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Surrogate-assisted multi-objective evolutionary algorithms have been paid much attention to solve expensive multi-objective problems in recent years. However, with the number of objectives increasing, an improper solution may be picked for expensive objective evaluation due to the accumulation error of approximated values on objective functions. Furthermore, the time to construct surrogate models for all objectives will significantly increase. Thus, in this paper, Gaussian process (GP) models are proposed for performance indicators instead of for objective functions. Furthermore, solutions are selected from either of two ways to be evaluated using the expensive objective function. When there are non-dominated solutions found so far that are approximated, they will be exactly evaluated using the objective function. Otherwise, the solution with the maximum approximation uncertainty among the current population will be evaluated using the real objective functions. The efficiency of the presented approach is validated on the DTLZ test suite with 3, 6, 10, 15, and 20 objectives, MaF benchmark problems with 3, 6, 10, 15, and 20 objectives, and a real-world optimization problem called filter design. The experimental results show that the method proposed in this paper is competitive compared to recently proposed peer algorithms for expensive many-objective problems. [ABSTRACT FROM AUTHOR]

Feature selection wrapper methods are powerful mechanisms for reducing the complexity of prediction models while preserving and even improving their precision. Meta-heuristic methods, such as multi-objective evolutionary algorithms, are commonly used as search strategies in feature selection wrapper methods since they allow minimizing the cardinality of the attribute subset and simultaneously maximizing the predictive capacity of the model. However, in high-dimensional problems, multi-objective evolutionary algorithms for wrapper-type feature selection may require excessive computational time, sometimes impractical, especially when the learning algorithm has a high computational cost, such as deep learning. To address this drawback, in this paper we propose a multi-surrogate assisted multi-objective evolutionary algorithm for feature selection, specially designed to improve generalization error. The proposed method has been compared with conventional feature selection wrapper methods that use random forest, support vector machine and long short-term memory learning algorithms to evaluate subsets of attributes. The experiments have been carried out with regression and classification problems with time series data for air quality forecasting in the south-east of Spain and for indoor temperature forecasting in a domotic house. The results demonstrate the superiority of the proposed multi-surrogate assisted method over conventional wrapper methods using the same run times. [ABSTRACT FROM AUTHOR]

Micromechanical modelling of particulate composites with non-ellipsoidal particle shapes presents significant challenges because analytical approaches based on the fundamental results of Eshelby cannot be used. On the other side, direct numerical evaluations by finite element analysis can involve high computational cost in the case when particle features have small radius of curvature, sharp edges and require extremely fine meshes. This paper proposes substituting the exact particle shape with a surrogate model producing approximately the same contribution to the effective elastic moduli. We illustrate our approach by considering rotationally symmetric 3D particle shapes with the external surface defined by the Laplace's spherical harmonics. In this case, spherical layered surrogates offer good accuracy of approximation, especially when the material parameters of each layer are determined by the particle swarm optimization algorithm. The proposed approach is presented by considering several highly undulated particle shapes and comparing the surrogate model results with direct finite element simulations of the original microstructure. [ABSTRACT FROM AUTHOR]

• A review and comparison of surrogate models used in single-objective SAEAs. • Review surrogate models in terms of absolute and relative fitness models. • The construction and prediction time of models, and model's accuracy are compared. • SAEAs with different surrogate models are compared. Surrogate-assisted evolutionary algorithms (SAEAs), which use efficient surrogate models or meta-models to approximate the fitness function in evolutionary algorithms (EAs), are effective and popular methods for solving computationally expensive optimization problems. During the past decades, a number of SAEAs have been proposed by combining different surrogate models and EAs. This paper dedicates to providing a more systematical review and comprehensive empirical study of surrogate models used in single-objective SAEAs. A new taxonomy of surrogate models in SAEAs for single-objective optimization is introduced in this paper. Surrogate models are classified into two major categories: absolute fitness models, which directly approximate the fitness function values of candidate solutions, and relative fitness models, which estimates the relative rank or preference of candidates rather than their fitness values. Then, the characteristics of different models are analyzed and compared by conducting a series of experiments in terms of time complexity (execution time), model accuracy, parameter influence, and the overall performance when used in EAs. The empirical results are helpful for researchers to select suitable surrogate models when designing SAEAs. Open research questions and future work are discussed at the end of the paper. [ABSTRACT FROM AUTHOR]

