A Depth-First Mutation-Based Genetic Algorithm for Flow Shop Scheduling Problems Pei-Chann Chang 1, 2 , Chen-Hao Liu 2 , Chin-Yuan Fan 2 1 Department of Information Management, Yuan-Ze University 2 Department of Industrial Engineering and Management, Yuan-Ze University e-mail : iepchang@saturn.yzu.edu.tw e-mail : s929510@mail.yzu.edu.tw e-mail : s948906@mail.yzu.edu.tw Abstract This paper presents a novel memetic genetic algorithm (GA) for the Flow Shop Scheduling problem by combining mutation-based local search with traditional genetic algorithm. The local search is based on the depth-first mutation-based searching process and the depth, i.e., the number of total mutation within each generation is according to the number of jobs to be scheduled. In traditional GA, the optimal solution may just next to the current best one however the combination of crossover and mutation may generate individuals with the solution jumping off the optimal zones. Therefore, in this research the classical mutation is replaced by depth-first multiple mutations within each generation. The multi-mutation can provide a more completely deep searching during each generation therefore there are more chances for the evolving searching procedure to reach to the optimal zone. In addition, the SA based acceptance rate is designed to be incorporated into the searching procedure; therefore the convergence rate of the hybrid GA can be further improved. The test problems are selected from the OR library, and the computational results show that the hybrid GA has a better solution quality than simple GA and NEH heuristic. Keyword: GA, Flow Shop Scheduling, Local Search 1. Introduction Flow shop scheduling is one of the most well-known and well-studied production scheduling problems with strong engineering background [19]. The permutation flow shop problem with n jobs and m machines as studied by many researchers is commonly defined as follows. Each of n jobs is to be sequentially processed on machine . The processing time of job i on machine j is given. At any time, each machine can process at most one job and each job can be processed on at most one machine. The sequence in which the jobs are to be processed is the same for each machine. The objective widely used is to find a permutation of jobs to minimize the maximum completion time, i.e. makespan, . Due to its significance both in theory and applications it is always an important and valuable study to develop effective optimization methods. m ,..., 2 , 1 j i p , max C Flow shop scheduling is a typical NP-hard combinational optimization problem [9]. Exact techniques are only applicable to small-size problems in practice. The solution quality of constructive methods such as CDS [1], NEH [21], etc. is not rather satisfied although the process is very quick. Therefore, a lot of improvement methods such as Simulated Annealing (SA) [23][24], Genetic Algorithms (GAs) [26][27], Tabu Search (TS) [11][22][29][32] can obtain fairly satisfied solutions, but they are often very time-consuming, parameter-dependent, as well as the stopping criteria are either impracticable or hard to determine. GAs is one of the most popular evolutionary computational algorithms with learning capability and has widely gained application in a variety of fields so far. Ref. [13] developed a branch and bound algorithm for the two-machine case, which was extended to the m-machine case by Ref. [1][5] derived a new machine-based lower bound for the m- machine case and conducted computational experiments where their bound was strictly better than Bansal’s in 75-95% of the time. These experiments did not show that the new bound improved the branch and bound algorithm’s performance. Note that all these papers assume unweighted flow time.