A Comparative Analysis of Metaheuristic Algorithms for Enhanced Parameter Estimation on Inverted Pendulum System Dynamics

We consider parameter estimation in dynamical systems from finite-time, partially observed trajectories. Rather than calibrating parameters within a prescribed model structure, we formulate parameter estimation as an inverse problem for a parameter-to-observation operator and learn its inverse directly from data using deep neural networks. Under appropriate identifiability assumptions, this inverse map is well-defined and continuous, making it amenable to approximation by neural networks. We discuss identifiability, stability, and noise sensitivity of the inverse problem and provide a simple error decomposition that separates approximation error from noise amplification. Numerical experiments on linear, nonlinear, nonautonomous, partially observed, noisy, and chaotic systems demonstrate accurate parameter recovery. For chaotic systems, recovery is validated through agreement of invariant dynamical quantities rather than pointwise trajectories.

Renewable energy is an attractive solution for water pumping systems particularly in isolated regions where the utility grid is unavailable. An attempt is made to improve the performance of solar photovoltaic water pumping system (SPVWPS) under partial shading condition. Under this condition, the power versus voltage curve has more than one maximum power point (MPP), which makes the tracking of global MPP not an easy task. Two MPP tracking (MPPT) strategies are proposed and compared for tracking MPP of SPVWPS under shading condition. The first method is based on the classical perturb and observe (P&O) and the other method is based on a Salp Swarm Algorithm (SSA). Based on extensive MATLAB simulation, it is found that the SSA method can provide higher photovoltaic (PV) generated power than the P&O method under shading condition. Consequently, the pump flowrate is increased. But, under normal distribution of solar radiation, both MPPT techniques can extract the maximum power but SSA is considered a time-consuming approach. Moreover, SSA is compared with particle swarm optimization (PSO) and genetic algorithm (GA). The obtained results ensure the superiority of SSA compared with PSO and GA. SSA has high successful rate of reaching true global MPP.

This study presents a comparative analysis of various optimization algorithms—Differential Evolution (DE), Particle Swarm Optimization (PSO), Arithmetic Optimization Algorithm (AOA), and Hippopotamus Optimization Algorithm (HOA)—for parameter identification in photovoltaic (PV) models. By utilizing RTC France solar cell data, we demonstrate that accurate parameter estimation is crucial for enhancing the efficiency of PV systems, ultimately supporting sustainable energy solutions. Our results indicate that DE achieves the lowest root mean square error (RMSE) of 0.0001 for the double-diode model (DDM), outperforming other methods in terms of accuracy and convergence speed. Both the HOA and PSO also show competitive RMSE values, underscoring their effectiveness in optimizing parameters for PV models. This research not only contributes to improved PV model precision but also aids in the broader effort to advance renewable energy technologies, thereby fostering a more sustainable future.

Research in the area of artificial neural networks has advanced at a rapid pace in recent times. The artificial neural network possesses a good ability to learn adaptively. The decision process in an artificial neural network is based on certain nonlinear operations. Such nonlinearities are useful: i) in improving the convergence speed (of the algorithm); ii) to provide more general nonlinear mapping between input-output signals; and iii) to reduce the effect of outliers in the measurements. One of the most successful artificial neural networks is the so-called feed forward neural network. In this chapter first the description of the feed forward neural network and its training algorithms is given. Next, parameter estimation using this approach is discussed. The presentation of training algorithms is such that it facilitates MATLAB implementation. Subsequently, recurrent neural networks are described. Several schemes based on recurrent neural networks are presented for parameter estimation of dynamical systems. Subsequently, the genetic algorithm is described and its application to parameter estimation considered.

Reasonable optimal operation policy for complex multiple reservoir systems is very important for the safe and efficient utilization of water resources. The operation policy of multiple hydropower reservoirs should be optimized to maximize total hydropower generation, while ensuring flood control safety by effective and efficient storage and release policy of multiple reservoirs. To achieve this goal, a new meta-heuristic algorithm, salp swarm algorithm (SSA), is used to optimize the joint operation of multiple hydropower reservoirs for the first time. SSA is a competitive bio-inspired optimizer, which has received substantial attention from researchers in a wide variety of applications in finance, engineering, and science because of its little controlling parameters and adaptive exploratory behavior. However, it still faces few drawbacks such as lack of exploitation and local optima stagnation, leading to a slow convergence rate. In order to tackle these problems, multiple strategies combining sine cosine operator, opposition-based learning mechanism, and elitism strategy are applied to the original SSA. The sine cosine operator is applied to balance the exploration and exploitation over the course of iteration; the opposition-based learning mechanism is used to enhance the diversity of the swarm; and the elitism strategy is adopted to find global optima. Then, the improved SSA (ISSA) is compared with six well-known meta-heuristic algorithms on 23 classical benchmark functions. The results obtained demonstrate that ISSA outperforms most of the well-known algorithms. Then, ISSA is applied to optimal operation of multiple hydropower reservoirs in the real world. A multiple reservoir system, namely Xiluodu Reservoir and Xiangjiaba Rservoir, in the upper Yangtze River of China are selected as a case study. The results obtained show that the ISSA is able to solve a real-world optimization problem with complex constraints. In addition, for the typical flood with a 100 return period in 1954, the maximum hydropower generation of multiple hydropower reservoirs is about 6671 GWh in the case of completing the flood control task, increasing by 1.18% and 1.77% than SSA and Particle Swarm Optimization (PSO), respectively. Thus, ISSA can be used as an alternative effective and efficient tool for the complex optimization of multiple hydropower reservoirs. The water resources in the river basin can be further utilized by the proposed method to cope with the increasingly serious climate change.

