Stochastic Fractal Search Research Articles

Efficient DC motor speed control using a novel multi-stage FOPD(1 + PI) controller optimized by the Pelican optimization algorithm.

This paper introduces a novel multi-stage FOPD(1 + PI) controller for DC motor speed control, optimized using the Pelican Optimization Algorithm (POA). Traditional PID controllers often fall short in handling the complex dynamics of DC motors, leading to suboptimal performance. Our proposed controller integrates fractional-order proportional-derivative (FOPD) and proportional-integral (PI) control actions, optimized via POA to achieve superior control performance. The effectiveness of the proposed controller is validated through rigorous simulations and experimental evaluations. Comparative analysis is conducted against conventional PID and fractional-order PID (FOPID) controllers, fine-tuned using metaheuristic algorithms such as atom search optimization (ASO), stochastic fractal search (SFS), grey wolf optimization (GWO), and sine-cosine algorithm (SCA). Quantitative results demonstrate that the FOPD(1 + PI) controller optimized by POA significantly enhances the dynamic response and stability of the DC motor. Key performance metrics show a reduction in rise time by 28%, settling time by 35%, and overshoot by 22%, while the steady-state error is minimized to 0.3%. The comparative analysis highlights the superior performance, faster response time, high accuracy, and robustness of the proposed controller in various operating conditions, consistently outperforming the PID and FOPID controllers optimized by other metaheuristic algorithms. In conclusion, the POA-optimized multi-stage FOPD(1 + PI) controller presents a significant advancement in DC motor speed control, offering a robust and efficient solution with substantial improvements in performance metrics. This innovative approach has the potential to enhance the efficiency and reliability of DC motor applications in industrial and automotive sectors.

Hybrid waterwheel plant and stochastic fractal search optimization for robust diabetes classification

Hybrid waterwheel plant and stochastic fractal search optimization for robust diabetes classification

A REVIEW ON OPTIMAL PLACEMENT AND SIZING METHODS OF DISTRIBUTION GENERATION SOURCES

This manuscript outlines various work carried out in the field of Distributed Generation (DG). Increase in power consumption and shortage in transmission capabilities are addressed by DGs. In order to maximize the potential benefits, it is imperative to place the DGs at optimal locations and the DGs should have optimal size pertaining to that location. There are several research works that are carried out on the placement and sizing of DGs. Nonetheless, the methodical principle for this issue is still unsettled. Various optimization strategies can be used to obtain the appropriate placement and sizing of distributed generation (DG) in grids. This study provides a comprehensive overview of several DG placement approaches, including stochastic fractal search algorithms, particle swarm optimization, symbiotic search algorithms, opposition-based tuneable chaotic differential evaluation, and more. The benefits and potential uses of each method are briefly covered in this study. The study sheds light on the efforts made to determine the best location and size of DGs.

Development of a mathematical model for investigation of hollow-fiber membrane contactor for membrane distillation desalination

This research investigates the predictive modeling of a dataset containing parameters denoted by r(m), z(m), and T(K) which is temperature. The considered process is a membrane distillation (MD) for separation of compounds based on temperature gradient. A membrane contactor is used for the process, and the computations are performed in the context of computational fluid dynamics (CFD) and machine learning. The dataset, which is generated by CFD modeling and encompasses over 5,000 data points, is analyzed using three distinct regression models: Support Vector Machine (SVM), Deep Neural Network (DNN), and Kernel Ridge Regression (KRR). Hyperparameter tuning is performed employing the Stochastic Fractal Search (SFS) algorithm. Our findings unraveled the nuanced intricacies of each model's performance, gauged through a comprehensive set of metrics. The RMSE, MAPE, and R2 score collectively offer a robust evaluation framework. The Deep Neural Network (DNN) exhibits a compelling RMSE of 7.7001E-01, a remarkably low MAPE of 2.05131E-03, and an impressive R2 score of 0.97054. Meanwhile, the Support Vector Machine (SVM) showcases a notable RMSE of 1.7215E-01, a minimal MAPE of 2.90820E-04, and a remarkably high R2 score of 0.99839. On the other hand, the Kernel Ridge Regression (KRR) model presents an RMSE of 1.3588E + 00, a MAPE of 2.63550E-03, and an R2 score of 0.90042.

