Prof. Allman is broadly interested in utilizing mathematical optimization, network theory, and machine learning to support efficient computational decision making for sustainable chemical systems. Specific research themes being pursued by the group are as follows:
- – Dimensionality reduction for many-objective optimization: We are developing methods which can systematically reduce an optimization problem with a larger (four or more) number of objectives, prevalent in any problem considering sustainability, to one of three or fewer, in order to overcome the curse of dimensionality of rigorously generating tradeoff solutions in many-objective problems. This work makes heavy use of concepts from linear algebra, global optimization, and network theory.
- – Learning classifier models for efficient moving horizon decision making: Modern chemical systems are becoming more complex due to trends in modularization, intensification, and intermittent operation for sustainability. However, optimal process control and operation problems must still be solved quickly for their solutions to be practically implementable. To this end, we are working on building ML models not to replace optimization, but to learn something about the problem that will allow us to solve it in a relevant amount of time (i.e. what method should be used to solve, what values should integer variables take).
- – Network structure detection for decomposing optimization problems: Network theoretic tools, such as community detection and stochastic blockmodeling learning, allow us to identify structure and sparsity within optimization problems that make them amenable to solving via, i.e. Lagrangian decomposition. However, some powerful decomposition methods require a specific structure which is not always identified using these tools. To this end, our team is developing approaches to solve constrained structure detection problems using tools from global optimization, with a particular interest in developing decomposition methods that can make use of quantum computing for solving parts of the optimization problem.