A novel optimization strategy combining hybrid surrogate modeling and hybrid optimization algorithms for multi-objective design of a rear seat backrest frame in a passenger car

To address the challenges of complex weight calculation in multi-criteria decision-making and the limited ability of single-surrogate models to accurately fit highly nonlinear response data in the traditional Multi-Objective Global Optimization (MOGO) technique for automotive seat skeletons, this study proposes the Modified Preference Selection Index (MPSI) and a hybrid surrogate model to overcome these limitations. First, a high-precision finite element model of the rear seat luggage compartment collision was developed and experimentally validated. Second, key design variables were identified based on engineering expertise. Additionally, sample points for constructing the hybrid surrogate model were generated using the experimental design method. Subsequently, Pareto Frontier Solutions (PFSs) were derived by integrating the hybrid surrogate model with the second-generation non-dominated sorting genetic algorithm. The optimal compromise solution was then selected from the PFSs using the MPSI method. Finally, to validate the feasibility of the proposed MOGO technique based on MPSI and the hybrid surrogate model, a series of tests—including rear seat luggage impact test, headrest static strength test, and modal test—were conducted on the optimized rear seat. The results demonstrated full compliance with regulatory requirements, further confirming the feasibility of the proposed optimization framework. This research provides significant contributions to the lightweight engineering of automotive components.

A global optimisation strategy based on the hybrid surrogate model method and the competitive mechanism-based multi-objective particle swarm optimisation (CMOPSO) algorithm was developed to improve the accuracy of the aerodynamic performance optimisation of a high-speed train running in open air without a crosswind. Free-form deformation was used to improve the optimisation efficiency without remodelling or remeshing. The sample points and their responses were obtained via optimal Latin hypercube sampling and computational fluid dynamics (CFD) simulations. The hybrid surrogate model (HSM) was constructed by using the theory of optimal weighted surrogate to combine a polynomial response surface (PRS) model with a radial basis function (RBF) model. Comprehensive error evaluation results indicated that the prediction accuracy achieved with the HSM was higher than that achieved with either the PRS model or the RBF model; thus, the HSM was selected for use in each iteration to approximate the CFD simulation model of the high-speed train in subsequent optimisation. Then, the CMOPSO algorithm was selected as the optimisation algorithm. After optimisation, a series of Pareto-optimal solutions was obtained, and the optimal and original head shapes were compared. The use of the hybrid surrogate model and the CMOPSO algorithm greatly improved the optimisation efficiency.

In the context of frequent automobile collisions, optimizing passenger car seat structures is critical for improving vehicle safety and economic efficiency. This paper proposes a novel multi-objective optimization method for rear seats. A finite element analysis model under luggage collision conditions was developed and validated to ensure numerical accuracy. The material type and structural thickness of key stress areas in the backrest skeleton were selected as design variables, while displacement at safety index test points, material cost, and mass were established as optimization objectives. Regulatory requirements were incorporated as constraints to construct the multi-objective optimization model. An adaptive optimal hybrid surrogate model (AOHSM) was then built using the optimal Latin hypercube design and a point-adding strategy, integrated with the non-dominated sorting genetic algorithm II to derive the Pareto front solution set. Compared with local optimization methods and global optimization based on static surrogate models, the proposed AOHSM achieves superior optimization efficiency and performance, highlighting its methodological novelty. Finally, the solutions were ranked using a multi-criteria decision-making method based on combined weighting and improvement degree evaluation to identify the optimal compromise solution. The results show that, while meeting safety regulations, the optimized seat material cost was reduced by 27.67% and the mass decreased by 17.51%, significantly improving economic and lightweight performance. The proposed method also demonstrates strong optimization efficiency, solution accuracy, and engineering practicality, for example, being directly applicable to real seat structure design and manufacturing, thereby providing a valuable reference for collaborative automotive seat design.

