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Yayın A modified artificial protozoa optimizer for robust parameter identification in nonlinear dynamic systems(Multidisciplinary Digital Publishing Institute (MDPI), 2026) İzci, Davut; Ekinci, Serdar; Yüksek, Gökhan; Rashdan, Mostafa; Bektaş Güneş, Burcu; Güngör, Muhammet İsmail; Salman, MohammadAccurate 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.Yayın A novel hyperbolic tangent-augmented controller framework for temperature control in jacketed continuous stirred tank reactors(Nature Research, 2026) İzci, Davut; Ekinci, Serdar; Ökten, İrfan; Çınar, Rıdvan Fırat; Rashdan, Mostafa; Salman, Mohammad; Bektaş Güneş, Burcu; Ahmad, Mohd AshrafAccurate temperature regulation of jacketed continuous stirred tank reactors (CSTRs) remains a challenging task due to strong nonlinearities, tight coupling between mass and energy balances, and sensitivity to disturbances and operating-point variations. In this study, a novel augmented proportional–integral–derivative (PID) controller incorporating a hyperbolic tangent nonlinearity (APID-T) is proposed for robust temperature control of an exothermic CSTR. The controller structure extends the classical PID framework by embedding a bounded nonlinear term that enhances transient shaping and robustness while preserving simplicity and practical implementability. The tuning of the APID-T parameters is formulated as a constrained nonlinear optimization problem, where a composite objective function combining normalized overshoot and integral squared error is minimized. To solve this problem efficiently, the recently developed Schrödinger optimizer (SRA) is employed, exploiting its balanced exploration–exploitation mechanism. A detailed nonlinear dynamic model of the jacketed CSTR is considered, and stability characteristics around the nominal operating point are examined to ensure meaningful closed-loop operation. The proposed SRA-based APID-T design is extensively evaluated through comparative simulations against several state-of-the-art metaheuristic optimizers and alternative controller structures, including PI, PID with filter, two-degree-of-freedom PID, and fractional-order PID controllers. Performance is assessed using statistical indicators, convergence behavior, and time-domain response metrics under identical optimization settings. In addition, widely used error performance criteria, including the integral squared error, integral time absolute error, and integral time squared error, are computed to provide a comprehensive quantitative assessment of the tracking performance. The results demonstrate that the SRA-tuned APID-T controller consistently achieves lower objective-function values, faster convergence, reduced settling time, and significantly smaller overshoot compared with the competing approaches. Furthermore, frequency-domain analysis based on the Bode characteristics of the linearized open-loop system confirms favorable stability margins, supporting the robustness of the proposed control structure. Additional stability and robustness evaluations are conducted under practical non-ideal conditions, including feed-temperature disturbances, measurement noise, and multiple setpoint variations, where the controller maintains stable and accurate temperature regulation across the considered operating scenarios.Yayın Global-best-guided electric eel foraging optimizer for robust parameter identification of Lorenz and memristive chaotic systems(Nature Research, 2026) İzci, Davut; Ekinci, Serdar; Ökten, İrfan; Tümen, Vedat; Bektaş Güneş, Burcu; Rashdan, Mostafa; Salman, MohammadAccurate parameter identification in chaotic dynamical systems constitutes a challenging inverse problem due to extreme sensitivity to initial conditions, pronounced nonlinearity, and highly multimodal error landscapes. To address these challenges, this study proposes a global-best-guided electric eel foraging optimization algorithm (g-EEFO), which enhances the original EEFO framework by embedding a behavior-aware and phase-dependent global learning mechanism. Unlike existing EEFO variants that rely solely on stochastic foraging dynamics, g-EEFO integrates global-best information as a soft cooperative signal that modulates the interacting, resting, hunting, and migrating behaviors without overriding them. In this way, global guidance acts as a directional bias rather than a dominant attractor, preserving ecological diversity while strengthening convergence coherence. For the first time, EEFO and its improved variant are applied to chaotic system parameter estimation. The proposed method is evaluated on two representative models: the classical Lorenz system and a structurally richer memristive chaotic system. Extensive numerical experiments, including statistical analysis, convergence profiling, boxplot distributions, and parameter-evolution trajectories, demonstrate the clear superiority of g-EEFO over several state-of-the-art metaheuristics. For the Lorenz system, g-EEFO achieves a best mean squared error of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:7.02\times\:{10}<^>{-26}$$\end{document}, which is six to twenty orders of magnitude lower than competing methods, while maintaining an exceptionally small standard deviation (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:4.58\times\:{10}<^>{-20}$$\end{document}). For the memristive system, g-EEFO attains a best error of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:8.19\times\:{10}<^>{-19}$$\end{document}, again outperforming all benchmarks by several orders of magnitude and exhibiting the highest run-to-run stability. In both cases, the estimated parameters match the true system values with near-perfect precision. These results confirm that the proposed behavior-aware global guidance fundamentally reshapes the search dynamics of EEFO, yielding substantial gains in convergence stability, numerical accuracy, and robustness. The g-EEFO therefore provides a powerful and reliable alternative for chaotic parameter identification and nonlinear system reconstruction across diverse dynamical regimes.Yayın Hybrid learning-driven golden jackal optimizer for reliable parameter estimation of nonlinear memristive chaotic systems(Springer Science and Business Media B.V., 2026) İzci, Davut; Ekinci, Serdar; Rizk-Allah, Rizk M.; Tümen, Vedat; Rashdan, Mostafa; Salman, Mohammad; Bektaş Güneş, Burcu; İnağ, YasinAccurate identification of parameters in chaotic and nonlinear systems is essential for ensuring precise modeling, control, and prediction of complex dynamical behaviors. However, conventional metaheuristic algorithms often struggle to maintain an effective balance between exploration and exploitation, leading to premature convergence and estimation inaccuracies. To address these challenges, this study proposes an enhanced golden jackal optimizer (en-GJO) that integrates three complementary mechanisms (Laplacian crossover learning, elite group learning, and opposition repair learning). These hybrid strategies collectively strengthen population diversity, accelerate convergence, and prevent stagnation, thereby improving both the global search capability and local refinement accuracy of the original GJO. The effectiveness of the en-GJO is first validated through extensive benchmarking on twenty-three standard test functions, including unimodal, multimodal, and fixed-dimensional multimodal problems. Comparative results against nine well-established metaheuristics (such as SSA, SCA, HHO, AEO, EO, GBO, RUN, and ARO) demonstrate that en-GJO achieves superior convergence precision and robustness, consistently yielding the lowest mean and standard-deviation values across all categories. To further verify its real-world applicability, the en-GJO is applied to the parameter identification of a memristive chaotic system, formulated as a nonlinear optimization problem using a least-squares-based objective function. Simulation results reveal that the proposed method attains the most accurate estimates of the system parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {a,b,c,d} \right)$$\end{document}, with negligible deviation from their true values. Statistical analyses and convergence profiles confirm that en-GJO not only converges faster but also delivers more stable and repeatable performance than competing algorithms. In comparative evaluations with reported techniques such as PSO, ABC, SPSSA, GWO, POA, and FPPOA, the en-GJO achieves the smallest cost value (1.3850 x 10-13) and with a mean fitness of 1.0507 x 10-9 and a standard deviation of 2.5392 x 10-9, outperforming all compared algorithms by several orders of magnitude. The estimated system parameters converge to their true values with error rates below 0.001%, confirming the high accuracy, stability, and repeatability of the proposed approach. In summary, the proposed en-GJO offers a highly accurate, stable, and computationally efficient solution for parameter estimation in nonlinear and chaotic systems.
