Teaching Learning Based Optimization Research Articles

Optimal Operation of a Village Energy System Considering Renewable Resources and Battery Energy Storage

In this paper, a village energy system is coupled with the wide-area energy network based on the energy hub concept. The village is modeled as an isolated energy hub while it could interact with the energy sub-networks including the electrical, and natural gas through the market. The energy demand of village is supplied with renewable resources such as photovoltaic (PV) system and other generation such as combined heat and power (CHP) technologies. The CHP unit is modeled by the part-load performance. In addition, the battery energy storage is presented beside the PV system to damp the intermittent generation of PV and to be utilized in the high prices of the market. The optimal operation problem is solved to maximize the profit from the energy hub operator point of view. The optimization problem is solved with the teaching-learning based optimization (TLBO) method. The results show that the proper interaction of the village energy system with the upstream sub-networks is so affordable for the system operator to increase the profit, in a way that the maximum benefit of village energy system is reached to 3.6456$.

Integrated multi-objective optimization of sodium bicarbonate pretreatment for the outer anatomical portion of corncob using central composite design, artificial neural networks, and metaheuristic algorithms

Effective pretreatment of raw biomass is crucial in establishing a successful biorefinery process, and response surface methodology (RSM), a statistical optimization method, is routinely employed for optimizing pretreatment methodologies. However, relying solely on statistical methods fails to capture the nonlinear relationships between pretreatment methodology and lignocellulose recalcitrance. Machine learning (ML) approaches excel at understanding these relationships. Therefore, combining statistical and ML optimization can establish better pretreatment parameters. This study presents a multi-stage approach to identify and optimize a chemical pretreatment for the outer anatomical portion of corncobs (CO). Various chemicals were screened using fixed factor screening and regular two-level factorial design (2FI), and among them NaHCO3 was chosen for further optimization, using central composite design (CCD). Moderate delignification (33.96%), minimum sugar loss (5.26 mg/g of CO), and a high enzymatic saccharification yield of up to 82% were achieved with the design. Three distinct metaheuristic algorithms, namely Teaching-Learning-Based Optimization (TLBO), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) were employed to optimize three specific hyperparameters of the artificial neural network (ANN), to create hybrid metaheuristic-optimized ANN models, which were subsequently used to validate the results obtained from the CCD. Among the different models, The TLBO-optimized ANN model provided the most accurate predictions than the CCD.

An Accurate Metaheuristic Mountain Gazelle Optimizer for Parameter Estimation of Single- and Double-Diode Photovoltaic Cell Models

Accurate parameter estimation is crucial and challenging for the design and modeling of PV cells/modules. However, the high degree of non-linearity of the typical I–V characteristic further complicates this task. Consequently, significant research interest has been generated in recent years. Currently, this trend has been marked by a noteworthy acceleration, mainly due to the rise of swarm intelligence and the rapid progress of computer technology. This paper proposes a developed Mountain Gazelle Optimizer (MGO) to generate the best values of the unknown parameters of PV generation units. The MGO mimics the social life and hierarchy of mountain gazelles in the wild. The MGO was compared with well-recognized recent algorithms, which were the Grey Wolf Optimizer (GWO), the Squirrel Search Algorithm (SSA), the Differential Evolution (DE) algorithm, the Bat–Artificial Bee Colony Optimizer (BABCO), the Bat Algorithm (BA), Multiswarm Spiral Leader Particle Swarm Optimization (M-SLPSO), the Guaranteed Convergence Particle Swarm Optimization algorithm (GCPSO), Triple-Phase Teaching–Learning-Based Optimization (TPTLBO), the Criss-Cross-based Nelder–Mead simplex Gradient-Based Optimizer (CCNMGBO), the quasi-Opposition-Based Learning Whale Optimization Algorithm (OBLWOA), and the Fractional Chaotic Ensemble Particle Swarm Optimizer (FC-EPSO). The experimental findings and statistical studies proved that the MGO outperformed the competing techniques in identifying the parameters of the Single-Diode Model (SDM) and the Double-Diode Model (DDM) PV models of Photowatt-PWP201 (polycrystalline) and STM6-40/36 (monocrystalline). The RMSEs of the MGO on the SDM and the DDM of Photowatt-PWP201 and STM6-40/36 were 2.042717 ×10−3, 1.387641 ×10−3, 1.719946 ×10−3, and 1.686104 ×10−3, respectively. Overall, the identified results highlighted that the MGO-based approach featured a fast processing time and steady convergence while retaining a high level of accuracy in the achieved solution.

