Framework for identifying the equivalence between Nature-Inspired Metaheuristics

TL;DR

This paper introduces a framework to measure the similarity between nature-inspired metaheuristics based on their behavior, addressing concerns about the novelty and duplication of algorithms in the field.

Contribution

It defines an equivalence theorem and develops a framework for identifying when two metaheuristics are behaviorally equivalent based on feature vector similarity.

Findings

High similarity between well-known metaheuristics is difficult to achieve in limited computational environments.

The framework effectively estimates the behavioral equivalence of different algorithms.

Many algorithms are not behaviorally equivalent despite superficial similarities.

Abstract

The domain of metaheuristic optimization has become vibrant due to a flood of new algorithms using a new nature-inspired metaphor but lacking clear methodological novelty. The Criticism behind the development of these algorithms has reached such an extent that the critics started to assert that all novel algorithms are only copies of already developed ones. In this study, we try to show that the situation is not so black and white. Therefore, we define a strong equivalence theorem for estimating the similarity between two nature-inspired metaheuristics, according to which two algorithms are equivalent if, and only if, the cosine similarity of their phenotypic and genotypic feature vectors, characterizing their behavior by searching for the optimal solutions, is above some threshold. On the theorem basis, a framework is developed for identifying the equivalence between nature-inspired metaheuristics. Extensive experimental work using the framework has shown that searching for conditions to achieve the high similarity of the more well-known nature-inspired metaheuristics is hard, or even not possible to achieve, in the limited computational environments.