Hybridizing Bees Algorithm with Firefly Algorithm for Solving Complex Continuous Functions

Hybridizing Bees Algorithm with Firefly Algorithm for Solving Complex Continuous Functions

Mohamed Amine Nemmich (Department of Computer Science, University Mustapha Stambouli of Mascara, Mascara, Algeria), Fatima Debbat (Department of Computer Science, University Mustapha Stambouli of Mascara, Mascara, Algeria) and Mohamed Slimane (Université de Tours, Laboratoire d'Informatique Fondamentale et Appliquée de Tours (LIFAT), Tours, France)
Copyright: © 2020 |Pages: 29
DOI: 10.4018/IJAMC.2020040102


In this article, two hybrid schemes using the Bees Algorithm (BA) and the Firefly Algorithm (FA) are presented for numerical complex problem resolution. The BA is a recent population-based optimization algorithm, which tries to imitate the natural behaviour of honey bees foraging for food. The FA is a swarm intelligence technique based upon the communication behaviour and the idealized flashing features of tropical fireflies. The first approach, called the Hybrid Bee Firefly Algorithm (HBAFA), centres on improvements to the BA with FA during the local search thus increasing exploitation in each research zone. The second one, namely the Hybrid Firefly Bee Algorithm (HFBA), uses FA in the initialization step for a best exploration and detection of promising areas in research space. The performance of the novel hybrid algorithms was investigated on a set of various benchmarks and compared with standard BA, and other methods found in the literature. The results show that the proposed algorithms perform better than the Standard BA, and confirm their effectiveness in solving continuous optimization functions.
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1. Introduction

Swarm intelligence (SI) is branch of metaheuristic algorithms that is based on the collective behaviour of populated, decentralized and self-organized systems. It focuses specifically on animals or insects behaviour to design different metaheuristics that can mimic the abilities of these agents in solving their problems such as effective foraging for food, colony re-location, nest building, prey evading and mating (Yu, & Estevez, 2018). These interactions have been effectively appropriated to deal with different types of optimization problems (Özbakır & Tapkan, 2011). For example, the behaviours of social insects in nature, such as ants, honey bees and fireflies, can be modelled by the Ant Colony Optimisation (ACO) (Dorigo & Di Caro, 1999), Artificial Bee Colony (ABC) (Karaboga, 2009) and Firefly Algorithm (FA) (Yang, 2008), respectively. These approaches are generally used to describe efficient social behaviour through self-organisation of the swarm.

The honey bees are one of the most social insects considered in SI studies, and it is in an increasing tendency in the literature for the recent years and it will continue. Many metaheuristic optimization algorithms are proposed such as Honeybees Mating Optimisation (HBMO), Beehive (BH), Honey Bee Optimisation (HBO), Artificial Bee Colony (ABC), Bee Colony Optimisation (BCO) and the Bees Algorithm (BA) (Yuce, Packianather, Mastrocinque, Pham, & Lambiase, 2013).

The Bees Algorithm (BA) is a new population-based optimisation algorithm, which tries to imitate the natural behaviour of honey bees in food foraging. It is proposed by Pham et al. (2006) for solving various complex optimisation problems. The main advantage of BA is it has power and equilibrate in local search (exploitation) and global random search (exploration), where both are completely decoupled, and can be clearly varied through the learning parameters (Pham & Castellani, 2009). It is easy to apply, stable, very efficient method for finding globally optimal solution and overcoming the local optima problem and available for hybridisation combination with other approaches (Yuce et al., 2013).

In recent years, the Bees Algorithm has been widely and successfully applied on a variety of engineering problems, such as pattern recognition (Nebti & Boukerram, 2013), data mining (Poonam & Dhaiya 2015; Nemmich, Debbat & Slimane, 2018a), supply chain optimisation (Mayteekrieangkrai & Wongthatsanekorn, 2015), image analysis (Azarbad et al., 2011), numerical functions optimisation (Pham & Castellani, 2009; Pham et al., 2006a; Yuce et al., 2013; Nemmich & Debbat, 2017), solving timetabling problems (Nguyen, Nguyen, & Tran, 2012), production scheduling (Packianather et al., 2014), control system tuning (Pham, Darwish, & Eldukhri, 2009), robotic swarm coordination (Jevtić, Gutiérrez, Andina, & Jamshidi, 2012), protein conformation search (Jana et al., 2015), wood defect classification (Packianather & Kapoor, 2015), test form construction (Songmuang & Ueno, 2011), mechanical design (Moradi et al., 2015), chemical process (Castellani, Pham, & Pham, 2012), project scheduling (Nemmich, Debbat & Slimane, 2018b), Printed Circuit Board (PCB) assembly optimisation (Pham, Otri, & Darwish, 2007b), Placements of FACTS devices (Idris, Kharuddi, & Mustafa 2009a), and several other applications (Hussein, Sahran & Sheikh Abdullah, 2017).

The BA has attracted a large attention among researchers because it has been demonstrated to be robust and efficient optimisation tool. It can be divided up into four components: parameter tuning, population initialisation, exploitative local search (i.e. intensification) and exploratory global search (i.e. diversification) (Hussein et al., 2017).

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