Optimal Design Variables Research Articles

An adaptive material-field series-expansion method for structural topology optimization

The material-field series-expansion (MFSE) method reduces the dimension of design variables in density-based topology optimization and avoids the checkerboard patterns. However, the constant correlation function of the MFSE method only accounts for the spatial dependency between material field points. Accordingly, the expanded material field using the constant correlation function has an obscure topology, which increases the iterations and computation burden of the MFSE method. This paper proposes an adaptive correlation function that considers the spatial dependency and the values of material field points simultaneously. It describes the correlation between material field points more accurately. As a result, the expanded material field based on the adaptive correlation function has a clearer topology than the constant correlation function. Moreover, the adaptive material-field series-expansion (AMFSE) method with dual-loop optimization is introduced leveraging the adaptive correlation function. The outer loop updates the adaptive correlation functions and expanded material fields. The inner loop searches for the optimal solution of the current topology optimization model based on the expanded material field. Finally, several examples of static compliance and dynamic modal loss factor topology optimization validate the effectiveness and applicability of the AMFSE method. Results show that the AMFSE method converges faster with fewer iterations than the MFSE method, despite it increasing the computing time of matrix decomposition in the outer loops. Therefore, the AMFSE method is suitable for topology optimization with complex responses such as modal loss factors to decrease the iterations and computation burden simultaneously.

Interpretable reduced-order optimization research for improving indoor environmental quality in buildings based on dimensional analysis and surrogate-based optimization

Implementing large-scale optimization designs and identifying optimal design variables in fields such as architectural engineering is crucial for improving indoor environmental quality. However, the high-dimensional nonlinear characteristics complicate the understanding of the optimization process and increase the difficulty of finding optimal solutions. This study proposes an interpretable reduced-order optimization (ROO) method based on dimensional analysis, which integrates numerous variables into a single reduced-order coefficient through a power form. The goal is to develop a reduced-order and approximately one-dimensional nonlinear relationship during the optimization process and to reveal the mechanisms of single-objective and multi-objective optimization, thereby enhancing the interpretability of the optimization process. The reliability of the ROO is validated through single-objective optimization of building thermal bridges and multi-objective optimization of squirrel cage fans. The study shows that the power in the reduced-order coefficient can be used to determine the sensitivity and impact of design variables on optimization targets. The nonlinear relationship between the composite structural parameters of the building thermal bridge and the total heat flux can be reduced to an approximately one-dimensional linear relationship, significantly reducing the total heat flux of the thermal bridge by 10.3 %. The ROO accurately describes the aerodynamic performance of the fan and its high-dimensional nonlinear relationship with eight design variables, eliminating optimization conflicts among multiple operating conditions and significantly enhancing the aerodynamic performance. The ROO method proposed in this study offers a new approach to making the optimization process more interpretable, playing a crucial role in optimization design and revealing optimization mechanisms in engineering applications.

The creation and assessment of an electrical all-terrain vehicle and its effects on efficiency

Abstract The suspension system consists of tires, tire air, springs, shock absorbers, and connections that facilitate the relative movement among the axles and the automobile. Although ride quality and road holding/handling are mutually exclusive, suspension components nevertheless need to provide both. Adjusting suspensions requires striking the ideal balance. Maintaining maximum contact between the road wheel and the road surface is crucial for the suspension. The vehicle’s suspension greatly affects its handling; since the vehicle must operate on all types of terrain and retain ideal steering geometry, an adaptable system of suspension should be employed. The EATV’s suspension elements will be designed in Solid works, and the resulting model will be examined utilizing Ansys software for optimizing design variables while taking into account how they may affect the efficiency of other automobile parts through simulator testing.

Isogeometric topology optimization for maximizing band gap of two-dimensional phononic crystal structures

A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations.

Multidisciplinary Optimization of Aircraft Aerodynamics for Distributed Propulsion Configurations

The combination of different aerodynamic configurations and propulsion systems, namely, aero-propulsion, affects flight performance differently. These effects are closely related to multidisciplinary collaborative aspects (aerodynamic configuration, propulsion, energy, control systems, etc.) and determine the overall energy consumption of an aircraft. The potential benefits of distributed propulsion (DP) involve propulsive efficiency, energy-saving, and emissions reduction. In particular, wake filling is maximized when the trailing edge of a blended wing body (BWB) is fully covered by propulsion systems that employ boundary layer ingestion (BLI). Nonetheless, the thrust–drag imbalance that frequently arises at the trailing edge, excessive energy consumption, and flow distortions during propulsion remain unsolved challenges. These after-effects imply the complexity of DP systems in multidisciplinary optimization (MDO). To coordinate the different functions of the aero-propulsive configuration, the application of MDO is essential for intellectualized modulate layout, thrust manipulation, and energy efficiency. This paper presents the research challenges of ultra-high-dimensional optimization objectives and design variables in the current literature in aerodynamic configuration integrated DP. The benefits and defects of various coupled conditions and feasible proposals have been listed. Contemporary advanced energy systems, propulsion control, and influential technologies that are energy-saving are discussed. Based on the proposed technical benchmarks and the algorithm of MDO, the propulsive configuration that might affect energy efficiency is summarized. Moreover, suggestions are drawn for forthcoming exploitation and studies.

Moving Morphable Components Using Strain-Based Beam Geometry Description for Topology Optimization

In the moving-morphable-component topology optimization, morphable components are introduced as a geometrical model mapped onto the background finite elements, and their shape parameters are utilized as design variables for topology optimization. Whereas a complex curved geometry ensuring C1 continuity can be generated using existing curved components, the component curvatures cannot be selected as design variables in the existing methods; thus geometric constraints associated with curvatures cannot also be directly imposed. To address this issue, this study proposes a curvature-based morphable component by introducing the curvilinear geometry representation in the strain-based beam formulation. Since the proposed component is parameterized by curvatures using the curvilinear equation, the component curvatures can be utilized as the design variables. This allows for directly imposing curvature constraints on structural members, thereby accounting for the manufacturability of an optimal topology. It is demonstrated that a symmetric placement of the design variables using the midpoint curvilinear coordinate system is critical in ensuring convergence of the proposed curvature-based component optimization. The symmetric curvature component is further extended to account for multiple curvatures within a single component while ensuring C1 continuity. Several examples are presented to demonstrate the benefits of the proposed multicurvature component for topology optimization.

An improved adaptive Kriging method for the possibility-based design optimization and its application to aeroengine turbine disk

Possibility-based design optimization (PBDO) can provide theoretical basis for the structural optimal design of fuzzy uncertainty model in engineering, so as to obtain the optimal design variables. The genetic algorithm (GA) based on adaptive Kriging method for PBDO requires high precision in the whole design space, while the region far from the limit state surface (LSS) of the constraint function has little effect on PBDO, thus greatly affects the computational efficiency. In order to improve the efficiency of PBDO, an improved adaptive Kriging method combined with active possibility constraint (I-AK-AC) is proposed in this paper. In I-AK-AC, the enhanced expected improvement learning function is first put forward to promote the convergence efficiency of Kriging model by reducing the accuracy of the region far from the LSS of the constraint function. Whereafter, the active possibility constraint is identified, and only the boundaries of active possibility constraint need to be approximated precisely by Kriging model. By these ways, the convergence speed of Kriging model is further ameliorated without affecting the computational accuracy, and the efficiency of PBDO is significantly improved. Three test examples and an engineering application of aeroengine turbine disk illustrate the validity and accuracy of the proposed I-AK-AC.

High-dimensional multi-objective optimization of coupled cross-laminated timber walls building using deep learning

This paper introduces a deep learning-based multi-objective optimization framework, applying for advancing the design of the Cross-Laminated Timber Coupled Wall system. While traditional optimization methods often struggle with the curse of dimensionality in high-dimensional problems, the approach proposed in this study employs an autoencoder to effectively reduce the dimensionality of the design space. Subsequently, a neural network establishes a mapping between input variables and latent spaces, with another neural network forming the crucial link between these latent variables and the output responses. The proposed framework is integrated into the design process of a 20-story Cross-Laminated Timber Coupled Wall system, where uncertainties inherent in connection elements are systematically addressed to optimize the structural parameters. The non-dominated sorting genetic algorithm-II is utilized to estimate optimal design variables by minimizing three conflicting objective functions, thereby generating a Pareto front. This optimized design is then bench-marked against three deterministic models with varying coupling beam shear strengths. A two-dimensional numerical model developed in OpenSees facilitates nonlinear time history analysis using 50 bi-directional ground motion records, representative of the seismicity of Vancouver, Canada. The results of this study not only highlight the efficacy of the deep learning-based framework in enhancing the structural integrity and resilience of high-rise timber structures in seismic regions but also significantly contribute to the evolution of computational approaches in structural engineering.

Analysis of different objective functions in petroleum field development optimization

Oilfield development optimization plays a vital role in maximizing the potential of hydrocarbon reservoirs. Decision-making in this complex domain can rely on various objective functions, including net present value (NPV), expected monetary value (EMV), cumulative oil production (COP), cumulative gas production (CGP), cumulative water production (CWP), project costs, and risks. However, EMV is often the main function when optimization is performed under uncertainty. The behavior and performance of different objective functions has been investigated in this paper, when EMV is the primary criterion for optimization under reservoir and economic uncertainty. One of the goals of this study is to provide insights into the advantages and limitations of employing EMV as the sole objective function in oil field development decision-making. The designed optimization problem included sequential optimization of design variables including well positions, well quantity, well type, platform capacity, and internal control valve placements. A comparative analysis is presented, contrasting the outcomes obtained from optimizing the EMV-based objective function against traditional objective functions. The study underscores the importance of incorporating multiple objective functions alongside EMV to guide decision-making in oilfield development. Potential benefits in minimizing CGP and CWP are revealed, aiding in the mitigation of environmental impact and optimization of resource utilization. A strong correlation between EMV and COP is identified, highlighting EMV’s role in improving COP and RF.

Learning experimental data to predict fluid-elastic instability and optimize configuration of tube arrays

Fluid-elastic instability (FEI) poses a particularly significant challenge to the safety of steam generators, given its potential to cause substantial damage in short periods. The tube bundle system model is inherently complex, resulting in expensive costs for experiments and numerical simulations during the design process. In this study, a substantial volume of FEI experimental data, conducted by various scholars, was compiled to create FEI surrogate model. The accuracy and feasibility of this surrogate model were demonstrated and compared to experimental results. This work represents the pioneering reference on the optimization of tube array configurations, achieved by combining FEI deep neural network (DNN) surrogate model with genetic algorithm (GA). The design variables for optimization encompassed tube array configurations and structural parameters. The optimization objective is to achieve a tubular array structure exhibiting a higher critical velocity, Ur, enabling safe operation of the heat exchanger tube bundle across a wider range of flow rates without any FEI accident. The developed approach holds promise for data-driven FEI analysis and optimized tube bundle design, resulting in substantial time and cost savings. We publicly share all code implementations, and we believe that our efforts open a door for the surrogate-model-assisted structural optimization of tube arrays.

Maximizing band gaps of single-phase phononic plates: Isogeometric optimal approach and 3D printing experimental validation

This work presents an effective isogeometric shape optimization approach for finding and widening the phononic band gaps of single-phase Mindlin plate structures. As the single-phase material phononic plate is easy to be manufactured by additive manufacturing, it has been investigated here by optimized its thickness profile to find and widen the band gaps. The proposed method utilizes a coarse B-spline surface to model the thickness profile of periodic plate and a fine B-spline surface to model the mid-surface of plate structure for simulation. The optimal design variables are the thickness variables, i.e., the z-components of the control points of the coarse B-spline surface. To avoid specifying the initial control point locations manually, the constrained dynamic maximization problem is solved by a particle swarm optimization (PSO) algorithm here. Various numerical examples demonstrate the effectiveness and reliability of the proposed method in finding optimal phononic band gaps of periodic plates. And the numerical results show that there is no band gap for hmax = 3 hmin, and the band gaps can be found and widen for hmax ≥ 5 hmin. The obtained band range is 638.9–823.6 Hz with a decreased central frequency of 731.25 Hz for hmax = 5 hmin and the width and the number of band gaps are increased as the maximum allowable thickness increases. Finally, one optimized design is fabricated through additive manufacturing, and the experimental frequency response is consistent with the results based on isogeometric analysis.

