Non-dominated Sorting Genetic Algorithm II Research Articles

Multitask scheduling on cloud additive manufacturing using NSGA-II

Purpose: Cloud manufacturing (CM) represents a new manufacturing paradigm that integrates distributed resources to provide on-demand services. The high consumer demand from various locations, coupled with the customizability and complexity of manufacturing, complicates task scheduling. In this context, 3D printers are crucial as innovative manufacturing technologies with significant potential in producing complex and custom products. Scheduling in CM falls under the non-deterministic polynomial time-hard category, where tasks must be scheduled and distributed rapidly. Considerations of distance, minimization of delays, and makespan become critical variables that must be considered. This research aims to schedule and distribute tasks in CM using the non-dominated sorting genetic algorithm II (NSGA-II) to minimize delays, reduce makespan, and decrease costs.Methodology: NSGA-II is employed to tackle the complexities of scheduling in CM. The strength of NSGA-II lies in its ability to determine optimal and efficient solutions for multiobjective problems. Tasks originating from requests at various locations are adjusted based on material parameters and dimensions and then distributed to providers while considering aspects such as makespan, delay minimization, and cost.Findings: The optimization results using NSGA-II demonstrate effective and efficient task distribution to providers. Across the four tested task distribution scenarios, the average computational time required was 5.59 seconds. Pareto analysis indicates a trade-off between various objective functions. Solutions with short distances tend to have increased maximum time and delays.Originality/value: NSGA-II is effective for task distribution with multiobjective considerations. Not all three objective functions can be optimized simultaneously, given the trade-offs between distance, maximum time, and lateness. The priority of the objective functions should be determined to achieve optimal results. If minimizing lateness is most important, the focus should be on points with low lateness values. Further development can be done by modifying the Pareto front to make data-driven decisions that consider these trade-offs.

Valley Path Planning on 3D Terrains Using NSGA-II Algorithm

Valley path planning on 3D terrains holds significant importance in navigating and understanding complex landscapes. This specialized form of path planning focuses on finding optimal routes that adhere to the natural contours of valleys within three-dimensional terrains. The significance of valley path planning lies in its ability to address specific challenges presented by valleys, such as varying depths, steep slopes, and potential obstacles. By following the natural flow of valleys, path planning can enhance the efficiency of navigation and minimize the risk of encountering difficult terrain or hazards. In recent years, an increasing number of researchers have focused on the study of valley path planning on 3D terrains. This study presents a valley path planning method utilizing the NSGA-II (Non-dominated Sorting Genetic Algorithm II) approach. To ensure that the paths generated by the algorithm closely follow the valley lines, the algorithm establishes an optimization function that includes three optimization criteria: mean altitude, flight route length, and mean offset. To test the performance of this algorithm, we conducted experiments based on workspaces based on three datasets full of 3D terrains and compared it with three baseline algorithms. The evaluation indicates that the suggested algorithm successfully designs routes that closely follow the valley contours.

An Optimization Framework for Waste Treatment Center Site Selection Considering Nighttime Light Remote Sensing Data and Waste Production Fluctuations

As urbanization accelerates, the management of urban solid waste poses increasingly intricate challenges. Traditional urban metrics, such as GDP and per capita consumption rates, have become inadequate for accurately reflecting the realities of waste generation; moreover, the linear correlation between these metrics and waste production is progressively diminishing. Consequently, this study introduces a novel methodology leveraging nighttime light remote sensing data to enhance the precision of urban solid waste production forecasts. By processing remote sensing data to mitigate noise and integrating it with conventional urban datasets, an innovative index system and predictive model were developed. Using Beijing as a case study, the gradient boosting regression algorithm yielded a prediction accuracy of 92%. Furthermore, in light of the substantial costs associated with waste recovery route planning and site selection for treatment facilities, this research further devised a location and distribution framework for waste treatment centers based on high-precision predictions of waste production while employing multi-objective evolutionary algorithms (MOEAs) alongside the non-dominated sorting genetic algorithm II (NSGA-II) for optimization. Distinct from prior studies, this study suggests that service point waste quantities are not fixed values but rather adhere to a normal distribution within specified ranges and thus provides a more realistic simulation of fluctuations in waste production while enhancing both the robustness and predictive accuracy of the model. In conclusion, by incorporating nighttime light remote sensing data along with advanced machine learning techniques, this study markedly improves forecasting accuracy for waste production while offering effective optimization strategies for site selection and recovery route planning—thereby establishing a robust data foundation aimed at refining urban solid waste management systems.