Predictive analysis of concrete slump using a stochastic search-consolidated neural network

Attaining a dependable measurement of concrete slump is crucial as it is a valuable indication of concrete workability. On the other hand, complexities associated with costly traditional approaches have driven engineers to use indirect efficient models such as metaheuristic-based machine learning for approximating the slump. While the literature shows promising application of some metaheuristic techniques for this purpose, the large variety of these algorithms calls for evaluating the most capable ones to keep the solution updated. Stochastic fractal search (SFS) is one of the most powerful optimization algorithms in the literature that has not received appropriate attention in analyzing concrete mechanical parameters. In the present research, a multi-layer perceptron neural network (NN-MLP), is enhanced using the SFS. The proposed SFS-NN-MLP model aims to predict the slump based on the amount of ingredients in the mixture, as well as the curing age of specimens. Accuracy assessment revealed that the proposed model can deal with the assigned task with excellent accuracy. It indicates that the SFS could properly tune the parameters required for training the NN-MLP, and consequently, the trained network could reliably calculate the slump of specimens that were not analyzed before. For comparative validation, the SFS was replaced with two similar optimizers, namely elephant herding optimization algorithm (EHO) and slime mould algorithm (SMA). Based on the calculated mean square errors of 5.6526, 6.1129, and 7.3561 along with mean absolute errors of 4.6657, 5.0078, and 6.3066, as well as the percentage-Pearson correlation coefficients of 78.06 %, 73.95 %, and 58.11 %, respectively for the SFS-NN-MLP, EHO–NN–MLP, and SMA–NN–MLP, it was shown that the SFS-NN-MLP is the most accurate predictor. Hereupon, the SFS-NN-MLP model is recommended to be effectively used for obtaining a cost-efficient approximation of concrete slump in real-world projects.

Improved stochastic fractal search algorithm involving design operators for solving parameter extraction problems in real-world engineering optimization problems

The characteristic parameters of renewable energy sources (RESs) are changes over time under changing operating conditions. Therefore, the accuracy of the model is important in order to establish appropriate control and operating plans for the stable operation of such systems. Determining the parameters of RESs and creating an accurate model of them is an inevitable reality and plays an important role in the success of system modeling. Many methods have been used to determine these parameters in the literature. Furthermore, optimization algorithms are now considered to be among the most significant approaches for resolving problems pertaining to system parameter extraction in many scientific areas. In the study, this parameter extraction is done by a new optimization method called stochastic fractal search algorithm (FDB-NSM-SFS-OBLs), which includes natural survivor updating (NSM) and fitness distance balance (FDB) guiding mechanisms, and opposite based learning (OBL) methods. The performance of the proposed FDB-NSM-SFS-OBL algorithm has been tested in two different experimental studies. In the first experimental study, the proposed approach is tested on CEC2020 benchmark test functions and the algorithm structure containing the best OBL approach is determined using nonparametric Wilcoxon and Friedman statistical analysis methods. The second experimental study is carried out with the proposed optimization algorithm to estimate the parameters of the photovoltaic cell used in the modeling, which is the building block of photovoltaic panels used in renewable energy systems, proton-exchange membrane fuel cell (PEMFC) that is another renewable energy source, and Li-Ion battery used as a backup power unit. The FDB-NSM-SFS-OBL algorithm, which is used both in the CEC2020 benchmark test functions and in determining the parameters of photovoltaic (PV) cells, PEMFC and Li-Ion batteries, performed better in searching and finding the global solution point during the optimization process.

Understanding the Impact of Mental Health on Academic Performance in Students Using Random Forest and Stochastic Fractal Search with Guided Whale Optimization Algorithm

Understanding the Impact of Mental Health on Academic Performance in Students Using Random Forest and Stochastic Fractal Search with Guided Whale Optimization Algorithm

Inspection policy optimization for hierarchical multistate systems under uncertain mission scenarios: A risk-averse perspective