Complex engineering multi-objective optimization problems that utilize high-fidelity simulation models often encounter challenges related to computational expense; however, surrogate-based optimization methods can effectively mitigate this limitation. This paper presents an integrated optimization framework that encompasses optimal Latin hypercube experimental design, a hybrid surrogate model combining a Pointer optimization algorithm with weighted prediction error reduction, a non-dominated sorting genetic algorithm-II, and the technique for order preference by similarity to ideal solutions (TOPSIS), which is based on grey relational analysis and the entropy weighting method as integral components of a comprehensive systematic optimization strategy. Subsequently, the feasibility of this strategy is validated through a case study centered on automotive seat engineering optimization, underscoring the benefits of the proposed hybrid surrogate model approach combined with the enhanced TOPSIS methodology. Thereafter, the thickness and number of layers of the carbon fiber-reinforced polymer (CFRP) automotive front bumper crossmember are established according to the principle of equal stiffness replacement. Ultimately, this optimization strategy is implemented in a multi-objective design concerning the layup sequence of the CFRP crash beam. The findings of this study indicate that the optimized CFRP crash beam demonstrates superior crashworthiness compared to the original steel crash beam, while achieving a significant reduction in overall weight. The optimized CFRP bumper demonstrates superior crash performance compared to the original steel structure, reducing the maximum crash force by 7.25%, while maintaining stable intrusion and energy absorption. Additionally, the optimized bumper achieves a substantial 67.5% weight reduction.

In order to improve the fitting accuracy and optimization efficiency of the surrogate model, a multi-response weighted adaptive sampling (MWAS) approach based on the hybrid surrogate model was proposed and implemented to a multi-objective lightweight design of car seats. In this approach, the sample discreteness index in the input design space was calculated by the maximum and minimum distance approach (MDA), the fitting uncertainty index of output response was calculated by a strategy based on the weighted prediction variance (WPV), and the two indices are combined by the weight coefficients. In the iterative process, the weight coefficients of the two indices were determined according to the accuracy of the hybrid surrogate model. The balance of global and local accuracy was realized by considering the sample dispersion and the fitting uncertainty of the surrogate model comprehensively. Numerical examples of single-response and multi-response systems showed that the proposed approach has excellent sampling efficiency and robustness. Moreover, the results of actual engineering application showed that the hybrid surrogate model constructed through MWAS could significantly improve the efficiency of model optimization. Hence, a high-precision optimization solution to the multi-objective lightweight design of passenger car rear seat was obtained.

Multi-objective optimization (MOO) algorithms usually require a high number of objective function evaluations to approximate the Pareto-optimal solutions, which can be time-consuming in many engineering applications . To overcome this issue, MOO algorithms using a small population, often referred to as micro-MOO algorithms, aim at approximating the true Pareto front using a smaller number of objective function evaluations. Such algorithms are not common in the evolutionary algorithms literature and their usage in building engineering is seldom. This paper proposes a micro-time variant multi-objective particle swarm optimization (micro-TVMOPSO), which is a revised version of the micro-MOPSO algorithm. First, the proposed algorithm is applied along with eight other MOO algorithms to 24 benchmark problems, and their performance is compared by using two metrics. Although the proposed micro-TVMOPSO algorithm faced difficulties in solving some complicated Pareto fronts, it outperformed the eight optimization algorithms on 10 of the 24 selected benchmark problems. After the comparison of proposed micro-TVMOPSO with several MOO algorithms for different benchmark problems, the micro-TVMOPSO is applied to a case study in engineering: the design optimization of a residential solar thermal combisystem using two conflicting objective functions, the life cycle cost (LCC) and energy use (LCE). Different patterns of variation of the decision variables were observed from the non-dominated solutions found by micro-TVMOPSO, which would have not been possible to notice by performing a single-objective optimization. For instance, the increase of number of solar collectors from 1 to 10 had the impact of increasing the LCC by 84% and decreasing the LCE by 63%. The results indicated that the number of solar thermal collectors is the variable having the most effect on both LCC and LCE. When the number of collectors increases, more energy is harvested, and larger tanks and less auxiliary electric power are needed.

The contact performance of high-contact-ratio asymmetrical planetary gears is comprehensively evaluated using multiple indicators. The relationship between the indicators and modification parameters is difficult to accurately describe with a single type of surrogate model due to their varying degrees of nonlinearity. This paper proposes an optimization design method for comprehensive modification parameters based on a hybrid surrogate model to improve the optimization accuracy of comprehensive modification. Firstly, a theoretical model of comprehensive modification for high-contact-ratio asymmetrical planetary gears and a dynamically selected hybrid surrogate model are proposed based on different contact performance indicators. Then, the explicit constraints of comprehensive modification and the implicit constraints of non-edge contact are modeled for the modification parameters. Finally, a multi-objective optimization algorithm for the modification parameters based on the hybrid surrogate model is established and validated through experiments and simulations. The results show that the proposed method improves the optimization accuracy and edge contact on the tooth surface is avoided while improving the contact performance, and they provide a reference for efficient and precise optimization of high-contact-ratio asymmetrical planetary gears.

