Teaching and Research Optimization Algorithms Based on Social Networks for Global Optimization and Real Problems

Solar photovoltaic systems are becoming increasingly popular due to their outstanding environmental, economic, and technical characteristics. To simulate, manage, and control photovoltaic (PV) systems, the primary challenge is identifying unknown parameters accurately and reliably as early as possible using a robust optimization algorithm. This paper proposes a newly developed cheetah optimizer (CO) and improved CO (ICO) to extract parameters from various PV models. This algorithm, inspired by cheetah hunting behavior, includes several basic strategies: searching, sitting, waiting, and attacking. Although this algorithm has shown remarkable capabilities in solving large-scale problems, it needs improvement concerning its convergence speed and computing time. Here, an improved CO (ICO) is presented to identify solar power model parameters for this purpose. The ICO algorithm’s search phase is controlled based on the leader’s position. The step length is adjusted following the sorted population. As a result of this updated operator, the algorithm can perform global and local searches. Furthermore, the interaction factor during the attack phase is adjusted based on the position of the prey, and a random value controls the turning factor. Single-, double-, and PV module models are investigated to test the ICO’s parameter estimation performance. Statistical analysis uses the minimum, mean, maximum, and standard deviation. Furthermore, to improve confidence in the test results, Wilcoxon and Freidman rank nonparametric tests are also performed. Compared with other state-of-the-art optimization algorithms, the CO and ICO algorithms are proven to be highly reliable and accurate when identifying PV parameters. According to the results, the ICO and CO obtained the first- and second-best sum ranking results for the studied PV models among 12 applied algorithms. Despite this, the ICO algorithm reduces the CO’s computation time by 40% on average. Additionally, ICO’s convergence speed is high, reaching an optimal solution in less than 25,000 function evaluations in most cases.

<abstract><p>With the widespread application of metaheuristic algorithms in engineering and scientific research, finding algorithms with efficient global search capabilities and precise local search performance has become a hot topic in research. The osprey optimization algorithm (OOA) was first proposed in 2023, characterized by its simple structure and strong optimization capability. However, practical tests have revealed that the OOA algorithm inevitably encounters common issues faced by metaheuristic algorithms, such as the tendency to fall into local optima and reduced population diversity in the later stages of the algorithm's iterations. To address these issues, a multi-strategy fusion improved osprey optimization algorithm is proposed (IOOA). First, the characteristics of various chaotic mappings were thoroughly explored, and the adoption of Circle chaotic mapping to replace pseudo-random numbers for population initialization improvement was proposed, increasing initial population diversity and improving the quality of initial solutions. Second, a dynamically adjustable elite guidance mechanism was proposed to dynamically adjust the position updating method according to different stages of the algorithm's iteration, ensuring the algorithm maintains good global search capabilities while significantly increasing the convergence speed of the algorithm. Lastly, a dynamic chaotic weight factor was designed and applied in the development stage of the original algorithm to enhance the algorithm's local search capability and improve the convergence accuracy of the algorithm. To fully verify the effectiveness and practical engineering applicability of the IOOA algorithm, simulation experiments were conducted using 21 benchmark test functions and the CEC-2022 benchmark functions, and the IOOA algorithm was applied to the LSTM power load forecasting problem as well as two engineering design problems. The experimental results show that the IOOA algorithm possesses outstanding global optimization performance in handling complex optimization problems and broad applicability in practical engineering applications.</p></abstract>

Global optimisation problems in high-dimensional and infinite-dimensional spaces arise in various real-world applications such as engineering, economics and finance, geophysics, biology, machine learning, optimal control, etc. Among stochastic approaches to global optimisation, biology-inspired methods are currently very popular in the literature. Bio-inspired approaches imitate natural ecological and evolutionary processes and are reported to be efficient in a large number of practical study cases. However, many bio-inspired methods can possess some vital drawbacks. For example, due to their semi-empirical nature, convergence to the globally optimal solution cannot always be guaranteed. Another major obstacle is that the existing methods often struggle with higher dimensionality of the space of parameters, which results in a slow convergence. Moreover, it is often difficult to adjust the dimensionality of the space of parameters in the corresponding computer code for a practical realisation of the optimisation method. Here, we present a bio-inspired global stochastic optimisation method applicable in Hilbert function spaces. The proposed method is an evolutionary algorithm inspired by the Darwin’s famous idea of survival of the fittest and is, therefore, referred to as the ‘Survival of the Fittest Algorithm’ (SoFA). Mathematically, the convergence of SoFA is a consequence of the fundamental property of localisation of probabilistic measure in a Hilbert space and we rigorously prove the convergence of the introduced algorithm for a generic class of functionals. The approach is simple in terms of practical coding. As an insightful, real-world problem, we apply our method to find the globally optimal trajectory for the daily vertical migration of zooplankton in the ocean and lakes, this phenomenon is considered to be the largest synchronised movement of biomass on Earth. We maximise fitness in a function space derived from a von-Foerster stage-structured population model with biologically realistic parameters. We show that for problems of fitness maximisation in high-dimensional spaces, SoFA provides better performance as compared to some other stochastic global optimisation algorithms. We highlight the links between the new optimisation algorithm and natural selection processes in ecosystems occurring within a population via gradual exclusion of competitive con-specific strains.