Comprehensive learning TLBO with recursive precedence-based solution construction and multilevel local search for the linear ordering problem

The linear ordering problem (LOP) is a difficult permutation-based optimization task with a multitude of practical applications in different areas. The objective of the LOP is to maximize the total of the benefits associated with the pairwise precedence relations between the permuted items. Since it is NP-hard, several approximate methods have been developed to quickly produce acceptable solutions. We aim to design a specialized teaching–learning-based optimization (TLBO) method that exploits the permutation structure of the LOP. TLBO is a modern population-based metaheuristic that mimics the conventional process of transmitting knowledge and skills in a classroom. Here we extend and improve TLBO by employing a comprehensive learning strategy. In this strategy, a selected group of learners from the current class are employed as exemplars to generate new solutions. The key component of our comprehensive learning TLBO (CL-TLBO) is a recursive permutation construction procedure. It is an effective pivot-based partitioning algorithm that focuses on the pairwise precedences between permutation items in exemplar solutions to generate new candidate solutions. For better performance, we investigate different ways of selecting the pivot item at each partitioning step. Furthermore, we offer a multilevel local search technique to refine the solutions of sub-problems that are constructed during the recursive partitioning process. The experimental evaluation demonstrates a very competitive performance of the developed CL-TLBO method when compared with various well-established techniques.

A Simulated-Annealing-Quasi-Oppositional-Teaching-Learning-Based Optimization Algorithm for Distributed Generation Allocation

Conventional evolutionary optimization techniques often struggle with finding global optima, getting stuck in local optima instead, and can be sensitive to initial conditions and parameter settings. Efficient Distributed Generation (DG) allocation in distribution systems hinges on streamlined optimization algorithms that handle complex energy operations, support real-time decisions, adapt to dynamics, and improve system performance, considering cost and power quality. This paper proposes the Simulated-Annealing-Quasi-Oppositional-Teaching-Learning-Based Optimization Algorithm to efficiently allocate DGs within a distribution test system. The study focuses on wind turbines, photovoltaic units, and fuel cells as prominent DG due to their growing usage trends. The optimization goals include minimizing voltage losses, reducing costs, and mitigating greenhouse gas emissions in the distribution system. The proposed algorithm is implemented and evaluated on the IEEE 70-bus test system, with a comparative analysis conducted against other evolutionary methods such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Honey Bee Mating Optimization (HBMO), and Teaching-Learning-Based Optimization (TLBO) algorithms. Results indicate that the proposed algorithm is effective in allocating the DGs. Statistical testing confirms significant results (probability < 0.1), indicating superior optimization capabilities for this specific problem. Crucially, the proposed algorithm excels in both accuracy and computational speed compared to other methods studied.

Multi‐criteria evolutionary optimization of a traffic light using genetics algorithm and teaching‐learning based optimization

AbstractToday, the development of urbanization and increasing the number of vehicles has resulted in displeased consequences like traffic congestion and vehicle queuing. The vast majority of countries in the world encounter the challenge of the explosive rise in traffic demand. In this regard, it is necessary to meet traffic demand in transport networks, especially in metropolitans. In traffic management and shortening the trip duration, traffic lights on the signalized intersections play an essential role in urban pathways. This work provides a multi‐criteria decision‐making method for optimum traffic light control in an isolated corner. The main idea involves establishing a set of sub‐optimal solutions for traffic light timing and selecting the best one among the diverse solutions. We have mathematically modelled the problem as an optimization problem to achieve an optimal solution with less waiting time for vehicles in intersections and the lowest cost. Genetic algorithm (GA) and Teaching‐Learning‐based Optimization (TLBO) are utilized for each phase to create a set of suitable timing scenarios. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to identify the best scenario, considering both waiting vehicles and traffic capacity as decision criteria. Its efficiency has been demonstrated over three different traffic volumes. Also, in a real‐world implementation, its practical capability has been approved at a crossroads in Mashhad, Iran. The simulations indicate the improvement in the number of vehicles waiting behind the crossroad and the traffic capacity by 10% and 6.76% compared to the existing signal timing of the studied intersection, respectively.

