TITLE:
Regression Neural Networks for Emulating Evolutionary Algorithm Predictions in Optimal Control
AUTHORS:
Iulian Arama, Viorel Mînzu
KEYWORDS:
Evolutionary Algorithm, Machine Learning, Optimal Control, Simulation
JOURNAL NAME:
Open Journal of Optimization,
Vol.15 No.2,
May
7,
2026
ABSTRACT: Many controlled processes, such as biochemical ones, are repetitive, similar to batch-organized processes. They generate Optimal Control Problems (OCPs) solved by optimal controllers, which often predict the best control values over a prediction horizon using a process model (PM). The latter can encompass imprecise, incomplete, and uncertain knowledge, nonlinearities, or may represent a distributed-parameter system, among other features. Using metaheuristics like the Evolutionary Algorithm (EA) within control structures is a practical approach for specific OCPs. The main drawback of this solution is its high computational demands, which can exceed the sampling period. Previously, the authors explored a new topic: whether a machine learning (ML) algorithm could “learn” the optimal behavior of the couple (EA and PM). Multilinear regression functions were trained and utilized within the ML controller, leading to a significant reduction in its execution time. This article extends the research and proposes using Regressive Neural Networks (RNNs) instead of regression functions, because they have limited capacity to capture nonlinearities. RNNs are more complex regression models, with a greater capacity to model EA-PM couples. The article meticulously describes how the training data is obtained. Algorithms for constructing the RNNs, developing the RNN predictor, and simulating the closed-loop are also proposed. The results are convincing: a) the control-loop dynamic was practically identical with that using the EA predictor; b) the performance indices were practically the same; c) the controller’s execution time decreased remarkably. Using MATLAB for the Park Ramirez Problem, this time was 38 seconds, with the multilinear regression functions, it was 0. 08 seconds, and now with the RNN predictor, it is 0.0549 seconds. This outstanding reduction in prediction time opens the possibility to apply Receding Horizon Control (RHC) not only to slow processes but also to fast ones, which have small time constants.