Multi-objective Design Optimization Research Articles

A parallel variable-fidelity algorithm for efficient constrained multi-objective aerodynamic design optimization

Modern aerodynamic design optimization aims to discover optimal configurations using computational fluid dynamics under complex flow conditions, which is a typical expensive multi-objective optimization problem. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) combined with efficient global optimization is a promising method but requires enhanced efficiency and faces limitations in its application to multi-objective aerodynamic design optimization (MOADO). To address the issues, an efficient parallel MOEA/D assisted with variable-fidelity optimization (VFO) is proposed for solving MOADO, called the MOEA/D-VFO algorithm. Variable-fidelity surrogates are built for objectives and constraints, achieving higher accuracy using fewer high-fidelity samples and a great number of low-fidelity samples. By retaining more good candidates, the sub-optimization problems defined by decomposing original objectives are capable of discovering more favorable samples using MOEA/D, which prompts optimization convergence. A constraint-handling strategy is developed by incorporating the probability of feasibility functions in the sub-optimizations. The selection of new samples for parallel evaluation is improved by filtering out poor candidates and selecting effective promising samples, which improves the feasibility and diversity of solved Pareto solutions. A Pareto front (PF) can be efficiently found in a single optimization run. The proposed approach is demonstrated by four analytical test functions and verified by two aerodynamic design optimizations of airfoils with and without constraints, respectively. The results indicate that the MOEA/D-VFO approach can greatly improve optimization efficiency and obtain the PF satisfying constraints within an affordable computational budget.

Multi-objective optimization design and experiment for a magnetic micro-vibration isolator considering stiffness trade-offs.

Vibration substantially degrades machining quality and measurement accuracy in ultra-precision processes, necessitating the implementation of vibration isolators to mitigate these effects. Magnetic vibration isolators represent a promising alternative due to their wide isolation frequency range, low energy consumption, and compatibility with vacuum environments. In designing the quasi-zero stiffness magnetic vibration isolator, the particle swarm optimization algorithm is employed to balance multiple performance indicators. To address the limitations of conventional optimization methods, which excessively prioritize stiffness and fail to encompass the entire performance spectrum of magnetic vibration isolators, this study presents an innovative optimization approach. This novel strategy directly enhances vibration isolation by integrating transmissibility and compliance considerations. Structural parameters for two types of magnetic vibration isolators were established through optimizations utilizing both conventional and innovative techniques. Simulations and experiments demonstrate that isolators developed using the proposed optimization method outperform those designed with conventional strategies, thereby validating the effectiveness of this advancement. The insights presented in this paper illuminate a novel and effective pathway for the conceptualization and refinement of magnetic vibration isolators.

Multi-objective optimal design of double-suction centrifugal pump impeller using agent-based models

Multi-objective optimal design of double-suction centrifugal pump impeller using agent-based models

Carbon emission warning method for machine tool manufacturing process based on dynamic adaptive EWMA control chart.

Machine tools constitute the backbone of the industrial sector, representing the largest global inventory of equipment. The carbon emissions resulting from the production of each machine tool merit attention. Effective management of carbon emissions in the machine tool manufacturing process is crucial. This paper introduces a novel method for early carbon emission warnings in the machine tool manufacturing process, utilizing an adaptive dynamic exponentially weighted moving average (EWMA) approach. This method addresses the challenges in identifying and monitoring abnormal carbon emissions, emerging from uncertainties and dynamic correlations. Utilizing dynamic sampling techniques and adaptive principles, this method constructs an adaptive dynamic EWMA control chart. The EWMA control chart incorporates a multi-objective optimization design model, concentrating on carbon emissions in the machine tool manufacturing process, and incorporates statistical, economic, and environmental objectives. To mitigate slow convergence rates and enhance optimization accuracy in complex control chart multi-objective optimization algorithms, this study proposes an enhanced Harris hawks optimization (HHO) algorithm as the solving algorithm. Finally, the application of this method is demonstrated through the monitoring of carbon emissions in the manufacturing process of a five-axis machine tool (EOC), as a case study. The results validate the method's rapid responsiveness to abnormal carbon emissions, providing alerts. This further confirms the efficacy and feasibility of the proposed approach. Ultimately, this approach offers a viable strategy for fostering environmentally conscious and high-quality growth in the machine tool industry.

