Swarm intelligence: past, present and future

Many optimization problems in science and engineering are challenging to solve, and the current trend is to use swarm intelligence (SI) and SI-based algorithms to tackle such challenging problems. Some significant developments have been made in recent years, though there are still many open problems in this area. This paper provides a short but timely analysis about SI-based algorithms and their links with self-organization. Different characteristics and properties are analyzed here from both mathematical and qualitative perspectives. Future research directions are outlined, and open questions are also highlighted.