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Article
Publication date: 1 August 2005

Balira O. Konfe, Yves Cherruault, Blaise Some and Titem Benneouala

This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).

611

Abstract

Purpose

This paper presents an efficient algorithm for solving general constrained optimization problems that arise in operational research (OR).

Design/methodology/approach

An unified approach is accomplished by converting the constrained optimization problem into an unconstrained one and by using Alienor method coupled to the new optimization preserving operator* (OPO*) technique for the resolution.

Findings

A new algorithm for solving general constrained optimization problems with continuous objective function contributes to research in this area and in particular, to applications to OR.

Research limitations/implications

Some improvements could probably be obtained at calculation time. We will in future work, develop an adaption of these methods and techniques to optimization problems with mixed variables or with integer and Boolean variables.

Practical implications

The new algorithm can be advantageously compared with other methods such as generalized reduced gradient. Small‐sized numerical examples are given.

Originality/value

A new algorithm is given which guarantees a global optimal solution is easily obtained in all cases.

Details

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

Keywords

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Article
Publication date: 1 August 2005

Balira O. Konfe, Yves Cherruault, Blaise Some and Titem Benneouala

To introduce Optimization‐Preserving‐Operators (O‐P‐Os), which are operators that are defined on classes of real functions that depend on a single variable, and allow us to…

226

Abstract

Purpose

To introduce Optimization‐Preserving‐Operators (O‐P‐Os), which are operators that are defined on classes of real functions that depend on a single variable, and allow us to eliminate local optima and to preserve global optima.

Design/methodology/approach

Outline a new method to build O‐P‐Os. These are introduced as O‐P‐O* and lead to a new approach for solving global optimization problems.

Findings

It was found that classical discretization methods for obtaining optimum of one variable function was too time‐consuming. The simple method introduced provided solutions to the test functions chosen as examples. The solutions were provided in a short time.

Research limitations/implications

Provides new tools for mathematical programming and in particular the global optimization problems. The O‐P‐O* introduced innovative technique for solving such problems.

Practical implications

O‐P‐O* produces solutions to global optimization problems in a much improved time. The algorithm derived, and the steps for its operation proved on implementation, the efficiency of the new method. This was demonstrated by numerical results for selected functions obtained using microcomputer systems.

Originality/value

Provides new way of solving global optimization problems.

Details

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

Keywords

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Article
Publication date: 1 August 2005

Titem Benneouala, Yves Cherruault and Karim Abbaoui

To find methods for solving non‐linear partial differential equations. The decomposition method may be applied, but a difficulty arises when applied to non‐linear partial…

562

Abstract

Purpose

To find methods for solving non‐linear partial differential equations. The decomposition method may be applied, but a difficulty arises when applied to non‐linear partial differential equations with initial and boundary conditions. In this work, two methods are described that take into account the boundary conditions.

Design/methodology/approach

The decomposition method whilst being a powerful tool for solving non‐linear functional equations encounters difficulties in finding solutions of partial differential equations with boundary conditions. In this paper, two methods are introduced which consist of setting boundary conditions to the equations so that the decomposition methods can be applied.

Findings

By using the two proposed methods the decomposition method can then be easily used. In this work the two methods taking account of the boundary conditions were found to be efficient and allows a solution to be found using the Adomian decomposition method.

Research limitations/implications

The two new methods provide solutions by the application of the decomposition method of George Adomian as extended by other researchers. Both are efficient: the first giving interesting results for linear and non‐linear problems; the second one is also efficient, but difficulties could arise from the calculations of the required series.

Practical implications

The research provides two efficient methods. The first method gives the demonstrated results for linear and non‐linear problems due to the use of symbolic software such as Mathematica or Maple.

Originality/value

Both methods illustrate the powerful use of the decomposition techniques pioneered by Adomian and as a result of their application may be applied to the solving of non‐linear functional equations of any kind. This paper tackles the problems by introducing new methods of applying the Adomian techniques to partial differential equations with boundary conditions.

Details

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

Keywords

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Article
Publication date: 1 August 2005

Balira O. Konfé, Yves Cherruault and Titem Benneouala

To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.

398

Abstract

Purpose

To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.

Design/methodology/approach

Use is made of the established Alienor method which has already been applied to biological and industrial processes. The problems tackled have a number of variables and the chosen optimization method is a variant of the Alienor method.

Findings

A new method for solving global optimization problem, called the Alienor method is now the subject of many variants. In this paper, it was found that a new reducing transformation α‐dense in Rn was successful in solving this type of problem when associated to a functional depending on a large number of variables. The reducing transformation is very efficient and accurate.

Research limitations/implications

This is a variant of the proven Alienor Method which has improved the resolution of global optimization problems. It showed that the reducing transformation has the advantage that a small calculation time is obtained even when the relevant series are slowly increasing. Further development of the method is anticipated.

Practical implications

Proved very effective for obtaining the global optimum with good precision and very short calculation time for large numbers of variables. Can be performed on micro‐calculators.

Originality/value

New variant of proven method. Of interest in solution of concrete problems in biology and industry.

Details

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

Keywords

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Article
Publication date: 1 August 2005

120

Abstract

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

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

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

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Article
Publication date: 1 August 2005

53

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Details

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

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