Estimating residential buildings’ energy usage utilising a combination of Teaching–Learning–Based Optimization (TLBO) method with conventional prediction techniques

Among the most significant solutions suggested for estimating energy consumption and cooling load, one can refer to enhancing energy efficiency in non-residential and residential buildings. A structure's characteristics must be considered when estimating how much heating and cooling is required. To design and develop energy-efficient buildings, it can be helpful to research the characteristics of connected structures, such as the kinds of cooling and heating systems needed to ensure sui interior air quality. As an important part of energy consumption and demand of buildings, the assessment of cooling load conditions from the envelope of large buildings has not been comprehensively understood yet. In the present paper, a new conceptual system has been developed to anticipate cooling load in the sector of residential buildings. Also, the paper briefly describes the major models of the developed system to maintain continuity and concentrate on the prediction model of the cooling load. To predict cooling load, authors have modelled two methods of artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) in conjunction with teaching-learning-based optimization (TLBO). This article aims to illustrate how artificial intelligence (AI) approaches play an essential role in addressing the mentioned necessity and help estimate the optimal design parameters for various stations. The value of the multiple determination coefficient is also determined. The values of the training R2 (coefficient of multiple determination) are 0.96446 and 0.97585 for TLBO-MLP and TLBO-ANFIS in the training stage and 0.95855 and 0.9721 in the testing stage, respectively, with an unknown dataset which is acceptable. The training RMSE values for TLBO-MLP and TLBO-ANFIS are 0.0685 and 0.11176 for training and 0.07074 and 0.12035 for testing, respectively, for the unknown dataset, which is acceptable. The lowest RMSE value and the higher R2 value indicate the favourable accuracy of the TLBO-MLP technique. According to the high value of R2 (97%) and the low value of RMSE, TLBO-MLP can predict residential buildings’ cooling load.

TLBO-trained ANN-based Shunt Active Power Filter for Mitigation of Current Harmonics

The increased utilization of nonlinear devices is resulting in damage to power distribution infrastructure by introducing harmonics into power system networks, which in turn causes distortion in voltage and current signals. A novel solution called Shunt Active Power Filter (SAPF) has been developed to address this issue using power electronics. This study aims to provide a method that is efficient and cost-effective for lowering harmonics and improving power quality in distribution infrastructure. The proposed method combines the Teaching learning-based optimization (TLBO) technique with an Artificial Neural Network Controller (TLBO-ANN) in conjunction with SAPF. The primary objective of the TLBO-ANN algorithms in SAPF is to minimise total harmonic distortion (THD) for maximum system efficiency. Initially, Gain values (Ki, Kp) for a regular Proportional-Integral controller are optimised with the Particle Swarm Optimisation (PSO) technique. Those optimized parameters obtained from the PSO-tuned PI controller serve as input and target datasets for training the ANN controller. Subsequently, the TLBO algorithm is utilized to further refine the ANN controller by finding the optimal weight and bias values. Using MATLAB/SIMULINK software, we compare the performance of the proposed algorithm to that of the PSO-tuned PI controller and traditional PI controller. The findings from the simulation suggest that a SAPF utilizing a TLBO-trained ANN controller could improve THD in the supplying current while maintaining harmonics within IEEE-519 accepting levels.

Optimization of Load Frequency Control Gain Parameters for Stochastic Microgrid Power System

Interconnected multi-area microgrids are vital for the future of sustainable and reliable power systems. Effective load frequency control (LFC) is indispensable for ensuring their stable operation. This paper introduces a PID-based LFC system tailored for a stochastic microgrid with diverse power sources, including solar, wind, diesel engine generators, and electrical batteries. The gain parameters of the proposed microgrid PID LFC controller are optimized using genetic algorithms (GA), teaching learning-based optimization (TLBO), and cohort intelligence algorithms. Integral time-multiplied absolute error (ITAE) and integral time-squared error (ITSE) serve as the cost functions for all optimization algorithms. The study evaluated the performance of these optimized microgrid PID LFC configurations under random step load disruptions. Our primary findings reveal that the cohort intelligence-optimized PID LFC controller excels in minimizing computation time (upto 76% and 94% lesser than GA and TLBO respectively) and exhibits superior robust response characteristics. Moreover, the cohort intelligence algorithm requires fewer iterations (upto 66% and 90% lesser than GA and TLBO respectively) and enhances power supply quality within the multi-power microgrid electrical framework, specifically in terms of effective load frequency control.

