EOptInterface.jl: Equation-Oriented Optimization Interface in Julia

We present the equation-oriented optimization interface EOptInterface.jl (EOI): an abstraction layer that interfaces componentized equation-oriented (EO) modeling with mathematical optimization in the Julia programming language. This work is motivated by an interoperability gap between simulation and optimization tasks within EO modeling: a modeling paradigm for hierarchical multicomponent models where systematic decision-making approaches are necessary. EOI directly addresses this gap by interfacing ModelingToolkit.jl (MTK)’s componentized EO modeling and simulation framework with the mathematical programming language JuMP.jl, which makes EOI the first package to integrate componentized EO modeling with mathematical optimization in Julia. In this paper, we detail EOI’s development and demonstrate its usage by formulating and solving nonlinear programs (NLPs) directly from algebraic and dynamic MTK models. For the algebraic process model example, our automatic reduced-space NLP formulation approach yields one and two orders of magnitude speedup for local and deterministic global solvers, respectively, compared to the equivalent full-space NLP formulation. For the dynamical system example, we showcase automatic direct transcription approaches with the automatic time-discretization for ordinary differential equations and subsequent equality constraint formulation.