Multi-objective optimization of supersonic separator for gas removal and carbon capture using three-field two-phase flow model and non-dominated sorting Genetic Algorithm-II (NSGA-II)

Supersonic separator (SS) is an efficient technology used for gas removal and carbon capture. To enhance its performance, many researchers have studied its structure; however, existing studies have primarily used traditional CFD models for single-objective structural optimization of the separator’s separation performance. However, in the SS, separation efficiency and pressure-loss ratio are the most important and conflicting performance parameters, and evaluating separation performance in isolation from either one is incomplete. Therefore, in this paper, a gas–liquid two-phase three-field CFD model considering a liquid film is firstly established, and then this model is combined with the non-dominated Sorting Genetic Algorithm-II (NSGA-II) for multi-objective optimization of the coupled multiple structural parameters with the objective of the separation efficiency and pressure-loss ratio. The results indicated that the maximum relative errors between simulated and predicted values for the four Pareto optimal solutions in computing pressure loss ratio and separation efficiency are 5.4% and 5.3%, respectively, with these solutions achieving the maximum reduction in pressure loss ratio of 28.3% at the same 90% separation efficiency compared to the original structure.

Multi-physical field coupling effect in micro pin-fin channel cooling with coaxial-like through-silicon via (TSV) for three-dimensional integrated chip (3D-IC)

Through-silicon via (TSV) technology offers significant advantages for three-dimensional integrated chip (3D-IC) by enabling higher integration densities and faster signal transmission rates. The increased power density of 3D-IC poses substantial thermal management challenges. Microchannel cooling is widely used for chip-level thermal management. However, the balance of heat dissipation and signal integrity between layers of 3D-IC with TSV remains elusive. This work presents a study on the electrical-thermal-force-flow-solid multi-physics field coupling effect of micro pin–fin channel cooling systems embedded with coaxial-like TSVs in 3D-IC, aiming to optimize signal integrity and thermal performance. We analyze the structural parameters of coaxial-like TSVs, such as TSV aspect ratio and pitch ratio, focusing on their impact on signal shielding efficiency and thermal conductivity. The results show that a coaxial-like TSV structure with an aspect ratio of 15 and a pitch ratio of 2.5 reduces the maximum temperature and insertion loss by 3.97% and 3.60%, respectively. This structure is then embedded in a micro pin–fin channel to explore the effect of pin–fin arrangement on heat dissipation at different Reynolds numbers. Using multi-objective optimization through response surface methodology (RSM) and the non-dominated sorting genetic algorithm II (NSGA-II), we obtain a series of optimal solutions for TSV-embedded micro pin–fin. When the weights of heat transfer and pressure drop are balanced, the average Nusselt number increases by 6.8% with a 2% rise in pressure drop. These findings provide valuable insights for the design and optimization of high-performance 3D-IC cooling systems.

A smart multiphysics approach for wind turbines design in industry 5.0

This paper aims to develop a smart multiphysics approach for wind turbine design utilizing Industry 5.0. A new blade profile is developed and optimized by non-dominated sorting genetic algorithm II (NSGA-II) for shape design, and a 3D modeling of wind turbines is proposed. The aerodynamic modeling of a horizontal axis wind turbine (HAWT) is an important step in the design of wind turbines. The blade geometry design plays an important role in a wind turbine to maximize the aerodynamic performance and extract as much kinetic energy as possible from the wind resource. This paper addresses a high-level design and optimization for the parameters of a new blade. Moreover, a 3D modeling of large wind turbines (>7 MW) is proposed that can be used in wind farms. This approach can be used in real-time design in Industry 5.0 using different data from sensors. Finally, the optimized blade increases the produced power by 10% (from 7.5 MW to 8.2 MW). The proposed approach allows people to work alongside machinery to improve processes and provide personalization for companies manufacturing wind turbines.