Multi-objective optimization design for the carcass of marine flexible pipes based on BP neural network and genetic algorithm

Multi-objective optimization design for the carcass of marine flexible pipes based on BP neural network and genetic algorithm

Multi-Objective Optimization of the Ultrasonic Scalpel Rod and Tip with Improved Performance: Vibration Frequency, Amplitude, and Service Life

Ultrasonic scalpel design for minimally invasive surgical procedures is mainly focused on optimizing cutting performance. However, an important issue is the low fatigue life of traditional ultrasonic scalpels, which affects their long-term reliability and effectiveness and creates hidden dangers for surgery. In this study, a multi-objective optimal design for the cutting performance and fatigue life of ultrasonic scalpels was proposed using finite element analysis and fatigue simulation. The optimal design parameters of resonance frequency and amplitude were determined. By setting the transition fillet and keeping the gain structure away from the node position to enable the scalpel to have a high service life with excellent cutting performance. The frequency modulation method of setting the vibration node bosses at the node position and setting the vibration antinode grooves at the antinode position was compared. Then, the mechanism of the influence of various design elements, such as tip, shank, node position, and antinode position, on the resonance frequency, amplitude, and fatigue life of the ultrasonic scalpel was analyzed, and the optimal design principles of the ultrasonic scalpel were obtained. The proposed ultrasonic scalpel design was confirmed by simulations, impedance measurements, and liver tissue cutting experiments, demonstrating its feasibility and enhanced performance. This research introduces innovative design strategies to improve the fatigue life and performance of ultrasonic scalpels to address an important issue in minimally invasive surgery.

Multi-objective optimization design of rail grinding profile in Curve Section of Subway based on wear Evolution and representative worn profile

Curve rail grinding has always been one of the key points of subway maintenance and repair. The appropriate grinding can effectively reduce wear. A multi-objective optimization design method for grinding profiles in curved sections is proposed. Firstly, representative grinding profiles are selected as the initial population using the dynamic time regularization algorithm (DTW). Then, the optimal design range is determined based on wear characterization analysis, and mathematical expressions of wheel profiles are chosen as design variables to establish a parametric model. Next, the prediction model considering the evolution of wheel wear is incorporated into the multi-objective function, and objective function adaptive weight adjustment coefficient factors are introduced to establish the multi-objective optimization model for wheel profiles. The Latin hypercubic sampling method is employed to establish the RBF agent model for simulation calculation, and the optimization design of wheel profiles is carried out using the TS-NSGA-II multi-objective algorithm.

Crashworthiness analysis and optimization design of special-shaped thin-walled tubes by experiments and numerical simulation

Thin-walled structures are widely used as typical high-efficiency energy-absorbing structures in crash safety protection. This paper aims to combine the characteristic of the square tube which concentrates energy dissipation through angle elements with the stable fold deformation of the circular tube, and innovatively propose a special-shaped thin-walled tube that contains both angle elements and arc elements. The failure behavior and energy absorption characteristics of the special-shaped tube were investigated by compression test and numerical simulation. The simulation results showed that the special-shaped thin-walled tubes have a significant advantage in energy absorption, and the specific energy absorption of the special-shaped tubes is 31.57% and 75.2% higher than that of the equal-mass circular and square tubes, respectively. Next, through finite element analysis, the effects of various parameters and initial imperfections on the crashworthiness of the special-shaped tubes were compared. The results indicated that adjustments to geometrical parameters significantly impact the energy absorption properties and crushing behavior of thin-walled tubes. Moreover, the tube with induced circular holes exhibited an optimal deformation mode. Further, a multi-objective optimal design of the metal special-shaped tube was carried out to obtain the best parameter configuration of the metal special-shaped tube. Finally, the special-shaped structure was extended to CFRP/AL hybrid thin-walled tubes. The failure behavior and energy absorption enhancement mechanism of the hybrid special-shaped tubes were investigated with experiments, and the absorbed energy of the hybrid tube was about 20% higher than the sum of the absorbed energy of the single constituent tubes. The effect of the CFRP lay-up pattern on the crashworthiness of the hybrid tube was investigated by numerical simulation, and it was found that the energy absorption capacity of the hybrid tube could be improved by appropriately increasing the number of layers and the proportion of axial fibers.