Random learning gradient based optimization for efficient design of photovoltaic models

As countries attach importance to environmental protection, clean energy has become a hot topic. Among them, solar energy, as one of the efficient and easily accessible clean energy sources, has received widespread attention. An essential component in converting solar energy into electricity are solar cells. However, a major optimization difficulty remains in precisely and effectively calculating the parameters of photovoltaic (PV) models. In this regard, this study introduces an improved rime optimization algorithm (RIME), namely ERINMRIME, which integrates the Nelder-Mead simplex (NMs) with the environment random interaction (ERI) strategy. In the later phases of ERINMRIME, the ERI strategy serves as a complementary mechanism for augmenting the solution space exploration ability of the agent. By facilitating external interactions, this method improves the algorithm’s efficacy in conducting a global search by keeping it from becoming stuck in local optima. Moreover, by incorporating NMs, ERINMRIME enhances its ability to do local searches, leading to improved space exploration. To evaluate ERINMRIME's optimization performance on PV models, this study conducted experiments on four different models: the single diode model (SDM), the double diode model (DDM), the three-diode model (TDM), and the photovoltaic (PV) module model. The experimental results show that ERINMRIME reduces root mean square error for SDM, DDM, TDM, and PV module models by 46.23%, 59.32%, 61.49%, and 23.95%, respectively, compared with the original RIME. Furthermore, this study compared ERINMRIME with nine improved classical algorithms. The results show that ERINMRIME is a remarkable competitor. Ultimately, this study evaluated the performance of ERINMRIME across three distinct commercial PV models, while considering varying irradiation and temperature conditions. The performance of ERINMRIME is superior to existing similar algorithms in different irradiation and temperature conditions. Therefore, ERINMRIME is an algorithm with great potential in identifying and recognizing unknown parameters of PV models.

The critical worldwide revolution towards clean energy has prompted the improvement of studies on the fabrication of high-performance solar cells. In this regard, rendering an accurate model of the solar cell for performance evaluation in the simulation could be essential. So far, several models have been proposed for the solar cell, including single-diode model (SDM), double-diode model (DDM), and three-diode model (TDM). By increasing the number of diodes considered in the equivalent circuit in order to deliver a more accurate model, the number of unknown parameters which must be identified will be increased as well. Therefore, presenting an efficient algorithm to estimate these parameters becomes an interesting issue in recent years. In this study, an improved optimization algorithm, called springy whale optimization algorithm (SWOA), is proposed to estimate the model parameters of solar cells. SWOA is a generalization of the WOA and has the advantages of high convergence speed, global search capability, and high robustness over it. In order to inquire the efficiency of SWOA, this algorithm is posed to estimate the parameters of models of solar cells and photovoltaic (PV) modules as well; the simulation results authenticate the supremacy of the proposed algorithm. Furthermore, the effectiveness of SWOA algorithm in the practical application has been evaluated using commercial modules, including polycrystalline (SW255), multi-crystalline (KC200GT), and monocrystalline (SM55). This assessment is carried out for various operating conditions under different irradiance and temperature conditions, which yield variations in the parameters of the PV model. The results obtained from various experimental setups confirm the high performance and robustness of the proposed algorithm.

A reconsideration on the resolution of phase stability analysis using stochastic global optimization methods: Proposal of a reliable set of benchmark problems

Computationally efficient and time‐memory saving compact algorithms become a keystone for solving global optimization problems, particularly the real world problems; which involve devices with limited memory or restricted use of battery power. Compact optimization algorithms represent a probabilistic view of the population to simulate the population behaviour as they broadly explores the decision space at the beginning of the optimization process and keep focus on to search the most promising solution, therefore narrows the search space, moreover few number of parameters need be stored in the memory thus require less space and time to compute efficiently. Role of population‐based algorithms remain inevitable as compact algorithms make use of the efficient search ability of these population based algorithms for optimization but only through a probabilistic representation of the population space in order to optimize the real world problems. Artificial bee colony (ABC) algorithm has shown to be competitive over other population‐based algorithms for solving optimization problems, however its solution search equation contributes to its insufficiency due to poor exploitation phase coupled with low convergence rate. This paper, presents a compact Artificial bee colony (cABC) algorithm with an improved solution search equation, which will be able to search an optimal solution to improve its exploitation capabilities, moreover in order to increase the global convergence of the proposed algorithm, an improved approach for population sampling is introduced through a compact distribution which helps in maintaining a good balance between exploration and exploitation search abilities of the proposed compact algorithm with least memory requirements, thus became suitable for limited hardware access devices. The proposed algorithm is evaluated extensively on a standard set of benchmark functions proposed at IEEE CEC'13 for large‐scale global optimization (LSGO) problems. Numerical results prove that the proposed compact algorithm outperforms other standard optimization algorithms.

