Advanced Optimization Methods Research Articles

Carbon Policies and Liner Speed Optimization: Comparisons of Carbon Trading and Carbon Tax Combined with the European Union Emissions Trading Scheme

This paper explores how optimizing vessel speeds can help reduce carbon emissions in the maritime industry. Focusing on liner shipping routes between China and Europe, it examines how carbon pricing mechanisms, including carbon taxes and emissions trading under the European Union Emissions Trading Scheme (EU ETS), impact operational costs and emissions reduction. With the use of advanced optimization methods, such as the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and the Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS), this research explores the balance between adjusting vessel speeds and minimizing emissions. The findings show that shipping companies on the China–Europe route can reduce the financial strain of carbon pricing by carefully managing speeds and voyage times. This study compares two scenarios of carbon tax policy and carbon trading rights in terms of voyage costs and carbon emissions. The results of this comparison based on the given parameters indicate a reduction of 1124 tons of carbon emissions with the carbon tax policy scenario, while the carbon trading rights scenario allows for more voyages yearly (5.24 vs. 5.30). This demonstrates one policy being more economical, while the other is also more environmentally efficient. These insights support the development of strategies that align environmental goals with economic priorities, paving the way for more sustainable maritime operations. The study introduces its objectives and reviews relevant literature by presenting a detailed methodology, incorporating emissions modeling with clearly defined parameters. The analysis presents results that undergo sensitivity testing and limitations using MATLAB (R2022a version). The study concludes by discussing policy implications and recommendations for future research and practical advancement

Advanced microgrid optimization using price-elastic demand response and greedy rat swarm optimization for economic and environmental efficiency

In this paper, a comprehensive energy management framework for microgrids that incorporates price-based demand response programs (DRPs) and leverages an advanced optimization method—Greedy Rat Swarm Optimizer (GRSO) is proposed. The primary objective is to minimize the generation cost and environmental impact of microgrid systems by effectively scheduling distributed energy resources (DERs), including renewable energy sources (RES) such as solar and wind, alongside fossil-fuel-based generators. Four distinct demand response models—exponential, hyperbolic, logarithmic, and critical peak pricing (CPP)—are developed, each reflecting a different price elasticity of demand. These models are integrated with a flexible elasticity matrix to assess the dynamic consumer response to fluctuating electricity prices. The study evaluates four operational scenarios, focusing on grid participation, DER utilization, and the impact of real-time pricing (RTP), time of use (TOU), and critical peak pricing strategies. Quantitative results demonstrate the significant cost-saving potential of integrating DRPs with microgrid operations. In the optimal scenario, the GRSO achieved a minimum generation cost of 882¥ for the base load profile. Further, when critical peak pricing (CPP) was applied, the generation cost was reduced to 746¥, representing a 15.4% reduction. For a scenario where the grid’s participation was limited, the logarithmic-based demand response model decreased the generation cost to 817¥, while full grid interaction led to higher cost reductions. Additionally, our results show a significant reduction in peak load, with load factor improvements of up to 87.7% across the studied demand profiles. Furthermore, limiting the grid’s upstream power capacity to 30 kW resulted in a 7% increase in generation cost across all cases, confirming the importance of grid participation in reducing operational costs. The GRSO algorithm outperformed traditional metaheuristics in terms of both execution time and convergence, making it a viable solution for real-time microgrid optimization. In conclusion, the proposed GRSO-based framework provides an efficient approach for microgrid cost minimization, achieving up to a 15.4% reduction in operational costs and notable environmental benefits by reducing emissions. This study highlights the importance of dynamic demand response strategies and grid participation for sustainable and cost-effective microgrid management.

Innovative Approaches of Optimization Methods Used in Geothermal Power Plants: Artificial Neural Networks and Genetic Algorithms

In this study, a general description of geothermal power plants is provided, and the optimization methods used are summarized. Following the review of these optimization methods, the advantages of heuristic methods and the success of the developed models are demonstrated. The challenges in optimizing geothermal systems, including the limitations due to their complexity and the use of multiple parameters, are discussed. Heuristic methods, particularly the widely used artificial neural networks and genetic algorithms, are explained in general terms. Recent studies highlight that the combined use of artificial neural networks and genetic algorithms can produce faster and more consistent results. This demonstrates the benefits of using advanced methods for geothermal resource utilization and power plant optimization. An innovative optimization method has been developed using the operational data of an ORC geothermal power plant in the city of Izmir. The computational method, using genetic algorithms with artificial neural networks as the fitness function, has identified the optimal operating conditions, achieving a 39.41% increase in net power output. The plant’s gross power generation has increased from 4943 kW to 6624 kW.