Multi-objective optimization design of NPR protection shell for hydrogen storage tank

In order to improve the safety of on-board hydrogen storage tanks during collision, a protective shell based on a negative Poisson’s ratio (NPR) core is designed in this paper. After analyzing and comparing the crashworthiness of three typical honeycomb structures, the concave hexagonal negative Poisson’s ratio honeycomb is selected as the energy-absorbing inner core of the hydrogen storage tank protection structure. The sensitivity analysis of the structural parameters of the NPR shell is conducted through orthogonal tests to identify parameters with a significant impact on crash performance. These parameters are then used as experimental variables for subsequent optimization design. Subsequently, a response surface approximation model between the optimization objective and the structural parameters is established based on the response surface method. Finally, the adaptive simulated annealing algorithm (ASA), neighborhood cultivation genetic algorithm (NCGA), and non-dominated sorting genetic algorithm-II (NSGA-II) are used to optimize the structural parameters, and the optimization results are verified by the whole-vehicle crash simulation. The simulation results demonstrate that all three algorithms achieve better optimization results, among which NCGA is more advantageous in improving the overall performance of the protective shell. After NCGA optimization, the specific energy absorption of the protective shell increases by 19.75%, the maximum collision force of the rigid wall decreases by 23.63%, and the maximum stress of the hydrogen storage tank body decreases by 22.77%. These findings indicate that the designed protection shell effectively improves the crashworthiness of the hydrogen storage tank during collisions.

On crashworthiness design of hybrid metal–composite battery-pack enclosure structure

Considering the crashworthiness and lightweight of the battery-pack enclosure structure (BPE), this article demonstrates multi-objective optimization design of BPE subjected to extrusion conditions by using a validated numerical model and an analytical approach. BPE is made with a unique combination of three materials: a high-strength steel (HSS) surrounding enclosure, an aluminum below enclosure, and a carbon fiber-reinforced polymer (CFRP) upper enclosure. First, the constitutive model of BPE material was determined based on the results obtained in material testing, meanwhile, the structural extrusion analysis of the initial BPE was performed and validated by the published experimental data. Second, a contribution analysis method based on modified TOPSIS (MTOPSIS) is adopted to screen the design parameters of the optimal structure. Based on this, the mass of the BPE and the maximum extrusion deformation of the BPE are employed as objectives to establish an optimization mathematical model. Furthermore, improved multi-objective particle swarm optimization (IMOPSO) has been exerted as the optimization algorithm to conduct optimization design, the results show the optimization model has a better optimization level and fitting ability. Finally, the performance comparison results before and after model optimization show the crashworthiness performance can be improved significantly, while the lightweight performance of BPE is ensured.

Multi-objective optimization design of a circular core paper sandwich panel

Abstract Ensuring sufficient mechanical performance while enabling lightweight design is critical for utilizing paper sandwich panels in the furniture industry. To design lightweight sandwich panels that balance mechanical properties and cost, this study developed a circular core paper sandwich panel (CCPSP) and investigated its structural efficiency using multi-objective optimization. The response surface method (RSM) based on Box–Behnken design was utilized to establish mathematical models relating the paper tube spacing, inner diameter, and height to the out-of-plane compressive strength, density, and cost. The resulting models effectively revealed the coupled effects of the parameters on the responses. Subsequently, the models were optimized using the non-dominated sorting genetic algorithm II (NSGA-II) to find the Pareto optimal trade-offs between maximizing compressive strength while minimizing its density and cost. The optimization solution resulted in an optimal set of paper tube geometries that maximized the structural efficiency of CCPSP. Overall, lower tube height conferred superior structural efficiency, while tube spacing and diameter were constrained. The results highlight the potential of CCPSP as an efficient and sustainable material for furniture manufacturing, enabled by multi-objective optimization of its structure.

Cellular gradient algorithm for solving complex mechanical optimization design problems

In mechanical optimization design problems, there are often some non-continuous or non-differentiable objective functions. For these non-continuous and non-differentiable optimization objectives, it is often difficult for existing optimal design algorithms to find the desired optimal solutions. In this paper, we incorporate the idea of gradient descent into cellular automata and propose a Cellular Gradient (CG) method. First, we have given the basic rules and algorithmic framework of CG and designed three kinds of growth and extinction rules respectively. Then, the three evolutionary rules for cellular within a single cycle are analyzed separately for form and ordering. The best expressions for the cellular jealous neighbor rule and the solitary regeneration rule are given, and the most appropriate order in which the rules are run is selected. Finally, the solution results of the cellular gradient algorithm and other classical optimization design algorithms are compared with a multi-objective multi-parameter mechanical optimization design problem as an example. The computational results show that the cellular gradient algorithm has an advantage over other algorithms in solving global and dynamic mechanical optimal design problems. The novelty of CG is to provide a new way of thinking for solving optimization problems with global discontinuities.

