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Hyperparameter optimization (HPO) is a necessary step to ensure the best possible performance of Machine Learning (ML) algorithms. Several methods have been developed to perform HPO; most of these are focused on optimizing one performance measure (usually an error-based measure), and the literature on such single-objective HPO problems is vast. Recently, though, algorithms have appeared that focus on optimizing multiple conflicting objectives simultaneously. This article presents a systematic survey of the literature published between 2014 and 2020 on multi-objective HPO algorithms, distinguishing between metaheuristic-based algorithms, metamodel-based algorithms and approaches using a mixture of both. We also discuss the quality metrics used to compare multi-objective HPO procedures and present future research directions.

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

This paper proposes an efficient Kriging-based subset simulation (KSS) method for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probability. In this method, Kriging metamodel is employed to replace the true performance function, and it is smartly updated based on the samples in the first and last levels of subset simulation (SS). To achieve the smart update, a new update strategy is developed to search out samples located around the projection outlines on the limit-state surface. Meanwhile, the number of samples in each level of SS is adaptively adjusted according to the coefficients of variation of estimated failure probabilities. Besides, to quantify the Kriging metamodel uncertainty in the estimation of the upper and lower bounds of the small failure probability, two uncertainty functions are defined and the corresponding termination conditions are developed to control Kriging update. The performance of KSS is tested by four examples. Results indicate that KSS is accurate and efficient for HRA-RI with small failure probability.

Model-based engineering (MBE) recognizes models as central in software construction with the possibility of their management in libraries and repositories with proper structuring of their spaces and operations. Due to this success, models (and metamodels) are becoming larger and larger and technics are needed in order to comprehend and exploit them, such as circumscribing sub(meta)models of interest, which is the subject of this paper. Following MBE, there are mainly two ways for circumscribing submodels: only at the model level (by selecting model elements of interest) or through the meta level (by selecting a submetamodeling dimension of interest). In a preceding paper, we deeply studied the first way. Here we concentrate on the second way. Model projection deeply relies on the concepts of submodels and submetamodels with their inclusion qualities for model space structuring and has to be systematically examined from this point of view. It is important to point out that model treatment has to deal with full models (as offered by “off the shelf” libraries) but also with not necessarily well-formed ones, such as unspecified model chunks, due, for example, to the storage in repositories of incomplete engineering choices or of intermediate results of operations. It is a difficulty to encompass all these forms of models, being well-formed or not, in a homogeneous manner through MBE operations. The operation for “Model projection relative to submetamodeling dimensions” presented here does take this difficulty into account.

Significant computational resources are required to obtain an optimised wing jig shape by solving a high-fidelity large-scale aero-structural design optimisation problem. Gradient-based methods are efficient; however, some of the features of real-life engineering problems including numerical noise that pollutes the function values and occurrences of failed evaluations in the optimisation may limit their performance. To address these issues, this paper presents the latest developments in the multipoint approximation method (MAM) based on a gradient-assisted metamodel assembly technique within a trust-region optimisation framework. The proposed method is tested by a benchmark case first, and then, an aircraft wing jig shape optimisation problem is offered to demonstrate its performance. The gradient-based optimisation is used as a benchmark case, and the metamodel-based optimisation utilises the latest developments in MAM to solve the same problem. The results show that the proposed method can achieve the same design goal as the gradient-based method but with enhanced robustness and efficient performance. In the wing jig shape optimisation, the difference in the design objective, the global equivalent drag coefficient, between the two aforementioned optimisation approaches is 0.20 counts, whose relative difference is approximately 0.10%. Three approximate sub-optimisations have been conducted in every iteration of the metamodel-based optimisation to reduce the possibility of local optimality, while the overall elapsed time of the metamodel-based optimisation is approximately 1.98 times that of one gradient-based optimisation, which confirms the competitiveness of the proposed method bearing in mind the added safeguards for numerical noise, failed evaluations and possible local optimality.

