Linear matrix genetic programming as a tool for data-driven black-box control-oriented modeling in conditions of limited access to training data

Abstract

In the paper, a new evolutionary technique called Linear Matrix Genetic Programming (LMGP) is proposed. It is a matrix extension of Linear Genetic Programming and its application is data-driven black-box control-oriented modeling in conditions of limited access to training data. In LMGP, the model is in the form of an evolutionarily-shaped program which is a sequence of matrix operations. Since the program has a hidden state, running it for a sequence of input data has a similar effect to using well-known recurrent neural networks such as Long Short-Term Memory (LSTM) or Gated Recurrent Unit (GRU). To verify the effectiveness of the LMGP, it was compared with different types of neural networks. The task of all the compared techniques was to reproduce the behavior of a nonlinear model of an underwater vehicle. The results of the comparative tests are reported in the paper and they show that the LMGP can quickly find an effective and very simple solution to the given problem. Moreover, a detailed comparison of models, generated by LMGP and LSTM/GRU, revealed that the former are up to four times more accurate than the latter in reproducing vehicle behavior.