Distributed generator and capacitor‐embedded reconfiguration in three‐phase unbalanced distribution systems using teaching learning‐based optimization

AbstractIn the transmission and distribution networks, both active and reactive power play significant roles. While active power does the beneficial work, reactive power maintains the voltage that necessitates management from a system reliability perspective. The voltage variation from the nominal range may result in unintentional operation and early component failure. To maximize the amount of real power that can be transported over the power‐transmitting media, the system must also control reactive power flow. In a three‐phase unbalanced distribution system reinforced with distributed generator units (DGUs) and shunt capacitor units (SCUs), this paper suggests a teaching learning‐based optimization (TLBO) approach to be applied to combinatorial problems for simultaneous reduction of real power loss and net reactive power flow, enhance voltage stability index (VSI) and minimize aggregated voltage deviation index. A multiobjective formulation based on TLBO has been implemented to choose the ideal sizes and placements of DGUs and SCUs in large distribution networks. The case studies have been carried out on an IEEE 33‐bus standard system and a large 123‐bus unbalanced system. The analysis of the IEEE 33‐ and 123‐bus test systems reveals the economic efficiency of the suggested TLBO algorithm. Notably, by applying DG and capacitor simultaneously in the 33‐bus system, a significant reduction of 59.35%, 55.05%, and 50.76% (phases a, b, and c), and for the 123‐bus system, a significant reduction of 43.65%, 19%, and 48.65% (phases a, b, and c) in total active power losses have been achieved. The results suggest that the proposed method renders significant improvement in voltage stability and reduces power losses concerning the base case for both test systems.

Gaussian bare-bones Levy circulatory system-based optimization for power flow in the presence of renewable units

The Optimal Power Flow (OPF) is a vital issue in electrical networks to ensure the economical and safe operation to transfer electrical energy that is very complex, non-linear, and limited. In the electrical networks with Renewable Energy Sources (RES), the OPF problem is a much more complex and constrained optimization problem because incorporating the intermittent nature of RESs, including Wind Turbine (WT) and Photovoltaic (PV), which have been used in this article, and OPF is often used to optimize various problems. In this research, an effort has been made to modify and improve the performance of a new algorithm named Circulatory System-Based Optimization (CSBO) to a more powerful algorithm for complex OPF problems, and the result of this research was to present a more effective and powerful algorithm named Gaussian Bare-bones Levy CSBO (GBLCSBO). CSBO mimics the mating behavior of the circulatory system in the body. The IEEE 30-bus and 118-bus test networks are adopted to validate the capability of the suggested approach in minimizing four objectives, which include the total generation cost, voltage deviation, power loss, and pollution emission.Finally, to know the performance and strength of GBLCSBO for solving various OPF problems, several new powerful algorithms include Seagull Optimization Algorithm (SOA), Teaching-Learning-Based Optimization (TLBO), Gray Wolf Optimizer (GWO), Multi-Verse Optimizer (MVO) have been used to compare with GBLCSBO. Also, the CEC 2017 test functions were used to measure the performance of GBLCSBO in a broader range of optimization problems.The optimization results in both topics of OPF problems and various test functions compared with various algorithms showed that GBLCSBO is both strong and robust and has a suitable and comparative performance in a wide range of different optimization problems such as OPF. According to the obtained results, the GBLCSBO demonstrates high potential in solving OPF problems.

Reliability analysis of floating offshore wind turbine generator based on failure prediction and preventive maintenance

Aiming at the failure problems of a floating offshore wind turbine (FOWT) generator, a preventive maintenance model based on failure prediction is established. Firstly, the fault tree method is adopted to calculate the generator reliability value under run or failure states. Secondly, quantitative analysis of the generator in a maintainable state is carried out by the Markov method. Finally, a system optimization model is established based on the failure prediction and preventive maintenance (FPPM) strategy. The single-objective teaching-learning-based optimization (TLBO) algorithm and multi-objective genetic algorithm (MOGA) are respectively used to solve the optimization problem. The results show that FPPM strategy can greatly improve the availability and mean time between failure (MTBF) value, which increase the system working time and efficiency. Multi-objective analysis can get the best combination of the system maintenance cost, availability, and risk than single-objective. The time interval of failure prediction is calculated as 19788 h and the system is in a safe state if the remaining life is predicted to be more than 101 h. Sensitivity analysis of the model is carried out to determine that the optimization objectives are less sensitive to variables, which verifies the rationality and accuracy of the proposed model.