Most engineered systems intend to perform missions with a pre-specified target success probability to reduce undesirable failure risks. Before executing the next mission, inspection activities are conducted across various physical levels for assessing the probability of mission success. However, due to the randomness of a system’s degradation behavior and the presence of measurement errors, inspection results inevitably contain uncertainty. Meanwhile, mission durations and acceptable system states may also be uncertain, due to uncontrollable factors, such as random operating environments and mission demands. In such a circumstance, it is of great significance to identify the optimal multilevel inspection policy to answer, as great confident as possible, the question that the system can complete the next mission with a target mission success probability. This paper develops a novel metric to gauge the effectiveness of a multilevel inspection policy to assess if the system can complete the next mission with a pre-specified target success probability from a risk-averse perspective, based on which an optimization method is proposed to seek an inspection policy under uncertain scenarios with the aim of minimizing the maximum regret of the proposed metric. A stochastic fractal search algorithm, along with two tailored local search rules, is designed to efficiently resolve the resulting optimization problem. Two cases, including a three-component system and a rocket fueling mechanism’s control system, are used to illustrate the efficacy of the proposed approach, which is capable of effectively identifying the risk of mission failures by inspection policies.

Validation of four optimization evolutionary algorithms combined with artificial neural network (ANN) for landslide susceptibility mapping: A case study of Gilan, Iran

Landslides, the most significant geohazards in Iran, adversely affect the region's socioeconomic conditions and the environment. Landslide susceptibility mapping is crucial for proactive risk management, sustainable development, and protecting human lives, infrastructure, and the environment. It enables decision-makers to make informed choices, implement appropriate mitigation measures, and plan for potential landslide events, leading to safer and more resilient communities. Using a recommended subdivision methodology, this research has developed a landslide susceptibility map for a significant Gilan, Iran region. The production of the map involved utilizing an artificial neural network (ANN) model. This model incorporated sixteen causal components from several characteristics, including topographic and geomorphologic features, geological factors, land use patterns, hydrological aspects, and hydrogeological properties. Three hundred seventy instances were identified using multiple verified sources and analyzing aerial photographs to create the landslide inventory map. Examining and verifying the weights assigned to the causal elements were conducted per accepted mathematical standards, incorporating sensitivity analysis, earlier research, and empirical data on landslides. The area under the receiver operating characteristic curve (AUROC) was used to compare the various models. The study's findings indicated that the best swarm size value for COA-MLP11Cuckoo Optimization Algorithm (COA). is equal to 450, and the accuracy indices for this algorithm were 0.998 and 0.995 in training and testing datasets, respectively. Similarly, the AUC22Area under the curve (AUC). for the HS-MLP,33Harmony Search Algorithm (HS). SFS-MLP,44Stochastic Fractal Search (SFS). and TLBO-MLP55Teaching- Learning-Based Optiization (TLBO). were 0.997, 0.999, and 0.999 in training and 0.995, 0.996, and 0.995 in the testing dataset, respectively. Therefore, the use of optimization algorithms leads to an increase in the performance and accuracy of the neural network, and the high accuracy of the SFS-MLP model demonstrates the existence of a dependable criterion for delineating the susceptibility zones about forthcoming landslide occurrences. The model is a cost-effective and potentially indispensable tool for urban planners in growing cities and municipalities. Its effectiveness is demonstrated by comparisons with previous susceptibility analyses conducted in the region.

Optimal Low-Thrust Earth Orbit Transfers with Eclipses Using Indirect Heuristic Approaches

Low-thrust propulsion allows substantial propellant saving if compared to high-thrust systems. However, multirevolution orbit transfers are affected by the unavailability of electrical power along eclipse arcs. This research addresses the identification of minimum-time low-thrust Earth orbit transfers with spacecraft eclipsing. Two different indirect heuristic approaches, based on the use of the analytical conditions for optimality, in conjunction with stochastic fractal search, are applied: 1) regularization through the hyperbolic tangent function and 2) multi-arc formulation of the problem. Both of them require no averaging, and the respective advantages and shortcomings are identified. Approach 2 leads to an extended set of multipoint conditions for optimality, which are shown to be solvable sequentially in the numerical solution process. Implicit costate transformation is proven to be a key ingredient for the purpose of obtaining closed-form solutions of the jump relations that hold for the adjoint variables at light/eclipse transitions. Some illustrative examples prove effectiveness of the two indirect heuristic approaches 1 and 2 in finding minimum-time low-thrust orbit transfers between either two coplanar or two noncoplanar Earth orbits. Approach 2 proves to be superior in terms of both computational efficiency and accuracy of the numerical results.

