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While performance demands in the natural world are varied, graded lattice structures reveal distinctive mechanical properties with tremendous engineering application potential. For biomechanical functions where mechanical qualities are required from supporting under external loading and permeability is crucial which affects bone tissue engineering, the geometric design in lattice structure for bone scaffolds in loading-bearing applications is necessary. However, when tweaking structural traits, these two factors frequently clash. For graded lattice structures, this study aims to develop a design-optimization strategy to attain improved attributes across different domains.

To handle diverse stress states, parametric modeling is used to produce strut-based lattice structures with spatially varied densities. The tailored initial gradients in lattice structure are subject to automatic property evaluation procedure that hinges on finite element method and computational fluid dynamics simulations. The geometric parameters of lattice structures with numerous objectives are then optimized using an iterative optimization process based on a non-dominated genetic algorithm.

The initial stress-based design of graded lattice structure with spatially variable densities is generated based on the stress conditions. The results from subsequent dual-objective optimization show a series of topologies with gradually improved trade-offs between mechanical properties and permeability.

In this study, a novel structural design-optimization methodology is proposed for mathematically optimizing strut-based graded lattice structures to achieve enhanced performance in multiple domains.

Currently, engineering project design lacks a design framework that fully combines subjective experience and objective data. This study develops an aided design decision-making framework to automatically output the optimal design alternative for engineering projects in a more efficient and objective mode, which synthesizes the design experience.

A database of design components is first constructed to facilitate the retrieval of data and the design alternative screening algorithm is proposed to automatically select all feasible design alternatives. Then back propagation (BP) neural network algorithm is introduced to predict the cost of all feasible design alternatives. Based on the gray relational degree-particle swarm optimization (GRD-PSO) algorithm, the optimal design alternative can be selected considering multiple objectives.

The case study shows that the BP neural network-cost prediction algorithm can well predict the cost of design alternatives, and the framework can be widely used at the design stage of most engineering projects. Design components with low sensitivity to design objectives have been obtained, allowing for the consideration of disregarding their impacts on design objectives in such situations requiring rapid decisions. Meanwhile, design components with high sensitivity to design objective weights have also been obtained, drawing special attention to the effects of changes in the importance of design objectives on the selection of these components. Simultaneously, the framework can be flexibly adjusted to different design objectives and identify key design components, providing decision reference for designers.

The framework proposed in this paper contributes to the knowledge of design decision-making by emphasizing the importance of combining objective data and subjective experience, whose significance is ignored in the existing literature.

The purpose of this paper is to review studies on mathematical optimization of the sustainable gasoline supply chain to help decision-makers understand the current situation, the exact dimensions of the problem and the models provided in the literature. So, a more realistic mathematical optimization model can be achieved by fully covering all dimensions of the supply chain of this product.

To evaluate and comprehend the mathematical optimization of the sustainable gasoline supply chain research area, a systematic literature review is undertaken that covers material collection, descriptive analysis, content analysis and material evaluation steps. Finally, based on this process, 69 related articles were carefully investigated.

The results of the systematic literature review show the main areas of the published papers on mathematical optimization of sustainable gasoline supply chain problems and the gaps for future research in this field presented based on them.

This approach is subject to limitations because the protocol of the systematic review of the research literature only included searching for the considered combination of keywords in the Scopus and ProQuest databases. Furthermore, the protocol used in this paper restricts documents to English.

The results have significant implications for both academicians and practitioners in this field. It can be useful for academics to comprehend the gaps and future trends in this field. Also, for practitioners, it can be useful to identify and understand the parts of the mathematical optimization model, which can help them model this problem effectively and efficiently.

No systematic literature review has been done in this field by considering gasoline to the best of the authors’ knowledge and delivers new facts for the future development of this field.

To improve the speed and accuracy of turbine blade film cooling design process, the most advanced deep learning models were introduced into this study to investigate the most suitable define for prediction work. This paper aims to create a generative surrogate model that can be applied on multi-objective optimization problems.

The latest backbone in the field of computer vision (Swin-Transformer, 2021) was introduced and improved as the surrogate function for prediction of the multi-physics field distribution (film cooling effectiveness, pressure, density and velocity). The basic samples were generated by Latin hypercube sampling method and the numerical method adopt for the calculation was validated experimentally at first. The training and testing samples were calculated at experimental conditions. At last, the surrogate model predicted results were verified by experiment in a linear cascade.

