  Citation: Zedadra, O.; Guerrieri, A.; Seridi, H. LFA: A Lévy Walk and Firefly-Based Search Algorithm: Application to Multi-Target Search and Multi-Robot Foraging. Big Data Cogn. Comput. 2022, 6, 22. https:// doi.org/10.3390/bdcc6010022 Academic Editor: Moulay A. Akhloufi Received: 16 December 2021 Accepted: 17 February 2022 Published: 21 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). big data and cognitive computing Article LFA: A Lévy Walk and Firefly-Based Search Algorithm: Application to Multi-Target Search and Multi-Robot Foraging Ouarda Zedadra 1, * , Antonio Guerrieri 2 and Hamid Seridi 1 1 LabSTIC, Department of Computer Science, 8 Mai 1945 University, P.O.Box 401, Guelma 24000, Algeria; seridi.hamid@univ-guelma.dz 2 Institute for High Performance Computing and Networking (ICAR), CNR—National Research Council of Italy, Via P. Bucci 8/9C, 87036 Rende, Italy; antonio.guerrieri@icar.cnr.it * Correspondence: zedadra.ouarda@univ-guelma.dz Abstract: In the literature, several exploration algorithms have been proposed so far. Among these, Lévy walk is commonly used since it is proved to be more efficient than the simple random-walk exploration. It is beneficial when targets are sparsely distributed in the search space. However, due to its super-diffusive behavior, some tuning is needed to improve its performance, specifically when targets are clustered. Firefly algorithm is a swarm intelligence-based algorithm useful for intensive search, but its exploration rate is very limited. An efficient and reliable search could be attained by combining the two algorithms since the first one allows exploration space, and the second one encourages its exploitation. In this paper, we propose a swarm intelligence-based search algorithm called Lévy walk and Firefly-based Algorithm (LFA), which is a hybridization of the two aforementioned algorithms. The algorithm is applied to Multi-Target Search and Multi-Robot Foraging. Numerical experiments to test the performances are conducted on the robotic simulator ARGoS. A comparison with the original firefly algorithm proves the goodness of our contribution. Keywords: swarm intelligence; swarm robotics; Lévy walk; Firefly algorithm; LFA; multi-target search (MTS); Multi-Robot Foraging (MRF) 1. Introduction In the future, Multi-Robots Systems (MRS) are intended to replace humans in some tasks, such as exploration, search and rescue, monitoring, surveillance, cleaning, and so on. To accomplish such tasks, mechanisms of distributed coordination and cooperation are desirable for MRS. Swarm robotics is a new approach to the coordination of large numbers of robots whose main inspiration stems from the observation of social insects [1]. Swarm robotics has recently come out as the realizations of the swarm intelligence (SI) toward the MRS. It emphasizes the incorporation of individuals and lifelike interactions, both among individuals and between the individuals and their environment. Swarm robotics exposes a synchronized behavior at the system level which emerges despite (i) the limited capabilities of the individuals, (ii) the absence of centralized coordination, and (iii) the easiness of interactions [2]. Firefly algorithm (FA) is an SI-based algorithm that takes advantage of lights to coordinate fireflies, which, in nature, emit bioluminescent light to allure their mates or preys. More is the brightness they emit, more is the attraction that they have. The light intensity is proportional to the associated luminescence quantity called luciferin, which attracts other fireflies within their neighborhood. The standard FA employs a full attraction model, which results in oscillations during the search process, and low attraction can also lead to premature convergence. Therefore, the number of attractions is very important [3]. The standard Firefly algorithm adopts a fixed step length which can cause it to become trapped in the local optima, thus causing low precision. The exploration rate of FA is very limited. FA is useful for MRS since its real application is guaranteed by Ambient Light Big Data Cogn. Comput. 2022, 6, 22. https://doi.org/10.3390/bdcc6010022 https://www.mdpi.com/journal/bdcc