Study of the Fractal decomposition based metaheuristic on low-dimensional Black-Box optimization problems

TL;DR

This study evaluates the Fractal Decomposition Algorithm's effectiveness on low-dimensional black-box optimization problems, revealing limited performance except on specific function groups.

Contribution

It investigates whether FDA, designed for high-dimensional problems, is effective for low-dimensional cases, providing empirical performance insights.

Findings

FDA performs poorly overall on low-dimensional problems.

FDA shows best results on Misc. moderate and Weak structure functions.

The algorithm's design for high-dimensional problems limits its low-dimensional effectiveness.

Abstract

This paper analyzes the performance of the Fractal Decomposition Algorithm (FDA) metaheuristic applied to low-dimensional continuous optimization problems. This algorithm was originally developed specifically to deal efficiently with high-dimensional continuous optimization problems by building a fractal-based search tree with a branching factor linearly proportional to the number of dimensions. Here, we aim to answer the question of whether FDA could be equally effective for low-dimensional problems. For this purpose, we evaluate the performance of FDA on the Black Box Optimization Benchmark (BBOB) for dimensions 2, 3, 5, 10, 20, and 40. The experimental results show that overall the FDA in its current form does not perform well enough. Among different function groups, FDA shows its best performance on Misc. moderate and Weak structure functions.