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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.

Many bio‐medical models leads to differential systems. Some coefficients (exchange parameters,…) must be identified from partial observation on the system's solution. We suggest methods to study the existence and unicity of the identification problem. Applications to numerical identification are also given, in particular when unicity is not ensured. Physiological systems, like respiratory system, are concerned with the identification of parameters.

Compartmental models allow us to visualise the behaviour of phenomena and simplify the formulation of some equations related to such systems. Mammillary systems are among the most interesting in pharmacokinetics. In the present study, a five compartment linear mammillary model is considered in which the central compartment 1 is connected reversibly to all other compartments, and elimination occurs from compartment 1. A reidentification of different distribution rate constants is made, with concentrations of drug in central compartment at different times of observation being known. In order to rninimise the difference between the set of given concentrations of drug and the calculated values of concentrations, an optimisation method is used which reduces the unknown parameters involved, to a single variable. Thus, the problem requires a global minimum of a function of single variable. The results obtained with present method are compared with those obtained by the generalised least squares method.

This paper deals with mathematical and numerical methods for defining optimal therapeutics associated with drugs action models. To obtain the optimal control corresponding to some criteria analytical and numerical methods are proposed. An original optimization technique giving the global optimum will be described and used. It is based on a space filling curve idea. A new variant of the dynamic programming method is also proposed, this leads to a simple optimization problem.

New methods for optimization and for solving nonlinear functional equations are given and are applied to the identification and optimal control of models coming from life sciences.

The purpose of this paper is to describe a general method for solving all problems arising in industrial processes and more generally in operational research.

The paper's aim is to present a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. This technique allows to solve all problems of operational research in a simple way. For instance, industrial problems leading to optimization or optimal control problems can be easily and precisely solved by this very general technique. The main idea consists in expressing n variables by means of a single one.

This new method, based on “alpha‐dense curves” allows to express n variables in function of a single variable. One of the most important applications is related to global optimization. Multivariable optimization problems can be quickly and easily solved, even for great numbers of variables and for integer or boolean variables. Every problem (linear or nonlinear) coming from operational research or from industry becomes simple to solve in a very short time on micro‐calculators.

This method is deduced from the original works of Yves Cherruault et al. of MEDIMAT laboratory. The reducing transformations were initiated at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. Then they were generalized by the notion of α‐dense curves. A lot of applications were derived covering entirely the operational research and a part of functional analysis.

We demonstrate an efficient numerical method for the solution of partial differential equations arising from a model suggested by BROCAS and CHERRUAULT and completed by CHERRUAULT and GUILLEZ.

This paper presents here a simulation model, the circulatory system being modelled on a heat installation. This installation is a heating system based on a distribution of dissolved fuel and removal of waste. One writes local equations for heat and chemical exchanges and for hydrodynamics; then one produces a thermodynamic synthesis, using a theorem of a constant output.

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.

Many biological systems give rise to optimization problems (for instance, when we have to identify the model or control of the system). Here, we propose a very simple method to find the extremum of a n‐variables function. This technique leads to the optimization of a one‐variable function. Our procedure can be applied to two kinds of cybernetic problems: resolution of equations with several variables and identification of the black box. It may also be used to solve optimal control problems arising from regulated or homeostatic systems. The technique gives a good approximation which may be used to seek a better solution.