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A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method. A progressive focusing on the most promising region, in combination with a variation of the density of the alpha-dense curve, is proposed.

ALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve: the curvilinear abscissa along the curve becomes the only design parameter for any design space. As a counterpart, the transformation of the objective function in the projected space is much more difficult to tackle.

A fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure. The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables, demonstrating the ability of the method in solving large scale optimization problem. Also an industrial application is presented.

In the knowledge of the author there is not a similar paper in the current literature.

This paper presents CoreLab, a sizing environment for electrical devices, based on a new software component standard, ICAR, which offers the possibility of multifaceted components. CoreLab supports the different steps of the sizing procedure of an electrical device by using an optimisation algorithm. It is open, which means that modules can be added to perform new functionalities.

The design of an electrical device has to comply with more and more constraints. In order to integrate and to manage all of these constraints during a design step, the paper proposes a sizing methodology based on an constrained optimisation by using analytical models of the device, and by encapsulating them into software components. Added to these services for the calculation of the sizing model, other services can be useful for the designer during the optimization phase, e.g. the geometry display of the device for each optimisation iteration. In this way, the approach proposes a new software component standard, Interfaces for Component Architecture (ICAR). It offers the possibility of multi‐facetted components. The paper also proposes an integrated environment to manage these software components, and their interactions: Core‐Lab. These components are then plugged to an optimisation component (algorithm), which manages the different constraints specified by the designer and finds the optimal sizing of the device.

The paper presents the ICAR standard and an environment to manage ICAR components: Core‐Lab: the creation of the components (from an analytical model or an existing computation); the projection from one component standard to another; and the composition of components to create a more complex one.

The use of software component approach is useful for the sizing of devices. The paper proposes a new standard to support the different aspects of the use of software components during the design of a device: ICAR. Complementary, an open integrated environment is proposed to use these components: CoreLab, but any environment being modified to accept ICAR standard can use ICAR component. So, components can be used in several environments, for example for calculation or optimisation. Components of different types can be gathered together to built a complete application for sizing, e.g. by connection of calculation components (for the sizing model), optimisation component and post‐processing components.

The n‐dimensional direct search algorithm, DIRECT, developed by Jones, Perttunen, and Stuckman has attracted recent attention from the multidisciplinary design optimization community. Since DIRECT only requires function values (or ranking) and balances global exploration with local refinement better than n‐dimensional bisection, it is well suited to the noisy function values typical of realistic simulations. While not efficient for high accuracy optimization, DIRECT is appropriate for the sort of global design space exploration done in large scale engineering design. Direct and pattern search schemes have the potential to exploit massive parallelism, but efficient use of massively parallel machines is non‐trivial to achieve. A fully‐distributed control version of DIRECT that is designed for massively parallel (distributed memory) architectures is presented. Parallel results are presented for a multidisciplinary design optimization problem – configuration design of a high speed civil transport.

Optimisation in electromagnetics, based on finite element models, is often very time‐consuming. In this paper, we present the space‐mapping (SM) technique which aims at speeding up such procedures by exploiting auxiliary models that are less accurate but much cheaper to compute.

The key element in this technique is the SM function. Its purpose is to relate the two models. The SM function, combined with the low accuracy model, makes a surrogate model that can be optimised more efficiently.

By two examples we show that the SM technique is effective. Further we show how the choice of the low accuracy model can influence the acceleration process. On one hand, taking into account more essential features of the problem helps speeding up the whole procedure. On the other hand, extremely simple auxiliary models can already yield a significant acceleration.

Obtaining the low accuracy model is not always straightforward. Some research could be done in this direction. The SM technique can also be applied iteratively, i.e. the auxiliary model is optimised aided by a coarser one. Thus, the generation of hierarchies of models seems to be a promising venue for the SM technique.

Optimisation in electromagnetics, based on finite element models, is often very time‐consuming. The results given show that the SM technique is effective for speeding up such procedures.

Using the ALIENOR transformation avoids the problem of determining the first and second derivatives of the objective functional f when using the multidimensional bissection method. Knowledge of the Lipschitzian constant C is generally sufficient for using this method, and therefore for determining the global maximum of f defined on a compact set.

Shows how a hi‐dimensional optimisation problem with linear inequalities constraints is converted into a global optimisation problem of one bounded variable function f*. Then, we reduce the feasible region f* before seeking its global optimum.

Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. The purpose of this paper is to use support vector regression with high dimensional model representation (SVR-HDMR) model to obtain accurate metamodels for high dimensional problems with a few sampling points.

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. Support vector regression (SVR) method can approximate the underlying functions with a small subset of sample points. Dividing Rectangles (DIRECT) algorithm is a deterministic sampling method.

This paper proposes a new form of HDMR by integrating the SVR, termed as SVR-HDMR. And an intelligent sampling strategy, namely, DIRECT method, is adopted to improve the efficiency of SVR-HDMR.

Compared to other metamodeling techniques, the accuracy and efficiency of SVR-HDMR were significantly improved. The SVR-HDMR helped engineers understand the essence of underlying problems visually.

The reducing transformation and global optimization technique called Alienor has been developed in the 1980s by Cherruault and Guillez. These methods are based on the approximating properties of α ‐dense curves. The aim of this work is to give a very large class of functions generating α ‐dense curves in a hyper‐rectangle of Rⁿ.

Describes the use of the decomposition method for solving the differential system governing the interaction between two species, based on the Lotka‐Volterra model. The Alienor method is applied for identifying the parameters of the model, which are the intrinsic rates of natural increase of the different species and their interaction coefficients.

Aims to present study of the coupling of the Alienor method with the algorithm of Piyavskii‐Shubert for global optimization applications.

The Alienor method allows us to transform a multivariable function into a function of a single variable for which it is possible to use an efficient and rapid method for calculating the global optimum. This simplification is based on the use of the established Alienor methodology.

The Alienor method allows us to transform a multidimensional problem into a one‐dimensional problem of the same type. It was then possible to use the Piyavskii‐Shubert method based on sub‐estimators of the objectives function. The obtained algorithm from coupling the two methods was found to be simple and easy to implement on any multivariable function.

This method does not require derivatives and the convergence of the algorithm is relatively rapid if the Lipschitz constant is small.

The classical multidimensional global optimization methods involve great difficulties for their implementation to high dimensions. The coupling of two established methods produces a practical easy to implement technique.

New method couples two established ones and produces a simple and user‐friendly technique.