生產排程依據生產類型、處理時間、生產約束及目標式等因素的不同，已發展出許多方法來解決排程的各種變化形式問題，在這些研究當中大多針對集中式生產製造系統，在面臨全球化快速發展階段，當企業版圖不斷擴大與供應鏈複雜化等因素產生，分散式生產製造系統逐漸成為主流，因其分散性具備風險分散、靠近商業行銷市場與原料供應地等優勢，可幫助企業創造更高價值的商業利益。
針對分散式製造系統，過往研究較少探討更複雜的分散式彈性零工式生產排程問題（Distributed Flexible Job Shop Scheduling Problem, DFJSP），為求解此NP-hard問題，本研究提出兩種混合基因簡化群體演算法（Hybrid Genetic Simplified Swarm Optimization, HGSSO），HGSSO結合簡化群體演算法（Simplified Swarm Optimization, SSO）之彈性更新機制與搜索空間記憶能力以強化基因演算法（Genetic Algorithm, GA）搜索能力，並運用兩種啟發式演算法針對DFJSP問題決策進行解碼，幫助縮小搜索空間加快找到高品質解，其中HGSSO2為首度將DFJSP運用事先分群技巧拆解為多個FJSP的求解方法，透過此種降維處理方式，能更大幅度縮小搜索空間以加快求解效率，而分群技巧則成為了此方法之關鍵要素，本研究發展出兩種分群策略並將HGSSO2算法使用DFJSP中71種資料集與過往研究進行比較，結果顯示在解品質上皆能優於其他算法。

Production scheduling is based on factors such as production type, processing time, production constraints, and objectives. Many methods have been developed to solve the problem of various forms of scheduling. Most of these studies are aimed at centralized manufacturing systems. When factors such as the continuous expansion of the company's territory and the complexity of the supply chain occur, the decentralized manufacturing system has gradually become the mainstream. Because of its decentralized nature, it has the advantages of risk dispersion, proximity to the commercial marketing market and raw material supply, which can help enterprises Create higher value business interests.
For distributed manufacturing systems, the more complex Distributed Flexible Job Shop Scheduling Problem (DFJSP) is rarely discussed in previous studies. To solve this NP-hard problem, this study proposes two hybrid algorithm. Hybrid Genetic Simplified Swarm Optimization (HGSSO), HGSSO combines the elastic update mechanism and search space memory capability of Simplified Swarm Optimization (SSO) to strengthen the Genetic Algorithm (GA) search capability, and Two heuristic algorithms are used to decode the DFJSP problem decision, which helps to narrow the search space and speed up the finding of high-quality solutions. Among them, HGSSO2 is the first solution method to disassemble DFJSP into multiple FJSPs using pre-grouping techniques. Through this dimensionality reduction The processing method can greatly reduce the search space to speed up the solution efficiency, and the clustering technique has become the key element of this method. This study developed two clustering strategies and used the HGSSO2 algorithm to compare with previous research on 71 data sets in DFJSP. The results show that the solution quality is better than other algorithms.

[1] Y. Fu, Y. Hou, Z. Wang, X. Wu, K. Gao, and L. Wang, "Distributed scheduling problems in intelligent manufacturing systems," Tsinghua Science and Technology, vol. 26, no. 5, pp. 625-645, 2021.
[2] M. Sambasivan and S. Yahya, "A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers," Computers & Operations Research, vol. 32, no. 3, pp. 537-555, 2005.
[3] B. Çaliş and S. Bulkan, "A research survey: review of AI solution strategies of job shop scheduling problem," Journal of Intelligent Manufacturing, vol. 26, no. 5, pp. 961-973, 2015.
[4] B. Naderi and R. Ruiz, "The distributed permutation flowshop scheduling problem," Computers & Operations Research, vol. 37, no. 4, pp. 754-768, 2010.
[5] L. De Giovanni and F. Pezzella, "An improved genetic algorithm for the distributed and flexible job-shop scheduling problem," European journal of operational research, vol. 200, no. 2, pp. 395-408, 2010.
[6] J. Gao, R. Chen, and W. Deng, "An efficient tabu search algorithm for the distributed permutation flowshop scheduling problem," International Journal of Production Research, vol. 51, no. 3, pp. 641-651, 2013.
[7] H. Li, X. Li, and L. Gao, "A discrete artificial bee colony algorithm for the distributed heterogeneous no-wait flowshop scheduling problem," Applied Soft Computing, vol. 100, p. 106946, 2021.
[8] G. Zhang, K. Xing, and F. Cao, "Scheduling distributed flowshops with flexible assembly and set-up time to minimise makespan," International Journal of Production Research, vol. 56, no. 9, pp. 3226-3244, 2018.