Fact Finding Instructor-based Clustering Technique for BP Estimation using Human Speech Signals

Blood Pressure (BP) is considered an essential factor that provides information regarding cardiovascular function. Regular monitoring of the BP is required for proper healthcare maintenance that avoids the high risk of life due to high and low BP. Several methods were devised for the estimation of BP, but the estimation accuracy is still a challenging task. Hence this research introduces an efficient BP estimation technique using the Fact Finding Instructor (FFI) based clustering method by considering the speech signal of the patients. An efficient BP extraction technique is introduced using the FFI Optimization algorithm an integration of the mannerism of the fact finder that identifies the suspect who commits the criminal offense and, with the instructor with good knowledge, these make the trainee more efficient. The detection and suspect’s arrest contain two phases, the fact-finding phase and the chasing phase. Initially, the speech signal is collected from the database and pre-processed for removing noise and artifacts. Then feature extraction is used for the minimization of the computation overhead that generates a feature vector. The clustering of BP is employed with the k-means clustering algorithm and the proposed FFI optimization algorithm. The FFI Optimization algorithm provides a fast convergence rate due to the fact-finding phase and provides accurate detection of the suspect’s location along with that the clustering of classes of patients’ BP by considering the feature of the speech signal. The clusters formed using the FFI optimization algorithm are combined with the K-means clustering, by multiplying the clusters the BP estimation is implemented on three criteria Low BP, Normal, and, High BP. Finally, the output generated by both the clustering operations is multiplied together for the estimation of the BP. The performance of the proposed method is evaluated using the metrics like Davies Bouldin score, Homogeneity score, Completeness score, Jacquard Similarity score, Silhouette score, and Dunn’s Index which acquired the improvement rate of 0.98, 0.96, 0.96, 0.98, 0.95, and 0.98 for training percentage 90, respectively to the existing Teaching Learning Based Optimization(TLBO) clustering technique.

Novel assessment tools for inland aquaculture in the western Godavari delta region of Andhra Pradesh.

The production of fisheries and shrimp has been twice every 10years for the previous five decades, making it the most rapidly expanding food industry. This growth is due to intensive farming and the conversion of agriculture into aquaculture in many parts of South Asia. Furthermore, intensive aquaculture generates positive economic growth but leads to environmental degradation without proper monitoring. Unfortunately, technical innovation is less in aquaculture than agricultural and manufacturing industries. The advent of remote sensing and soft computing has expanded various opportunities for utilizing and integrating technological advances in civil and environmental disciplines. This paper presents the aquaculture scenario in the western Godavari delta region of Andhra Pradesh and proposes various novel assessment tools to monitor the aquaculture environment. An experimental investigation was carried out on the physicochemical characteristics of the inland aquaculture ponds to evaluate water quality in the aquaculture ponds. Furthermore, to assess the intensity of inland aquaculture, the current work concentrates on the potential application of remote sensing and soft computing approaches. Geospatial models of kriging and inverse distance weighing (IDW) show higher performance in estimating ammonia levels in the intensive aquaculture groundwaters with coefficient of determination (R2) values of 0.947 and 0.901, respectively. Teaching learning-based optimization (TLBO) and adaptive particle swarm optimization (APSO), two of the five soft computing techniques utilized in the study, perform better than the others. Additionally, it was found that remote sensing-based assessment tools and soft computing prediction models were both trustworthy, accurate, and easy to use. Furthermore, these methods could assist in the real-time evaluation of inland aquaculture waters by stakeholders and policymakers.