Optimization of Submersible LNG Centrifugal Pump Blades Design Based on Support Vector Regression and the Non-Dominated Sorting Genetic Algorithm Ⅱ

Optimizing the impeller blade design of submersible LNG centrifugal pump significantly enhances mechanical efficiency, reducing energy consumption and carbon emissions during LNG storage and transportation. This study focuses on optimizing blades of the centrifugal pump, combining Bezier blade design, CFD simulations, optimal Latin Hypercube sampling, Support Vector Regression (SVR), and Non-Dominated Sorting Genetic Algorithm Ⅱ(NSGA-II) multi-objective optimization into a systematic method. During the development of this optimization method, it was found that directly applying sampled CFD simulation data for machine learning led to poor overall predictive performance of the models. To address this, a data augmentation method based on Gaussian noise was proposed. Through Bayesian optimization of the machine learning model’s hyperparameters, the R2 of the predictive model was successfully increased from below 0.8 to above 0.99. The optimized design improved the prototype pump's efficiency from 70% to 77.8% under rated flow and head conditions. This efficiency gain is due to the significant reduction in flow separation vortices between blades and decreased turbulent kinetic energy between the impeller and diffuser vanes. Additionally, sensitivity and linear relationship analyses using the Sobol method and Pearson correlation provided valuable insights for blade optimization design.

A Stochastic Sustainable Closed-Loop Supply Chain Networks for Used Solar Photovoltaic Systems: Meta-Heuristic Comparison and Real Case Study

This research presents a novel approach to setting up a sustainable Closed-Loop Supply Chain (CLSC) network for used solar photovoltaic (PV) systems, addressing end-of-life product waste from solar panel installations and manufacturing centers. The model accounts for uncertainties in PV systems and aims to efficiently collect, refurbish, and recycle used solar PV systems, promoting a circular and environmentally responsible waste management strategy. The supply chain network comprises vendors, collection centers, hybrid centers, distribution centers, and manufacturing centers, with objectives to maximize total profit, minimize environmental risk, and maximize service levels by demonstrating the profitable reuse of used solar photovoltaic systems by manufacturers. The epsilon-constraint method is utilized to handle the model's multi-objectiveness and identify Pareto optimal solutions. A case study in Iran is conducted to validate the methodology's performance, comparing results obtained from three meta-heuristic methods: Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), and Multi-Objective Gray Wolf Optimization (MOGWO). The average error rates are 0.0358 for MOGWO, 0.1248 for MOPSO, and 0.2066 for NSGA-II. Sensitivity analysis highlights the significant impact of demand variations on all objective functions. Lastly, the numerical results are discussed to provide managerial insights for informed decision-making.

Multi‐objective optimization of ultrasonic vibration‐assisted drilling in carbon fiber reinforced polyetherketoneketone laminate

AbstractCarbon fiber reinforced polyetherketoneketone (CF/PEKK) possess excellent mechanical properties and also meet low‐carbon environmental standards, leading to their increasingly widespread application in recent years. To ensure the strength of mechanical connections, it is crucial to minimize drilling damage. This paper utilizes Ultrasonic Vibration‐Assisted Drilling (UVAD) to enhance hole‐making quality, comparing multiple drilling performance indicators with Conventional Drilling (CD), including thrust force, drilling temperature, delamination factor, and burr factor. The results demonstrate that UVAD significantly reduces thrust force and drilling temperature, decreases delamination and burring damage, and effectively improves hole quality. To further optimize processing parameters, the Non‐dominated Sorting Genetic Algorithm II (NSGA‐II) was used, targeting thrust force, Material removal rate (MRR), and delamination factor as optimization goals. The reliability of the model was verified through experimentations. This paper provides an effective technical approach for high‐quality drilling in CF/PEKK materials, offering significant practical application value for material processing in aerospace and other fields.Highlights The quality of CF/PEKK processed by CD and UVAD was compared. UVAD can effectively improve the quality of drilling. The drilling parameters were optimized by NSGA‐II. The reliability of the prediction model was verified by experiments.

A method for dynamic parameter identification of an industrial robot based on frequency response function

AbstractHaving accurate values of the dynamic parameters is necessary to characterize the dynamic behaviors of mechanical systems and for the prediction of their responses. To accurately describe the dynamic characteristics of industrial robots (IRs), a new method for dynamic parameter identification is proposed in this study with the goal of developing a real IR dynamics model that combines the multibody system transfer matrix method (MSTMM) and the nondominated sorting genetic algorithm‐II (NSGA‐II). First, the multibody dynamics model of an IR is developed using the MSTMM, by which its frequency response function (FRF) is calculated numerically. Then, the experimental modal analysis is conducted to measure the IR's actual FRF. Finally, the objective function of the minimum errors between the calculated and measured eigenfrequencies and FRFs are constructed to identify the dynamic parameters of the IR by the NSGA‐II algorithm. The simulated and experimental results illustrate the effectiveness of the methodology presented in this paper, which provides an alternative to the identification of IR dynamic parameters.