Formulation of a Practical Algorithm for Parameter Estimation with Process and Measurement Noise

Optimization methods have been developed by many researchers. Especially, the methods based on Evolutionary Algorithms (EAs) have received increased attention from diversity fields. Recently, bacterial foraging algorithm mimicked bacterial behavior has been introduced by Passino. However, his work did not implement an important bacterial behavior regulating division so-called 'quorum sensing'. The quorum-sensing is a chemical communication including producing, releasing, detecting, and responding to small hormone-like molecules termed auto inducers. This communication allows bacteria to coordinate the behavior of the group. This paper proposes an optimization algorithm based on the bacterial quorum sensing. In order to estimate the performance of the algorithm, we use Lorenz Chaotic systems to identity unkonwn parameters. Experimental results show that this proposed method can achieve good performance.

This paper describes the evaluation of the spreading factor inertia weight Particle Swarm Optimization (PSO) for the fuzzy logic control (FLC) of FES-assisted paraplegic indoor rowing exercise (FES-rowing). The FES-rowing is introduced as a total body exercise for rehabilitation of lower extremities through the application of functional electrical stimulation (FES). FLC is used to control the knee trajectories for smooth rowing manoeuvre and minimize the total electrical stimulation required by the muscles. PSO is implemented to optimize the parameter of the FLC. The objective function specified is to minimize the mean squared error of knee angle trajectory. The inertia weight of the PSO is updated using spreading factor technique and it performance is compared to the performance of PSO with time variant inertia weight. In view of good results obtained, it is concluded that Spreading Factor Inertia weight PSO is able to obtain the optimal parameter for FLC of FES-rowing.

A newly hybrid nature-inspired algorithm called HSSGWOA is presented with the combination of the salp swarm algorithm (SSA) and grey wolf optimizer (GWO). The major idea is to combine the salp swarm algorithm's exploitation ability with the grey wolf optimizer's exploration ability to generate both variants' strength. The proposed algorithm uses to tune the parameters of the integral sliding mode controller (ISMC) that design to improve the dynamic performance of the two-link flexible joint manipulator. The efficiency and the capability of the proposed hybrid algorithm are evaluated based on the selected test functions. It is clear that when compared to other algorithms like SSA, GWO, differential evolution (DE), gravitational search algorithm (GSA), particles swarm optimization (PSO), and whale optimization algorithm (WOA). The ISMC parameters were tuned using the SSA, which was then compared to the HSSGWOA algorithm. The simulation results show the capabilities of the proposed algorithm, which gives an enhancement percentage of 57.46% compared to the standard algorithm for one of the links, and 55.86% for the other.

Salp Swarm Algorithm (SSA) is a new type of metaheuristic and has shown superiority over other well-known algorithms such as Particle Swarm Optimization and Grey Wolf Optimizer in solving challenging optimization problems. Despite its superior performance, SSA still has problems such as insufficient convergence speed. Moreover, its local optima avoidance ability is not as good as those evolutionary algorithms using crossover operators. In this paper, we propose a modified Salp Swarm Algorithm (m-SSA) which improves the exploitation and exploration of SSA by integrating random walk strategy and especially enhances exploration by adding a new controlling parameter. In addition, a simulated annealing-type acceptance criterion is adopted to accept the fittest follower position as the new best leader position. The performance of the proposed algorithm is benchmarked on a set of classical functions and CEC2014 test suite. The proposed algorithm (m-SSA) outperforms SSA significantly on most test functions. When compared with other state-of-the-art metaheuristics, it also presents very competitive results. Besides, we apply the proposed algorithm on training feedforward neural networks (FNNs) and the results prove the effectiveness and efficiency of m-SSA.

