Integer optimization by dense curves

Purpose To use dense curves for solving an optimization problem with constraints involving integer variables. Designmethodologyapproach dense curves are curves in Rn depending on a single variable able to approximate a compact KRn with precision . It is proposed dense curves allowing to obtain all i...

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Bibliographic Details
Published in:Kybernetes 2007-02, Vol.36 (2), p.257-266
Main Authors: Mora, G., Cherruault, Y.
Format: Article
Language:English
Subjects:
Algorithms
Cybernetics
Euclidean space
Linear equations
Linear programming
Mathematical models
Optimization techniques
Studies
Variables
Online Access:Get full text
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Summary:Purpose To use dense curves for solving an optimization problem with constraints involving integer variables. Designmethodologyapproach dense curves are curves in Rn depending on a single variable able to approximate a compact KRn with precision . It is proposed dense curves allowing to obtain all integer points of a compact domain in Rn. This transformation allows to transform the functional into a new function depending on a single variable. Then we can calculate the global optimum of the functional. Findings Alienor method invented by Y. Cherruault allows to find global minimum of ncontinuous variables functions. Here, dense curves are extended to problems involving integer variables. The curves pass through all points having integer coordinates and belonging to the compact domain. By this method integer programming nonlinear problems arising in operational research have been easily and exactly solved. Originalityvalue It is the first time the technique based on dense curves to optimization problems with integer variables are extended. This approach is totally original and allows to solve very easily and fastly nonlinear optimization problems.
ISSN:0368-492X
1758-7883
DOI:10.1108/03684920710741260