Resolution of industrial problems by a simple and universal new method

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.