The influence of invariant horizontal projection area constraint on shape optimization of free-form surface structure with openings

Free-form curved surface shell roof is favored by architects, but the openings for daylighting will decline its mechanical properties. In the shell shape optimization under the vertical load, when the outer contour of the openings or the shell changes, the total load of the structure also changes with the changes in its horizontal projection area. This contradicts the premise of structural optimization, that is, to maintain the principle of unchanging total loads. To solve this problem, the invariant horizontal projection area of the shell was taken as constraints in the shell shape optimization in which the objective function was structural strain energy and optimization design variables were internal and external boundary points of the curved surfaces with openings, and the key points on the curved surface which were design variables of the overall shape of the curved surface. The numerical examples verified the validity of the method, and the influence of the invariant horizontal projection area constraint of the curved surface with openings on the optimization results of the minimum strain energy, optimization with the frequency constraint, and the initial surface with the different support distribution were discussed. The results of the numerical examples showed that the invariant horizontal projection area constraint has a greater impact on the results of the curved surface with opening optimization, and its influence should be considered in the engineering design.

Optimizing the Honeycomb Spoke Structure of a Non-Pneumatic Wheel to Reduce Rolling Resistance

Traditional pneumatic tyres are prone to puncture or blowout and other safety hazards. Non-pneumatic tyres use a high-strength, high-toughness support structure to replace the “airbag body” structure of pneumatic tyres, which is made of fibre skeleton materials and rubber laminated layers, thus effectively avoiding the problems of blowout and air leakage. However, discontinuous spokes undergo repeated bending deformation when carrying loads, which leads to energy loss, of which the rolling resistance of non-pneumatic tyres is one of the main sources of energy loss. This paper focuses on the study of gradient honeycomb non-pneumatic tyres. Firstly, a finite element model was established, and the accuracy of the model was verified by numerical simulation and stiffness tests. Secondly, the order of the effect of different spoke thicknesses on rolling resistance was obtained through orthogonal test analysis of four-layer honeycomb spoke thicknesses. Then, four optimized design variables were selected in combination with the spoke angles, and the effects of the design variables on rolling resistance were analyzed in detail by means of the Latin hypercube experimental design. Finally, the response surface model was established, and the non-linear optimization model was solved by the EVOL optimization algorithm considering the tyre stiffness limitations so that the rolling resistance was minimized. The results of the study laid down theoretical and methodological guidance for the design concept and technological innovation of low rolling resistance comfort non-pneumatic tyres.

An improved evolutionary structure optimization method considering stress minimization and smooth design

AbstractThe design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P‐norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element‐node sensitivity. This method addresses the singularity issue commonly found in density‐based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post‐processing, helping to drive innovation and development in engineering.

Analysis and Optimization of a Novel Compact Compliant 2-DOF Positioner for Positioning to Assess Bio-Specimen Characteristics

A novel compact 2-DOF compliant positioner is developed for the purpose of achieving good characteristics such as high natural frequency, high displacement amplification ratio, good linear motion, and compact structure based on its symmetrical structure. To be specific, the developed stage is proposed according to an advanced six-lever displacement amplifier arranged at an inclination angle of the rigid bar utilizing right circular hinges and a parallel guiding mechanism with integrated flexure leaf hinges to attain the above-mentioned characteristics and reduce the decoupling mobility error. First, to quickly assess the initial quality response, an integration method of kinetostatic analysis, the Lagrange method, and finite element analysis was applied to evaluate and verify the quality characteristic of the stage. The experimental result showed that the error between the analytical method and the FEA method was 1.3%, which was relatively small and reliable for quickly assessing the primary quality response of the proposed positioner. Next, to boost the important output characteristics of the developed positioner, the integration approach of the response surface method and NSGA-II algorithm was utilized to find the optimal design variables. Finally, a prototype was manufactured based on the CNC milling method to validate the experimental and FEA analysis results. The attained results show that the optimal results of safety factor and output displacement were 2.4025 and 248.9 µm. Moreover, the FEA verification results were 2.4989 and 242.16 µm, with errors for safety factor and output displacement between the optimal result and the FEA result of 3.86% and 2.78%, respectively. In addition, the simulation and experimental results of the first natural frequency were 371.83 Hz and 329.59 Hz, respectively, and the error between the FEA result and experimental result for the first natural frequency was 11.36%. Furthermore, the achieved results show that the relationship between input displacement and output displacement of the experimental result and the FEA result of the developed structure achieved a good linear connection. These results suggest that the proposed positioner will be a potential structure employed in precise positioning systems and nanoindentation testing positioning systems for checking bio-specimens’ behaviors.