Multi-criteria study and machine learning optimization of a novel heat integration for combined electricity, heat, and hydrogen production: Application of biogas-fueled S-Graz plant and biogas steam reforming

The current research introduces an environmentally friendly heat design method by employing biogas fuel, aiming to yield electricity, hydrogen, and heating load simultaneously. The proposed arrangement consists of a biogas-powered S-Graz plant and a biogas steam reforming cycle. Although methane-fueled S-Graz plants for multigeneration purposes have been studied in previous studies, research on employing biogas fuel to launch a S-Graz plant and integrating a biogas steam reforming cycle with such a plant has yet to be examined. The model is simulated using the engineering equation solver software, and the study includes thermodynamic, exergoeconomic, and sustainability assessments to show the potential of the suggested configuration. By conducting a sensitivity study, a machine learning optimization method within MATLAB is implemented to exhibit the final optimal solution for the proposed arrangement. This optimization uses artificial neural networks and a non-dominated sorting genetic algorithm-II algorithm in a triple-objective framework based on energy efficiency, sustainability index, and products’ specific cost. The optimization demonstrates that the mentioned objectives reach optimal values of 58.26 %, 4.56, and 15.56 $/GJ, respectively. Also, the optimal net output power and hydrogen production rate equal 5746 kW and 1.45 m3/s, respectively. Besides, the process determines the optimal exergy efficiency, total net present value, and payback period as 52.70 %, 50.3 M$, and 8.96 years, respectively. The total investment cost rate for this system also is found to be 219.8 $/h.

Tri-objective and multi-parameter geometric optimization of two-stage radioisotope thermoelectric generator based on NSGA-II

Radioisotope thermoelectric generator (RTG) is one of ideal power sources for deep space exploration due to the long service life and high stability. To further extend service life and improve electrical output, this study is first to simultaneously optimize electrical output and mechanical stability induced by thermal stress of the two-stage RTG using non-dominated sorting genetic algorithm-II. Skutterudite and bismuth telluride are used as the thermoelectric materials in hot-stage and cold-stage thermoelectric generators, respectively. The maximum von Mises stress of the skutterudite-stage (VonSKD) and bismuth telluride-stage (VonBT) thermoelectric generator and the conversion efficiency of the two-stage RTG (ηtwo) are set to the three objectives, and twelve geometrical parameters of two-stage RTG are used as variables. Electrical output and mechanical stability are simulated with COMSOL 6.0 Multiphysics software based on the finite element method. Results show that the ranges of ηtwo, VonSKD, and VonBT in the Pareto front are 4.81–7.57 %, 112.2–228.46 and 19.24–87.33 MPa, respectively, when the temperature difference is 300 K. TOPSIS decision-making method is used to select the specific optimal solution on the Pareto front according to the weight of the different objectives. Comparisons between tri- and bi-objective as well as single-stage optimization are also carried. Results show that there are strong influences among these three objectives. The performance of one objective would improve at the expense of the performance of the remaining objectives decrease if a larger weight was given. The VonSKD has the greatest importance among the three objectives, followed by ηtwo, and the smallest is VonBT. Skutterudite-stage thermoelectric generator should be particularly considered in the design of two-stage RTGs. The two-stage RTGs with different weight factors exhibit different electrical performances due to different geometrical parameters. This research can provide references for two-stage thermoelectric generators in more scenarios to improve electrical performances and extend service life.

Multi-objective optimization towards cooling performance of teardrop section Kagome trusses array jet impingement composite cooling structure with cross-flow

Teardrop Section Kagome trusses array can be a spoiler for a new generation of advanced combustion chambers. In this study, multi-objective optimizations are applied to optimize a jet impingement composite cooling structure with cross-flow. Four structural parameters with five levels and three performance parameters are calculated in design of experiment and fitted by response surface methodology. The database is expanded by non-dominated sorting genetic algorithm-II, and then technique for order preference by similarity to an ideal solution is used to calculate the optimal structures under different operating conditions by different weights of the performance parameter. The conclusions are as follows: The minimal Equality of variances and fitting accuracy are 35.4371 and 93.6%. Diameter of the cross-section has the largest positive main effect on average Nusselt number and pressure loss coefficient, while angle between the rod and the horizontal plane has the largest positive effect on temperature uniformity coefficient. The interaction of trailing edge angle with angle between the front rod and the back rod in the horizontal plane is large. Case15 is chosen, where the weight ratio is 1:5:5, improvement of the corresponding optimized performance parameters of the simulation results with respect to the Origin of three performance parameters are 26.72%, −2.93%, 91.59% respectively. It provides a feasible reference for future advanced combustion chambers and accelerates their development process.