A Hybrid Framework for Dynamic Clustering and Anomaly Detection in SAP ERP Systems

The growing complexity of enterprise data in SAP ERP systems demands advanced methods for real-time anomaly detection and dynamic clustering optimization. Traditional clustering techniques, such as Standard K-Means, need to adapt to evolving data patterns, while existing AI/ML-based methods like GMM with EM and Self-Organizing Maps (SOM) face challenges in scalability and computational efficiency. This research proposes a hybrid model that integrates GMM, SOM, and adaptive K-Means to address these limitations, offering improved detection accuracy, precision, and recall. Tested on datasets of varying sizes (small, medium, large), the hybrid model consistently outperforms baseline methods, achieving up to 94% detection accuracy and high precision (95.5%) with strong scalability and interpretability. The model leverages distributed computing on a Spark cluster for efficient processing, ensuring seamless integration with SAP ERP environments. Results demonstrate the hybrid model’s ability to detect anomalies effectively, adapt to dynamic data streams, and provide actionable insights through intuitive visualizations. This comprehensive approach makes it a robust solution for maintaining data integrity and enhancing operational decision-making in increasingly complex and data-rich enterprise environments.

OPTIMIZATION METHODS FOR PARAMETER IDENTIFICATION MODEL OF TEST ELECTRORETINOSIGNAL TO ASSESS NEUROTOXICITY RISKS

Introduction. The development of advanced optimization methods plays a crucial role in the enhancement of diagnostic tools in the biomedical field, particularly in the analysis of complex physiological signals. Electroretinography (ERG) is a widely used diagnostic technique that records electrical responses generated by the retina in response to light stimuli, providing valuable insights into the functional health of retinal cells. ERG is instrumental in diagnosing conditions such as retinitis pigmentosa, diabetic retinopathy, and neurotoxicity. However, the analysis of low-intensity electroretinograms (ERG) presents numerous challenges, particularly due to noise and signal distortion, which complicate accurate signal interpretation. Main purpose of this study.This paper is dedicated to developing an expert system for real-time analysis of electroretinographic signals (ERS), focusing on optimizing the parameters of a mathematical model for ERS analysis in conditions where noise and other distortions are present. The primary aim is to improve the accuracy and efficiency of ERG data processing, enabling early detection of neurotoxicity and other retinal conditions. To achieve this, we applied advanced optimization techniques, such as the Nelder-Mead method, known for its effectiveness in handling non-smooth, noisy functions. Conclusions. 1. The application of the Nelder-Mead algorithm for optimizing the complex and noisy ERS model significantly improved the performance of ERG data analysis. The algorithm's adaptability to varying optimization conditions allowed for more accurate model parameter determination, particularly in the context of real-time neurotoxicity detection. Reduction in Processing Time: The time complexity analysis revealed that the Nelder-Mead method reduced the time required to compute the model coefficients by approximately 15%. This improvement was achieved while maintaining the necessary precision for reproducing the test electroretinosignal, making it suitable for real-time applications. Computational Efficiency: One of the key findings of this study is that the use of the Nelder-Mead algorithm reduced the computational load by up to 30%. This makes the method feasible for use in expert systems designed for real-time ERS analysis, allowing for the monitoring of functional changes in the retina during the early stages of neurotoxicity detection.

Integrating Evolutionary Algorithms and Mathematical Modeling for Efficient Neural Network Optimization

Optimizing neural network architectures presents significant challenges due to the vast search spaces and computational costs involved. This study explores the integration of evolutionary algorithms (EAs) and mathematical modeling techniques to enhance neural network optimization. We propose a novel framework combining EAs with dimensionality reduction, surrogate modeling, and hybrid optimization strategies to reduce computational complexity and improve performance. Our results demonstrate that the adapted EAs significantly increase accuracy and F1-scores while reducing the number of generations required for convergence. The hybrid approach, combining EAs with local search techniques, achieves superior performance and robustness across various datasets. These findings provide a foundational basis for future research in advanced optimization methods for neural networks

