Island-based harmony search for optimization problems Mohammed Azmi Al-Betar a,⇑ , Mohammed A. Awadallah c , Ahamad Tajudin Khader b , Zahraa Adnan Abdalkareem d a Department of Information Technology, Al-Huson University College, Al-Balqa Applied University, P.O. Box 50, Al-Huson, Irbid, Jordan b School of Computer Sciences, Universiti Sains Malaysia, 11800 Pinang, Malaysia c Faculty of Computer Science, Al-Aqsa University, P.O. Box 4051, Gaza, Palestine d Department of Quality Assurance and Performance, College of Imam Azam University, P.O. Box 72002, Baghdad, Iraq article info Article history: Available online 23 October 2014 Keywords: Harmony search Island model Structured population Diversity abstract Harmony search (HS) algorithm is a recent meta-heuristic algorithm that mimics the musical improvisa- tion concepts. This algorithm has been widely used for solving optimization problems. Moreover, many modifications in this algorithm have been carried out in order to improve the performance of the search. Island model is a structured population mechanism used in evolutionary algorithms to preserve the diversity of the population and thus improve the performance. In this paper, the island model concepts are embedded into the main framework of HS algorithm to improve its convergence properties where the new method is refer to as island HS (iHS). In the proposed method, the individuals in population are dis- tributed into separate sub-population named (islands). Then the breeding loop is separately involved in each island. After specific generations, a number of individuals run an exchange through a process called migration. This process is performed to keep the diversity of population and to allow islands to interact with each other. The experimental result using a set of benchmark function shows that the island model context is crucial to the performance of iHS. Finally the sensitivity analysis and the comparative study for iHS prove the efficiency of the island model. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Harmony search (HS) algorithm, a recent Evolutionary Algo- rithm (EA), was proposed by Geem, Kim, and Loganathan (2001) to emulate the musical phenomena of the improvisation process. In musical rehearsal, a group of musicians play the tunes of their musical tools, practice after practice to formulate a pleasing har- mony. Analogously in optimization, a set of variables, taken selec- tive values, iteration by iteration, to formulate most probably an optimal solution. The set of successful stories introduced by adapt- ing HS algorithm to a wide variety of optimization problems gets credit from the emergence of the tremendous research tendency to the domain. Some examples that adopted HS solutions include Engineering, timetabling, nurse rostering, space allocations, bioin- formatics, image processing (Abual-Rub, Al-Betar, Abdullah, & Khader, 2012; Al-Betar & Khader, 2012; Al-Betar, Khader, & Zaman, 2012b; Alkareem, Venkat, Al-Betar, & Khader, 2012; Awadallah, Khader, Al-Betar, & Bolaji, 2013, 2012; Geem, Yang, & Tseng, 2013; Landa-Torres, Manjarres, Salcedo-Sanz, Del Ser, & Gil-Lopez, 2013), and many others as recorded in Manjarres et al. (2013). The main merits of HS over other optimization methods are summarized as follows: a novel stochastic derivative is embedded within the HS (Geem, 2008); it needs less mathematical require- ments which iteratively generate a new solution after manipulat- ing all existing solutions (Mahdavi, Fesanghary, & Damangir, 2007). Put simply, it is simple, flexible, adaptable, general, and scalable (Al-Betar, Khader, Geem, Doush, & Awadallah, 2013b). However, the performance of HS has continuously attracted researcher attention account for the optimization problems combi- natorial nature (Alia & Mandava, 2011). Therefore, the HS theory has been improved by either replacing, adding, tailoring its opera- tors or hybridizing HS with other effective algorithms (Al-Betar, Khader, & Doush, 2014; Awadallah, Khader, Al-Betar, & Bolaji, 2014; Maheri & Narimani, 2014; Zhao, Suganthan, Pan, & Fatih Tasgetiren, 2011). Furthermore, adaptive parameters of HS have been also studied (Geem & Sim, 2010; Gholizadeh & Barzegar, 2013). The majority of improvements in HS performance have adjusted the process of its operators to cope with the ‘‘survival of the fittest’’ principle of natural selection (Al-Betar, Doush, Khader, & Awadallah, 2012a; Xiang, An, Li, He, & Zhang, 2014). http://dx.doi.org/10.1016/j.eswa.2014.10.008 0957-4174/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: mohbetar@cs.usm.my (M.A. Al-Betar), ma.awadallah@alaqsa. edu.ps (M.A. Awadallah), tajudin@cs.usm.my (A.T. Khader), zahraa2010@yahoo. com (Z.A. Abdalkareem). Expert Systems with Applications 42 (2015) 2026–2035 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa