This article introduces and investigates the optimization of the Vehicle Routing Problem for Security Dispatch (VRPSD). VRPSD focuses on security and patrolling applications, which involve precise timing and strict time-window constraints. When the number of sites to visit is large, the problem becomes extremely difficult. In this work, three algorithms are proposed to tackle this problem. The first algorithm combines single-phase adaptive large neighbourhood search (ALNS) with threshold accepting (TA). The second employs a multiphase ALNS with TA, and the third integrates multiphase ALNS, TA and tabu search (TS). Experiments are conducted on a real-world instance comprising 251 customer requests, followed by a structured hyperparameter sensitivity analysis and expanded scope of experiments through synthetic instance generation with varying sizes and constraints for robustness and scalability study. The results demonstrate that the hybrid multiphase ALNS-TS-TA algorithm solves large-scale VRPSD problems effectively with promising scalability and shows potential for continuous improvement with increased computation time.

Combinatorial Route Optimization (CRO) problems, such as the Vehicle Routing Problem (VRP) or the Travelling Salesman Problem (TSP), are commonly seen in scheduling, logistics, and transportation. While current machine learning (ML) methods can overcome certain limitations of traditional approaches, including exact and heuristic algorithms, they typically require substantial computational resources, large training datasets, and carefully designed models, thereby limiting their scalability and practical deployment. In this paper, we develop a method to address such concerns in a data-efficient and near-training-free manner using foundation models. We select TSP, one of the most well-known combinatorial optimization problems, to solve in our experiments and employ the Tabular Prior-Data Fitted Network (TabPFN), one of the newly designed foundation models. Specifically, we develop a node-based formulation that converts TSP into a sequence of localized prediction tasks and constructs a complete route through in-context learning provided by TabPFN. The proposed method enables TabPFN, a model developed for regression and classification, to be applied to CRO problems with only one TSP sample for fine-tuning. We evaluate the proposed method across varying TSP instance sizes and demonstrate that our approach generalizes effectively without retraining, maintains competitive solution quality, and exhibits promising scalability. These findings suggest that CRO problems can be approached through foundation models, enabling scalability as well as generating rapidly deployable solutions with near-training-free adaptation.

Deep generative models for engineering design often require substantial computational cost, large training datasets, and extensive retraining when design requirements or datasets change, limiting their applicability in real-world engineering design workflow. In this work, we propose a zero-shot generation framework for parametric engineering design based on TabPFN, enabling conditional design generation using only a limited number of reference samples and without any task-specific model training or fine-tuning. The proposed method generates design parameters sequentially conditioned on target performance indicators, providing a flexible alternative to conventional generative models. The effectiveness of the proposed approach is evaluated on three engineering design datasets, i.e., ship hull design, BlendedNet aircraft, and UIUC airfoil. Experimental results demonstrate that the proposed method achieves competitive diversity across highly structured parametric design spaces, remains robust to variations in sampling resolution and parameter dimensionality of geometry generation, and achieves a low performance error (e.g., <2% in generated ship hull designs' performance). Compared with diffusion-based generative models, the proposed framework significantly reduces computational overhead and data requirements while preserving reliable generation performance. These results highlight the potential of zero-shot, data-efficient generation as a practical and efficient tool for engineering design, enabling rapid deployment, flexible adaptation to new design settings, and ease of integration into real-world engineering workflows.

Digital twin (DT) has emerged as a powerful tool to facilitate monitoring, control, and other decision-making tasks in real-world engineering systems. Online update methods have been proposed to update DT models. Considering the degradation behavior in the system lifecycle, these methods fail to enable DT models to predict the system responses affected by the system degradation over time. To alleviate this problem, degradation models of measurable parameters have been integrated into DT construction. However, identifying the degradation parameters relies on prior knowledge of the system and expensive experiments. To mitigate those limitations, this paper proposes a lifelong update method for DT models to capture the effects of system degradation on system responses without any prior knowledge and expensive offline experiments on the system. The core idea in the work is to represent the system degradation during the lifecycle as the dynamic changes of DT configurations (i.e., model parameters with a fixed model structure) at all degradation stages. During the lifelong update process, an Autoencoder is adopted to reconstruct the model parameters of all hidden layers simultaneously, so that the latent features taking into account the dependencies among hidden layers are obtained for each degradation stage. The dynamic behavior of latent features among successive degradation stages is then captured by a long short-term memory model, which enables prediction of the latent feature at any unseen stage. Based on the predicted latent features, the model configuration at future degradation stage is reconstructed to determine the new DT model, which predicts the system responses affected by the degradation at the same stage. The test results on two engineering datasets demonstrate that the proposed update method could capture effects of system degradation on system responses during the lifecycle.

The present study aims to develop a novel optimal design of hybrid energy systems based on exergy and lifecycle concepts using genetic algorithms. The model consists of both stand-alone and on-grid options with scenarios for exchanging energy with the grid. The objectives include cost minimization or benefit maximization primarily, and lifecycle exergy efficiency, i.e., cost as the sustainability index secondarily. This research considers renewable sources such as solar, wind, hydropower, and hydrogen production and storage in addition to conventional diesel generators. The optimization was performed subject to weather conditions and solar radiation profiles, demand, and environmental or economic aspects. Also, the model contains various modules such as water-heating, waste energy utilization, as well as the options of power exchange with the distribution network and injection of hydrogen produced from excess renewable sources into the gas network. The application was demonstrated in a case study, where specific demands and the climate of Tehran were assumed. The case study considers four scenarios, including standalone, completely on-grid, on-grid with a non-backup generator, and on-grid without an energy sale option. The first optimal objective, the levelized unit cost of energy for the standalone system, is $0.22 per kWh. Moreover, the second optimal objective, the lifecycle exergy cost, ranges from 1.93 to 4.13 in different grid-connection states.

Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical for preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions. Machine learning models, on the other hand, rely heavily on high-quality datasets, which can be costly and difficult to obtain in the metal AM domain. Existing studies on physics-informed neural networks (PINNs) have made progress in integrating physics with machine learning but often lack in-situ data integration, which is essential for capturing real-time thermal dynamics. Additionally, their methodologies are typically heavily dependent on specific process characteristics, limiting their flexibility. Our work addresses these gaps by introducing a PINNbased framework specifically designed for temperature field prediction in metal AM. The framework incorporates in-situ temperature data gathered during the manufacturing process, combining it with physics-informed inputs and a custom loss function. The approach is demonstrated through two case studies. In the first case, using a small set of experimental data, the model achieves an error below 3 % with a mean absolute error (MAE) of 11 degrees C. In the second case, using simulation data, the model achieves an error below 1 % with an MAE of 7 degrees C. In addition, the framework shows promising adaptability for different metal AM scenarios with different geometries, deposition patterns, and process parameters.

Optimization problem formulation, a crucial but manually performed process, can present an obstacle to applying optimization in engineering since many practitioners find it challenging. This article explores the use of ChatGPT to address this challenge. It evaluates the efficacy of self-designed prompts with different ChatGPT models. Using analysis of variance and Tukey's test, assessments are conducted to determine the influence of variations in wording on the quality of solutions. The sequential learning approach is also tested to assess its impact on ChatGPT responses. This article confirms the importance of specificity in word choice and the relevance of domain-specific engineering terminology in crafting prompts for problem modelling. The analysis shows that a combination of properly selected words can lead to high-quality optimization problem formulations. Furthermore, it is found that sequential learning can enhance formulations. This work may bring more attention to the use of ChatGPT for formulating problems in engineering optimization.

This paper investigates the optimization of the Vehicle Routing Problem for Security Dispatch (VRPSD). VRPSD focuses on security and patrolling applications which involve challenging constraints including precise timing and strict time windows. We propose three algorithms based on different metaheuristics, which are Adaptive Large Neighborhood Search (ALNS), Tabu Search (TS), and Threshold Accepting (TA). The first algorithm combines single-phase ALNS with TA, the second employs a multiphase ALNS with TA, and the third integrates multiphase ALNS, TS, and TA. Experiments are conducted on an instance comprising 251 customer requests. The results demonstrate that the third algorithm, the hybrid multiphase ALNS-TS-TA algorithm, delivers the best performance. This approach simultaneously leverages the large-area search capabilities of ALNS for exploration and effectively escapes local optima when the multiphase ALNS is coupled with TS and TA. Furthermore, in our experiments, the hybrid multiphase ALNS-TS-TA algorithm is the only one that shows potential for improving results with increased computation time across all attempts.

Hot-wire directed energy deposition using a laser beam (DED-LB/w) is a method of metal additive manufacturing (AM) that has benefits of high material utilization and deposition rate, but parts manufactured by DED-LB/w suffer from a substantial heat input and undesired surface finish. Hence, regulating the process parameters and monitoring the process signatures to control the final quality during the deposition is crucial to ensure the quality of the final part. This paper explores the dynamic modeling of the DED-LB/w process and introduces a parameter-signature-quality modeling and control approach to enhance the quality of modeling and control of part qualities that cannot be measured in situ. The study investigates different process parameters that influence the melt pool width (signature) and bead width (quality) in single and multi-layer beads. The proposed modeling approach utilizes a parameter-signature model as F1 and a signature-quality model as F2. Linear and nonlinear modeling approaches are compared to describe a dynamic relationship between process parameters and a process signature, the melt pool width (F1). A fully connected artificial neural network is employed to model and predict the final part quality, i.e., bead width, based on melt pool signatures (F2). Finally, the effectiveness and usefulness of the proposed parameter-signature-quality modeling is tested and verified by integrating the parametersignature (F1) and signature-quality (F2) models in the closed-loop control of the width of the part. Compared with the control loop with only F1, the proposed method shows clear advantages and bears potential to be applied to control other part qualities that cannot be directly measured or monitored in situ.

Considering data insufficiency in metal additive manufacturing (AM), transfer learning (TL) has been adopted to extract knowledge from source domains (e.g., completed printings) to improve the modeling performance in target domains (e.g., new printings). Current applications use all accessible source data directly in TL with no regard to the similarity between source and target data. This paper proposes a systematic method to find appropriate subsets of source data based on similarities between the source and limited target datasets. Such similarity is characterized by the spatial and model distance metrics. A Pareto frontier-based source data selection method is developed, where the source data located on the Pareto frontier defined by two similarity distance metrics are selected iteratively. This method is integrated into an instance-based TL method (decision tree regression model) and a model-based TL method (fine-tuned artificial neural network). Both models are then tested on several regression tasks in metal AM. Comparison results demonstrate that (1) the source data selection method is general and supports integration with various TL methods and distance metrics, (2) compared with using all source data, the proposed method can find a subset of source data from the same domain with better TL performance in metal AM regression tasks involving different processes and machines, and (3) when multiple source domains exist, the source data selection method could find the subset from one source domain to obtain comparable or better TL performance than the model constructed using data from all source domains.

Laser wire directed energy deposition (DED-LB/w) offers notable efficiency in metal additive manufacturing (AM), allowing rapid component fabrication with high material utilization. Despite its advantages, challenges such as anisotropy and uneven mechanical properties arise from unregulated heat application, highlighting the need for precise temperature control during deposition. This study evaluates the use of visible light images to predict melt pool temperature, leveraging Convolutional Neural Networks (CNN), Gaussian Process Regression (GPR), and Artificial Neural Networks (ANN). While CNN is trained directly on images, GPR and ANN utilize extracted features such as melt pool dimensions. The CNN model notably excels, achieving an R-squared value of 0.981, root mean square error of 44.46, and mean absolute percentage error of 2.74%, demonstrating the superior capability of visible light imaging in accurately predicting the melt pool temperature. This success illustrates the considerable potential of integrating predictive models with visible light imaging as a cost-effective alternative to traditional sensory systems. Such integration not only offers a pragmatic solution to the high costs and complexities associated with thermal imaging but also opens new avenues for combining other measurement techniques such as pyrometers to further enhance the prediction accuracy for AM process control. Future efforts will concentrate on implementing these models in real-time metal printing, aiming to enhance microstructure control and advance process automation.

Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.

A digital twin (DT) is a model that mirrors a physical system and is continuously updated with real-time data from the physical system. Recent implementations of reduced-order-model-based DT (DT-ROM) have been applied in aerodynamics and structural health monitoring, where partial differential equations (PDEs) are utilized to update reduced bases and coefficients. However, these methods are not directly applicable when the PDEs of the system are unknown. This paper addresses the online update challenge for DT-ROM in scenarios lacking known PDEs of the system. To tackle the challenge, a systematic online update and application method is proposed. During the online update, the projection residual of online data on the reduced bases determines the necessity of updating reduced bases; the prediction residual of online data obtained by the current DT-ROM is used to decide whether to update the coefficient model. By sequentially evaluating both criteria, the method selectively incorporates essential online data for the online DT model update. During the online application, a criterion defined based on online data is adopted to determine whether the offline DT-ROM or the online one is applied to output final predictions. The capability of the proposed method is tested through three numerical and three engineering problems. Results indicate that the proposed online update method consistently reduces both projection and prediction residuals, thereby progressively enhancing the performance of the online DT-ROM on test data. Meanwhile, the online application method provides a prediction performance better than using offline DT-ROM only. Both demonstrate that the proposed work could be applied to online DT updates where the PDEs of the system are unknown.

Multiple-input multiple-output (MIMO) systems are fundamental in numerous advanced engineering applications, from aerospace to telecommunications, where precise system identification is critical for optimal performance. However, the identification of such systems often faces significant hurdles due to data scarcity, with existing approaches typically requiring substantial amounts of data for effective training. Addressing this challenge, this paper introduces a novel transfer learning framework designed specifically for MIMO system identification under conditions of limited data and inherent uncertainties. The proposed framework is applied to two case studies: the first in metal additive manufacturing, specifically the laser-blown powder-directed energy deposition as the source domain and the laser hot wire-directed energy deposition as the target domain, and the second involving a nonlinear case study of a continuous stirred-tank reactor (CSTR) with a temperature-dependent reaction. The results underscore the framework's effectiveness in capturing the dynamics of the target systems, including the ability to effectively model nonlinear dynamics. Comparative analyses highlight the benefits of employing dimensionless numbers in dynamic system modelling, offering reduced dimensionality, more physical meaning, and increased model accuracy. Overall, the proposed framework presents a promising approach to enhance system identification in MIMO systems with limited data and uncertainties, with potential applications across diverse domains.

Digital twin (DT) refers to any model that reflects a physical system and remains updated with the real-time data from the physical system. Recently, DT constructed with a reduced-order model (DT-ROM) has been applied to aerodynamics and structure health monitoring tasks, whose partial differential equations (PDEs) are used to design the online update formula for reduced bases and coefficients in DT-ROM. Although such online update methods improve the performance of DT-ROM, they are not applicable when the PDEs of a system are unknown. This paper focuses on the online update task where a system is modeled with a DT-ROM, but the system's PDEs are unknown. To tackle the task, an online sequential update method is proposed. During the update process, the projection residual of online data on the reduced bases is applied to determine whether to update the reduced bases in ROM, and the prediction residual of online data obtained by the offline DT-ROM is adopted to infer whether to update the coefficient models. By checking both criteria sequentially, the online update method selects the necessary online data for the DT update. Three numerical problems and one engineering problem are designed to test the proposed online update method. Testing results demonstrate that (a) the proposed online update method reduces both the projection and prediction residuals gradually, and (b) the performance of the offline DT-ROM model on the testing data is improved gradually during the online update process. Both indicate that the proposed method could be applied to online DT update tasks where the PDEs of the system are unknown.

In metal additive manufacturing (AM), precise temperature field prediction is crucial for process monitoring, automation, control, and optimization. Traditional methods, primarily offline and data-driven, struggle with adapting to real-time changes and new process scenarios, which limits their applicability for effective AM process control. To address these challenges, this paper introduces the first physics-informed (PI) online learning framework specifically designed for temperature prediction in metal AM. Utilizing a physics-informed neural network (PINN), this framework integrates a neural network architecture with physics-informed inputs and loss functions. Pretrained on a known process to establish a baseline, the PINN transitions to an online learning phase, dynamically updating its weights in response to new, unseen data. This adaptation allows the model to continuously refine its predictions in real-time. By integrating physics-informed components, the PINN leverages prior knowledge about the manufacturing processes, enabling rapid adjustments to process parameters, geometries, deposition patterns, and materials. Empirical results confirm the robust performance of this PI online learning framework in accurately predicting temperature fields for unseen processes across various conditions. It notably surpasses traditional data-driven models, especially in critical areas like the Heat Affected Zone (HAZ) and melt pool. The PINN’s use of physical laws and prior knowledge not only provides a significant advantage over conventional models but also ensures more accurate predictions under diverse conditions. Furthermore, our analysis of key hyperparameters—the learning rate and batch size of the online learning phase—highlights their roles in optimizing the learning process and enhancing the framework’s overall effectiveness. This approach demonstrates significant potential to improve the online control and optimization of metal AM processes.

Cold metal transfer wire arc additive manufacturing (CMT-WAAM) has attracted attention in recent years due to its ability to print walls with higher dimensional accuracy than regular WAAM. To print near-net shape parts by CMT-WAAM, there is a need to define a set of height-related geometrical parameters (HGPs) that can capture, quantify, and compare the quality of the height of the produced parts. In the presenting study, a set of HGPs, namely, the average height error, maximum height variation, and average absolute slope are defined and assessed. Fifteen single-track multi-layer walls are printed to check the effect of process parameters on the defined HGPs. It is found that the stability and quality of the print cannot be guaranteed by checking the visual appearance of the single beads and at least five-to-ten-layer walls should be printed. It is also found that the travel speed and the wire feed speed have positive monotonic relationships with average absolute slope and maximum height variation, respectively. Correlations between process parameters and HGPs are modeled and optimized using multi-objective optimization, and a validation test is performed to check the validity of the developed models. Moreover, HGPs of walls printed using unidirectional and bidirectional path strategies are calculated and compared. Defined HGPs are able to quantify, capture, and compare the quality of height of a wall with only three parameters. The HGPs can be used in further studies to report and compare the quality of height of thin wall structures.

The computational cost of modern simulation-based optimization tends to be prohibitive in practice. Complex design problems often involve expensive constraints evaluated through finite element analysis or other computationally intensive procedures. To speed up the optimization process and deal with expensive constraints, a new dimension selection-based constrained multi-objective optimization (MOO) algorithm is developed combining least absolute shrinkage and selection operator (LASSO) regression, artificial neural networks, and grey wolf optimizer, named L-ANN-GWO. Instead of considering all variables at each iteration during the optimization, the proposed algorithm only adaptively retains the variables that are highly influential on the objectives. The unselected variables are adjusted to satisfy the constraints through a local search. With numerical benchmark problems and a simulation-based engineering design problem, L-ANN-GWO outperforms state-of-the-art constrained MOO algorithms. The method is then applied to solve a highly complex optimization problem, the design of a high-temperature superconducting magnet. The optimal solution shows significant improvement as compared to the baseline design.

This paper aims to propose an online two-stage thermal history prediction method, which could be integrated into a metal AM process for performance control. Based on the similarity of temperature curves (curve segments of a temperature profile of one point) between any two successive layers, the first stage of the proposed method designs a layer-to-layer prediction model to estimate the temperature curves of the yet-to-print layer from measured temperatures of certain points on the previously printed layer. With measured/predicted temperature profiles of several points on the same layer, the second stage proposes a reduced order model (ROM) (intra-layer prediction model) to decompose and construct the temperature profiles of all points on the same layer, which could be used to build the temperature field of the entire layer. The training of ROM is performed with an extreme learning machine (ELM) for computational efficiency. Fifteen wire arc AM experiments and nine simulations are designed for thin walls with a fixed length and unidirectional printing of each layer. The test results indicate that the proposed prediction method could construct the thermal history of a yet-to-print layer within 0.1 seconds on a low-cost desktop computer. Meanwhile, the method has acceptable generalization capability in most cases from lower layers to higher layers in the same simulation, as well as from one simulation to a new simulation on different AM process parameters. More importantly, after fine-tuning the proposed method with limited experimental data, the relative errors of all predicted temperature profiles on a new experiment are smaller than 0.09, which demonstrates the applicability and generalization of the proposed two-stage thermal history prediction method in online applications for metal AM.

Modeling plays an important role in the additive manufacturing (AM) process and quality control. In practice, however, only limited data are available for each product due to the relatively high AM cost, which brings challenges in building either a high-quality physics-based or data-based model. Transfer learning (TL) is a new and promising group of approaches where the model of one product (source) may be reused for another product (target) with limited new target data. This paper focuses on reviewing applications of TL in AM modeling to help advance research in this area. First, notations, definitions, and categories of TL methods are introduced along with their application scenarios. Then current applications of TL in AM modeling are summarized along with their limitations. Based on reviewed applications, recommendations are given on how to apply TL for a certain AM problem, from the perspectives of source domain determination, TL method selection, target data generation, and data preprocessing. Finally, future research directions about TL in AM modeling are discussed in the hope to explore more potential of TL in improving the AM model quality with limited data.