Nature-Inspired Mateheuristic Algorithms: Success and New Challenges

TL;DR

This paper discusses the current state, challenges, and future directions of nature-inspired metaheuristic algorithms, emphasizing the need for a solid theoretical framework to understand and improve their practical effectiveness.

Contribution

It highlights the gap between theory and practice in metaheuristics and advocates for developing mathematical frameworks using Markov chains and dynamical systems.

Findings

Limited convergence analysis studies exist

Current practice relies heavily on trial and error

Mathematical methods can enhance understanding

Abstract

Despite the increasing popularity of metaheuristics, many crucially important questions remain unanswered. There are two important issues: theoretical framework and the gap between theory and applications. At the moment, the practice of metaheuristics is like heuristic itself, to some extent, by trial and error. Mathematical analysis lags far behind, apart from a few, limited, studies on convergence analysis and stability, there is no theoretical framework for analyzing metaheuristic algorithms. I believe mathematical and statistical methods using Markov chains and dynamical systems can be very useful in the future work. There is no doubt that any theoretical progress will provide potentially huge insightful into meteheuristic algorithms.