Enterprises exist in a competitive manufacturing environment. To reduce production costs and effectively use production capacity to improve competitiveness, a hybrid production system is necessary. The flexible job shop (FJS) is a hybrid production system, and the FJS problem (FJSP) has drawn considerable attention in the past few decades. This paper examined the FJSP and, like previous studies, aimed to minimize the total order completion time (makespan). We developed a novel method that involves encoding feasible solutions in the genes of the initial chromosomes of a genetic algorithm (GA) and embedding the Taguchi method behind mating to increase the effectiveness of the GA. Two numerical experiments were conducted for evaluating the performance of the proposed algorithm relative to that of the Brandimarte MK1-MK10 benchmarks. The first experiment involved comparing the proposed algorithm and the traditional GA. The second experiment entailed comparing the proposed algorithm with those presented in previous studies. The results demonstrate that the proposed algorithm is superior to those reported in previous studies (except for that of Zhang et al.: the results in experiment MK7 were superior to those of Zhang, the results in experiments MK6 and MK10 were slightly inferior to those of Zhang, and the results were equivalent in other experiments) and effectively overcomes the encoding problem that occurs when a GA is used to solve the FJSP. INDEX TERMSFlexible job shop, genetic algorithm, optimization, Taguchi method. HAO-CHIN CHANG received the B.S. and M.S. degrees in marine engineering from National Kaohsiung Marine University, Kaohsiung, Taiwan, in 2009 and 2011, respectively, where he is currently pursuing the Ph.D. degree with the Institute of Engineering Science and Technology. His research interests include artificial intelligence and applications of multiobjective optimization genetic algorithms.

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Over the last few decades, there has been considerable concern over the multifactory manufacturing environments owing to globalization. Numerous studies have indicated that flexible job-shop scheduling problems (FJSPs) and the distributed and FJSPs (DFJSPs) belong to NP-hard puzzle. The allocation of jobs to appropriate factories or flexible manufacturing units is an essential task in multifactory optimization scheduling, which involves the consideration of equipment performance, technology, capacity, and utilization level for each factory or manufacturing unit. Several variables and constraints should be considered in the encoding problem of DFJSPs when using genetic algorithms (GAs). In particular, it has been reported in the literature that the traditional GA encoding method may generate infeasible solutions or illegal solutions; thus, a specially designed evolution process is required. However, in such a process, the diversity of chromosomes is lost. To overcome this drawback, this paper proposes a refined encoding operator that integrates probability concepts into a real-parameter encoding method. In addition, the length of chromosomes can be substantially reduced using the proposed algorithm, thereby, saving computation space. The proposed refined GA algorithm was evaluated with satisfactory results through two-stage validation; in the first stage, a classical DFJSP was adopted to show the effectiveness of the algorithm, and in the second stage, the algorithm was used to solve a real-world case. The real-world case involved the use of historical data with 100 and 200 sets of work orders of a fastener manufacturer in Taiwan. The results were satisfactory and indicated that the proposed refined GA algorithm could effectively overcome the conflicts caused by GA encoding algorithms.INDEX TERMS Genetic algorithms, probability-based encoding operator, distributed and flexible job-shop, flexible job-shop, scheduling problems.

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