Validation of a general-use high flux isotope reactor–specific metaheuristic optimization framework for isotope production target design

Currently, advanced optimization methods are limited for isotope production (IP) campaigns at the US Department of Energy’s High Flux Isotope Reactor (HFIR) located at Oak Ridge National Laboratory (ORNL), leading to years of conservative and historical approaches with minimal innovation. Moreover, the growing demand for new and existing isotopes is beginning to challenge the capacity of HFIR. This work explores the development and integration of metaheuristic (MH) optimization techniques for more efficient target design and irradiation strategies. As a test case, the optimization framework was applied to a routinely produced isotope at HFIR, 188W, with the objective of maximizing the specific activity (SA), a key production metric. The framework includes Gnowee, a Python-based MH optimization algorithm, coupled with the Monte Carlo N-Particle version 6 (MCNP6) and Oak Ridge Isotope Generation (ORIGEN) activation/depletion/decay codes to design, simulate, and evaluate thousands of potential target design and irradiation scheme candidates. The framework relies on mock input files, design and irradiation variables for the algorithm to select, as well as a user-defined objective function to score each candidate based on the returned SA. Given the inherent complexities and computational time required when modeling and simulating the full HFIR model, a novel simplified MCNP6 model is presented in this article to increase the computational efficiency of the framework. The variables explored include irradiation location, number of cycles, and the number of W samples. Over 1,000 simplified model candidates were simulated in the same amount of time as a single full HFIR model run. By comparing the simplified model optimization’s top candidate(s) with the full HFIR model results, the framework was verified to accurately explore the design space and converge on the top performing candidates. Lastly, past experimental data was compared to the data generated by the framework/model and both show that fewer W rings return higher SA, as expected. The verified and validated techniques provide a standardized solution to increase IP efficiencies by exploring thousands of unique target designs and irradiation strategies in a similar time as that required to run a single case in the full HFIR MCNP6 model. Both the novel simplified model and the full HFIR model show a more than 30% increase in SA if all presented modifications are applied to the current design and strategy. Thus, the objective of building a general-use, computationally efficient optimization framework for HFIR IP was accomplished, and has the potential to be applied to other IP campaigns.

Topology Optimization Enabled High Performance and Easy‐to‐Fabricate Hybrid Photonic Crystals

AbstractPhotonic crystals (PtCs) can confine and guide electromagnetic waves within specific frequency ranges, forming the foundation for promising optical applications. To numerically design PtCs with broad bandgaps, materials with high dielectric constants are favored. However, fabricating these high dielectric constant materials into microstructures is extremely challenging and it suffers from limitation of low fabricating resolution. To address this problem, this paper proposes hybrid microstructures composed of an easy‐to‐fabricate core and a high dielectric constant coating layer, which leverages the strength of both materials. This paper establishes a topology optimization algorithm to generate these PtCs with maximized bandgaps. Numerical examples demonstrate the effectiveness of the proposed method in generating optimized unit cells for both transverse magnetic (TM) and transverse electric (TE) modes. The hybrid PtCs offer unprecedented opportunities for the fabrication of optical devices, encouraging further research on multimaterial optical systems and advanced optimization methods to explore photonic bandgap materials beyond those offered by the current photonic technology.

Quasinormal mode expansion in thin elastic plates

Elastic wave manipulation using large arrays of resonators is driving the need for advanced simulation and optimization methods. To address this we introduce and explore a robust framework for wave control: quasinormal modes (QNMs). Specifically, we consider the problem for thin elastic plates, where the Green's function formalism is well known and readily exploited to solve multiple scattering problems. By studying the associated nonlinear eigenvalue problem we derive a dispersive QNM expansion, providing a reduced-order model for efficient forced response computations which reveals physical insight into the resonant mode excitation. Furthermore, we derive eigenvalue sensitivities with respect to resonator parameters and apply a gradient-based optimization to design quasi-bound states in the continuum and position eigenfrequencies precisely in the complex plane. Scattering simulations validate our approach in structures such as graded line arrays and quasicrystals. Drawing on QNM concepts from electromagnetism we demonstrate significant advances in elastic metamaterials, highlighting their potential for tailored wave manipulation. Published by the American Physical Society 2024