• A novel Kriging-assisted two-phase optimization framework is proposed based on TLBO's unique structure. • A data management approach is proposed to collect and organize the dynamically updated expensive samples. • Two prescreening operators are proposed in Kriging-assisted Teaching and Learning Phases to select elite individuals. • KTLBO performs efficient on 18 benchmark cases and can successfully solve actual engineering applications. In this paper, a novel algorithm KTLBO is presented to achieve computationally expensive constrained optimization. In KTLBO, Kriging is adopted to develop dynamically updated surrogate models for costly objective and inequality constraints. A data managing method aiming at solving expensive constrained problems is developed to archive, classify and update expensive samples, where a penalty function is set to adaptively select elite individuals. Moreover, based on the Teaching-Learning-based Optimization (TLBO), a Kriging-assisted two-phase optimization framework is presented to alternately conduct local and global searches. In Kriging-assisted Teaching and Learning Phases, two different prescreening operators considering the probability of feasibility are respectively proposed to select the high-quality samples around the present best solution and the samples exhibiting better space-filling performance, as an attempt to balance exploitation of surrogates and exploration of unknown area. In brief, KTLBO retains the meta -heuristic search mechanism of TLBO while adopting Kriging to accelerate its search, thereby acting as a novel idea for surrogate-assisted constrained optimization. Lastly, KTLBO is compared with 6 well-known methods on 27 benchmark cases, and then its significant advantages in expensive constrained optimization are verified. Furthermore, KTLBO is adopted to design the structure of a Blended-Wing-Body underwater glider, and the satisfactory solution is yielded. [ABSTRACT FROM AUTHOR]

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node, referred to as log-sum-exp (LSE) network, is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of network maps to a family of subtraction-free ratios of generalized posynomials (GPOS), which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for a design that possesses a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing an effective optimization-based design. We illustrate the proposed approach by applying it to the data-driven design of a diet for a patient with type-2 diabetes and to a nonconvex optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp ($\mathrm {LSE}_{T}$). Under a suitable exponential transformation, the class of $\mathrm {LSE}_{T}$ functions maps to a family of generalized posynomials $\mathrm {GPOS}_{T}$ , which we similarly show to be universal approximators for log-log-convex functions. A key feature of an $\mathrm {LSE}_{T}$ network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a $\mathrm {GPOS}_{T}$ model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models. [ABSTRACT FROM AUTHOR]

• New approach for physics-based machine learning using POD expansions. • Machine learning methods learn map between inputs and POD coefficients. • Particular solutions in the POD expansion embed physical constraints in ML models. • Particular solutions enforce boundary conditions and other physical solution features. • Incorporating physics in ML models is critical when we have limited training data. This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional output quantities of interest, such as pressure, temperature and strain fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using the proper orthogonal decomposition (POD), and combines this parametrization with machine learning methods to learn the map between the input parameters and the POD expansion coefficients. The use of particular solutions in the POD expansion provides a way to embed physical constraints, such as boundary conditions and other features of the solution that must be preserved. The relative costs and effectiveness of four different machine learning techniques—neural networks, multivariate polynomial regression, k-nearest-neighbors and decision trees—are explored through two engineering examples. The first example considers prediction of the pressure field around an airfoil, while the second considers prediction of the strain field over a damaged composite panel. The case studies demonstrate the importance of embedding physical constraints within learned models, and also highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models. [ABSTRACT FROM AUTHOR]

Purpose – Fostered by the development of new technologies, micro-electro-mechanical systems (MEMS) are massively present on board of vehicles, within information equipment, as well as in medical and healthcare equipment. The purpose of this paper is to approach here the shape design of MEMS in terms of the optimization of a vector objective function, subject to a set of constraints. Objectives and constraints are non-linear, dependent on the unknown device shape. When multiple objective functions should be optimized simultaneously, the set of solutions minimizing the degree of conflict (Pareto front) can be searched for. Design/methodology/approach – This paper proposes an automated optimal design method based on connecting the MATLAB surrogate modeling (SUMO) toolbox with COMSOL Multiphysics finite element analysis tool, and the evolutionary algorithm NSGA-II as well. Findings – The efficiency of the optimization method proposed is approximately doubled in terms of runtime (5 vs 10 h for the referred platform), when compared with the same computational job without using surrogate models. This way, a cost-effective and accurate approximation of the Pareto front, trading off drive and levitation force components in a comb-drive electrostatic microactuator, was found. Research limitations/implications – More in-depth models of MEMS devices could be obtained by simulating multi-domain physical processes, i.e. encompassing a coupled-field analysis in the multiphysics sense. Originality/value – Under this framework, the proposed approach lays the ground for a very general method devoted to the optimal shape design of any MEMS configuration; in fact, the application of multiobjective optimizations to these kind of devices is quite new. [ABSTRACT FROM AUTHOR]

