Are metaheuristics worth it? A computational comparison between nature-inspired and deterministic techniques on black-box optimization problems

TL;DR

This paper compares nature-inspired and deterministic derivative-free optimization methods across various benchmarks, revealing that nature-inspired techniques excel with cheap evaluations, while deterministic methods are preferable for costly evaluations.

Contribution

It provides an extensive computational comparison of representative methods from both branches on multiple benchmarks, highlighting their relative strengths and weaknesses.

Findings

Nature-inspired methods outperform deterministic ones with cheap evaluations.

Deterministic methods are more consistent with costly evaluations.

Performance varies significantly based on evaluation cost.

Abstract

In the field of derivative-free optimization, both of its main branches, the deterministic and nature-inspired techniques, experienced in recent years substantial advancement. In this paper, we provide an extensive computational comparison of selected methods from each of these branches. The chosen representatives were either standard and well-utilized methods, or the best-performing methods from recent numerical comparisons. The computational comparison was performed on five different benchmark sets and the results were analyzed in terms of performance, time complexity, and convergence properties of the selected methods. The results showed that, when dealing with situations where the objective function evaluations are relatively cheap, the nature-inspired methods have a significantly better performance than their deterministic counterparts. However, in situations when the function evaluations are costly or otherwise prohibited, the deterministic methods might provide more consistent and overall better results.