Mathematical Optimization of Electric Motor Designs

When designing and improving the performance of electric motors, mathematical optimization is very important. The main goals are usually to make the motors more efficient, lower their costs, and work within certain limits. The main topic of this study is how to improve electric motor designs using advanced optimization methods, such as multi-objective optimization. The study looks at how to use different types of computer algorithms together, like gradient-based methods, genetic algorithms, and particle swarm optimization, to solve difficult design problems. Some of these problems are reducing energy loss, making the best use of materials, and finding the right balance between different performance measures such as speed, power density, and temperature management. Building mathematical models of the motor's physical and functional features is the first step in this method. Then, optimization methods are applied to these models. Finite element analysis (FEA) is used to correctly model the motor's electric behavior. This makes sure that the optimization process considers physical limits and nonlinearities that happen in the real world. The study also looks into how different design factors, like the shape of the motor's core, the way the windings are set up, and the materials used, affect its total performance. The study also looks at the fact that motor design has more than one goal by using Pareto front analysis to find the best ways to balance different goals. This lets people come up with motor designs that are good for speed, efficiency, and cost-effectiveness. Case studies of the design of different kinds of electric motors, such as induction motors, permanent magnet synchronous motors (PMSMs), and brushless DC motors (BLDCs), show that the proposed optimization method works well. The results show that mathematical optimization has the ability to make the planning process a lot better. This could lead to motors that work better, cost less, and are better suited to certain uses. The study ends with a talk of how optimization methods could be used in the future to improve the design of electric motors, especially for new technologies like electric cars and green energy systems.

The Development of Nano Si Materials in the Application of Lithium-Ion Batteries Anode

Electric vehicles (EVs) have become a practical alternative to conventional fuel vehicles due to their environmental friendliness, high energy efficiency, low operating costs, etc. In EVs, lithium-ion batteries (LIBs) play a crucial role. It provides a power source for EVs and directly affects their performance. Among them, LIBs with silicon nanomaterials as negative electrodes show great potential in improving EV performance. This article aims to conclude Si-based anode LIBs’ present challenges and introduce advanced optimization methods with nano-Si material according to these challenges. It starts with the principle of Li-ion storage in Si. Then, problems faced by pure Si anodes and the preliminarily improved Si-based anodes are listed. Finally, further optimization methods in the nano Si anodes during these years are introduced. The optimization methods mainly include improving the service life of nano-Si-based anode and reducing the cost of manufacture. This comprehensive review provides reference and inspiration for developing Si-based anode LIBs applied in EVs.

Multi-Objective Optimal Power Flow Analysis Incorporating Renewable Energy Sources and FACTS Devices Using Non-Dominated Sorting Kepler Optimization Algorithm

In the rapidly evolving landscape of electrical power systems, optimal power flow (OPF) has become a key factor for efficient energy management, especially with the expanding integration of renewable energy sources (RESs) and Flexible AC Transmission System (FACTS) devices. These elements introduce significant challenges in managing OPF in power grids. Their inherent variability and complexity demand advanced optimization methods to determine the optimal settings that maintain efficient and stable power system operation. This paper introduces a multi-objective version of the Kepler optimization algorithm (KOA) based on the non-dominated sorting (NS) principle referred to as NSKOA to deal with the optimal power flow (OPF) optimization in the IEEE 57-bus power system. The methodology incorporates RES integration alongside multiple types of FACTS devices. The model offers flexibility in determining the size and optimal location of the static var compensator (SVC) and thyristor-controlled series capacitor (TCSC), considering the associated investment costs. Further enhancements were observed when combining the integration of FACTS devices and RESs to the network, achieving a reduction of 6.49% of power production cost and 1.31% from the total cost when considering their investment cost. Moreover, there is a reduction of 9.05% in real power losses (RPLs) and 69.5% in voltage deviations (TVD), while enhancing the voltage stability index (VSI) by approximately 26.80%. In addition to network performance improvement, emissions are reduced by 22.76%. Through extensive simulations and comparative analyses, the findings illustrate that the proposed approach effectively enhances system performance across a variety of operational conditions. The results underscore the significance of employing advanced techniques in modern power systems enhance overall grid resilience and stability.

Refined transmission line ice-cover prediction model and optimization study

Abstract This study aims to develop a fine-grained transmission line ice-cover prediction model and conduct an optimization study. Ice cover is one of the important factors leading to transmission line accidents, so accurately predicting the ice cover of transmission lines is crucial to ensure the safe operation of power grids. In this paper, an efficient ice-cover prediction model is constructed based on advanced machine learning algorithms and optimization methods and is validated and optimized with a large amount of experimental data. The results show that the proposed model has high accuracy and prediction capability in ice cover prediction, which provides important support for the safe operation of transmission lines.

