Global optimization with alpha‐dense curves: resolution of Boolean equations

Abstract

Purpose

The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

Design/methodology/approach

The paper's aim is to present the applications in Boolean algebra and 0‐1 integer programming of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. The main idea consists in expressing n variables by means of a single one.

Findings

Apply the method to Boolean algebra and 0‐1 integer programming.

Originality/value

The paper presents a new method based on α‐dense curves for solving Boolean equations and 0‐1 integer programming problems.

Citation

Claudine Bitye Mvondo, E., Cherruault, Y. and Mazza, J. (2012), "Global optimization with alpha‐dense curves: resolution of Boolean equations", Kybernetes, Vol. 41 No. 1/2, pp. 68-83. https://doi.org/10.1108/03684921211213115