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Article
Publication date: 1 March 1990

Y. Cherruault

The Alienor technique for global optimisation is described. The method is deterministic and uses the approximate properties of Archimedes' spirals, reducing n variables to a…

Abstract

The Alienor technique for global optimisation is described. The method is deterministic and uses the approximate properties of Archimedes' spirals, reducing n variables to a single one. It is shown that Monte Carlo methods are less efficient than Alienor, they need more computing time and convergence is not absolutely guaranteed. The application of the Alienor technique to many concrete problems is discussed.

Details

Kybernetes, vol. 19 no. 3
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 25 January 2021

Daniele Peri

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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

Details

International Journal of Intelligent Computing and Cybernetics, vol. 14 no. 2
Type: Research Article
ISSN: 1756-378X

Keywords

Article
Publication date: 20 February 2007

J.C. Mazza, Y. Cherruault, G. Mora, B. Konfé and T. Benneouala

To use a new method based on α‐dense curved for solving problems of operational research.

Abstract

Purpose

To use a new method based on α‐dense curved for solving problems of operational research.

Design/methodology/approach

The method of global optimization (called Alienor) is used for solving problems involving integer or mixed variables. A reducing transformation using α‐dense curves allows to transforms a n‐variables problem into a problem of a single variable.

Findings

Extends the basic method valid for continuous variables to problems involving integer, Boolean or mixed variables. All problems of operational research, linear or nonlinear, may be easily solved by or technique based on α‐dense curves (filling a n‐dimensional space). Industrial problems can be quickly solved by this technique obtaining the best solutions.

Originality/value

This method is deduced from the original works of Y. Cherruault and colleagues about global optimization and α‐dense curves. It proposes new techniques for solving operational research problems.

Details

Kybernetes, vol. 36 no. 1
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 August 2005

Z. Zaidi, M. Bezzina and Y. Cherruault

A two‐compartmental open model to study metabolism/elimination that arise in clinical observation and pharmacokinetics, is presented. The purpose of this work is to show how it is…

Abstract

Purpose

A two‐compartmental open model to study metabolism/elimination that arise in clinical observation and pharmacokinetics, is presented. The purpose of this work is to show how it is possible to combine the two methods of Alienor and Adomian with observability identification and controllability principles to optimize drug doses.

Design/methodology/approach

Cliniciansa try to know how to detect patients at high risk of 5‐Fu (intravnous administration). The approach is to use a two‐compartmental open model to study its metabolism/elimination and assume that it has a nonlinear behaviour. The methodology chosen brings together two proven techniques to solve the arising differential system. A case study “5‐Fu pharmacokinetics” provides an illustrative application of the combined methods.

Findings

On the basis of the numerical results obtained in the case study it was found that a chart could be set up for individual dose adjustment according to individual parameters relating to dose and plasma concentration. The use of mathematical modeling in this field was shown to be justified.

Research limitations/implications

This research is especially important in the pharmaceutical industry since it allows the prediction of drug behaviour in the body. In future work, we will consider the controllability of this problem.

Practical implications

Improved mathematical modelling would allow physicians to treat patients in an optimal way without compromising their comfort or safety. The practitioner would need only to follow a specified procedure.

Originality/value

The new procedure will be especially important to the pharmaceutical industry and this methodology, combined with statistical analysis, will help to improve drug benefits.

Details

Kybernetes, vol. 34 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 February 2000

A. Ziadi and Y. Cherruault

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…

Abstract

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.

Details

Kybernetes, vol. 29 no. 1
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 August 2005

Abdelkader Ziadi, Djaouida Guettal and Yves Cherruault

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

249

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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

Practical implications

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.

Originality/value

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

Details

Kybernetes, vol. 34 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 August 2005

T. Benneouala and Y. Cherruault

To show the usefulness of the Alienor method when applied to the global optimization problems that depend on large number of variables.

Abstract

Purpose

To show the usefulness of the Alienor method when applied to the global optimization problems that depend on large number of variables.

Design/methodology/approach

The approach is to use reducing transformations. The first is due to Cherruault and the second to Mora.

Findings

It was found that the Alienor method was very efficient and reliable in solving global optimization problems of many variables. Results produced to confirm this conclusion.

Research limitations/implications

The numerical results presented showed that the Alienor method was suitable for finding global minimum even in the case of a very large number of variables. The research provides a new methodology for solving such problems.

Practical implications

No other method, we believe, can obtain such results in so short a time for hundreds or even thousands of variables.

Originality/value

The new approach relies on the originality of both the Cherruault and the Mora transformations and their earlier invention of the Alienor method.

Details

Kybernetes, vol. 34 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 July 1995

H. Ammar and Y. Cherruault

Using the ALIENOR transformation avoids the problem of determining the first and second derivatives of the objective functional f when using the multidimensional bissection…

Abstract

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.

Details

Kybernetes, vol. 24 no. 5
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 December 2006

S. Manseur, N. Messaoudi and Y. Cherruault

The purpose of this paper is to show that a combination of Adomian and Alienor methods can be used to solve the problem of parameters identification of HIV/AIDS model. This model…

Abstract

Purpose

The purpose of this paper is to show that a combination of Adomian and Alienor methods can be used to solve the problem of parameters identification of HIV/AIDS model. This model involves a system of three ordinary differential equations.

Design/methodology/approach

Parameters identification leads to the minimization of an error functional given by the sum of variations between measured variables and calculated variables obtained by solving the system of differential equations. We assume that the quantity of healthy cells CD4 + T and the viral load contents in the blood are measured.

Findings

The identification was realized by applying the combined Adomian/Alienor method allowing to reduce the problem to a minimization problem in dimention one.

Practical implications

Simulation results are given for illustration.

Originality/value

Application to parameter identification in an HIV model‐compatible, results to other methods.

Details

Kybernetes, vol. 35 no. 10
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 August 2005

S. Manseur, K. Attalah and Y. Cherruault

This paper aims at applying the proven Adomian and Alienor methods to solve the problem of optimal chemotherapy of HIV model.

Abstract

Purpose

This paper aims at applying the proven Adomian and Alienor methods to solve the problem of optimal chemotherapy of HIV model.

Design/methodology/approach

The combination of the Adomian decomposition method and the Alienor reduction method allows us to solve the control problem as if it were a classical one‐dimensional minimization problem. The methodology is applied to a HIV model and simulation results given.

Findings

A general abstract framework for the control of a non‐linear evolution system has been developed. It was shown that it is possible to control a system by using the powerful techniques of Adomian and Alienor, and produce results comparable with those obtained by classical methods where other cost functions are used.

Research limitations/implications

The benefit of this work is based on the CD4 healthy cells being maximized and the cost based on a drug dose being minimized. The new methodology could be used after further research for solving many control problems in biology and in other areas such as those involving industrial processes.

Practical implications

New methodology is cost‐effective in controlling the drug dose affecting rate of infection of cells by HIV virus.

Originality/value

New application of proven methodology will solve many control problems in biocybernetics/biomedicine/industry and other fields.

Details

Kybernetes, vol. 34 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

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