Surrogate-Based Optimization of Simulated Energy Systems

Standard optimization techniques fall short of being able to solve simulated systems or, more generally, black-box systems since these techniques require the use of first and second derivatives of algebraic objectives and constraints. In these cases, black-box or derivative-free optimization (DFO) solvers are used. However, when the design of a process involves discrete variables and complex decisions, the resulting problem topology is often too complex for these DFO methods to solve reliably. To access standard algebraic optimization methods to solve simulated systems, we first build a set of algebraic surrogate models to describe the system. These models can be combined with design constraints and algebraic objectives or cost functions to formulate an algebraic optimization problem. This optimization model is to design all discrete and continuous process alternatives, technology choices, etc., while simultaneously solving for continuous operating conditions across the process network using a superstructure optimization framework. In order to solve such a large superstructure 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 test, exploited, and improved using an adaptive sampling method we refer to as error maximization sampling. New simulation points are strategically chosen to help rule out the previous iterates’ surrogate with the goal of increasing model accuracy using relatively few costly simulation. By using low complexity, accurate surrogate models we are able to optimize energy systems by efficiently exploring the full set of process alternatives to design low cost, environmentally conscious energy systems.