Surrogate mixed integer nonlinear models by means of regression splines
Complex phenomena can be accurately described by means of data-driven mathematical models. However, being able to integrate these models within a mathematical optimization framework can be, in general, very challenging. In fact, many of these data-driven models are `black-box', in the sense that they do not have an explicit mathematical formula which describes them. In other cases, even if an explicit expression exists, including it into a mathematical optimization model may make solving the problem computationally intractable. We propose to use a special kind of surrogate models, regression splines, to deal with functions of this kind which appear in Mixed Integer Nonlinear Programming (MINLP) problems. The choice of spline functions is not arbitrary. On one hand, they offer a good compromise between accuracy and complexity. On the other hand, their functional form allows us to exploit separability and approximate general non-convex MINLPs by a more tractable subclass of problems.
Keywords: MINLP Regression splines