Multi-objective Design Optimization Research Articles

PB-MNSGA-II algorithm and its application for multi-objective optimization design of under-vehicle equipment

Structural damage caused to under-vehicle equipment under adverse working conditions affects the safe operation of high-speed electric multiple units (EMUs). To address the low optimization efficiency and take into account vibration fatigue in traditional under-vehicle equipment design, herein, a multi-objective optimization design method (PB-MNSGA-II) that combines particle swarm optimization-back propagation (PSO-BP) neural network and modified non-dominated sorting Genetic Algorithm II (MNSGA-II) was proposed. It can help engineers choose better equipment component thickness and achieve efficient and accurate design. First, MNSGA-II, the core content of PB-MNSGA-II, was proposed, which improved four aspects of NSGA-II: Latin hypercube sampling population initialization, adaptive crossover and mutation probability, mutation interference of Levy flight strategy, and optimal elite strategy. Then, zero-ductility transition (ZDT) series functions were employed to test MNSGA-II, thereby verifying its convergence and computational efficiency. Subsequently, utilizing the frame structure of the traction transformer (TTR) as an illustrative example, the PB-MNSGA-II approach was employed to enable multi-objective optimization. During this optimization process, the focus was on random vibration fatigue damage, thus enhancing the rationality of the optimization outcomes. After structural optimization, the mass of the TTR decreased by 20.1 kg, and the maximum vibration fatigue damage value decreased from 1.09 to 0.808, verifying the effectiveness and feasibility of the proposed method. The findings of this study provide important insights for the multi-objective optimization design of under-vehicle equipment under complex operating conditions.

Multi-objective Optimization Design Framework and Flight Performance Prediction for Reentry Module Using a Rapid Analysis Program

Multi-objective Optimization Design Framework and Flight Performance Prediction for Reentry Module Using a Rapid Analysis Program

Multi-objective optimization of automotive seat frames using machine learning

The optimal design of automobile seats plays an important role in passenger safety in high-speed accidents. In order to enhance the accuracy of the prediction of the input variables and output response of the seat, a hybrid machine learning prediction model that combines the improved gray wolf optimizer (IGWO) and back propagation neural network (BPNN) has been proposed, and the prediction effect of the model was validated using the seat simulation data. Initially, based on the experimental data, finite element models were developed for eight typical working conditions of automobile seats and their accuracy was validated. Subsequently, the energy absorption to mass ratio method was employed to screen the design variables, resulting in the selection of 17 thickness variables and 15 material variables. Thereafter, the gray wolf optimizer (GWO) algorithm underwent enhancement through the incorporation of the dynamic leadership hierarchy (DLH) mechanism and the revision of the positional formula, yielding the IGWO algorithm. Following this, the IGWO algorithm was applied to optimize the hyperparameters of BPNN, culminating in the establishment of the IGWO-BPNN model. Ultimately, the seat multi-objective optimization design process was addressed using multi-objective gray wolf optimizer (MOGWO) to achieve the Pareto frontier, while the decision-making was conducted using the combined compromise solution (CoCoSo) method to determine the best trade-off solution. Furthermore, the effectiveness of the proposed optimal design method is evidenced by comparing the baseline design, simulation analysis, and optimal design methods. The results indicate that the optimized automotive seat frame achieves a reduction in cost by 20.7 % and mass by 22.9 %, simultaneously maintaining safety performance. Consequently, the proposed optimization design methodology is demonstrated to be highly effective for the multi-objective optimization design of automotive seat frames.

Multi-objective optimization design of automobile seat backrest considering coupling effect

To investigate the impact of the coupling effects of carbon fiber reinforced polymer in the seat back layer on the performance of car seats, this paper presents a comprehensive optimization design method for composite materials. In detail, the finite element models firstly established and validated through five typical working conditions of automotive seats based on experimental data. Then, the optimized variables are divided and determined through backrest stress nephograms for each working conditions of the automotive seats, in which the various perspective are taken into account, such as the total mass of seat backrest, safety performance, and comfort index. Subsequently, an optimization strategy for unequal thickness layers lay-up design is constructed, which combines strength factors, optimal Latin hypercube sampling, best-worst method, gray relational analysis, and Visekriterijumsko KOmpromisno Rangiranje method for the optimal design of the automotive CFRP seat backrest. Additionally, the impact of layer coupling effects on different performance indices of the seat is examined through simulating and analyzing the seat backrest with various layer coupling types, while incorporating the classical laminate theory. The study reveals that by minimizing the laminate coupling effect, the comfort of the seat can be enhanced. Finally, a comprehensive comparative analysis of the optimal trade-off solution is carried out in terms of optimization strategies. The results show that ensuring the safety performance, the total mass of the seat backrest decreased by 21.3%, as a result of the optimization strategy proposed in this paper, and the comfort performance is also improved to some extent. Therefore, the multi-objective optimization strategy proposed in this paper performs well in terms of effectiveness and provides a reliable reference for related composite material multi-objective optimization.