Multi-surrogate-assisted stochastic fractal search based on scale-free network for high-dimensional expensive optimization

Surrogate-assisted meta-heuristic algorithms (SAMAs) have been increasingly popular in recent years for solving challenging optimization problems. However, the majority of recent studies concentrate on low-dimensional problems. In this paper, a scale-free network based multi-surrogate-assisted stochastic fractal search (SF-MSASFS) algorithm is proposed. Specifically, based on the stochastic fractal search (SFS) algorithm, multiple surrogate models, namely RBF and Kriging models, are used to enhance the robustness of the algorithm. The scale-free network is used to build the topology structure of the SFS algorithm, and the offspring particles are generated by means of the connection relationship between the parent particles. In addition, to further enhance adaptability, an adaptive mechanism is implemented, tailoring three distinct update mechanisms based on their corresponding reward values. Finally, the performance of the proposed algorithm is demonstrated by comparing the proposed algorithm with a number of state-of-the-art SAMAs on several well-known benchmark functions, in particular in solving high-dimensional expensive problems (HEOPs). The results underscore the SF-MSASFS algorithm’s commendable optimization performance. (The MATLAB code can be found at the authors github: https://github.com/xiaodi-Cheng/SF-MSASFS)

Solving the inverse kinematics problem of discretely actuated hyper-redundant manipulators using the multi-module searching method

AbstractHyper-redundant manipulators are produced by cascading several mechanisms on top of each other as modules. The discrete actuation makes their control easier because discrete actuators usually do not need any feedback to control. So far, several methods have been proposed to solve the inverse kinematic problem of discretely actuated, hyper-redundant manipulators. The two-by-two searching method is better than the other methods in terms of CPU time and error. In this article, the mentioned method is generalized by choosing an arbitrary number of modules as pending modules in each step of the solution instead of the necessary two. For validation, the proposed method is compared with nine meta-heuristic searching algorithms: simulated annealing, genetic algorithm, particle swarm optimization, ant colony optimization, gray wolf optimizer, stochastic fractal search, whale optimization algorithm, Giza pyramid construction, and flying fox optimization. Furthermore, the effect of the number of pending modules on CPU time and error is investigated. All the numerical problems have been solved for two case studies, one is planar and the other is spatial.

Guided learning strategy: A novel update mechanism for metaheuristic algorithms design and improvement

Meta-heuristic algorithms (MH) are naturally inspired global optimization algorithms. They are often relatively simple and can solve problems in a short period of time, with certain benefits. However, as the problem becomes more complex, the solution that the algorithm can obtain is often not the optimal solution to the problem, which limits its application scenarios. Therefore, improving the performance and solving accuracy of existing algorithms is crucial for expanding their application ability. In traditional optimization algorithms, there are often two concepts, namely exploration and exploitation. Exploration refers to a wide range of discrete search, used to avoid falling into local optima, and exploitation refers to a small range of focused exploration, used to improve algorithm accuracy. How to balance exploration and exploitation is the key to enhancing algorithm performance and problem adaptability. This paper proposes a brand new strategy named Guided Learning Strategy (GLS) to solve above problem. GLS obtains the dispersion degree of the population by calculating the standard deviation of the historical locations of individuals in recent generations, and infers what guidance the algorithm currently needs. When the algorithm is biased towards exploration, it will guide the algorithm to exploit. Otherwise, it will guide the algorithm to explore. It is precisely because this strategy can identify the current needs of the algorithm and provide assistance that it can improve the performance of most algorithms. This article improves three types of algorithms based on evolution (LSHADE_SPACMA), Stochastic Fractal Search (SFS), and Marine Predators Algorithm (MPA) with better performance, and tests their performance on 57 constrained engineering problems and CEC2020. The effectiveness of this strategy has been confirmed and proved for optimization problem. The source codes of the proposed GLS (GLS_MPA) can be accessed by https://github.com/luchenghao2022/Guided-Learning-Strategy

A Modified Artificial Hummingbird Algorithm for solving optimal power flow problem in power systems