Optimal Design of the Modular Joint Drive Train for Enhancing Cobot Load Capacity and Dynamic Performance

Automation advancements prompts the extensive integration of collaborative robot (cobot) across a range of industries. Compared to the commonly used design approach of increasing the payload-to-weight ratio of cobot to enhance load capacity, equal attention should be paid to the dynamic response characteristics of cobot during the design process to make the cobot more flexible. In this paper, a new method for designing the drive train parameters of cobot is proposed. Firstly, based on the analysis of factors influencing the load capacity and dynamic response characteristics, design criteria for both aspects are established for cobot with all optimization design criteria normalized within the design domain. Secondly, with the cobot in the horizontal pose, the motor design scheme is discretized and it takes the joint motor diameter and gearbox speed ratio as optimization design variables. Finally, all the discrete values of the optimization objectives are obtained through the enumeration method and the Pareto front is used to select the optimal solution through multi-objective optimization. Base on the cobot design method proposed in this paper, a six-axis cobot is designed and compared with the commercial cobot. The result shows that the load capacity of the designed cobot in this paper reaches 8.4 kg, surpassing the 5 kg load capacity commercial cobot which is used as a benchmark. The minimum resonance frequency of the joints is 42.70 Hz.

Artificial neural network-based sequential approximate optimization of metal sheet architecture and forming process

Abstract This paper introduces a sequential approximate optimization method that combines the finite element method (FEM), dynamic differential evolution (DDE), and artificial neural network (ANN) surrogate models. The developed method is applied to address two optimization problems. The first involves metamaterial design optimization for metal sheet architecture with binary design variables. The second pertains to optimizing process parameters in multi-stage metal forming, where the discrete nature arises owing to changing tool geometries across stages. This process is highly nonlinear, accumulating contact, geometric, and material nonlinear effects discretely through forming stages. The efficacy of the proposed optimization method, utilizing ANN surrogate models, is compared with traditionally used polynomial response surface (PRS) surrogate models, primarily based on low-order polynomials. Efficient learning of ANN surrogate models is facilitated through the FEM and Python integration framework. Initial data for surrogate model training is collected via Latin hypercube sampling and FEM simulations. DDE is employed for sequential approximate optimization, optimizing ANN or PRS surrogate models to determine optimal design variables. PRS surrogate models encounter challenges in dealing with nonlinear changes in sequential approximate optimization concerning discrete characteristics such as binary design variables and discrete nonlinear behavior found in multi-stage metal forming processes. Owing to the discrete nature, PRS surrogate models require more data and iterations for optimal design variables. In contrast, ANN surrogate models adeptly predict nonlinear behavior through the activation function's characteristics. In the optimization problem of Metal Sheet Architecture for design target C, the ANN surrogate model required an average of 4.6 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. Furthermore, in the optimization of multi-stage deep drawing processes, the ANN surrogate model required an average of 6.1 times fewer iterations to satisfy stopping criteria compared to the PRS surrogate model. As a result, the sequential global optimization method utilizing ANN surrogate models achieves optimal design variables with fewer iterations than PRS surrogate models. Further confirmation of the method's efficiency is provided by comparing Pearson correlation coefficients and locus plots.