NVH multiobjective and robust optimization of electric motor design, including power losses

As part of electric motor design, compromises between NVH considerations, electrotechnical design and performance targets must be made. Electromagnetic excitation within the airgap results in structure-borne and airborne noise transmission to the vehicle. High-frequency tones are characteristic of this noise. Efficient computation methods exist to estimate these vibration and noise levels. From the early design stage, NVH performance can be diagnosed and optimized. The focus on NVH can no longer be separated from efficiency optimization. Simulation workflows and optimization loops, developed for NVH-related targets, are updated to consider copper and iron losses. The modification of the geometrical design must be addressed to reduce both dynamic excitation and energy loss, or at least offer compromises. Electric motor design optimization requires the handling of multiple objectives and constraints from multiple physics. In addition, design robustness must be ensured as part of the industrial process: manufacturing tolerances have to be considered to define a robust optimized design.

Hybrid extreme gradient boosting regressor models for the multi-objective mixture design optimization of cementitious mixtures incorporating mine tailings as fine aggregates

The design of cementitious mixtures incorporating mine tailings as fine aggregates is a multi-objective optimization (MOO) problem, in which both the uniaxial compressive strength (UCS) and cost of the mixtures need to be considered simultaneously. Given that data-driven methods have shown promising results when solving similar MOO problems, this study developed an extreme gradient boosting regressor (XGBR) model on a dataset extracted from the literature to predict the UCS. Among the efforts taken to improve the models, a genetic algorithm (GA)-based XGBR model demonstrated the optimal prediction performance, with an R2 of 0.959. Next, the GA-XGBR model and a cost equation were used as objective functions in the MOO problem. The non-dominated sorting genetic algorithm with elite strategy (NSGA-II) was selected to solve the optimization problem. A case study was conducted, generating mixture designs that offered improved trade-offs between cost and UCS compared to experimental designs. Finally, a graphical user interface was developed to provide access to the prediction model and optimization method. Overall, this work can be used as a guide for optimal mixture designs as it facilitates informed decision-making before the actual applications.

Design optimization and off-design performance analysis of one-dimensional supercritical CO2 Brayton cycle

Supercritical carbon dioxide (SCO2) recompression Brayton cycle (RBC) is an encouraging technology for thermal power conversion and heat harvest for a wide range of heat sources due to its high-efficiency, low auxiliary power consumption, and compact size. However, most studies on its design and off-design performance analysis have been limited to the simple zero-dimensional component models without considering aerothermodynamics and ambient conditions. In this study, we developed a set of fully one-dimensional components models for SCO2 compressors, turbines, and heat exchangers, and, then, applied them to the multi-objective design optimization of a SCO2 cycle targeting a 50 MW net power output. The cycle off-design performance analysis methods and the control strategies were developed to countermeasure the performance degradation against the varying cooling water temperatures and part loads. The multi-objective cycle design optimization demonstrates that the cycle thermal efficiency and total product unit cost can be 0.476 and 11.652$/GJ, respectively, for the 50 MW SCO2 RBC cycle. The choke margin of the main compressor is 0.136 less than that of the re-compressor, and condensation can lead to a sharp decline in efficiency under high-flow conditions, causing the earlier onset of choking. The off-design performance analysis shows that the turbine inlet pressure control improves cycle efficiency below the design point of 317 K but does otherwise above the point. In contrast, inventory control strategies can maintain stable cycle efficiency and achieve adjustable net power output between 10 % and 110 %. The findings have the potential to advance further the commercial application of SCO2 cycles in high-temperature thermal energy systems.

