The Challenge for the Nature-Inspired Global Optimization Algorithms: Non-Symmetric Benchmark Functions

Along with the increasing number of nature-inspired algorithms, more and more benchmark functions were also involved in the initial verification experiments. The benchmark functions were introduced to verify the capability of algorithms in optimization, but not all of them could be optimized, because they were different from each other in dimensionality, separability, scalability, and modality et.al.. In this paper, we introduced another property called symmetry or non-symmetry, which should be another embedded characteristic of functions affecting the capability of algorithms in optimization. 67 non-symmetric benchmark functions were collected and 9 popular capability-verified algorithms were introduced in four types of simulation experiments. Experimental results show that most of the non-symmetric algorithms could not be optimized. And none of the algorithms involved could optimize them all. Efforts remain in need of new methods and improvements of nature-inspired algorithms.

Automated summary

With the introduction of symmetry or non-symmetry as a new characteristic affecting the capability of algorithms in optimization, experimental results showed that most of the non-symmetric benchmark functions were difficult to optimize. None of the algorithms involved could optimize all functions, indicating the need for new methods and improvements for nature-inspired algorithms.