Abstract

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

Abstract

DC motors are frequently utilized in industrial and automation applications where accurate speed control is crucial. Although conventional Proportional-Integral-and Derivative (PID) controllers are widely utilized, their constant gain values make them less effective in managing dynamic loads and disturbances. It’s difficult to get optimal transient and steady-state performance with traditional PID tuning methods. To overcome these limitations, more adaptable and dependable control systems are needed. This study introduces a novel control strategy by optimizing a Fractional-Order PID (FOPID) controller using the Ant Lion Optimization (ALO) method. Mathematical modeling is used to determine the DC motor’s transfer function. An ALO, a metaheuristic algorithm, is then implemented to improve five FOPID parameters using Integral Timeweighted Absolute Error (ITAE). The simulation is done in MATLAB-Simulink software. According to the findings, the enhanced ALO-FOPID controller decreased settling time (0.0728 s) and rising time (0.0455 s) when compared to the PID controller, which is taken as a reference. It is noted that the proposed ALO-tuned FOPID demonstrated enhanced response over the conventional methods, demonstrating the usefulness of bioinspired algorithms for precision control applications. The comparison of the proposed methodology is also done with other studies during different operating conditions. The results show that intelligent optimizationbased control in industrial systems is feasible, which aids in the creation of reliable and flexible automation solutions.

Abstract

sup>Efficient service placement is a critical challenge in large-scale Internet of Things (IoT) environments, where fog computing must balance deployment cost and resource utilization under heterogeneous and dynamic conditions. To address this challenge, this paper proposes a hybrid metaheuristic approach that combines Rat Swarm Optimization (RSO) and Sunflower Optimization (SFO), leveraging the strong global exploration capability of RSO and the efficient local exploitation behavior of SFO. The proposed RSO–SFO framework integrates both strategies within a unified fitness function designed to minimize deployment cost while ensuring efficient allocation of fog resources. Extensive simulation results demonstrate that the proposed hybrid algorithm consistently outperforms state-of-the-art optimization techniques, including Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and the standalone RSO and SFO methods. Specifically, the RSO–SFO approach achieves a fitness improvement of 45.38%, reduces deployment costs by 43.71%, and maintains a high average resource utilization of 78.83%. These results confirm the effectiveness and robustness of the proposed hybrid strategy for optimal service placement in fog-based IoT environments.