Optimized hybrid osprey with PSO control for improved VSC-HVDC-wind power integration

Innovative power systems include offshore wind farms (OWFs) to generate electricity from renewable sources. So, reliable control systems are also necessary to make sure these power systems run smoothly. The purpose of this study is to combine the Osprey Optimization with Particle Swarm Optimization (OOPSO) to fine-tune the gains of Proportional-Integral (PI) controllers within the investigated wind energy conversion system (WECS) to enhance its performance. The study confirms the effectiveness of using the Hybrid OOPSO algorithm to optimize PI controllers in a WECS. The WECS includes two voltage source converter (VSC) stations at each end of a high voltage direct current (HVDC) transmission system. The transmission system links OWFs to the grid. The research demonstrates that the Hybrid OOPSO algorithm is superior to the genetic algorithm (GA) and PSO by enhancing setup stability and allowing fast voltage regaining following different fault cases. The introduced method performs more remarkably than traditional methods such as GA and PSO. The results of this study have shown that the proposed OOPSO enhances the overshoot in onshore voltage transient response under a symmetrical fault condition by 26% over PSO, 24% over GA, and 16% over OOA. The study is conducted using MATLAB/Simulink. The study underscores the importance of advanced optimization methods to guarantee offshore wind energy systems' efficient and dependable functioning.

Comparative Analysis of Inverse Problem-Solving Techniques: Integrating Deep Learning with Advanced Optimization Methods

This paper presents a comparative analysis of four distinct approaches to solving inverse problems in engineering and scientific applications. The studies under comparison integrate deep learning techniques, specifically using TensorFlow, with various optimization methods: Genetic Algorithm (GA), Ant Colony Optimization (ACO), LMFIT (employing Nelder-Mead and Powell methods), and Particle Swarm Optimization (PSO). All four approaches aim to predict design parameters for achieving desired response profiles. This analysis examines the methodologies, performance metrics, and unique features of each approach, providing insights into their relative strengths and potential applications.

Grid Integration Strategies for Optimizing Renewable Energy Deployment and Grid Resilience

This study explores the integration of renewable energy sources, namely, solar and wind, focusing on strategies to optimize their deployment into the electrical grid, and increasing the resiliency of the grid. Using four-year comprehensive data from Spain, including energy consumption, generation, pricing, and the condition of the weather, advanced statistical analysis, regression models, and optimization methods have been employed. Based on the results, it is clear that solar energy is seasonal, and wind energy is variable, with the weather playing a considerable role in the energy output. The optimization analysis showed that when the renewable capacity was increased to include 30 MW of solar and 120 MW of wind, the energy demand would be met at a significantly lower total system cost of $12.60 per unit. The costs related to operation and emissions would also decrease notably. However, with the regression models giving modest values of R² equal to 0.19 for solar and R² equal to 0.21 for wind, the extent of these developments and prediction can be fairly modest. Still, these results provide a strong backbone for the prediction of energy generation and show that modernization of the grid and adaptive management are of crucial importance. The results of the study could provide a guideline for policymakers and energy managers on how these goals can be achieved.

Modeling and validation of purification of pharmaceutical compounds via hybrid processing of vacuum membrane distillation

This study provides an in-depth examination of forecasting the concentration of pharmaceutical compounds utilizing the input features (coordinates) r and z through a range of machine learning models. Purification of pharmaceuticals via vacuum membrane distillation process was carried out and the model was developed for prediction of separation efficiency based on hybrid approach. Dataset was collected from mass transfer analysis of process to obtain concentration distribution in the feed side of membrane distillation and used it for machine learning models. The dataset has undergone preprocessing, which includes outlier detection using the Isolation Forest algorithm. Three regression models were used including polynomial regression (PR), k-nearest neighbors (KNN), and Tweedie regression (TWR). These models were further enhanced using the Bagging ensemble technique to improve prediction accuracy and reduce variance. Hyper-parameter optimization was conducted using the Multi-Verse Optimizer algorithm, which draws inspiration from cosmological concepts. The Bagging-KNN model had the highest predictive accuracy (R2 = 0.99923) on the test set, indicating exceptional precision. The Bagging-PR model displayed satisfactory performance, with a slightly reduced level of accuracy. In contrast, the Bagging-TWR model showcased the least accuracy among the three models. This research illustrates the effectiveness of incorporating bagging and advanced optimization methods for precise and dependable predictive modeling in complex datasets.

