Multi-PBil: an estimation distribution algorithm applied to multimodal optimization problems

Abstract

The Estimation Distribution Algorithms (EDAs) compose an evolutionary metaheuristic whose main characteristic is the construction of solutions in randomly form, using a distribution of probabilities that evolves during the execution. The Population-Based Incremental Learning Algorithm (PBIL) is a type of EDA where the variables are independent, that is, they do not have significant interactions between themselves. The PBIL considers that the solutions can be represented as vectors of discrete variables, what makes it more adequate for combinatorial optimization problems. This paper presents a method called Multi-PBil that is an extension of PBIL with applications in multimodal problems. The Multi-PBil was developed with the goal to have an efficient and non expensive algorithm of search in multimodal spaces. From PBIL, it was implemented a routine that allows the Multi-PBil to create a probability model to act in the search space. A formula that allows initiating the probability models in regions of the search space next to the searched global points was applied in the process of the probability model initialization rule. The Multi-PBil method was tested and analyzed, presenting some experimental results that highlight its viability and characteristics. It is also shown a comparison of the performance between the Multi-PBil and a traditional Genetic Algorithm using the sharing method.