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1 – 10 of 67The 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.
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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…
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.
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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.
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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.
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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.
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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.
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.
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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.
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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.
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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.
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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.
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