Study on the Effect of Chaotic Maps in the Formation of New Universes in the Multiverse Optimizer Algorithm

Abstract

In this work, we study the effect of using chaotic maps to replace random values in the formation of new solutions over the Multi-Verse Optimizer algorithm (MVO). We present new variations of the MVO algorithm, where we use Fuzzy Logic in combination with chaotic maps, to achieve a better improvement on the universes generated by the algorithm with respect to only using Fuzzy Logic. The use of chaotic maps substitutes a random parameter in the generation of universes, so, in this work, we are analyzing the effect of this parameter over the generation of better solutions for the problems that are being applied. For testing, we use 13 mathematical functions, to do a comparison with the original MVO and other variations such as Fuzzy-MVO and Chaotic-MVO; we use 10 chaotic maps to do our main tests for the comparison between the variants. The objective of this work is, to study the effect of chaotic maps in the MVO algorithm, by generating new universes when using the chaotic map in a specific parameter of the algorithm, and then, go through further testing on more complex problems, like optimizing fuzzy controllers.