Metaheuristic methods in hybrid flow shop scheduling problem F. Choong ⇑ , S. Phon-Amnuaisuk, M.Y. Alias Taylor’s University Lakeside Campus, School of Engineering, No. 1, Jalan Taylor’s, 47500 Subang Jaya, Selangor, Malaysia article info Keywords: Memetic algorithms Particle swarm optimization Simulated annealing Tabu search abstract Memetic algorithms are hybrid evolutionary algorithms that combine global and local search by using an evolutionary algorithm to perform exploration while the local search method performs exploitation. This paper presents two hybrid heuristic algorithms that combine particle swarm optimization (PSO) with simulated annealing (SA) and tabu search (TS), respectively. The hybrid algorithms were applied on the hybrid flow shop scheduling problem. Experimental results reveal that these memetic techniques can effectively produce improved solutions over conventional methods with faster convergence. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Multiprocessor task scheduling is a generalized form of classical machine scheduling where a task is processed by more than one processor. It is a challenging problem encountered in wide range of applications and it is vastly studied in the scheduling literature (Chan & Lee, 1999; Drozdowski, 1996) for a comprehensive intro- duction on this topic). However, Drozdowski (1996) showed that multiprocessor task scheduling is difficult to solve even in its sim- plest form. Hence, many heuristic algorithms were presented in the literature to tackle multiprocessor task scheduling problem. Jin, Schiavone, and Turgut (2008) presented a performance study of such algorithms. However, most of these studies are primarily concerned with a single stage setting of the processor environ- ment. There are many practical problems where multiprocessor environment is a flow-shop made up of multiple stages and tasks have to go through one stage to another. Flow-shop scheduling problem is also vastly studied in sched- uling context though most of these studies concerned with single processor at each stage (Dauzère-Pérès & Paulli, 1997; Linn & Zhang, 1999). With the advances made in technology, in many practical applications, we encounter parallel processors at each stage instead of single processors such as parallel computing, power system simulations, operating system design for parallel computers, traffic control in restricted areas, manufacturing and many others (Caraffa, Ianes, Bagchi, & Sriskandarajah, 2001; Kra- wczyk & Kubale, 1985; Lee & Cai, 1999). This particular problem is defined as hybrid flow-show with multiprocessor tasks in scheduling terminology and minimizing the schedule length (makespan) is the typical scheduling problem addressed. How- ever, Brucker and Kramer (1995) showed that multiprocessor flow-shop problem to minimize makespan is also NP-hard. Gupta (1988) showed that hybrid flow-shop even with two stages is NP- hard. Furthermore, the complexity of the problem increases with the increasing number of stages. Multiprocessor task scheduling in a hybrid flow-shop environ- ment has recently gained the attention of the research community. However, due to the complexity of the problem, in the early studies (Lee & Cai, 1999; Oðuz, Ercan, Cheng, & Fung, 2003) researchers targeted two layer flow-shops with multiprocessors. Simple list based heuristics as well as meta-heuristics were introduced for the solution (Jdrzêjowicz & Jdrzêjowicz, 2003; Oðuz et al., 2003, 2004). Apparently, a broader form of the problem will have arbi- trary number of stages in the flow-shop environment. This is also studied recently and typically metaheuristic algorithms applied to minimize the makespan such as population learning algorithm (Jdrzêjowicz & Jdrzêjowicz, 2003), tabu search (Oðuz et al., 2004), genetic algorithm (Oðuz et al., 2003) and ant colony system (Ying & Lin, 2006). Minimizing the makespan is not the only scheduling problem tackled; recently Shiau, Cheng, and Huang (2008) focused on minimizing the weighted completion time in proportional flow shops. These metaheuristic algorithms produce impressive results though they are sophisticated and require laborious programming effort. However, of late particle swarm optimization (PSO) is gain- ing popularity within the research community due to its simplicity. The algorithm is applied to various scheduling problems with nota- ble performance. For instance, Sivanandam, Visalakshi, and Bhuv- aneswari (2007) applied PSO to typical task allocation problem in multiprocessor scheduling. Chiang, Chang, and Huang (2006) and Tu, Hao, and Chen (2006) demonstrate application of PSO to well known job shop scheduling problem. PSO, introduced by Kennedy and Eberhart (1995), is another evolutionary algorithm which mimics the behavior of flying birds and their communication mechanism to solve optimization 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.01.173 ⇑ Corresponding author. E-mail address: florence.choong@gmail.com (F. Choong). Expert Systems with Applications 38 (2011) 10787–10793 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa