Study of the Fractal decomposition based metaheuristic on low-dimensional Black-Box optimization problems
This is an incremental study that addresses the applicability of an existing metaheuristic to low-dimensional optimization problems, which is relevant for researchers in optimization algorithms.
The paper investigated whether the Fractal Decomposition Algorithm (FDA), originally designed for high-dimensional optimization, is effective for low-dimensional black-box problems, finding that it generally performs poorly, with best results only on specific function groups like Misc. moderate and Weak structure functions.
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.