The increasing adoption of solar energy as a clean and sustainable power source has intensified research efforts toward developing more efficient photovoltaic (PV) cells. These cells exhibit nonlinear characteristics that are significantly influenced by variations in irradiance and temperature. Accurate estimation of PV model parameters plays a crucial role in maximizing performance, particularly via precise maximum power point (MPP) tracking. This paper presents a new hybrid metaheuristic algorithm that combines the global exploration capability of the Bat Algorithm (BA) with local exploitation efficiency of the Crow Search Algorithm (CR) to optimize PV parameter estimation. The proposed approach is tested using Single-Diode (SDM), Double-Diode (DDM), and Triple-Diode (TDM) models based on the RTC France dataset. The hybrid model demonstrates better convergence behavior and robustness compared to conventional approaches. Qualitatively, it effectively manages parameter uncertainty; quantitatively, it achieves RMSE values of 0.00077299 (SDM), 0.0008215 (DDM), and 0.0008068 (TDM), outperforming traditional algorithms such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

A prediction method based on an improved salp swarm algorithm (ISSA) and extreme learning machine (ELM) was proposed to improve line heating and forming. First, a three-dimensional transient numerical simulation of line heating and forming was carried out by applying a finite element simulation, and the influence of machining parameters on deformation was studied. Second, a prediction model for the ELM network was established based on simulation data, and the deformation of hull plate was predicted by the training network. Additionally, swarm intelligence optimization, particle swarm optimization (PSO), the seagull optimization algorithm (SOA), and the salp swarm algorithm (SSA) were studied while considering the shortcomings of the ELM, and the ISSA was proposed. Input weights and hidden layer biases of the ELM model were optimized to increase the stability of prediction results from the PSO, SOA, SSA and ISSA approaches. Finally, it was shown that the prediction effect of the ISSA–ELM model was superior by comparing and analyzing the prediction effect of each prediction model for line heating and forming.

This paper addresses the economic dispatch problem in thermal power systems using four metaheuristic optimization algorithms: Particle Swarm Optimization (PSO), Crow Search Algorithm (CSA), Salp Swarm Algorithm (SSA), and JAYA algorithm. A deterministic formulation is adopted to minimize the total generation cost over a 24-hour horizon while meeting generator operating constraints and ensuring load balance. A randomly generated dispatch strategy is also included as a baseline. Each algorithm is independently executed 100 times to evaluate robustness, repeatability, and associated CO2 emissions. Among all methods, PSO achieves the best performance, yielding the lowest total dispatch cost of $82,412.78 and the smallest relative standard deviation (0.12%), along with total CO2 emissions of 1901.65 kg. Compared to other techniques, PSO provides cost improvements of 0.20% over CSA, 0.28% over SSA, 0.94% over JAYA, and a substantial 29.23% reduction with respect to the random baseline. Moreover, all metaheuristic strategies significantly outperform the random dispatch, demonstrating their ability to generate high-quality and feasible solutions. The PSO-based dispatch strategy efficiently allocates hourly power outputs within technical constraints, introducing a controlled overgeneration margin to compensate for system losses. These results confirm the effectiveness of metaheuristic approaches in complex power system optimization tasks and establish a foundation for future work involving renewable integration, emission constraints, and uncertainty modeling.

This study introduces a derivative of the well-known optimization algorithm, Big Bang–Big Crunch (BB–BC), named Nuclear Fission–Nuclear Fusion-based BB–BC, simply referred to as N2F. Broadly preferred in the engineering optimization community, BB–BC provides accurate solutions with reasonably fast convergence rates for many engineering problems. Regardless, the algorithm often suffers from stagnation issues. More specifically, for some problems, BB–BC either converges prematurely or exploits the promising regions inefficiently, both of which prevent obtaining the optimal solution. To overcome such problems, N2F algorithm is proposed, inspired by two major phenomena of nuclear physics: fission and fusion reactions. In N2F, two concepts named “Nuclear Fission” and “Nuclear Fusion” are introduced, replacing the “Big Bang” and “Big Crunch” phases of BB–BC, respectively. With the “Nuclear Fission” phase represented through a parameter named amplification factor, premature convergence issues are eliminated to a great extent. Meanwhile, convergence rate and exploitation capability of the algorithm are enhanced largely through a precision control parameter named magnification factor, in the “Nuclear Fusion” phase. The performance of N2F algorithm is investigated through unconstrained test functions and compared with the conventional BB–BC and other metaheuristics including genetic algorithm, Particle Swarm Optimization (PSO), Artificial Bee Colony Optimization (ABC), Drone Squadron Optimization (DSO) and Salp Swarm Algorithm (SSA). Then, further analyses are performed with constrained design benchmarks, validating the applicability of N2F to engineering problems. With superior statistical performance compared to BB–BC, GA, PSO, ABC, DSO and SSA in unconstrained problems and improved results with respect to the literature studies, N2F is proven to be an efficient and robust optimization algorithm.

The marine main diesel engine rotational speed automatic control plays a significant role in determining the optimal main diesel engine speed under impacting on navigation environment conditions. In this article, the application of fuzzy logic control theory for main diesel engine speed control has been associated with Particle Swarm Optimization (PSO). Firstly, the controller is designed according to fuzzy logic control theory. Secondly, the fuzzy logic controller will be optimized by Particle Swarm Optimization (PSO) in order to obtain the optimal adjustment of the membership functions only. Finally, the fuzzy logic controller has been completely innovated by Particle Swarm Optimization algorithm. The study results will be represented under digital simulation form, as well as comparison between traditional fuzzy logic controller with fuzzy logic control–particle swarm optimization speed controller being obtained.