Study of Multiverse Optimizer Variations with Chaos Theory and Fuzzy Logic Over Benchmark Optimization

In this work, we are presenting multiple variations of the Multiverse Optimizer algorithm incorporating the use of Fuzzy inference systems and chaotic maps (FCMVO) with the purpose of analyzing their performance in a benchmark with some mathematical functions. We implement some of the most used chaotic maps over literature for metaheuristics in order to replace multiple parameters of the original algorithm, and change the original behavior, and by the other hand, we use Fuzzy Logic to adapt dynamically some of the parameters. By adding both Chaos theory and Fuzzy Logic, the resulting algorithm can have the best of both, resulting in a competitive variant. By using Chaos theory, we saw that not all the chaotic maps behave a good behavior in MVO, then we select a set of six variants that we called Elitist FCMVO. In the study, we do a brief comparison between the resulting variants with the benchmark functions, where each variant changes a set of three selected chaotic maps. The main objective is to define the best set of chaotic maps that FCMVO can used, and it could be used in other cases of study.