Multi-Objective Optimization of an Inertial Wave Energy Converter for Multi-Directional Wave Scatter

To advance wave energy devices towards commercialization, it is essential to optimize their design to enhance system performance. Additionally, a thorough economic evaluation is crucial for making these technologies competitive with other renewable energy sources. This study focuses on the techno-economic optimization of an innovative inertial system, the so-called SWINGO system, which is based on gyropendulum technology. SWINGO stands out due to its high energy efficiency in multi-directional installation sites, where wave directions vary significantly throughout the year. The study introduces the application of a multi-objective Evolutionary Algorithm (EA), specifically the Non-dominated Sorting Genetic Algorithm II (NSGA-II), to optimize the techno-economic performance of the SWINGO system. This approach aims to identify optimal design parameters that maximize energy extraction while considering economic viability. By deriving a Pareto frontier, a set of optimal devices is selected for further analysis. The performance of the SWINGO system is also compared to an alternative (mono-directional) inertial wave energy converter, the Inertial Sea Wave Energy Converter (ISWEC), to highlight the differences in techno-economic outcomes. Both systems are evaluated at two different installation sites: Pantelleria island and the North Sea in Denmark, with a focus on the directional wave scatter at each location.

Efficiency improvement and pressure pulsation reduction of volute centrifugal pump through diffuser design optimization

To investigate the effects of load distribution parameters of the diffuser vanes on the efficiency and pressure pulsation of the volute centrifugal pump, the diffuser shape was designed using an inverse design method, and an optimization method was proposed for the diffuser blade load distribution based on the combination of Latin hypercubic sampling, artificial neural network, and non-dominated sorting genetic algorithm-II. Steady and unsteady simulations were performed by solving the three-dimensional Reynolds-averaged Navier–Stokes equations using the shear stress transport k−ω turbulence model. The results obtained from Pearson correlation analysis revealed that the slope values Ks and Kh of the shroud and hub load distribution curves had the most significant effect on the pump head and efficiency. Compared with those of the original model, the efficiency and head of the optimized volute centrifugal pump under the design conditions increased by 3.8 and 3.5 %, respectively. The pressure pulsation intensities in the vaneless regions were effectively mitigated for the optimized volute centrifugal pump. The pressure pulsation coefficients at three times the diffuser vane frequency (3fDIF) reduced by 58.5 and 43.8 % at monitoring points M1 and M2, in the impeller outlet, respectively. The pressure pulsation coefficients at the impeller blade passing frequency (fBPF) reduced by 6.5 and 14.4 % at monitoring points M3 and M4 in the diffuser inlet, respectively. The results showed that the optimized diffuser improved the overall performance of the volute centrifugal pump, and demonstrated the feasibility of the optimization method.

Optimal Capacity Allocation for Life Cycle Multiobjective Integrated Energy Systems Considering Capacity Tariffs and Eco-Indicator 99

Traditional energy systems pose a significant threat to human social development due to fossil fuel depletion and environmental pollution. Integrated energy systems (IESs) are widely studied and applied due to their clean and low-carbon characteristics to achieve sustainable development. However, as integrated energy systems expand, their impact on ecosystems becomes more pronounced. This paper introduces the concept of the ecological damage index (EDI) to promote the sustainable development of integrated energy systems. Moreover, the introduction of a capacity tariff mechanism will impact the energy structure, making it essential to consider its effects on capacity allocation within integrated energy systems. This paper proposes a multiobjective optimization framework for constructing a capacity planning model for integrated energy systems, focusing on achieving a multidimensional balance between the economy, environment, and ecosystem using the life cycle assessment (LCA) method. Finally, the nondominated sorting genetic algorithm-II (NSGA-II) is employed to optimize the three objectives and obtain the Pareto frontier solution set. The optimal solution is selected from the solution set by combining the technique for order preference by similarity to ideal solution (TOPSIS) and Shannon entropy method. In comparison to scenarios with incomplete considerations, the multiobjective capacity optimization model proposed in this study exhibits significant improvements across the three metrics of cost, carbon emissions, and the ecological damage index, with a 19.05% reduction in costs, a 26.24% decrease in carbon emissions, and an 8.85% decrease in the ecological damage index. The study demonstrates that the model abandons traditional single-objective research methods by incorporating a multidimensional balance of the economy, environment, and ecosystems. This approach forms a foundational basis for selecting the optimal energy mix and achieving sustainable development in integrated energy systems. The life cycle assessment methodology evaluates impacts across all stages of integrated energy systems, providing a comprehensive basis for assessing and planning the sustainable development of the systems. The study offers guidance for the rational allocation of the integrated energy system capacity and advances the sustainable development of such systems.

