Towards a Multi-Output Kaizen Programming Algorithm

A model obtained from solving a symbolic regression problem is a surrogate model that represent a system with high accuracy. In the area of process system engineering, surrogate models substitute rigorous models in optimization and design process problems. As chemical processes have several outputs with a common physical-chemical phenomena, it is expected that the surrogate models generated for the outputs share terms or function basis. Kaizen Programming (KP) is a novel technique to solve symbolic regression problems, which do not assume any supposition of the form of the model in advance. This technique has shown a better performance than Genetic Programming on benchmarking functions. In this work, we propose an extension of Kaizen Programming, Multi-Output KP (MO-KP), to construct multi-output models in a single execution.The experimental evaluation was conducted on an extension of three classical benchmarking functions to multi-output scenarios, considering three different schemes of function basis sharing. The experimental results shown that MO-KP builds well fitted models, and it is even able to construct better models than single-output KP in some scenarios. The results also confirm that MO-KP favors the sharing of terms between the generated models. Finally, we found that the median execution time of MO-KP is in general shorter than the equivalent executions of single-output KP, but with larger variability in the distribution of the runtimes.