Application of a novel stall margin improvement indicator in optimizing casing treatment for a transonic compressor

This paper presents a multi-objective design optimization of axial slot casing treatments in a 1.5 stage transonic compressor. To perform the optimization, an in-house optimization design platform is constructed using genetic algorithm and Kriging surrogate model. The optimization objectives are the peak efficiency at the design rotating speed and the stall margin improvements at both design and off-design rotating speeds. Instead of massive unsteady simulations that are required to accurately predict the stall margin, a stall margin improvement indicator is introduced based on the time-averaged axial momentum budget analysis at the rotor tip region. With this indicator, only one steady simulation is needed to evaluate the stall margin enhancement ability of a new casing treatment design at a given rotating speed. The axial slots are parameterized with a total of eight design parameters. The meridional profiles are described with two B-spline curves to define parameters such as the size, axial position, and shape of the slots. Circumferential parameters include the open area ratio and inclination angle. When the optimization finally converges, different optimal variants are selected from the database and their effects are investigated with both experiments and numerical simulations. The detailed flow fields are analyzed in depth with results from unsteady simulations. The application of the optimal casing treatments exerts a suction and re-injection effect, pushes the interface between tip leakage flow and incoming main flow downstream and reduced flow blockage in the blade tip region. Consequently, the stability of the compressor is significantly improved.

Towards maximum cost-effectiveness: multi-objective design optimisation of insulating glass flat-plate collectors

A significant challenge in the advancement of solar thermal heating systems lies in the unexplored techno-economic potential of insulating glass flat-plate collectors. These collectors are constructed in accordance with the specifications of standard insulating glass units and have emerged over the past decade as a promising design concept for enhancing the cost-effectiveness of solar thermal systems. However, substantial findings regarding the techno-economic viability of their production are still pending. The aim of this paper is to optimise insulating glass collector designs for solar district heating applications by identifying key design parameters that maximise cost-effectiveness. This study employed a five-stage methodology. It included thermo-hydraulic collector modelling using MATLAB/Simscape and the CARNOT Toolbox. The model was validated against experimental performance tests. A Latin hypercube computational design with 250,000 samples was set up to train supervised machine learning metamodels and perform a multi-objective optimisation using an elitist genetic algorithm. The study identified the argon concentration, collector length, and width as critical parameters influencing efficiency. Larger, thinner collectors demonstrated superior performance due to reduced convective losses and increased aperture-to-surface ratios. The optimisation revealed that the insulating glass collectors could achieve a 7.7 percentage point increase in efficiency, a 19.4 % reduction in material cost, and a 14.5 % decrease in weight compared to market-available flat-plate collectors. However, the direct economic comparison was not considered strong in evidence due to a lack of economic data from technology providers. The most cost-effective designs featured an argon concentration of 99 %, sealing thickness of 31.2 mm, and a glazing thickness of 4.1 mm, and 4.5 mm, while collector length and width varied more significantly. The research findings indicate the techno-economic potential of insulating glass collectors, demonstrating their ability to outperform conventional flat-plate collectors in terms of cost-effectiveness and efficiency. Future studies should focus on producing and testing larger modules and incorporating production costs to fully realise their potential for solar district heating applications. This study provides valuable guidelines for IGU designers and producers aiming to develop cost-effective and efficient solar thermal collectors for district heating systems.

Multi-objective design optimization for aerodynamic performance of centrifugal compressor impeller

Multi-objective design optimization for aerodynamic performance of centrifugal compressor impeller

Multi-objective optimization design of high-speed diaphragm coupling based on RSM and NSGA-II

Multi-objective optimization design of high-speed diaphragm coupling based on RSM and NSGA-II

Multi-objective optimization of energy demand and net zero energy building design based on climatic conditions (Case study: Iran)

Multi-objective optimization of energy demand and net zero energy building design based on climatic conditions (Case study: Iran)

Multi-objective Topology Optimization Design for a Certain Launcher Bracket

To achieve weight reduction and enhance the firing accuracy of a specific type of launch device, the bracket was selected as the optimization subject for multi-objective topology optimization. Single-objective optimization often overlooks other influencing factors. To address the limitations of single-objective optimization, this study adopts the variable density method from the SIMP approach and proposes a multi-objective topology optimization based on compromise programming. This study, through multi-objective topology optimization of the bracket, obtained an optimized topology structure that maximizes static stiffness and the dynamic low-order natural frequencies of the launch device bracket at launch angles of 0°, 53°, and 85°, with an azimuth angle of 0°. Finally, the obtained topology structure was validated using finite element software. The design method presented in this paper not only enhanced the stiffness of the bracket structure for such launch devices and increased the first two natural frequencies of the bracket but also achieved weight reduction. The optimization design process also provides a reference for other mechanical structures.

