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Top1. Introduction
Swarm Intelligence is one of the most promising research fields in Optimization (Ma, Ye, Simon, & Fei, 2017; Nayyar & Singh, 2016). These techniques are inspired by the collective behavior of decentralized and self-organized systems (Hassanien & Emary, 2016; Mahant, Choudhary, Kesharwani, & Rathore, 2012). Some of the most well-known algorithms of this segment are the Particle Swarm Optimization (PSO) (Engelbrecht, 2007; Kennedy & Eberhart, 1995; Simon, 2013) and the Ant Colony Optimization (ACO) (Colorni, Dorigo, & and Maniezzo, 1991; Engelbrecht, 2007; Simon, 2013). These approaches were also the first ones to be developed in this area. Other examples of Swarm Intelligence algorithms are the Artificial Bee Colony (ABC) (Karaboga & Basturk, 2007) and the Fish School Search (FSS) (Bastos Filho, de Lima Neto, Lins, Nascimento, & Lima, 2008). The FSS presents exciting features, especially for multi-modal problems, and is the object of analysis of this paper.
The Fish School Search was introduced in 2008 and is inspired by the swimming behavior of schools to catch food or escape from predators (Bastos Filho, de Lima Neto, Lins, Nascimento, & Lima, 2008; Chiong, 2009). Some aspects related to the individual and collective behavior of schools, e.g., the avoidance of predators and the seek for food, were observed and applied to the development of this new solution to optimization problems. In the algorithm, each fish is a simple reactive agent of the population, and the seek for food regards the process of searching better solutions in the search space. The fish moves along a limited search space with n dimensions, where a maximum and a minimum value bound to each dimension.
The first version of the FSS has gone through several modifications over the years. They aimed to improve the algorithm performance and allow its implementation in a more significant number of optimization problems. We can cite variations for monomodal (Bastos Filho, de Lima Neto, Lins, Nascimento, & Lima, 2008) and multimodal (de Lima Neto & de Lacerda, 2014) functions. For both mono-objective (Bastos Filho, de Lima Neto, Lins, Nascimento, & Lima, 2008) and multi-objective (Bastos-Filho & Guimarães, Multi-objective fish school search, 2015) problems. We also observed a version for binary applications (Sargo, 2013). Despite those improvements, there are still some aspects to be considered concerning the algorithm performance, e.g., the fish feeding strategy and the equalization of the swimming operators (Monteiro Filho, Albuquerque, Neto, & Ferreira, 2016).
Regarding the feeding operation, it is possible that in some situations there will be inconsistent correlations between the relative weight of the fish and their cumulative success along the optimization process. Furthermore, some remarkable improvements in the FSS algorithm have been developed over the years and have not been applied yet, suggesting that studies about those changes might be promising.