# A Modified Artificial Protozoa Optimizer for Robust Parameter Identification in Nonlinear Dynamic Systems

## TL;DR

A modified optimization algorithm is developed to improve parameter identification in complex nonlinear and chaotic systems.

## Contribution

The mAPO algorithm integrates global exploration and local refinement mechanisms for robust optimization in dynamic systems.

## Key findings

- mAPO outperforms original APO on CEC2017 benchmarks with better mean performance and reduced variability.
- mAPO achieves exact parameter reconstruction in PMSM with zero error across all runs.
- mAPO shows superior convergence and stability in both static and time-varying scenarios.

## Abstract

Accurate parameter identification in nonlinear and chaotic dynamic systems requires optimization algorithms that can reliably balance global exploration and local refinement in complex, multimodal search landscapes. To address this challenge, a modified artificial protozoa optimizer (mAPO) is developed in this study by embedding two complementary mechanisms into the original artificial protozoa optimizer: a probabilistic random learning strategy to enhance population diversity and global search capability, and a Nelder–Mead simplex-based local refinement stage to improve exploitation and fine-scale solution adjustment. The general optimization performance and scalability of the proposed framework are first evaluated using the CEC2017 benchmark suite. Statistical analyses conducted over shifted and rotated, hybrid, and composition functions demonstrate that mAPO achieves improved mean performance and reduced variability compared with the original APO, indicating enhanced robustness in high-dimensional and complex optimization problems. The effectiveness of mAPO is then examined in nonlinear system identification applications involving chaotic dynamics. Offline and online parameter identification experiments are performed on the Rössler chaotic system and a permanent magnet synchronous motor, including scenarios with abrupt parameter variations. Comparative simulations against APO and several state-of-the-art optimizers show that mAPO consistently yields smaller objective function values, more accurate parameter estimates, and superior statistical stability. In the PMSM case, exact parameter reconstruction with zero error is achieved across all independent runs, while rapid and smooth convergence is observed under both static and time-varying conditions.