Optimal power flow (OPF) problem solution is a crucial task for the operators and decision makers to assign the best setting of the system components to obtain the most economic, environmental, and technical suitable state. Artificial Hummingbird Algorithm is a recent optimization algorithm that has been applied to solving several optimization problems. In this paper, a Modified Artificial Hummingbird Algorithm (MAHA) is proposed for improving the performance of the orignal Artificial Hummingbird Algorithm as well as effectivelly solve the OPF problem. The proposed MAHA is based on improving the searching capability by boosting the exploitation using the bandwidth motion around the best solution, while the exploration process is improved using the Levy flight distribution motion and the fitness-distance balance selection. This modified version helps overcome issues such as stagnation, premature convergence, and a propensity for local optima when tackling complex, nonlinear, and non-convex optimization problems like OPF. In order to confirm the effectiveness of the proposed algorithm, a series of tests are conducted on 23 standard benchmark functions, including CEC2020. The resulting outcomes are then compared to those obtained using other algorithms such as fitness-distance balance selection-based stochastic fractal search (FDBSFS), antlion optimizer (ALO), whale optimization algorithm (WOA), sine-cosine algorithm (SCA), fitness-distance balance and learning based artificial bee colony (FDB-TLABC), and traditional artificial hummingbird algorithm (AHA).The proposed algorithm is evaluated by solving the OPF problem with multiple objective functions on the IEEE 30-bus system. These objectives include fuel cost, fuel cost with valve loading effects, power losses, emissions, and voltage profile. Additionally, the algorithm's effectiveness is further assessed by testing it on single objective functions using medium and large-scale IEEE 57 and 118-bus networks.The results obtained by the proposed MAHA demonstrate its power and superiority for solving the OPF problem as well as the standard benchmark functions , surpassing the performance of other reported techniques.

Enhancing K-Nearest Neighbors Algorithm in Wireless Sensor Networks through Stochastic Fractal Search and Particle Swarm Optimization

The utilization of wireless sensor networks (WSNs) holds significant importance in diverse data collection applications. Efficient operation of computers, especially in predictive tasks, is imperative for obtaining accurate results within WSNs. This research introduces an innovative approach employing Stochastic Fractal Search-Particle Swarm Optimization (SFS-PSO) to enhance the performance of the K-Nearest Neighbors (KNN) algorithm. The proposed methodology initiates with the establishment of a particle population, dynamically adjusting their positions and velocities and integrating a diffusion process. Through an iterative process of incremental adjustments and evaluations, the algorithm fine-tunes its parameters, resulting in a refined KNN regression model. The enhanced model exhibits substantial improvements, as indicated by the notable reduction in root mean square error (RMSE) and mean absolute error (MAE), accompanied by a strengthened correlation between variables. The favorable outcomes underscore the efficacy of the SFS-PSO optimization technique in augmenting the KNN algorithm's performance within wireless sensor networks. In simpler terms, the application of SFS-PSO in conjunction with KNN leads to a significant decrease in RMSE, reaching a value as low as 0.00894, demonstrating the notable effectiveness of this optimization approach in refining the predictive capabilities of the KNN algorithm in the context of WSNs.

Memory backtracking strategy: An evolutionary updating mechanism for meta-heuristic algorithms

The search domain of meta-heuristic algorithms is always constantly changing, which make it difficult to adapt the diverse optimization issues. To overcome above issue, an evolutionary updating mechanism called Memory Backtracking Strategy (MBS) is proposed, which contains thinking stage, recall stage, and memory stage. Overall, the adoption of the MBS enhances the efficiency of MHSs by incorporating group memory, clue recall, and memory forgetting mechanisms. These strategies improve the algorithm's ability to explore the search space, optimize the search process, and escape local optima. MBS will be applied to three different types of MHS algorithms: evolutionary based (LSHADE_SPACMA), physical based (Stochastic Fractal Search, SFS), and biological based (Marine Predators Algorithmnm, MPA) to demonstrate the universality of MBS. In the experimental section including 57 engineering problems, algorithm complexity analysis, CEC2020 Friedman ranking, convergence curve, Wilcoxon statistical, and box plot. Among them, 21 algorithms participated in the Friedman experiment, including MBS_LSHADE_SPACMA ranked first, LSHADE_SPACMA ranked second, MBS_MPA ranked 6th, MPA ranked 8th, MBS_SFS ranked 9th and SFS ranked 12th. Combined with the analysis of "MBS testing analysis" and the experimental results of engineering problems, it has proven that MBS has universality and good ability to improve optimization algorithm performance. The source codes of the proposed MBS (MBS_MPA) can be accessed by https://github.com/luchenghao2022/Memory-Backtracking-Strategy