Highlights: [•] We modeled a representative helical micro-swimmer by a commercial CFD package. [•] We extracted necessary force coefficients and corrections from hydrodynamic forces. [•] We employed the coefficients and corrections in a RFT-based surrogate model. [•] We tested the validity of the surrogate within a bounded design space against CFD. [•] We demonstrated the use of surrogate to investigate optimal helical tail geometry. [Copyright &y& Elsevier]

• Current recurrent neural network (RNN) models are sensitive to path sampling. • A self-consistent RNN architecture is proposed and implemented. • This architecture replicates elasto-plastic behavior with 2500 parameters. • Surrogate models are validated in explicit finite element simulations. Recurrent neural networks could serve as surrogate material models, removing the gap between component-level finite element simulations and numerically costly microscale models. Recent efforts relied on gated recurrent neural networks. We show the limits of that approach: these networks are not self-consistent, i.e. their response depends on the increment size. We propose a recurrent neural network architecture that integrates self-consistency in its definition: the Linearized Minimal State Cell (LMSC). While LMSCs can be trained on short sequences, they perform best when applied to long sequences of small increments. We consider an elastoplastic example and train small models with fewer than 5000 parameters that precisely replicate the deviatoric elastoplastic behavior, with an optimal number of state-variables. We integrate these models into an explicit finite element framework and demonstrate their performance on component-level simulations with tens of thousands of elements and millions of increments. [Display omitted]. [ABSTRACT FROM AUTHOR]

• New, data-driven and physics constrained subgrid scale terms for dynamic turbulent flows. • An unclosed component that is reduced in dimension by orders of magnitude. • Easier subsequent surrogate construction. Recent years have seen a growing interest in using data-driven (machine-learning) techniques for the construction of cheap surrogate models of turbulent subgrid scale stresses. These stresses display complex spatio-temporal structures, and constitute a difficult surrogate target. In this paper we propose a data-preprocessing step, in which we derive alternative subgrid scale models which are virtually exact for a user-specified set of spatially integrated quantities of interest. The unclosed component of these new subgrid scale models is of the same size as this set of integrated quantities of interest. As a result, the corresponding training data is massively reduced in size, decreasing the complexity of the subsequent surrogate construction. [ABSTRACT FROM AUTHOR]

Sound wave propagation in a shallow water environment is complex due to e.g. the uncertainties of sound speed profile being inhomogeneous and imprecisely measured, the bottom reflections, etc. The propagation and influence of several uncertainty parameters are quantified in this paper. A four-layer model, which can approximately represent a wide range of shallow water environments, is considered; six parameters representing sound speed profile and water depth are considered as random variables. We investigate how the wave field (pressure) in this model is influenced by these uncertainties. For this purpose, the sound field is computed for different realizations of the random variables, when the medium is excited with sources whose frequencies are appropriate, for example, for marine seismic exploration applications. Since classical Monte Carlo methods require a huge sample size to converge, we use three surrogate modeling techniques (Kriging, Polynomial Chaos, and Polynomial Chaos-based Kriging). The proposed methods require much smaller sample sizes, which makes the uncertainty quantification (UQ) possible. Wavelength-to-depth ratio (λ ∕ d) is introduced as the key parameter that defines the degree of interaction (reflection and transmission) of the sound waves with the boundaries of the shallow water waveguide. The results show that for small and large values of λ ∕ d , the wave field is more sensitive to the variations of the water depth and the velocity of the bottom layer, respectively. The robustness (precision) of the surrogate models is shown to decrease for lower values of λ ∕ d. The proposed UQ methodology can be used for more complicated underwater environments; it is even more advantageous because it can efficiently deal with a large number of model uncertainty parameters and identify the most influential ones. [ABSTRACT FROM AUTHOR]