Computational Resolution of a Boolean Equation of 21 Variables

Abstract

The Alienor method has been elaborated at the beginning of the 1980s by Yves Cherruault and Arthur Guillez (1983). The following people have also greatly contributed to the improvement of this new optimization method: Blaise Somé, Gaspar Mora, Balira Konfé, Jean Claude Mazza and Esther Claudine Bityé Mvondo. The basic idea consists in using a reducing transformation allowing us to simplify a multivariable optimization problem to a new optimization problem according to a single variable. The rational gestion of enterprises leads generally to the use of Operational Research, often called management science. The term Operational Research means a scientific approach to decision making, that seeks optimization in a system. Consequently, it is better to take the right decisions. Otherwise, fatal consequences can occur instantaneously [1]. Generally, we have to maximize the global profit margin, taking into account some constraints. For instance, in an integer programming problem, some or all the variables are required to be nonnegative integers. In this paper, we present new reducing transformations for global optimization in integer, binary and mixed variables as well as the applications in Boolean algebra by solving a Boolean Equation of 21 variables. The applications in Operational Research are presented on various examples, resolved by using the tabulator Excel of Microsoft.