Crashworthiness analysis and multi-objective optimization design for foam-filled spiral tube

Thin-walled structures, due to their favorable mechanical properties and exceptional energy absorption capabilities, find extensive applications across various engineering fields. This study, drawing inspiration from natural spiral structures, introduces a novel foam-filled spiral tube (FFST) to further enhance the crashworthiness of thin-walled structures. The spiral tubes (STs) and random foam are additively manufactured. Quasi-static compression tests are undertaken to investigate the energy absorption properties of STs, foam and FFSTs. Unlike conventional methods, this study adopts micro-computed tomography (micro-CT) technology to understand the mechanisms of interaction between the foam and ST. The parametric study is performed based on the finite element model to evaluate the influence of meso‑structure properties of tubes and foam fillers on the crashworthiness and deformation modes. The experimental results indicate that an increase in the wall thickness of both the ST and foam leads to a simultaneous increase in specific energy absorption (SEA) and initial peak crushing force (IPCF). Conversely, a decrease in the wavelength and an increase in the amplitude of waves results in the reduction of both SEA and IPCF, along with an enhancement of crushing force efficiency (CFE). Micro-CT images indicate mutual extrusion between the foam and ST and with a reduction in wavelength, the number of folds in the samples increased, thus enhancing the energy-dissipation capacity. The numerical results reveal a strengthening of interaction between the foam and ST with decreasing wavelength and increasing foam cell wall thickness. A theoretical model is proposed for predicting the plateau stress of FFSTs based on the energy conservation principle and the plastic hinge theory. Comparisons between theoretical and test results exhibit good agreement. Comparing the FFST obtained through multi-objective optimization design with an ST featuring same structural parameters, it is observed that the IPCF increases by 8.00 %, SEA increases by 18.10 %, and the undulation of load-carrying capacity (ULC) decreases by 31.96 %. Finally, through a comparative analysis with other energy-absorbing structures, the outstanding performance of this structure is established. This study offers a new approach for investigating interaction effects and provides useful guidelines for the design of future high-performance light-weight materials and structures.

Multi-objective optimal sizing and design of renewable and diesel-based autonomous microgrids with hydrogen storage considering economic, environmental, and social uncertainties

The multifaceted nature of human society necessitates the consideration of various indicators when planning and designing energy systems. The success of energy systems is contingent on their ability to reliably meet demands while satisfying different objectives that align with societal needs. This paper presents the multi-objective optimal design and configuration of hydrogen-storage-based microgrids to reliably meet electric load demands in remote regions while considering economic, environmental and social uncertainties. A comprehensive Mixed Integer Linear Programming (MILP) was adopted to model the microgrid consisting of renewable energy systems (RES), hydrogen energy storage system (HESS), battery energy storage system (BESS), and diesel generator (DG). Advanced Interactive Multidimensional Modelling System (AIMMS) was used to perform the deterministic and robust optimisation with special consideration on cost-greenhouse emissions minisation and employment generation maximisation. This study further performs a comparative analysis between hydrogen-based microgrids and lithium-ion battery-based microgrids in terms of the key objectives. In overall performance, the configuration consisting of photovoltaic (PV), wind turbine (WT), fuel cell (FC), electrolyser (EL) and low-pressure tank (LPT) outplays the other configurations considered in terms of total job factor, levelised cost of electricity, renewable energy penetration factor, carbon emission reduction capability. Considering both deterministic and robust solutions of the configuration, the levelised cost of electricity ranges between 0.131 and 0.169 $/kWh, the total lifetime cost varies from $2,002,100 to $6,784,740, and the job provision factor ranges between 0.339 and 0.447. Nevertheless, there is a need for further reduction of the investment cost for its continued technological and market penetration. This is a good basis for the adoption of hydrogen-based storage systems with renewable energy systems.

Vibration source analysis and structural optimization design of rotary table based on OTPA.