The results indicated that comparing with the Multi-Scale Pix2Pix Model, the Swin-Transformer U-Net model presented higher accuracy and computing speed on the prediction of contour results. The computation time for each step of the Swin-Transformer U-Net model is one-third of the original model, especially in the case of multi-physics field prediction. The correlation index reached more than 99.2% and the first-order error was lower than 0.3% for multi-physics field. The predictions of the data-driven surrogate model are consistent with the predictions of the computational fluid dynamics results, and both are very close to the experimental results. The application of the Swin-Transformer model on enlarging the different structure samples will reduce the cost of numerical calculations as well as experiments.

The number of U-Net layers and sample scales has a proper relationship according to equation (8). Too many layers of U-Net will lead to unnecessary nonlinear variation, whereas too few layers will lead to insufficient feature extraction. In the case of Swin-Transformer U-Net model, incorrect number of U-Net layer will reduce the prediction accuracy. The multi-scale Pix2Pix model owns higher accuracy in predicting a single physical field, but the calculation speed is too slow. The Swin-Transformer model is fast in prediction and training (nearly three times faster than multi Pix2Pix model), but the predicted contours have more noise. The neural network predicted results and numerical calculations are consistent with the experimental distribution.

This paper creates a generative surrogate model that can be applied on multi-objective optimization problems. The generative adversarial networks using new backbone is chosen to adjust the output from single contour to multi-physics fields, which will generate more results simultaneously than traditional surrogate models and reduce the time-cost. And it is more applicable to multi-objective spatial optimization algorithms. The Swin-Transformer surrogate model is three times faster to computation speed than the Multi Pix2Pix model. In the prediction results of multi-physics fields, the prediction results of the Swin-Transformer model are more accurate.

This paper aims to investigate the optimization of window and shading designs to reduce the building energy consumption of a standard office room while improving occupants' comfort in Tehran and Auckland.

The NSGA-II algorithm, as a multi-objective optimization method, is applied in this study. First, a comparison of the effects of each variable on all objectives in both cities is conducted. Afterwards, the optimal solutions and the most undesirable scenarios for each city are presented for architects and decision-makers to select or avoid.

The results indicate that, in both cities, the number of slats and their distance from the wall are the most influential variables for shading configurations. Additionally, occupants' thermal comfort in Auckland is much better than in Tehran, while the latter city can receive more daylight. Furthermore, the annual energy use in Tehran can be significantly reduced by using a proper shading device and window-to-wall ratio (WWR), while building energy consumption, especially heating, is negligible in Auckland.

To the best of the authors' knowledge, this is the first study that compares the differences in window and shading design between two cities, Tehran and Auckland, with similar latitudes but located in different hemispheres. The outcomes of this study can benefit two groups: firstly, architects and decision-makers can choose an appropriate WWR and shading to enhance building energy efficiency and occupants' comfort. Secondly, researchers who want to study window and shading systems can implement this approach for different climates.

The purpose of this study is to evaluate and minimize the losses of alternating current (AC) in the winding of electrical machines. AC winding losses are frequently disregarded at low frequencies, but they become a significant concern at high frequencies. This is the situation where applications require a high speed. The most significant applications in this category are electrical propulsion and drive systems.

An analytical model is used to predict the AC losses in the winding of electrical machines. The process involves dividing the slot into separate layers and then calculating the AC loss factor for each layer. The model aims to calculate AC losses for two different winding arrangements involving circular conductors. This application focuses on the stator winding of a permanent magnet synchronous motor that is specifically designed for electric vehicles. The model is integrated into an optimization process that makes use of the genetic algorithm method to minimize AC losses resulting from the arrangement of conductors within the slot.

This study and its findings demonstrate that the arrangement of the conductors within the slot has a comparable effect on the AC losses in the winding as the machine's geometric and physical properties. The effectiveness of electrical machines depends heavily on optimizing the arrangement of conductors in the slot to minimize AC winding losses.

The proposed strategy seeks to minimize AC winding losses in high-speed electric machines by providing a cost-effective and precise solution to improve energy efficiency.

