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Metamodels are widely used to replace simulation models in engineering design optimization to reduce the computational cost. The purpose of this paper is to develop a novel sequential sampling strategy (weighted accumulative error sampling, WAES) to obtain accurate metamodels and apply it to improve the quality of global optimization.

A sequential single objective formulation is constructed to adaptively select new sample points. In this formulation, the optimization objective is to select a sample point with the maximum weighted accumulative predicted error obtained by analyzing data from previous iterations, and a space-filling criterion is introduced and treated as a constraint to avoid generating clustered sample points. Based on the proposed sequential sampling strategy, a two-step global optimization approach is developed.

The proposed WAES approach and the global optimization approach are tested in several cases. A comparison has been made between the proposed approach and other existing approaches. Results illustrate that WAES approach performs the best in improving metamodel accuracy and the two-step global optimization approach has a great ability to avoid local optimum.

The proposed WAES approach overcomes the shortcomings of some existing approaches. Besides, the two-step global optimization approach can be used for improving the optimization results.

The purpose of this study is to enable performing reliability-based design optimisation (RBDO) for a composite component while accounting for several multi-scale uncertainties using a large representative volume element (LRVE). This is achieved using an efficient finite element analysis (FEA)-based multi-scale reliability framework and sequential optimisation strategy.

An efficient FEA-based multi-scale reliability framework used in this study is extended and combined with a proposed sequential optimisation strategy to produce an efficient, flexible and accurate RBDO framework for fibre-reinforced composite laminate components. The proposed RBDO strategy is demonstrated by finding the optimum design solution for a composite component under the effect of multi-scale uncertainties while meeting a specific stiffness reliability requirement. Performing this using the double-loop approach is computationally expensive because of the number of uncertainties and function evaluations required to assess the reliability. Thus, a sequential optimisation concept is proposed, which starts by finding a deterministic optimum solution, then assesses the reliability and shifts the constraint limit to a safer region. This is repeated until the desired level of reliability is reached. This is followed by a final probabilistic optimisation to reduce the mass further and meet the desired level of stiffness reliability. In addition, the proposed framework uses several surrogate models to replace expensive FE function evaluations during optimisation and reliability analysis. The numerical example is also used to investigate the effect of using different sizes of LRVEs, compared with a single RVE. In future work, other problem-dependent surrogates such as Kriging will be used to allow predicting lower probability of failures with high accuracy.

The integration of the developed multi-scale reliability framework with the sequential RBDO optimisation strategy is proven computationally feasible, and it is shown that the use of LRVEs leads to less conservative designs compared with the use of single RVE, i.e. up to 3.5% weight reduction in the case of the 1 × 1 RVE optimised component. This is because the LRVE provides a representation of the spatial variability of uncertainties in a composite material while capturing a wider range of uncertainties at each iteration.

Fibre-reinforced composite laminate components designed using reliability and optimisation have been investigated before. Still, they have not previously been combined in a comprehensive multi-scale RBDO. Therefore, this study combines the probabilistic framework with an optimisation strategy to perform multi-scale RBDO and demonstrates its feasibility and efficiency for an fibre reinforced polymer component design.

The purpose of this paper is to study joint inventory and pricing strategy for a continuous inventory review system. While dynamic pricing decisions are often studied in the literature along with inventory management, the authors' aim in this study is to obtain a single long‐run optimal price; also to gain insight about how to obtain the optimal price and inventory control variables simultaneously and then the benefits of joint optimization of the inventory and pricing decisions over the sequential optimization policy often followed in practice.

A general (R;Q) policy system with fixed cost of ordering is modelled and then the case where unsatisfied demand is lost is studied. General forms of both the additive and multiplicative demand models are used to obtain structural results.

By showing optimality conditions on the price and inventory decision variables, two algorithms on how to obtain optimal decision variables, one for additive and another for multiplicative demand‐price model are provided. Through extensive numerical analyses, the potential profit increases are reported if the price and inventory problem are solved simultaneously instead of sequentially. In addition, the sensitivities of optimal decision variables to system parameters are revealed.

Although there are several studies in the literature investigating emergency price change models, they use arbitrary exogenous prices menus. However, the value of a price change can be better appreciated if the long‐run price is optimal for the system.

Very few researchers have investigated constant price and inventory optimization, and while there are several past studies demonstrating the benefits of dynamic pricing over a static one, there still are not many findings on the benefit of joint price and inventory optimization.

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

This paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching transformers. The considered methods involve surrogate modeling techniques and variable-fidelity electromagnetic (EM) simulations. In contrary to majority of conventional approaches, they do not rely on population-based metaheuristics, which permit lowering the design cost and improve reliability.

There are two algorithmic frameworks presented, both fully deterministic. The first algorithm involves creating a path covering the Pareto front and arranged as a sequence of patches relocated in the course of optimization. Response correction techniques are used to find the Pareto front representation at the high-fidelity EM simulation level. The second algorithm exploits Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front by means of solving appropriately defined local constrained optimization problems. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving expensive EM-simulation models of impedance transformer structures.

It is possible, by means of combining surrogate modeling techniques and constrained local optimization, to identify the set of alternative designs representing Pareto-optimal solutions, in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures. Multi-objective optimization for the considered class of structures can be realized using deterministic approaches without defaulting to evolutionary methods.

The present study can be considered a step toward further studies on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

The proposed algorithmic solutions proved useful for expedited multi-objective design optimization of miniaturized microwave structures. The problem is extremely challenging when using conventional methods, in particular evolutionary algorithms. To the authors’ knowledge, this is one of the first attempts to investigate deterministic surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

For complex engineering problems, multidisciplinary design optimization (MDO) techniques use some disciplines that need to be run several times in different modules. In addition, mathematical modeling of a discipline can be improved for each module. The purpose of this paper is to show that multi-modular design optimization (MMO) improves the design performances in comparison with MDO technique for complex systems.

MDO framework and MMO framework are developed to optimum design of a complex system. The nonlinear equality and inequality constrains are considered. The system optimizers included Genetic Algorithm and Sequential Quadratic Programming.

As shown, fewer design variables (optimization variables) are needed at the system level for MMO. Unshared variables are optimized in the related module when shared variables are optimized at the system level. The results of this research show that MMO has lower elapsed times (14 percent) with lower F-count (16 percent).

The monopropellant propulsion upper-stage is selected as a case study. In this paper, the efficient model of the monopropellant propulsion system is proposed. According to the results, the proposed model has acceptable accuracy in mass model (error < 2 percent), performance estimation (error < 6 percent) and geometry estimation (error < 10 percent).

The monopropellant propulsion system is broken down into the three important modules including propellant tank (tank and propellant), pressurized feeding (tank and gas) and thruster (catalyst, nozzle and catalysts bed) when chemical decomposition, aerothermodynamics, mass and configuration, catalyst and structure have been considered as the disciplines. The both MMO and MDO frameworks are developed for the monopropellant propulsion system.

Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal.

The chosen model problem for the design is a two‐phase material, with one phase related to plasticity and another to damage. The design problem is set in terms of shape optimization of the interface between two phases. The solution procedure proposed herein is compatible with the multi‐scale interpretation of the inelastic mechanisms characterizing the chosen two‐phase material and it is thus capable of providing the optimal form of the material microstructure. The original approach based upon a simultaneous/sequential solution procedure for the coupled mechanics‐optimization problem is proposed.

Several numerical examples show a very satisfying performance of the proposed methodology. The latter can easily be adapted to other choices of design variables.

Confirms that one can thus achieve the optimal design of the nonlinear behavior of a given two‐phase material with respect to the goal specified by a cost function, by computing the optimal form of the shape interface between the phases.

This paper aims to introduce an original application of the corrected response surface method (CRSM) in the context of the optimal design of a permanent magnet synchronous machine used as an integrated starter generator. This method makes it possible to carry out this design in a very efficient manner, in comparison with conventional optimization approaches.

The search for optimal conditions is achieved by the joint use of two multi-physics models of the machine to be optimized. The former models most finely the physical functioning of the machine; it is called “fine model”. The second model describes the same physical phenomena as the fine model but must be much quicker to evaluate. Thus, to minimize its evaluation time, it is necessary to simplify it considerably. It is called “coarse model”. The lightness of the coarse model allows it to be used intensively by conventional optimization algorithms. On the other hand, the fine reference model makes it possible to recalibrate the results obtained from the coarse model at any instant, and mainly at the end of each classical optimization. The difference in definition between fine and coarse models implies that these two models do not give the same output values for the same input configuration. The approach described in this study proposes to correct the values of the coarse model outputs by constructing an adjustment (correcting) response surface. This gives the name to this method. It then becomes possible to have the entire load of the optimization carried over to the coarse model adjusted by the addition of this correction response surface.

The application of this method shows satisfactory results, in particular in comparison with those obtained with a traditional optimization approach based on a single (fine) model. It thus appears that the approach by CRSM makes it possible to converge much more quickly toward the optimal configurations. Also, the use of response surfaces for optimization makes it possible to capitalize the modeling data, thus making it possible to reuse them, if necessary, for subsequent optimal design studies. Numerous tests show that this approach is relatively robust to the variations of many important functioning parameters.

The CRSM technique is an indirect multi-model optimization method. This paper presents the application of this relatively undeveloped optimization approach, combining the features and benefits of (Indirect) efficient global optimization techniques and (multi-model) space mapping methods.

The purpose of this paper is to make easily accessible models to test and compare the optimization algorithms we develop.

For this, the paper proposes an optimization framework based on software component, web service, and plugin to exploit these models in different environments.

The paper illustrates the discussion with optimizations in Matlab™ and R (www.r-project.org) of a transformer described and exploitable from the internet.

The originality is to make easy implementation of simulation model and optimization algorithm coupling using software component, web service, and plugin.

The purpose of this paper is to efficiently use as few sample points as possible to get a sufficiently explored design space and an accurate optimum for adaptive metamodel-based design optimization (AMBDO).

A parameterized lower confidence bounding (PLCB) scheme is proposed in which a cooling strategy is introduced to guarantee the balance between exploitation and exploration by varying weights of the predicting error and optimum of a metamodel. The proposed scheme is investigated by a set of test functions and a structural optimization problem, in which PLCB with four kinds of cooling control functions are studied. Moreover, other infill criteria (such as expected improvement and its extension versions) are taken into comparison.

Results show that the proposed PLCB (especially PLCB with the first cooling control function) based AMBDO method can find the optimum with fewer evaluations and maintain good accuracy, which means the proposed PLCB contributes to the excellent efficiency and accuracy in finding global optimal solutions.

The parameterized version of the lower confidence bound metric is proposed for AMBDO, typically used in the context of adaptive sampling in efficient global optimization.