As an important force transmission component of mortars, the seat plate affects some core indicators of mortars such as range, shooting accuracy, and maneuverability. In order to withstand huge impact loads, the seat plate was previously made of metal, which accounts for approximately 30%–45% of the total weight of the gun. The drawbacks of the heavy weight of the seat plate, which are not conducive to transportation and transfer, run counter to the current direction of the mortar’s lightweight development. The application of composite materials can greatly reduce the weight of the seat plate, but it exacerbates the contradiction between the mobility and combat effectiveness of mortars. In order to achieve the best match between mortar stability and maneuverability, a multiobjective optimization of composite material layers for seat plates is proposed, utilizing the designability of composite material layers. First, a fiber continuity model based on dropout sequence is adopted to solve the problems existing in the design of inherent continuity classes for composite layered fibers. Second, a hybrid surrogate model that considers the composite material seat plate quality, structural strength, shooting stability, shooting accuracy, and various working conditions is considered. Then, in order to improve the optimization efficiency and robustness of the algorithm, a multiobjective optimization algorithm based on the Chebyshev combination pattern is used to solve the mixed surrogate model. Finally, the optimization results are comprehensively evaluated against the optimization objectives. Research has shown that the method proposed in this article can effectively solve the time‐consuming problem of multiobjective optimization, improve the accuracy of hybrid surrogate models, and meet the expected requirements of multiobjective optimization of composite material seat plates. While ensuring shooting stability, the weight of the seat plate is reduced by 18.43% compared to the metal seat plate, which has important application value for lightweight design of mortars.

In the multi-objective optimization design of automotive seats based on Approximation-Based Design Optimization, a single approximation model may not adequately address the requirement of accurately fitting highly nonlinear feature data. For this reason, the Hybrid Approximation Models based on the Multi-Species Approximation Model (HAM-MSAM) is proposed to meet the requirement for high fitting accuracy. Subsequently, this study introduces a HAM-MSAM-based Approximation-Based Global Multi-Objective Optimization Design (ABGMOOD) strategy. This strategy is employed in the multi-objective optimization of the rear seat of a passenger car. HAM-MSAM was constructed from an experimentally validated finite element model and a training set generated through experimental design. The advantages of HAM-MSAM in capturing the highly nonlinear response under seat crash conditions were validated through comparison with hybrid model construction methods reported in existing literature. Finally, the optimization results obtained by the ABGMOOD strategy were compared to those of the classical local multi-objective optimization strategy, demonstrating the substantial advantages of the ABGMOOD optimization scheme in economy and weight reduction. In addition, the safety of the rear seats is slightly lower than that of the local optimization scheme but remains in compliance with regulatory requirements. The final optimized rear seat demonstrates notable improvements in safety, economy, and weight reduction, validating the feasibility of the ABGMOOD strategy and providing valuable insights for similar engineering optimization challenges.

In order to reduce the complexity of multi-objective design for automotive seat structures under crash scenarios, this study applies the MO-SHERPA algorithm to the automotive seat frame optimization problem for the first time. Based on a validated high-fidelity finite element model of a passenger car rear seat backrest, key design variables, material alternatives, and thickness ranges are defined to formulate the multi-objective optimization problem. The adaptive hybrid search capability of MO-SHERPA within HEEDS is leveraged to explore the design space efficiently, reducing reliance on deep theoretical knowledge and extensive surrogate modeling. To balance prediction accuracy and computational effort, a genetic aggregation response surface surrogate model is constructed using limited finite element samples. The optimization process evaluates different iteration schemes, revealing that increasing the number of evaluations significantly improves the Pareto front quality. The modified technique for order preference by similarity to an ideal solution decision-making method is then applied to select the optimal compromise solution from the Pareto sets. Comparative results show that with only 200 evaluations, the MO-SHERPA approach achieves a weighted improvement of 19.3%, outperforming local optimization and achieving similar or better performance than the non-dominated sorting genetic algorithm-III algorithm, which requires more than five times the evaluations. This demonstrates that MO-SHERPA can deliver robust, high-quality solutions for nonlinear crashworthiness problems with reduced computational resources. The proposed strategy provides practical guidance for multi-objective lightweight design of automotive seat structures, highlighting the potential of adaptive intelligent search algorithms to simplify and enhance complex engineering optimizations.