Many practical control problems require achieving multiple objectives, and these objectives often conflict with each other. The existing multi-objective evolutionary reinforcement learning algorithms cannot achieve good search results when solving such problems. It is necessary to design a new multi-objective evolutionary reinforcement learning algorithm with a stronger searchability.

The multi-objective reinforcement learning algorithm proposed in this paper is based on the evolutionary computation framework. In each generation, this study uses the long-short-term selection method to select parent policies. The long-term selection is based on the improvement of policy along the predefined optimization direction in the previous generation. The short-term selection uses a prediction model to predict the optimization direction that may have the greatest improvement on overall population performance. In the evolutionary stage, the penalty-based nonlinear scalarization method is used to scalarize the multi-dimensional advantage functions, and the nonlinear multi-objective policy gradient is designed to optimize the parent policies along the predefined directions.

The penalty-based nonlinear scalarization method can force policies to improve along the predefined optimization directions. The long-short-term optimization method can alleviate the exploration-exploitation problem, enabling the algorithm to explore unknown regions while ensuring that potential policies are fully optimized. The combination of these designs can effectively improve the performance of the final population.

A multi-objective evolutionary reinforcement learning algorithm with stronger searchability has been proposed. This algorithm can find a Pareto policy set with better convergence, diversity and density.

The aerodynamic differences between the head car (HC) and tail car (TC) of a high-speed maglev train are significant, resulting in control difficulties and safety challenges in operation. The arch structure has a significant effect on the improvement of the aerodynamic lift of the HC and TC of the maglev train. Therefore, this study aims to investigate the effect of a streamlined arch structure on the aerodynamic performance of a 600 km/h maglev train.

Three typical streamlined arch structures for maglev trains are selected, i.e. single-arch, double-arch and triple-arch maglev trains. The vortex structure, pressure of train surface, boundary layer, slipstream and aerodynamic forces of the maglev trains with different arch structures are compared by adopting improved delayed detached eddy simulation numerical calculation method. The effects of the arch structures on the aerodynamic performance of the maglev train are analyzed.

The dynamic topological structure of the wake flow shows that a change in arch structure can reduce the vortex size in the wake region; the vortex size with double-arch and triple-arch maglev trains is reduced by 15.9% and 23%, respectively, compared with a single-arch maglev train. The peak slipstream decreases with an increase in arch structures; double-arch and triple-arch maglev trains reduce it by 8.89% and 16.67%, respectively, compared with a single-arch maglev train. The aerodynamic force indicates that arch structures improve the lift imbalance between the HC and TC of a maglev train; double-arch and triple-arch maglev trains improve it by 22.4% and 36.8%, respectively, compared to a single-arch maglev train.

This study compares the effects of a streamlined arch structure on a maglev train and its surrounding flow field. The results of the study provide data support for the design and safe operation of high-speed maglev trains.

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

This study aims to address the inherent uncertainties within closed-loop supply chain (CLSC) networks through the application of a multi-objective approach, specifically focusing on the optimization of integrated production and transportation processes. The primary purpose is to enhance decision-making in supply chain management by formulating a robust multi-objective model.

In dealing with uncertainty, this study uses Pythagorean fuzzy numbers (PFNs) to effectively represent and quantify uncertainties associated with various parameters within the CLSC network. The proposed model is solved using Pythagorean hesitant fuzzy programming, presenting a comprehensive and innovative methodology designed explicitly for handling uncertainties inherent in CLSC contexts.

The research findings highlight the effectiveness and reliability of the proposed framework for addressing uncertainties within CLSC networks. Through a comparative analysis with other established approaches, the model demonstrates its robustness, showcasing its potential to make informed and resilient decisions in supply chain management.

This study successfully addressed uncertainty in CLSC networks, providing logistics managers with a robust decision-making framework. Emphasizing the importance of PFNs and Pythagorean hesitant fuzzy programming, the research offered practical insights for optimizing transportation routes and resource allocation. Future research could explore dynamic factors in CLSCs, integrate real-time data and leverage emerging technologies for more agile and sustainable supply chain management.

This research contributes significantly to the field by introducing a novel and comprehensive methodology for managing uncertainty in CLSC networks. The adoption of PFNs and Pythagorean hesitant fuzzy programming offers an original and valuable approach to addressing uncertainties, providing practitioners and decision-makers with insights to make informed and resilient decisions in supply chain management.