Accurate parameter estimation for photovoltaic (PV) cell or module models is crucial for enhancing the performance of PV systems through simulation, evaluation, and control. However, due to the nonlinear and multi-modal nature of PV models, parameter extraction remains a challenging task. To address this issue, this study proposes an improved mayfly optimization algorithm (MOA) for PV cell parameter estimation using measured current–voltage data. To strengthen the algorithm’s global search capability, Lévy-distributed random numbers are introduced to replace uniformly distributed numbers in the mayflies’ position updates. The heavy-tailed property of Lévy flight enables a broader search range, effectively preventing the algorithm from converging to local optima. Furthermore, a chaotic local search operator is incorporated into MOA to refine its local exploitation ability. The proposed algorithm, termed LFC-MOA (Lévy Flight and Chaos-based Mayfly Optimization Algorithm), is rigorously evaluated on three benchmark PV cell datasets. Experimental results demonstrate its effectiveness in accurately identifying PV cell parameters.

To address the problems of local optima and insufficient convergence accuracy in parameter identification of primary frequency regulation (PFR) for steam turbines, this paper proposed a hybrid identification method that integrated an Improved Bayesian Optimization (IBO) algorithm and an Improved Whale Optimization Algorithm (IWOA). By initializing the Bayesian parameter population using Tent chaotic mapping and the reverse learning strategy, employing a radial basis kernel function hyperparameter training mechanism based on the Adam optimizer and optimizing the Expected Improvement (EI) function using the Limited-memory Broyden–Fletcher– Goldfarb–Shanno with Bounds (L-BFGS-B) method, IBO was proposed to obtain the optimal candidate set with the smallest objective function value. By introducing a nonlinear convergence factor and the adaptive Levy flight perturbation strategy, IWOA was proposed to obtain locally optimized optimal solutions. By using the reverse-guided optimization mechanism and employing a fitness-oriented selection strategy, the optimal solution was chosen to complete the closed-loop process of reverse learning feedback. Nine standard test functions and the Proportional Integral Derivative (PID) parameter identification of the electro-hydraulic servo system in a 330 MW steam turbine were presented as examples. Compared with Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Bayesian Optimization (BO) and Particle Swarm Optimization-Grey Wolf Optimizer (PSO-GWO), the Improved Bayesian Optimization-Whale Optimization Algorithm (IBO-WOA) proposed in this paper has been validated to effectively avoid the problem of getting stuck in local optima during complex optimization and has high parameter recognition accuracy. Meanwhile, an Out-Of-Distribution (OOD) Test based on noise injection had demonstrated that IBO-WOA had good robustness. The time constant identification of the steam turbine were carried out using IBO-WOA under two experimental conditions, and the identification results were input into the PFR model. The simulated power curve can track the experimental measured curve well, proving that the parameter identification results obtained by IBO-WOA have high accuracy and can be used for the modeling and response characteristic analysis of the steam turbine PFR.

Parameters identification of photovoltaic models by using an enhanced adaptive butterfly optimization algorithm

Optimal foraging algorithm for global optimization

This paper presents the estimation method of solar irradiance in W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> based on the short circuit current output produce by the photovoltaic module. The proposed solar irradiance estimation method is derived using photovoltaic mathematical model. Therefore, photovoltaic module modeling is required to develop the proposed estimation method. The modeling includes the identification of photovoltaic module diode ideality factor using recursive iteration and series resistance identification using photovoltaic model equation. The reminding modeling parameters can be obtained from the given photovoltaic module manufacturer datasheet. With all the required parameters in place the solar irradiance can be estimated using equation derived from the photovoltaic model. The proposed solar irradiance estimation method is evaluated using a 80W 36 cells polycrystalline photovoltaic module in the field and the results are validated with a World Meteorological Organization certified second class pyranometer. This paper demonstrates that the solar irradiance can be estimated by the short circuit current output measured from the photovoltaic module with acceptable accuracy. This contributes to the elimination of the installation of expensive pyranometer.

To address the challenge of quantitatively identifying mixed gases, we developed a gas concentration identification algorithm based on the sparrow search algorithm (SSA) and optimized support vector regression (SVR). The Tent chaotic mapping operator is employed to initialize the population, enhancing population diversity, and improving the algorithm’s global search capability. By optimizing SVR parameters with SSA, we propose an enhanced TSSA-SVR model. Evaluated on mixed gas datasets, TSSA-SVR achieves a prediction accuracy of 94.47%, outperforming comparative algorithms such as Genetic Algorithm (GA)-SVR and PSO-SVR, while demonstrating improved convergence compared to the baseline SSA-SVR. The experimental results demonstrate significant performance enhancements, offering an effective solution for precise gas concentration identification in complex environments.

Particle swarm optimisation with adaptive mutation strategy for photovoltaic solar cell/module parameter extraction