An opportunity to optimize a black box system using algebraic substitution models identified using a symbolic regression approach.
Performing optimization is a very interesting task. In our daily lives, we might be interested in the best way to get to work in the shortest possible time, or perhaps the best grain size of our ground coffee to get a very tasty cup of coffee ☕. Industries also want to optimize things like supply chains, carbon emissions or waste accumulation.
There are a large number of possibilities for implementing optimization, depending on how the particular situation looks. Let me divide these situations into two parts for this article:
On the one hand, we may have knowledge about the physics, chemistry or biological products that govern the system under study. With this we could set up algebraic equations which accurately describe what we observe (first principles). These situations allow the use of commercially available solvers, such as GLPK, BARON, ANTIGONE, SBBor others, since we have closed form expressions and can calculate their derivatives.
On the other hand, we may not really have a sense of how our system looks or behaves. One way to derive information from this would be to perform experiments, that is, define certain inputs and observe what happens in the output. To optimize such a system, we could use heuristics, like particle swarm optimization, apply a genetic algorithm, or use powerful techniques like Bayesian optimization.
We could now dive deep into the literature and lots of discussion. But let’s keep it simple here. Let’s focus only on the second case, where we don’t have a closed and precise mathematical description of our system, or we don’t have time to find one because we are busy drinking coffee ☕. Let’s also assume that we have some past observations, but we can’t sample new data from our system for some reason.
Such a situation can arise when working with very expensive equipment, such as pharmaceuticals. You may have produced some batches of drug products in the past, but you can’t produce another one just for fun…