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A survey of the state‑of‑the‑art swarm intelligence techniques and their application to an inverse design problem Talha Ali Khan1   · Sai Ho Ling1 Received: 27 April 2020 / Accepted: 3 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract This paper encompasses a detailed review of state-of-the-art swarm-based algorithms, with a focus on their applications along with a discussion on the merits and limitations of each algorithm. Further, a recently developed advanced particle swarm optimization (APSO) algorithm is compared with the different state-of-the-art algorithms through solving an electromagnetic inverse problem. Results show that the APSO algorithm outperforms the other algorithms. This research provides a scientific guideline for the comparison of different swarm-based algorithms and their utilization regarding specific applications. Keywords  Artificial intelligence · Evolutionary computation · Swarm intelligence · Optimization

1 Introduction In the course of this planet’s history, evolution has been the constant driver enabling many animal species to accomplish complicated tasks by learning from their environment, building resilience, and adapting. Examples of such evolutionary capabilities are numerous, but some specific ones which revolve around animal social behavior include flocks of birds, colonies of ants, and bees in their hives. These examples illustrate the fundamental concept of swarm intelligence (SI) and stigmergy, where the collective movement of these species improves the mechanism allowing them to explore complicated spaces, which is achieved without any central command and just by agents following local rules. The results from this technique help the swarm achieve much more than the sum of the individual actions. Swarm intelligence (SI) has been the focal point of numerous researchers of diverse research backgrounds. SI is defined as “the emergent collective intelligence of groups of simple agents” [1]. SI is the cumulative intelligence demeanor of self-formulated and dispersed systems such as an artificial group of simple agents. Examples of SI include (a) nest building, (b) food hunting, (c) unified clustering, and (d) categorization of insects. The two principal concepts that are essential

parameters of SI are self-management and labor allocation. Self-management is the capability of an order to independently allocate its resources in a useful manner. Chakraborty et al. [2] established that self-management depends upon four main characteristics: negative feedback, positive feedback, variations, and frequent communication. The positive and negative feedback aid in maintaining equilibrium and expansions. Variations are, however, usually used only for haphazardness. Frequent communication takes place when swarms communicate with one another restricted to their search areas. The other important characteristic of SI is the allocation of labor, which is illustrated by entities carrying out many feasible and simple tasks. This is how individuals grouped a