Parameter-less Hierarchical BOA: A Fully Parameter-less Optimization Algorithm

Title: Parameter-less Hierarchical BOA: A Fully Parameter-less Optimization Algorithm

Abstract: The parameter-less hierarchical Bayesian optimization algorithm (hBOA) is a powerful optimization technique that can solve complex, nearly decomposable, and hierarchical problems without the need for any user-defined parameters. This groundbreaking algorithm is an advanced version of the hierarchical BOA, which was initially designed with the assumption that certain parameters must be set to achieve optimal performance. However, the parameter-less hBOA eliminates this requirement by adopting a population-sizing technique inspired by the parameter-less genetic algorithm. This technique allows hBOA to simulate a collection of populations of different sizes, ensuring that the computational overhead is still reasonable, even with an unknown number of populations. The paper presents a number of experiments to verify the scalability and effectiveness of the parameter-less hBOA.

Main Research Question: Can a fully parameter-less optimization algorithm be designed to solve nearly decomposable and hierarchical problems effectively and efficiently?

Methodology: The research team developed the parameter-less hierarchical Bayesian optimization algorithm (hBOA) by incorporating a population-sizing technique inspired by the parameter-less genetic algorithm. This technique simulates a collection of populations of different sizes, ensuring that the computational overhead is still reasonable, even with an unknown number of populations. The algorithm uses a two-step procedure: probabilistic model building and sampling. It replaces traditional variation operators with machine learning techniques that allow the automatic discovery of problem regularities from populations of promising solutions.

Results: The experiments demonstrated that the parameter-less hBOA performs within a logarithmic factor from the case with the optimal population size, verifying its scalability and effectiveness. The algorithm was able to solve a variety of nearly decomposable and hierarchical problems, proving that it can handle complex optimization tasks without the need for any user-defined parameters.

Implications: The development of the parameter-less hBOA has significant implications for the field of optimization algorithms. It offers a fully parameter-less approach that can solve nearly decomposable and hierarchical problems effectively and efficiently. This breakthrough can lead to advancements in various fields, such as machine learning, artificial intelligence, and operations research, where complex optimization tasks are common. The parameter-less hBOA serves as a benchmark for other optimization algorithms and opens up new research directions in the field.

Link to Article: https://arxiv.org/abs/0402031v1 Authors: arXiv ID: 0402031v1