Feature extraction from optimization samples via ensemble based symbolic regression

Abstract

We demonstrate a means of knowledge discovery through feature extraction that exploits the search history of a search-based optimization run. We regress a symbolic model ensemble from optimization run search points and their objective scores. The frequency of a variable in the models of the ensemble indicates to what the extent it is an influential feature. Our demonstration uses a genetic programming symbolic regression software package that is designed to be “off-the-shelf”. By default, the only parameter needed in order to evolve a suite of models is how long the user is willing to wait. Then the user can easily specify which models should go forward in terms of sufficient accuracy and complexity. For illustration purposes, we consider a sequencing heuristic used to chain remote sensors from one to the next: “place the most reliable sensor last”. The heuristic is derived based on the mathematical form of the optimization objective function which places emphasis on the decision variable pertaining to the last sensor. Feature extraction on optimized sensor sequences demonstrates that the heuristic is usually effective though it is not always trustworthy. This is consistent with knowledge in sensor processing.