Simultaneous Energy Optimization of Heating Systems by Multi-Zone Predictive Control—Application to a Residential Building

Climate change has made energy management a global priority. In France, the Grenelle Environment has set very ambitious progress targets for positive-energy buildings, particularly in terms of reducing and managing energy consumption. However, effective energy management in multi-zone buildings presents significant challenges, particularly when considering the inter-zone dynamics and heat transfer. This study examines multi-zone heating control, using a data-driven model for predictive indoor temperature modeling in intelligent buildings taking into account the influence of interconnected adjacent zones. The research methodology uses dynamic thermal simulation, parallel predictive models based on multiple linear regressions, and a multi-objective non-dominated sorting genetic algorithm II (NSGA-II) for the optimization process, which evaluates various generated heating strategies. This research introduces an approach to improve building energy efficiency by considering inter-zone dynamics and reducing heating-related energy consumption compared to a conventional heating strategy. By applying this model predictive control on a simulated case, a reduction in energy consumption due to heating is observed while respecting thermal comfort. This work contributes by implementing a method that independently controls temperatures in different building zones simultaneously while applying distinct constraints to each zone. This approach empowers occupants to manage heating consumption based on their preferences, ensuring personalized comfort. In addition, a comparison was made using a model that did not account for inter-zone interactions. This comparison demonstrates that incorporating these interactions into the predictive model enhances the effectiveness of the model predictive control approach. The multi-zone approach was also validated experimentally by using real experimental data, demonstrating significant reductions in energy consumption.

Research on Multi-Objective Optimization Methods of Urban Rail Train Automatic Driving Based on NSGA-II

In order to improve the control performance of automatic train operation (ATO) in urban rail trains, five typical operating sequences of urban rail trains were studied. Under the condition of meeting the safety and comfort principles of train operation, a train dynamics model was established to achieve the goals of low energy consumption, short running time, and high stopping accuracy in urban rail transit trains. In the process of finding a multi-objective solution to this problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used with an elite retention strategy, and the optimal Pareto multi-objective solution set was sought. In the process of optimal solution weight assignment, the hierarchical analysis Mahalanobis distance method, which combines subjective and objective analysis, was used. Finally, taking the Beijing Yizhuang subway line as the background design example, the simulation verified the effectiveness and feasibility of the algorithm and obtained high-quality automatic train driving curves under various working conditions. This research has important reference significance for the actual operation of automatic driving in urban rail trains.

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

Optimization of Flange Design for Engine Assembly Stand using RSM and NSGA-II Based on FEA Data

This article presents the results of a research study that focused on optimizing the flange design for engine assembly stands using the Response Surface Methodology (RSM) and Nondominated Sorting Genetic Algorithm II (NSGA-II) based on finite element analysis (FEA) simulation data. The study investigated the impact of three main dimensions (d1, d2, d3) of the flange as independent variables on the mass (m, kg), Von Mises stress (V, MPa), and displacement (D, mm) as dependent variables. The regression models developed using the RSM exhibited high R2 values of 0.9896, 0.998, and 0.9997 for m, V, and D, respectively. The multi-objective optimization results obtained through NSGA-II yielded 39 Pareto solutions, with d1 ranging from 10 to 27.43 mm, d2 ranging from 30 to 50 mm, and d3 ranging from 75 to 85 mm. These values corresponded to m values ranging from 2.93 to 7.58 kg, V values ranging from 54.8 to 342.6 MPa, and D values ranging from 0.006 to 0.270 mm. For verification purposes, Solution No.17 was selected. The results showed that the redesigned flange's mass, Von Mises stress, and displacement deviated by 0.95%, 2.28%, and 1.14%, respectively, from the optimal values obtained through the optimization process. These findings provide strong evidence for the high reliability of the optimization method employed in this study.