Hydrogen vs. conventional sector-coupling residential energy systems: An economic and environmental comparison based on multi-objective design optimization

Planning residential energy systems faces economic, environmental, and technical challenges, necessitating cost-effective and environmentally friendly solutions. Hydrogen technologies in districts have recently gained interest. However, their economic and environmental potential relative to conventional technologies remains largely unexplored. Therefore, we quantitatively compared the impacts of designing hydrogen-based and conventional sector-coupling systems on total costs and CO2 emissions.We developed a multi-objective optimization model for the design and operation of generation and storage units, aiming to minimize total costs and CO2 emissions. We created three energy system configurations for an exemplary German district, each involving photovoltaics, heat storage, and batteries, while varying the main heat supplier. The first configuration includes a gas combined heat and power unit, the second features a heat pump, and the third incorporates a fuel cell, an electrolyzer, and hydrogen storage.Our comparison of the Pareto fronts revealed that the hydrogen system’s cost is 83% higher than the gas-based system and 33% higher than the heat-pump-based system. Environmentally, the hydrogen system emits 11% less than the gas-based system but 47% more than the heat-pump-based system. In conclusion, hydrogen units offer environmental benefits through improved photovoltaic utilization but perform poorly economically due to high investment and operating costs.

The study of design and optimisation for CFRP combined pier anti-collision device

A CFRP honeycomb combination anti-collision device with a larger anti-collision level, greater crashworthiness, and longer service life was designed to safeguard the ship and piers in the event of an unintentional collision. Taking large-tonnage cargo ships and common bridge piers in the middle reaches of the Yangtze River as the research objects, the energy conversion response, impact force response and impact depth response of the collision were studied considering the collision conditions between the ship and the bare pier and the collision avoidance device. On this basis, the response surface method, variance analysis method and efficacy coefficient method were further used to take the shell thickness of the collision avoidance device and the thickness of the internal steel structure as the design parameters. The multi-objective optimisation design of the CFRP composite anti-collision device is carried out by selecting the ship impact force, the total internal energy absorbed by the anti-collision device, the total mass, and the inner diameter of the honeycomb steel structure as the optimisation objectives. The results show that the impact force reduction rate reaches 82.7%, the overall mass is greatly reduced, the maximum deformation is within a reasonable range, and the collision resistance is optimised.

Numerical simulation and multi-objective optimization design of conjugate heat transfer in novel double shell-passes multi-layer helically coiled tubes heat exchangers

A novel double shell-passes multi-layer helically coiled tubes heat exchanger (DSMHCTHE) is proposed to improve the flow and heat transfer performance of the shell side. It was studied by using conjugate heat transfer numerical model. By changing coil diameter and pitch, the influence of coil torsion on the performance of the heat exchangers was investigated in the range of 0.0637–0.3183, and compared with the conventional multi-layer helically coiled tubes heat exchangers (MHCTHE). Two kinds of heat exchangers were optimized by using multi-objective optimization differential evolution algorithm. The results indicate that the coil pitch has a greater effect on the overall heat transfer coefficient, and the effects of coil pitch variations in the inner and outer helically coiled tubes follow different patterns. Compared with MHCTHE, the heat transfer rate of DSMHCTHE are increased by 13.9 %–19.1 %, the comprehensive performance is increased by 13.0 %–18.0 %, and the heat transfer entropy generation number and friction entropy generation number are lower. It shows that DSMHCTHE have better application potential as heat exchangers.

Multiobjective Optimization Design of a MDOF Structure with Attached Nonlinear Gas–Spring Damper

