Automatic Generation of Reduced-Space Optimization Formulations of Process Systems for Faster Deterministic Global Optimization in Julia

Optimization plays a critical role in engineering because of its ability to address decision-making problems. For problems involving nonconvexity, which is inherent to many chemical engineering systems of interest, deterministic global optimization solvers are required to guarantee a certificate of optimality. However, global solvers are ill-suited for large-scale applications because of their worst-case exponential runtime with respect to problem dimension. This has prompted research into the generation and use of reduced-space optimization formulations, where a model is algebraically transformed from a high-dimensional space into its intrinsic dimension, to reduce computational cost and therefore broaden the scope of problems for which global solvers can be applied.

In this work, we detail the development of user-defined functions that provide a bridge between an easy-to-use open-source modeling framework and a robust open-source deterministic global optimization solver, namely EAGO.jl, within the Julia programming language. Specifically, we utilize ModelingToolkit.jl’s intuitive modeling interface and structural simplification features along with Symbolics.jl’s function compilation tools to automatically generate reduced-space models as numerically usable functions, which can then be used as EAGO-compatible equality constraints in JuMP models.

We then apply our methods to formulate and solve a process design optimization problem with the objective of minimizing capital and operational costs, where we demonstrate improvements in convergence times and reductions in memory allocations compared to its full-space formulation. These advantages are further exemplified through the provision of our novel approaches to automatically generate reduced-space models by using powerful and highly accessible open-source tools, advancing the applicability and availability of global solvers for optimizing large-scale nonconvex chemical engineering systems.