Multi-Objective Feature Selection Algorithm using Beluga Whale Optimization

Optimum design of distributed energy hubs using hybrid surrogate models (HSM)

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This paper describes a two-step design using optimization method for a six-phase synchronous reluctance motor mounted with a centrifugal compressor to achieve minimum cost, lower torque ripple, maximum efficiency and higher power factor. In the first-step optimization, the multiobjective design of adopted altered bee colony optimization (BCO) and Taguchi method combined with finite element analysis (FEA) are used for optimizing the barrier shape and layer number in the rotor to reduce torque ripple and raise power factor. In the second-step optimization, the adopted multiobject design method can be emplyed for optimizing the geometry of stator to achieve minimum cost and maximum efficiency. Experimental results show that these techniques can not only improve the efficiency and power factor but also reduce the material cost and torque ripple. The multiphase machine offers numerous advantages over the conventional threephase motor drives such as increased torque per ampere for the same volume machine, reduction of the stator current per phase, improvement of torque density and increase of the fault tolerance [1–2]. Some of the most suitable applications are electric, hybrid electric vehicles [3] and ship propulsion [4]. An multiobjective optimization design of a six-phase synchronous reluctance motor applied in a centrifugal compressor provides an important role in helping the consumption systems. The factors of design optimization in the six-phase synchronous reluctance motor are minimizing material cost, minimizing torque ripple, maximizing efficiency, and maximizing power factor. One of the popular design methods of the electromagnetic devices is the use of finite-element analysis (FEA) coupled with optimization algorithms. However, the classical optimization algorithms, such as deterministic and stochastic methods, seem to be not very efficient by using the FEA because it needs longer computing time. Therefore, a multiobjective optimization design of a six-phase synchronous reluctance motor used in both the altered bee colony optimization (BCO) [5], [6] and the Taguchi method [7], [8] with FEA [9], [10] in practical methodology is applied in a centrifugal compressor system. In this paper, the motor is rated at a power of 3kW, rotating at 1800r/min. The initial design of the motor consists of a stator having 36 slots that carry two-layer windings, as shown in Fig. 1 and Table I. The losses of the motor include iron loss in the stator, copper loss in the winding, eddy current loss in the rotor, and rotational losses due to friction and wind resistance. The iron and copper losses were the dominant contributor in a centrifugal compressor. The finite-element method with the measurement that combined the BCO and the Taguchi method is a very efficient and effective approach in the robust design of a high-performance motor. This paper presents the optimization design of a six-phase synchronous reluctance motor using two-stage optimization processes, which mainly depends on the stator and rotor regions between cost and efficiency. The stator region is applied to reduce the use of the iron and the winding to minimize cost and maxmimize efficiency in the first stage, while the rotor parameters are kept unchanged. An optimization design based on the altered BCO and the Taguchi method with FEA is employed to further enhance the machine performance. The Taguchi method can optimize the machine parameter of performance characteristics in electrical discharge machining. The experimental results are then converted into a signal-to-noise (S/N) ratio. The S/N ratio can be used to measure the deviation of the show characteristics from the desired values. In the second-stage optimization, the objectives are the maximization of power factor and minimization of toque ripple. while the stator parameters are kept unchanged. An optimization design based on the altered BCO and the Taguchi method with FEA is employed to further enhance the machine performance. In summary, it is seen that the two-stage optimization can reduce both cost and torque ripple, and further increase efficiency and power factor from the experimental values. Finally, the photo view of a six-phase synchronous reluctance motor is shown Fig. 2. The views of stator, rotor and winding combination in the six-phase synchronous reluctance motor mounted with a centrifugal compressor is shown in Fig. 2(a)–(b). This paper has presented an optimization design using the altered BCO and Taguchi method with FEA for tacking multiobjective optimization problems on a six-phase synchronous reluctance motor mounted with a centrifugal compressor compressor. The results of this paper confirm the effectiveness of the proposed technique for obtaining lower cost and better performance characteristics. This technique can be applied to solve multiobjective optimization problems of any electromagnetic devices.