Standard optimization techniques fall short of being able to solve simulated systems or, more generally, black-box systems since these techniques rely on first and second derivatives of algebraic objectives and constraints to identify search directions and test for optimality. In these cases, derivative-free optimization (DFO) solvers can be used. However, when the design of a process involves discrete variables and complex nonlinear objectives and constraints, the resulting problem topology is often too complex for DFO methods to solve reliably.
To facilitate use of standard algebraic optimization methods for the solution of simulated or experimental systems, we developed ALAMO to generate a set of algebraic surrogate models to describe these systems. The surrogate models can be combined with design constraints and algebraic objectives to formulate an algebraic optimization problem. This optimization model can then be used to design all discrete and continuous process alternatives, technology choices, etc., while simultaneously solving for continuous operating conditions across a process network using, for instance, a superstructure modeling framework.
To solve such a large optimization model, we aim to build not only accurate but also simple surrogate models. A combination of machine learning, statistical, and optimization techniques are used to build low complexity algebraic models. These models are tested, exploited, and improved using an adaptive sampling method we refer to as error maximization sampling (EMS). New simulation/experimental points are strategically chosen to help rule out the previous iterates’ surrogate with the goal of increasing model accuracy using relatively few costly simulation/experimentation.
By using low complexity, accurate surrogate models we are able to optimize large systems. Additionally, the surrogate models obtained by this approach provide insights to the system under study as they may reveal relationships and interactions between system variables and components.