To maximize vibration reduction efficiency and reduce the risk of detuning, this study proposes a multiobjective optimization design method for shape parameters affecting the nonlinear characteristics of nonlinear gas-spring damper (NGSD) based on the NSGA-II algorithm. A numerical model of a MDOF structure with attached NGSD is developed and optimized under white noise excitation, and the effectiveness of the optimized NGSD in mitigating structural seismic responses is validated through shaking table tests. By comparing with the optimal TMD, the control effectiveness and parameter sensitivity of the optimized NGSD under various near- and far-field seismic excitations are investigated. Results show that the optimization design is carried out with the performance objective of minimizing the RMS of structural displacement and acceleration response, and a set of relatively optimal piston radius and initial volume parameters are obtained, resulting in the control effectiveness of NGSD on the RMS response of MDOF structure’s displacement and acceleration as high as 77% and 39%, respectively. The maximum reduction effectiveness of optimized NGSD on the peak structural acceleration and displacement response under seismic excitation is 18% and 19% respectively, and the RMS reduction ratios are even as high as 56% and 61%, indicating the efficacy of using NSGA-II for parameter optimization. Moreover, the optimized NGSD demonstrates comparable control effectiveness to the optimal TMD with a shorter stroke and stable performance across different seismic excitations, indicating low sensitivity of optimal parameters to excitation frequency.

Multi-objective optimization design of low-power-driven, large-flux, and fast-response three-stage valve

Intrinsically safe solenoids drive solenoid valves in coal mining equipment. The low power consumption of these solenoids limits the response time of the solenoid valves. Additionally, the low viscosity and high susceptibility to dust contamination of the emulsion fluid often lead to leakage and sticking of hydraulic valves. This study proposes a low-power-driven, large-flux, fast-response three-stage valve structure with an internal displacement feedback device to address these issues. The critical parameters of the valve were optimized using a novel multi-objective optimization algorithm. A prototype was manufactured based on the obtained parameters and subjected to simulation and experimental verification. The results demonstrate that the valve has an opening time of 21 ms, a closing time of 12 ms, and a maximum flow rate of approximately 225 L/min. The driving power of this structure is less than 1.2 W. By utilizing this valve for hydraulic cylinder control, a positioning accuracy of ± 0.15 mm was achieved. The comparative test results show that the proposed structural control error fluctuation is smaller than that of the 3/4 proportional valve.

Design of Vibration and Noise Reduction for Ultra-Thin Cemented Carbide Circular Saw Blades in Woodworking Based on Multi-Objective Optimization

Cemented carbide circular saw blades are widely used for wood cutting, but they often suffer from vibration and noise issues. This study presents a multi-objective optimization method that integrates ANSYS and MATLAB to optimize the design of noise reduction slots in circular saw blades. A mathematical model was developed to correlate the emitted sound power with the overall vibration intensity. A multi-objective optimization model was then formulated to map the slot shape parameters to the deformation, equivalent stress, and vibration intensity during sawing. The ABAQUS thermal–mechanical coupling analysis was used to determine the sawing force and temperature field. The NSGA-II algorithm was applied on the ANSYS–MATLAB platform to iteratively compute slot shape parameters and conduct optimization searches for a globally optimal solution. Circular saw blades were fabricated based on the optimization results, and experimental results showed a significant reduction in sawing noise by 2.4 dB to 3.0 dB on average. The noise reduction effect within the specified frequency range closely agreed with the simulation results, validating the method’s efficiency. This study provides a feasible and cost-effective solution to the multi-objective optimization design problem of noise reduction slots for circular saw blades.

Multi-objective optimization of high Mach waverider based on small-sample surrogate model

Advancements have been achieved in the optimization of waverider designs with the aid of machine learning to expedite the design process. However, these approaches are hampered by the need for extensive sample sizes and susceptibility to becoming ensnared in local optima. This study undertakes a parametric design based on the wedge-derived, power-law-shaped waverider, increasing configuration diversity and creating a dataset with limited samples by calculating waverider geometry and aerodynamic parameters. At a Mach number of 10, a multi-objective optimization design is implemented using the Young's double-slit experiment-least squares support vector regression (YDSE-LSSVR) surrogate model in conjunction with improved congestion distance multi-objective particle swarm optimization algorithm, focusing on maximizing the lift-to-drag ratio and volumetric efficiency as much as possible. The results indicated that, under conditions of limited samples, the YDSE-LSSVR model outperforms standard models such as support vector regression, LSSVR, Kriging, and Polynomial Chaos Expansions-Kriging regarding prediction accuracy. The Pareto solutions for both concave and convex waveriders, obtained through multi-objective optimization, improve the lift-to-drag ratio by 17.36% and 21.70%, respectively, and increase the volumetric efficiency by 88.89% and 105.56%, in comparison to baseline configurations. In addition, the research examines the impact of various design parameters on the Pareto solutions. Finally, the study applies the K-means method to conduct a cluster analysis of the Pareto solutions, generating three-dimensional waverider configurations based on distinguished solutions from different clusters.