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The purpose of study is to overcome the error estimation of standard deviation derived from Expected improvement (EI) criterion. Compared with other popular methods, a quantitative model assessment and analysis tool, termed high-dimensional model representation (HDMR), is suggested to be integrated with an EI-assisted sampling strategy.

To predict standard deviation directly, Kriging is imported. Furthermore, to compensate for the underestimation of error in the Kriging predictor, a Pareto frontier (PF)-EI (PFEI) criterion is also suggested. Compared with other surrogate-assisted optimization methods, the distinctive characteristic of HDMR is to disclose the correlations among component functions. If only low correlation terms are considered, the number of function evaluations for HDMR grows only polynomially with the number of input variables and correlative terms.

To validate the suggested method, various nonlinear and high-dimensional mathematical functions are tested. The results show the suggested method is potential for solving complicated real engineering problems.

In this study, the authors hope to integrate superiorities of PFEI and HDMR to improve optimization performance.

This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.

The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency.

To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations.

The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.

The purpose of this paper is threefold: to make explicitly clear the range of efficient multi‐objective optimization algorithms which are available with kriging; to demonstrate a previously uninvestigated algorithm on an electromagnetic design problem; and to identify algorithms particularly worthy of investigation in this field.

The paper concentrates exclusively on scalarizing multi‐objective optimization algorithms. By reviewing the range of selection criteria based on kriging models for single‐objective optimization along with the range of methods available for transforming a multi‐objective optimization problem to a single‐objective problem, the family of scalarizing multi‐objective optimization algorithms is made explicitly clear.

One of the proposed algorithms is demonstrated on the multi‐objective design of an electron gun. It is able to identify efficiently an approximation to the Pareto‐optimal front.

The algorithms proposed are applicable to unconstrained problems only. One future development is to incorporate constraint‐handling techniques from single‐objective optimization into the scalarizing algorithms.

A family of algorithms, most of which have not been explored before in the literature, is proposed. Algorithms of particular potential (utilizing the most promising developments in single‐objective optimization) are identified.

Reflow soldering process is an important step of the surface mount technology. The purpose of this paper is to minimize the maximum warpage of shielding frame by controlling reflow soldering control parameters.

Compared with other reflow-related design methods, both time and temperate of each extracted time region are considered. Therefore, the number of design variable is increased. To solve the high-dimensional problem, a surrogate-assisted optimization (SAO) called adaptive Kriging high-dimensional representation model (HDMR) is used.

Therefore, the number of design variable is increased. To solve the high-dimensional problem, a surrogate-assisted optimization (SAO) called HDMR is used. The warpage of shield frame is significantly reduced. Moreover, the correlations of design variables are also disclosed.

Compared with the original Kriging HDMR, the expected improvement (EI) criterion is used and a new projection strategy is suggested to improve the efficiency of optimization method. The application suggests that the adaptive Kriging HDMR has potential capability to solve such complicated engineering problems.

This paper aims to introduce a method based on the optimizer of the particle swarm optimization (PSO) algorithm to improve the efficiency of a Kriging surrogate model.

PSO was first used to identify the best group of trend functions and to optimize the correlation parameter thereafter.

The Kriging surrogate model was used to resolve the fuselage optimization of an unmanned helicopter.

The optimization results indicated that an appropriate PSO scheme can improve the efficiency of the Kriging surrogate model.

Both the STANDARD PSO and the original PSO algorithms were chosen to show the effect of PSO on a Kriging surrogate model.

Kriging model has been widely adopted to reduce the high computational costs of simulations in Reliability-based design optimization (RBDO). To construct the Kriging model accurately and efficiently in the region of significance, a local sampling method with variable radius (LSVR) is proposed. The paper aims to discuss these issues.

In LSVR, the sequential sampling points are mainly selected within the local region around the current design point. The size of the local region is adaptively defined according to the target reliability and the nonlinearity of the probabilistic constraint. Every probabilistic constraint has its own local region instead of all constraints sharing one local region. In the local sampling region, the points located on the constraint boundary and the points with high uncertainty are considered simultaneously.

The computational capability of the proposed method is demonstrated using two mathematical problems, a reducer design and a box girder design of a super heavy machine tool. The comparison results show that the proposed method is very efficient and accurate.

The main contribution of this paper lies in: a new local sampling region computational criterion is proposed for Kriging. The originality of this paper is using expected feasible function (EFF) criterion and the shortest distance to the existing sample points instead of the other types of sequential sampling criterion to deal with the low efficiency problem.

Variable-fidelity optimization (VFO) frameworks generally aim at taking full advantage of high-fidelity (HF) and low-fidelity (LF) models to solve computationally expensive problems. The purpose of this paper is to develop a novel modified trust-region assisted variable-fidelity optimization (MTR-VFO) framework that can improve the optimization efficiency for computationally expensive engineering design problems.

Though the LF model is rough and inaccurate, it probably contains the gradient information and trend of the computationally expensive HF model. In the proposed framework, the extreme locations of the LF kriging model are firstly utilized to enhance the HF kriging model, and then a modified trust-region (MTR) method is presented for efficient local search. The proposed MTR-VFO framework is verified through comparison with three typical methods on some benchmark problems, and it is also applied to optimize the configuration of underwater tandem wings.

The results indicate that the proposed MTR-VFO framework is more effective than some existing typical methods and it has the potential of solving computationally expensive problems more efficiently.

The extreme locations of LF models are utilized to improve the accuracy of HF models and a MTR method is first proposed for local search without utilizing HF gradient. Besides, a novel MTR-VFO framework is presented which is verified to be more effective than some existing typical methods and shows great potential of solving computationally expensive problems effectively.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

This paper aims to study the sampling methods (or design of experiments) which have a large influence on the performance of the surrogate model. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study.

The high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. First, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set uniformly distributed. Third, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated.

The SCSM has better performance in efficiency, accuracy and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence.

The SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimisation problems.

This paper aims to investigate a multi-objective electric vehicle’s (EV’s) synergetic scheduling problem in the automotive industry, where a synergetic delivery mechanism to coordinate multiple EVs is proposed to fulfill part feeding tasks.

A chaotic reference-guided multi-objective evolutionary algorithm based on self-adaptive local search (CRMSL) is constructed to deal with the problem. The proposed CRMSL benefits from the combination of reference vectors guided evolutionary algorithm (RVEA) and chaotic search. A novel directional rank sorting procedure and a self-adaptive energy-efficient local search strategy are then incorporated into the framework of the CRMSL to obtain satisfactory computational performance.

The involvement of the chaotic search and self-adaptive energy-efficient local search strategy contributes to obtaining a stronger global and local search capability. The computational results demonstrate that the CRMSL achieves better performance than the other two well-known benchmark algorithms in terms of four performance metrics, which is inspiring for future researches on energy-efficient co-scheduling topics in manufacturing industries.

This research fully considers the cooperation and coordination of handling devices to reduce energy consumption, and an improved multi-objective evolutionary algorithm is creatively applied to solve the proposed engineering problem.