Multiple models of a physical phenomenon are sometimes available with different levels of approximation. The high fidelity model is more computationally demanding than the coarse approximation. In this context, including information from the lower fidelity model to build a surrogate model is desirable. Here, the study focuses on the design of a miniaturized photoacoustic gas sensor which involves two numerical models. First, a multifidelity metamodeling method based on Radial Basis Function, the co-RBF, is proposed. This surrogate model is compared with the classical co-kriging method on two analytical benchmarks and on the photoacoustic gas sensor. Then an extension to the multifidelity framework of an already existing RBF-based optimization algorithm is applied to optimize the sensor efficiency. The co-RBF method does not bring better results than co-kriging but can be considered as an alternative for multifidelity metamodeling.

Model transformation lies at the very core of model-driven engineering, and a large number of model transformation languages and tools have been proposed over the last few years. These tools can be used to develop, transform, merge, exchange, compare, and verify models and metamodels. In this paper, we present a comprehensive catalog of existing metamodel-based transformation tools and compare them using a qualitative framework. We begin by organizing the 60 tools we identified into a general classification based on the transformation approach used. We then compare these tools using a number of particular facets, where each facet belongs to one of six different categories and may contain several attributes. The results of the study are discussed in detail and made publicly available in a companion website with a capability to search for tools using the specified facets as search criteria. Our study provides a thorough picture of the state-of-the-art in model transformation techniques and tools. Our results are potentially beneficial to many stakeholders in the modeling community, including practitioners, researchers, and transformation tool developers.

Drone Forensics (DRF) is one of the subdomains of digital forensics, which aims to capture and analyse the drone’s incidents. It is a diverse, unclear, and complex domain due to various drone field standards, operating systems, and infrastructure-based networks. Several DRF models and frameworks have been designed based on different investigation processes and activities and for the specific drones’ scenarios. These models make the domain more complex and unorganized among domain forensic practitioners. Therefore, there is a lack of a generic model for managing, sharing, and reusing the processes and activities of the DRF domain. This paper aims to develop A Drone Forensic Metamodel (DRFM) for the DRF domain using the metamodeling development process. The metamodeling development process is used for constructing and validating a metamodel and ensuring that the metamodel is complete and consistent. The developed DRFM consists of three main stages: (1) identification stage, (2) acquisition and preservation stage, and (3) examination and data analysis stage. It is used to structure and organize DRF domain knowledge, which facilitates managing, organizing, sharing, and reusing DRF domain knowledge among domain forensic practitioners. That aims to identify, recognize, extract and match different DRF processes, concepts, activities, and tasks from other DRF models in a developed DRFM. Thus, allowing domain practitioners to derive/instantiate solution models easily. The consistency and applicability of the developed DRFM were validated using metamodel transformation (vertical transformation). The results indicated that the developed DRFM is consistent and coherent and enables domain forensic practitioners to instantiate new solution models easily by selecting and combining concept elements (attribute and operations) based on their model requirement.

This paper proposes a novel multiscale concurrent topology optimization for cellular structures with continuously varying microstructures in space to obtain a superior structural performance at an affordable computation cost. At microscale, multiple prototype microstructures are topologically optimized to represent all the microstructures within macrostructure by incorporating a numerical homogenization approach into a parametric level set method (PLSM), whose connectivity is guaranteed by a kinematical connective constraint approach. A shape interpolation technology is developed to map these optimized prototype microstructures and generate a series of nonuniform microstructures, which are considered as sample points and used to construct a kriging metamodel. The built kriging metamodel is then employed to predict the effective properties of all the nonuniform microstructures within macrostructure. At macroscale, the variable thickness sheet (VTS) method is employed to generate an overall free material distribution patterns using the predicted effective properties of all the nonuniform microstructures. With the help of shape interpolation technology, all the nonuniform microstructures within macrostructure are well connected with each other due to the similar topological features at their interfaces. Using the proposed method, the macrostructural topology as well as the locations and configurations of the spatially varying nonuniform microstructures can be simultaneously optimized to ensure a sufficiently large multiscale design space. Numerical examples are provided to demonstrate the validity and advantages of the proposed method.

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.