Due to the influence of coal rock shape, hardness, working environment and other factors in the cutting process of cantilever roadheader, the cutting head will produce irregular and violent vibration. As the rotary table of key stress components, its operation process stability, dynamic reliability and life affect the cutting efficiency and cutting stability of cantilever roadheader. In order to study the vibration characteristics of the rotary table in the cutting process, firstly, based on the theory of spatial force analysis and calculation, the spatial mechanical model of the rotary table of the cantilever roadheader is established. By solving the balance equation of the rotary table force system, the variation law of the load at the hinge ear of the rotary table with the cutting pitch angle and the horizontal angle is obtained. Secondly, based on the path transfer analysis method of working condition, the vibration data of cutting head, cutting cantilever, cutting lifting and rotary hydraulic cylinder under stable cutting condition are taken as input signals. By constructing the transfer path analysis model of rotary table working condition, the synthetic vibration of rotary table in cutting process is simulated, and the main vibration source of rotary table is determined. Then, the vibration contribution and contribution degree of each vibration excitation point to the hinge ear of rotary table are studied. By building a cutting test bench, the vibration response of rotary table in cutting process is tested to verify the correctness of the theoretical model.Thirdly, based on the frequency domain analysis method of random vibration fatigue life, combined with the S-N curve of the rotary table, the PSD curve at the maximum stress of the rotary table is obtained by modal excitation method, and the load data is imported into ANSYS nCode software to obtain the life cloud diagram and damage cloud diagram of the rotary table, and then the fatigue life of the rotary table under symmetrical cyclic load is solved. Finally, based on the response surface optimization analysis method, the maximum stress and maximum deformation of the rotary table are taken as the optimization objectives, and the aperture of each hinge ear of the rotary table is taken as the optimization variable. Based on Design Expert, a second-order regression model is established to realize the multi-objective optimization design of the key stress parts of the rotary table in the cutting process. The simulation results show that under the same cutting conditions, the maximum stress of the optimized rotary table is reduced by 15.82% year-on-year, and the maximum deformation is reduced by 24.70% year-on-year. The optimized rotary table structure can better adapt to the cutting process, which is beneficial to improve the service life of the rotary table and enhance its operation stability. The research results are beneficial to enrich the relevant research theory in the field of rotary table vibration of cantilever roadheader, and are beneficial to improve the service life of the rotary table and the efficiency of tunneling and mining.

Multi-Objective Optimization Design of Dynamic Performance of Hydrofoil with Gurney Flap

The horizontal axis tidal turbine, as a crucial device for capturing tidal energy, has gained significant attention because it has better energy efficiency performance. Enhancing the performance of foils, a vital part of tidal turbine blades, can significantly improve tidal turbine performance. Among numerous methods to enhance the foil performance, the Gurney flap has gained significant attention due to its avoidance of complex structural design. Currently, there is limited research on optimizing the design of Gurney flaps while considering the dynamic performance of foils. In this study, the S809 foil with a blade cross-section was selected as the research subject, a multi-objective optimization design platform was created by integrating a multi-objective optimization algorithm with Computational Fluid Dy-namics (CFD) numerical simulation techniques. The objective of this platform is to enhance the dynamic performance of the hydrofoil by optimizing the geometric structure of the Gurney flap. The improvement of dynamic lift and the size of the dynamic stall hysteresis loop are used as objective variables in this study to evaluate the hydrofoil’s dynamic performance. The optimal Latin hypercube design method is used in the optimization process to choose sample locations, and the Kriging approximation model is used to determine the relationship between the design variables and the objective variables. Meanwhile, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is used to create a multi-objective optimization platform for solving the optimization problem, and the optimized results are validated using CFD. Comparative validation results show that quantifying the dynamic performance during hydrofoil pitching oscillation and using the optimal Latin hypercube design method and Kriging approximation model for optimizing the Gurney flap structure is rational and accurate. This study explores the mechanism of the Gurney flap through in-depth CFD numerical simulations and finds that the Gurney flap affects the flow characteristics at the hydrofoil’s trailing edge, thereby influencing the performance. It increases the pressure difference between the pressure and suction surfaces, thus enhancing the hydrofoil’s lift. Finally, this article provides three recommended parameters to improve the dynamic performance of the hydrofoil. This research can serve as a reference for the application of Gurney flaps in tidal turbine blade design.

