming problems are presented. Each advancement is accompanied with an application from the grand challenges faced in the engineering domain including, food-energy-water nexus considerations, energy systems design with economic and environmental considerations, thermal cracking of natural gas liquids, and oil production optimization. Second, key modeling challenges in environmental and biomedical systems are addressed through employing advanced data analysis techniques. Chemical contaminants created during environmental emergencies, such as hurricanes, pose environmental and health related risks for exposure. The goal of this work is to alleviate challenges associated with understanding contaminant characteristics, their redistribution, and their biological potential through the use of data analytics