Dynamic-fitness-distance-balance stochastic fractal search (dFDB-SFS algorithm): an effective metaheuristic for global optimization and accurate photovoltaic modeling

Dynamic-fitness-distance-balance stochastic fractal search (dFDB-SFS algorithm): an effective metaheuristic for global optimization and accurate photovoltaic modeling

An Improved Stochastic Fractal Search Based on Entropy Multitrust Fusion Model for IoT-Enabled WSNs Clustering

An Improved Stochastic Fractal Search Based on Entropy Multitrust Fusion Model for IoT-Enabled WSNs Clustering

A novel voting classifier for electric vehicles population at different locations using Al-Biruni earth radius optimization algorithm

The rising popularity of electric vehicles (EVs) can be attributed to their positive impact on the environment and their ability to lower operational expenses. Nevertheless, the task of determining the most suitable EV types for a specific site continues to pose difficulties, mostly due to the wide range of consumer preferences and the inherent limits of EVs. This study introduces a new voting classifier model that incorporates the Al-Biruni earth radius optimization algorithm, which is derived from the stochastic fractal search. The model aims to predict the optimal EV type for a given location by considering factors such as user preferences, availability of charging infrastructure, and distance to the destination. The proposed classification methodology entails the utilization of ensemble learning, which can be subdivided into two distinct stages: pre-classification and classification. During the initial stage of classification, the process of data preprocessing involves converting unprocessed data into a refined, systematic, and well-arranged format that is appropriate for subsequent analysis or modeling. During the classification phase, a majority vote ensemble learning method is utilized to categorize unlabeled data properly and efficiently. This method consists of three independent classifiers. The efficacy and efficiency of the suggested method are showcased through simulation experiments. The results indicate that the collaborative classification method performs very well and consistently in classifying EV populations. In comparison to similar classification approaches, the suggested method demonstrates improved performance in terms of assessment metrics such as accuracy, sensitivity, specificity, and F-score. The improvements observed in these metrics are 91.22%, 94.34%, 89.5%, and 88.5%, respectively. These results highlight the overall effectiveness of the proposed method. Hence, the suggested approach is seen more favorable for implementing the voting classifier in the context of the EV population across different geographical areas.

The impact of thermal insulating materials in heat loss control in smart green buildings using experimental and swarm intelligent analysis.

The efficacy of saving energy standards depends on the ability to anticipate the heat loss of buildings. Environmentally friendly materials, also known as eco-friendly or sustainable materials, have a minimal negative impact on the environment throughout their life cycle. These materials are designed to conserve resources, reduce pollution, and promote sustainability. The characteristics of non-stationary and non-linear heat loss through environmentally friendly materials make it challenging to anticipate accurately. At the same time, many of the industry's presently accessible computational models have been created with this in mind; the majority call for powerful computers and time-consuming computations. The artificial neural network (ANN) has been utilized for prediction, and ground-breaking research has shown the viability of this strategy. This research proposes an artificial neural network (ANN) prototype to estimate construction cooling load usage. ANN is integrated with the vortex search algorithm (VS), stochastic fractal search (SFS), and multi-verse optimizer (MVO) models to compare the three models' outcomes and suggest a more accurate strategy. These techniques make a linear mapping among the output and input parameters, often utilized for modeling and regression. The value of the multiple determination coefficient is also determined. The values of the training R2 (coefficient of multiple determination) are 0.9464, 0.99827, and 0.99522 for VS-MLP, SFS-MLP, and MVO-MLP, respectively, with an unknown dataset which is acceptable. The training RMSE amounts for VS-MLP, SFS-MLP, and MVO-MLP are 0.06433, 0.00619, and 0.01028 for the unknown dataset, which is acceptable. According to the MAE values of 0.0082902, 0.0047834, and 0.0076534 in the training phase for VS-MLP, SFS-MLP, and MVO-MLP approaches and the values of testing MAE error of 0.029107, 0.018167, and 0.029212 for VS-MLP, SFS-MLP, and MVO-MLP approaches, respectively, it is obtained that the SFS-MLP has a lower MAE value. The lowest RMSE value and the higher R2 value indicate the favorable accuracy of the SFS-MLP technique.