Abstract—This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems. Keywords—Flow Shop, Genetic Algorithm, Simulated Annealing, Tabu Search. I. INTRODUCTION CHEDULING is allocating limited resources (machine, gate, people, etc) to certain task to optimize objective functions [1]. Hybrid or Flexible Flow Shop (HFS) is one kind of scheduling problem. HFS is combination of Parallel machine and Flow shop scheduling [2]-[4]. In addition, it is a generalization of flow shop problem [5]. In HFS, jobs are processed through some stages l. in each stage l, there are two or more identical machine i that can process the job. Fig. 1 shows HFS scheme. The job in each stage will be processed by every machine that idle. The machines have capacity constraint so that only one job machine can process at a time. Fig. 1 n-stages 2-parallel machine Hybrid Flow Shop Wahyudin P. Syam is a MS student at Industrial Engineering Department, King Saud University, Riyadh, 11421, Kingdom of Saudi Arabia and researcher at Princess Fatimah Alnijris’s Research Chair for Advance Manufacturing Technology at King Saud University, Riyadh (corresponding author e-mail: wsyam@ksu.edu.sa, gebe_top@yahoo.com). Ibrahim M. Al-Harkan is an associate professor at Industrial Engineering Department, King Saud University, Riyadh, 11421, Kingdom of Saudi Arabia and Chairman of Saudi Council of Engineer (e-mail: imalhark@ksu.edu.sa, ialharkan@gmail.com). The notation for this scheduling problem is as follows: HFm | perm | Cmax [2]. The meaning of this notation is as follows: hybrid flow shop scheduling environment with all jobs have identical sequence and minimizing total time to finish all jobs is the objective to be solved. Mathematical formulation for HFS is as follows as given in [6]: Notation of the HFS model: J: The set of the job to be scheduled |J| = N: number of jobs s: Number of stages that all jobs will be processed with the same order. j: Subscript letter representing job j. l: Subscript letter representing stage l. i: Subscript letter representing machine i. : l m Number of identical parallel machine in stage l. B: A very large positive number. : jl S Starting time of job j in stage l. , , , , J j j s l l ∈ ∀ ∈ ∀ m i J j j s l l otherwise l stage at i machine on is j job if X jli .., .......... , 1 , , , , 0 . , 1 = ∈ ∀ ∈ ∀ ⎩ ⎨ ⎧ = m i J j j s l l otherwise l stage on i machine on g job before is f job if Y fgli .., .......... , 1 , , , , 0 , 1 = ∈ ∀ ∈ ∀ ⎩ ⎨ ⎧ = : lj p Processing time of job j at stage l. , , , , J j j s l l ∈ ∀ ∈ ∀ Objective Function: Q Minimize Subject to: j Q p S js js ∀ ≤ + ; (1) s l l j S p S l j jl jl ≠ ∀ ≤ + + , , ; 1 , (2) g f g f i l Y B S p S fgli gl fl fl ≠ ∀ − + ≤ + , , , , ); 1 ( (3) Comparison of Three Meta Heuristics to Optimize Hybrid Flow Shop Scheduling Problem with Parallel Machines Wahyudin P. Syam, and Ibrahim M. Al-Harkan S World Academy of Science, Engineering and Technology International Journal of Industrial and Manufacturing Engineering Vol:4, No:2, 2010 267 International Scholarly and Scientific Research & Innovation 4(2) 2010 ISNI:0000000091950263 Open Science Index, Industrial and Manufacturing Engineering Vol:4, No:2, 2010 publications.waset.org/699/pdf