Sustainability evaluation of C3MR natural gas liquefaction process: Integrating life cycle analysis with Energy, Exergy, and economic aspects

In a transition towards a clean energy future, natural gas serves as an interim fuel due to its lower emissions whereas the C3MR (propane pre-cooled mixed refrigerant process) is widely recognized for high efficiency and commercial scale application converting natural gas to LNG. Previously, numerous studies have been conducted to optimize the energy efficiency and performance of C3MR process but very little contribution has been made towards its sustainability analysis. To address this, a life cycle analysis approach is established to evaluate the carbon footprint of C3MR process. In order to showcase its link with energy consumption and put forward the groundwork of analyses, the research focuses on using simulation – assisted optimization to reduce the specific energy consumption (SEC) of C3MR process by optimizing design variables. The study highlights the use of mixed refrigerant (MR) as a process variable and validates that its optimal implementation has decreased SEC to 0.2195 kWh/kg LNG, while achieving a minimum inlet temperature approach (MITA) of main cryogenic heat exchanger (MCHX), less than 3 °C. The knowledge − based optimization approach applied in this research, developed comparative case studies on which multiple analyses are performed to verify scientific findings. Energy and exergy analyses are conducted to determine thermal efficiency of the process where the optimized case exhibits a reduced difference in its composite curves and an 8.65 % improvement in exergetic performance compared to the base case. The economic indicators assessment reveals that optimized case demonstrates lower capital and operating costs, establishing economic viability. Furthermore, the energy consumption parameters are utilized for evaluation of ecological impact ofLNGsupply chain through life cycle assessment (LCA) which reflects reduced greenhouse gas (GHG) emissions for optimized case. Hence, the current study fills existing research knowledge gaps in terms of providing a comprehensive process system engineering by evaluating energy synergistic point, thermodynamic irreversibility, process viability and sustainability using life cycle assessment.

Design optimization of the cooling systems with PCM-to-air heat exchanger for the energy saving of the residential buildings

Driven by a rapid surge in cooling demand in buildings, the energy consumption dedicated to cooling has experienced remarkable growth. To address this challenge, the adoption of latent heat thermal energy storage utilizing phase change materials (PCM) has gained significant momentum in recent years. This paper presents the design and evaluation of an integrated latent heat thermal energy storage (ILHTES) system tailored for residential buildings. This system integrates a PCM-to-air heat exchanger (PAHX) with an air conditioning unit. Modelica language is utilized to develop a numerical model for the ILHTES system. The heat transfer model of the PAHX is developed and validated using existing literature data. To simulate the dynamic behavior and energy consumption of the residential building, the open-source library AixLib is adopted. The developed ILHTES system model is used for the optimization of key design variables, including the PCM slab thickness and air flow rate, based on the results of long-term simulations covering the entire cooling season. Evaluation of the energy saving potential of the optimized ILHTES systems is carried out in comparison to conventional air conditioning systems, considering various climatic conditions in five European cities. The results highlight the profound impact of PCM types on the Energy Saving Ratio (ESR) throughout the entire cooling season. Among the four commercially available PCMs examined—RT27, RT25, RT20, and RT18—RT25 consistently outperforms the others. Across all five cities investigated, using RT25 leads to a minimum ESR of 16% in Catania and a maximum ESR of 44.7% in Stockholm for the entire cooling season.

Optimization of a non-pneumatic tire using design of experiments and machine learning techniques

In this paper, the spoke structure of a non-pneumatic tire is optimized. The finite element model of the spoke structure is created and structural dynamic analysis is made using ABAQUS. The optimization goal is to simultaneously reduce three characteristics of the spoke structure, the mass, vertical displacement and acceleration. Simulations are performed according to the center composite design table, and the objective function is estimated using response surface analysis (RSA), random forest regression (RFR), gradient boosting regression (GBR) and artificial neural network (ANN). The genetic algorithm is used for minimization, and the optimization results of each objective function are analyzed through verification simulation. As a result of the optimization, the error between the predicted value and the actual value is 18.6% for RSA 3.1% for RFR, 1.7% for GBR, and 15.0% for the ANN. The ANN proposes the optimum design variables which derive output values smaller than the current minimum value because the ANN properly represents the nonlinear characteristics of the spoke model generated in this study. Highlights Simulation based optimization of the spoke structure of a non-pneumatic tire Various regression models are used and their accuracy is compared A two-step genetic algorithm is used for optimization