Spiral-refraction mutation prairie dog algorithm: Optimization framework for engineering design of interconnected multimachine power system

Many real-world engineering problems, characterized by high-dimensionality, nonlinearity, nonconvexity, and multi-modality, demand advanced optimization methods. Traditional algorithms may struggle with these challenges. Prairie dog optimization (PDO) was proposed for function optimization but faces limitations in balancing exploration and exploitation due to two reasons. The first one is related to diversity features which may not be efficient, and the second one is related to having no leading mechanism for direct search feature towards the promising regions. With that in mind, this study introduces an enhanced PDO variant, improved PDO (IPDO), addressing PDO's drawbacks through two key strategies: refraction-based learning (RBL) and spiral search learning (SSL). RBL enhances exploration by generating refraction solutions, while SSL conducts deep local searches around the best solution, strengthening exploitation. IPDO's performance is evaluated on benchmarks, IEEE CEC2017/CEC2020 test suites, and real-world constraint engineering optimization problems. Comparative analyses, including statistical measures, convergence analysis, and boxplot analysis, demonstrate IPDO's superiority. Besides, the IPDO is applied to estimate more promising parameters of power system stabilizer utilized in an interconnected multimachine power system using Western System Coordinating Council three-machine, nine-bus power system. Results illustrate that the IPDO harvests the better estimation among the other methods, making it to be an efficient and powerful tool for dealing with the efficient operation of an interconnected multimachine power system which is a challenging real-world engineering problem.

Optimizing hybrid energy storage: A multi-objective approach for hydrogen-natural gas systems with carbon-emission management

This article addresses the challenges of load curve variability in integrated energy systems (IES) and emphasizes carbon neutralization in response to global environmental concerns. It introduces a game-theoretic approach to understand the collaborative dynamics within an integrated energy-hydrogen system (HGESS). The study develops a collaborative game model for the IES-HGESS partnership, focusing on carbon neutralization considerations. Using game theory, it investigates the determinants shaping this partnership and extends to create a hybrid model for day-ahead and real-time markets. To foster enduring cooperation, the study introduces a cooperation profit coefficient and devises an income distribution strategy for HGESS-IES interactions. A load management program is incorporated to reduce costs and enhance profitability. Addressing complexity and constraints, the article introduces an advanced multi-objective particle swarm optimization method. Tested on a sample system under various conditions, the results demonstrate that the alliance between IES and HGESS can significantly enhance net profits, achieving mutual benefit and a win-win outcome while advancing sustainability in energy management.

A Retinal Vessel Segmentation Method Based on the Sharpness-Aware Minimization Model.

Retinal vessel segmentation is crucial for diagnosing and monitoring various eye diseases such as diabetic retinopathy, glaucoma, and hypertension. In this study, we examine how sharpness-aware minimization (SAM) can improve RF-UNet's generalization performance. RF-UNet is a novel model for retinal vessel segmentation. We focused our experiments on the digital retinal images for vessel extraction (DRIVE) dataset, which is a benchmark for retinal vessel segmentation, and our test results show that adding SAM to the training procedure leads to notable improvements. Compared to the non-SAM model (training loss of 0.45709 and validation loss of 0.40266), the SAM-trained RF-UNet model achieved a significant reduction in both training loss (0.094225) and validation loss (0.08053). Furthermore, compared to the non-SAM model (training accuracy of 0.90169 and validation accuracy of 0.93999), the SAM-trained model demonstrated higher training accuracy (0.96225) and validation accuracy (0.96821). Additionally, the model performed better in terms of sensitivity, specificity, AUC, and F1 score, indicating improved generalization to unseen data. Our results corroborate the notion that SAM facilitates the learning of flatter minima, thereby improving generalization, and are consistent with other research highlighting the advantages of advanced optimization methods. With wider implications for other medical imaging tasks, these results imply that SAM can successfully reduce overfitting and enhance the robustness of retinal vessel segmentation models. Prospective research avenues encompass verifying the model on vaster and more diverse datasets and investigating its practical implementation in real-world clinical situations.