On the optimal multi-objective design of fractional order PID controller with antlion optimization

This study introduces an optimal multi-objective design approach for a robust multimachine Fractional Order PID Controller (FOPID) using the Antlion algorithm. The research focuses on the need for effective stabilizers in multimachine power systems by employing traditional speed-based lead-lag FOPID controllers. The study formulates a multi-objective problem, optimizing the damping factor and damping ratio of lightly damped electromechanical modes to maximize a composite set of objective functions, tackled through the Antlion algorithm. Stability analysis of Single-Machine Infinite-Bus (SMIB) and multimachine power systems is conducted based on rotor speed and power deviation minimization in the time domain response, along with damping ratio and eigenvalue analysis. The proposed approach is implemented and tested on three IEEE test cases, showcasing significant improvements in stability through the reduction of maximum overshoot (Mp) and settling time (ts) of speed deviation. Comparative analysis with other optimization-based FOPID controllers underscores the superiority of the proposed approach in enhancing stability in multimachine power systems. The main impact of this research lies in its contribution to the advancement of stability enhancement techniques in multimachine power systems, offering a systematic framework for optimal FOPID controller design and empowering decision-making processes in power engineering.

Multi-objective topology optimization design of silicon carbide metal oxide semiconductor field effect transistors power module liquid-cooled heatsink for electric vehicles

Silicon carbide (SiC) metal oxide semiconductor field effect transistors (MOSFETs) is gradually replacing silicon-based insulated gate bipolar transistor (IGBT) as the switching devices in electric vehicle power inverters due to its higher operating temperatures, switching speeds, and frequencyies. However, the high switching frequency of SiC MOSFETs can increase the losses of the power inverter, resulting in an increase in the temperature, which will limit the performance of power inverters. The improvement of power module performance is mainly controlled by optimizing its control methods during operation and improving its cooling system. Currently, the liquid-cooled heatsink used in power modules have disadvantages such as large flow resistance and poor heat dissipation performance. In order to enhance the performance of the heatsink, this study first established a three-dimensional finite element model of SiC MOSFETs power module based on a pin fin heatsink. The accuracy of the model was verified by numerical and experimental methods. Secondly, based on numerical analysis, a multi-objective topology optimization method for the power module liquid-cooled heatsink is proposed. This method takes heat exchange and fluid dissipation energy as the objective function and uses weight factors to adjust the influence of each on the objective functions. Additionally, the temperature distribution of the heatsink is considered to optimize its performance. Finally, the numerical results show that the topology-optimized heatsink exhibits better performance at high coolant volumetric flow rates. When the coolant volumetric flow rate is 14 L/min, the pressure drops of topology-optimized heatsink is reduced by 63.94 % and the junction temperature of the power module is reduced by 0.24 % compared with the pin fin heatsink. This topologically optimized heatsink could be helpful to improve the performance of existing power module heatsinks.

Multi-Objective Intelligent Optimization Design Method of Microstrip Antenna Based on Back Propagation Neural Network

Multi-Objective Intelligent Optimization Design Method of Microstrip Antenna Based on Back Propagation Neural Network

Surrogate-based multi-objective design optimization of tree-shaped fins with uniform branch end distribution for latent heat thermal energy storage

The enhancement of latent heat thermal energy storage (LHTES) systems through fin geometry optimization remains a critical challenge for leveraging the full potential of renewable energy sources. This study focuses on optimizing the geometries of tree-shaped fins to enhance power and energy densities in LHTES systems. The goal is to find branch designs with high energy and power density through a novel surrogate model-based optimization strategy that explores a broad design space. The surrogate models applied, including linear regression, principal component analysis-based linear regression, artificial neural networks, and random forest, are evaluated for their predictive performance. The random forest model demonstrates superior accuracy in predicting targets. The optimization process results in a Pareto-optimal design with a volume fraction of 33.9%. This optimal design substantially enhances the system's power density by 61.6% compared to conventional plate fins at an equivalent energy density. This optimized design improves energy and power density, achieving a uniform end-to-branch distribution, which is a pivotal factor for consistent temperature distribution and improved thermal efficiency. By integrating surrogate-based optimization with broad ranges of the tree-shaped fin design, this research has significantly improved the operational efficiency of LHTES systems. This research promises more effective thermal management and provides a methodological framework for design innovation in thermal energy storage.