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Top1. Introduction
Metaheuristic algorithms are a class of optimization, which generally mimic the most successful behaviours and processes in nature. These methods present best tools in reaching the optimal or near optimal solutions for complex engineering optimisation problems (Saka, Hasançebi, & Geem, 2016).
Swarm intelligence (SI) is a class of metaheuristic methods which are interested by the collective behaviour of populated, self-organized and decentralized systems. It concentrates specifically on insects or animals’ behaviour in order to develop different metaheuristics that can imitate the capabilities of these agents in solving their problems like nest building, mating and foraging. These interactions have been effectively appropriated to solve large and complex optimisation problems (Özbakır & Tapkan, 2011). For instance, the behaviours of social insects, such as ants and honey bees that can be patterned by the Ant Colony Optimisation (ACO) (Dorigo & Di Caro, 1999) and Artificial Bee Colony (ABC) (Karaboga, 2009) algorithms. These methods are generally utilized to describe effective food search behaviour through self-organisation of the swarm.
In SI, honey bees are one of the most well studied social insects. Furthermore, it is in a growing tendency in the literature for the past few years and it will continue. Many intelligent popular search algorithms are developed such as Honey Bee Optimisation (HBO), Beehive (BH), Honeybees Mating Optimisation (HBMO), Bee Colony Optimisation (BCO), Artificial Bee Colony (ABC) and the Bees Algorithm (BA) (Yuce, Packianather, Mastrocinque, Pham, & Lambiase, 2013).
Today, the Bees Algorithm (BA) is one of the most recent foraging-based algorithms. It is a population-based search technique that imitates the foraging bees’ behaviour, it is proposed by Pham et al. (2006) for solving complex optimisation problems. It equilibrates between local neighbourhood search, i.e. exploitation and global random search, i.e. exploration, where both are completely decoupled, and can be clearly varied through the learning parameters (Pham & Castellani, 2009). It is very efficient in finding optimal solutions and overcoming the problem of local optima, easy to apply, and available for hybridisation combination with other methods (Yuce et al., 2013). Also, BA shares many similarities with Particle Swarm Optimization (Mishra, Bisht, Singh, & Chang, 2018) and presents good alternative. The system is initialized with a population of random solutions and searches for optima by updating generations.
Recently, the BA has been widely applied in many different engineering problems, such as supply chain optimisation (Mayteekrieangkrai & Wongthatsanekorn, 2015), production scheduling (Packianather et al., 2014), numerical functions optimisation (Pham & Castellani, 2009; Pham et al., 2006a; Yuce et al., 2013; Nemmich & Debbat, 2017), solving timetabling problems (K. Nguyen, P. Nguyen, & Tran, 2012), control system tuning (Pham, Darwish, & Eldukhri, 2009), protein conformation search (Jana, Sil, & Das, 2015), test form construction (Songmuang & Ueno, 2011), Placements of FACTS devices (Idris, Khairuddin, & Mustafa, 2009a), pattern recognition (Nebti & Boukerram, 2013), robotic swarm coordination (Jevtić, Gutierrez, Andina, & Jamshidi, 2012), data mining (Hamou, Amine, & Boudia, 2013; Poonam & Dhaiya, 2015; Nemmich, Debbat, & Slimane, 2019), chemical process (Castellani, Q. T. Pham, & D. T. Pham, 2012), mechanical design (Moradi, Nafchi, & Ghanbarzadeh, 2015), wood defect classification (Packianather & Kapoor, 2015), Printed Circuit Board (PCB) assembly optimisation (Pham, Otri, & Darwish, 2007b), image analysis (Azarbad, Ebrahimzade, & Izadian, 2011), and many other applications (Hussein, Sahran, & Sheikh Abdullah, 2017).