RETRACTED: Optimum operation of energy hub by considering renewable resources by considering risk tolerance and risk taking with Teaching–learning-based optimization

Amidst growing concerns over climate change, the conventional energy landscape faces critical challenges associated with fossil fuel usage. In response, this study explores alternative approaches by investigating an energy hub system leveraging wind turbine-generated power. This hub integrates seamlessly with electricity and natural gas grids, offering a comprehensive energy supply encompassing electricity, natural gas, and thermal loads. The research strategy encompasses a multi-pronged approach. A Time-of-Use (TOU) load management program optimizes the distribution of electrical and thermal loads. To address the unpredictability of wind speed, the information gap decision theory (IGDT) is introduced to manage risk and deviations effectively. The central objective involves optimizing the energy hub's operations, focusing on minimizing operational costs and emissions. To address this intricate challenge, the study employs the Teaching–Learning-Based Optimization (TLBO) method. This advanced technique concurrently optimizes cost and environmental impact, exemplifying its efficacy in the energy hub context. The research culminates in demonstrating the TLBO algorithm's swift convergence, highlighting its aptitude for addressing complex cost and emission optimization dynamics. In sum, this study offers innovative insights into sustainable energy systems, where economic and environmental considerations converge harmoniously.

Advances in teaching–learning-based optimization algorithm: A comprehensive survey(ICIC2022)

Teaching-learning-based optimization (TLBO) algorithm which imitates the teaching–learning process in a classroom, is one of population-based heuristic stochastic swarm intelligent algorithms. TLBO executes through similar iterative evolution processes as utilized by a standard evolutionary algorithm. Unlike traditional evolutionary algorithms and swarm intelligent algorithms, the iterative computation process of teaching–learning-based optimization is divided into two phases and each phase executes iterative learning operation. In this paper, we present a comprehensive survey on the recent advances in TLBO. A review of the current literature reveals intriguing challenges and suggests potential future research directions.

Optimal load frequency control of multi-area multi-source deregulated power system with electric vehicles using teaching learning-based optimization: a comparative efficacy analysis

Optimal load frequency control of multi-area multi-source deregulated power system with electric vehicles using teaching learning-based optimization: a comparative efficacy analysis

Enhanced Economic Load Dispatch by Teaching–Learning-Based Optimization (TLBO) on Thermal Units: A Comparative Study with Different Plug-in Electric Vehicle (PEV) Charging Strategies

This research paper presents an enhanced economic load dispatch (ELD) approach using the Teaching–Learning-Based Optimization (TLBO) algorithm for 10 thermal units, examining the impact of Plug-in Electric Vehicles (PEVs) in different charging scenarios. The TLBO algorithm was utilized to optimize the ELD problem, considering the complexities associated with thermal units. The integration of PEVs in the load dispatch optimization was investigated, and different charging profiles and probability distributions were defined for PEVs in various scenarios, including overall charging profile, off-peak charging, peak charging, and stochastic charging. These tables allow for the modeling and analysis of PEV charging behavior and power requirements within the power system. By incorporating PEVs, additional controllable resources were introduced, enabling more effective load management and grid stability. The comparative analysis showcases the advantages of the TLBO-based ELD model with PEVs, demonstrating the potential of coordinated dispatch strategies leveraging PEV storage and controllability. This paper emphasizes the importance of integrating PEVs into the load dispatch optimization process, utilizing the TLBO algorithm, to achieve economic and reliable power system operation while considering different PEV charging scenarios.

Experimental Analysis and Artificial Neural Network Teaching–Learning-Based Optimization Modeling on Electrical Discharge Machining Characteristics of AZ91 Composites

Experimental Analysis and Artificial Neural Network Teaching–Learning-Based Optimization Modeling on Electrical Discharge Machining Characteristics of AZ91 Composites

Experimental and theoretical verification of TLBO and PSO for solving the inverse kinematic model of continuum robots

This paper presents a comprehensive exploration of two meta-heuristic optimization techniques, Teaching Learning-Based Optimization (TLBO) and Particle Swarm Optimization (PSO), applied to solve the inverse kinematic problem of continuum robots. The study encompasses both theoretical investigations and realistic simulations, including tracking a spiral trajectory and utilizing real measurements to follow a trajectory. TLBO demonstrates exceptional precision in solving the inverse kinematic problem for continuum robots, consistently outperforming PSO in terms of accuracy. On the other hand, PSO showcases notable advantages in terms of computational efficiency, exhibiting faster convergence and reduced time consumption. The research findings suggest promising avenues for the application of meta-heuristic approaches in real-world scenarios involving continuum robots, particularly in domains such as medical devices and industrial automation. However, the challenge remains to develop modified algorithms that strike a balance between accuracy and efficiency to address the diverse requirements of practical applications in this field. Nevertheless, the versatility of meta-heuristic methods in handling complex robotic systems offers exciting prospects for the future of continuum robotics.