[9] W. Xu, Y. Hu, W. Luo, L. Wang, and R. Wu, "A multi-objective scheduling method for distributed and flexible job shop based on hybrid genetic algorithm and tabu search considering operation outsourcing and carbon emission," Computers & Industrial Engineering, vol. 157, p. 107318, 2021.
[10] F. T. Chan, S. H. Chung, and P. Chan, "Application of genetic algorithms with dominant genes in a distributed scheduling problem in flexible manufacturing systems," International Journal of Production Research, vol. 44, no. 3, pp. 523-543, 2006.
[11] W.-C. Yeh, "A two-stage discrete particle swarm optimization for the problem of multiple multi-level redundancy allocation in series systems," Expert Systems with Applications, vol. 36, no. 5, pp. 9192-9200, 2009.
[12] D. Lei, Y. Yuan, J. Cai, and D. Bai, "An imperialist competitive algorithm with memory for distributed unrelated parallel machines scheduling," International Journal of Production Research, vol. 58, no. 2, pp. 597-614, 2020.
[13] B. Naderi and A. Azab, "An improved model and novel simulated annealing for distributed job shop problems," The International Journal of Advanced Manufacturing Technology, vol. 81, no. 1, pp. 693-703, 2015.
[14] J.-Q. Li, P. Duan, J. Cao, X.-P. Lin, and Y.-Y. Han, "A hybrid Pareto-based tabu search for the distributed flexible job shop scheduling problem with E/T criteria," IEEE Access, vol. 6, pp. 58883-58897, 2018.
[15] H.-B. Song and J. Lin, "A genetic programming hyper-heuristic for the distributed assembly permutation flow-shop scheduling problem with sequence dependent setup times," Swarm and Evolutionary Computation, vol. 60, p. 100807, 2021.
[16] E. M. Gonzalez-Neira, D. Ferone, S. Hatami, and A. A. Juan, "A biased-randomized simheuristic for the distributed assembly permutation flowshop problem with stochastic processing times," Simulation Modelling Practice and Theory, vol. 79, pp. 23-36, 2017.
[17] J. Zheng, L. Wang, and J.-j. Wang, "A cooperative coevolution algorithm for multi-objective fuzzy distributed hybrid flow shop," Knowledge-Based Systems, vol. 194, p. 105536, 2020.
[18] M. Komaki and B. Malakooti, "General variable neighborhood search algorithm to minimize makespan of the distributed no-wait flow shop scheduling problem," Production Engineering, vol. 11, no. 3, pp. 315-329, 2017.
[19] K.-C. Ying, S.-W. Lin, C.-Y. Cheng, and C.-D. He, "Iterated reference greedy algorithm for solving distributed no-idle permutation flowshop scheduling problems," Computers & Industrial Engineering, vol. 110, pp. 413-423, 2017.
[20] J.-f. Chen, L. Wang, and Z.-p. Peng, "A collaborative optimization algorithm for energy-efficient multi-objective distributed no-idle flow-shop scheduling," Swarm and Evolutionary Computation, vol. 50, p. 100557, 2019.
[21] G. Gong, R. Chiong, Q. Deng, and Q. Luo, "A memetic algorithm for multi-objective distributed production scheduling: minimizing the makespan and total energy consumption," Journal of Intelligent Manufacturing, pp. 1-24, 2020.
[22] P. Brucker and R. Schlie, "Job-shop scheduling with multi-purpose machines," Computing, vol. 45, no. 4, pp. 369-375, 1990.
[23] H. Jia, J. Y. Fuh, A. Y. Nee, and Y. Zhang, "Web-based multi-functional scheduling system for a distributed manufacturing environment," Concurrent Engineering, vol. 10, no. 1, pp. 27-39, 2002.
[24] H. Jia, A. Y. Nee, J. Y. Fuh, and Y. Zhang, "A modified genetic algorithm for distributed scheduling problems," Journal of Intelligent Manufacturing, vol. 14, no. 3, pp. 351-362, 2003.
[25] H. Jia, J. Y. Fuh, A. Y. Nee, and Y. Zhang, "Integration of genetic algorithm and Gantt chart for job shop scheduling in distributed manufacturing systems," Computers & Industrial Engineering, vol. 53, no. 2, pp. 313-320, 2007.
[26] B. Naderi and A. Azab, "Modeling and heuristics for scheduling of distributed job shops," Expert Systems with Applications, vol. 41, no. 17, pp. 7754-7763, 2014.
[27] I. Chaouch, O. B. Driss, and K. Ghedira, "Elitist ant system for the distributed job shop scheduling problem," in International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, 2017: Springer, pp. 112-117.
[28] I. Chaouch, O. B. Driss, and K. Ghedira, "A modified ant colony optimization algorithm for the distributed job shop scheduling problem," Procedia computer science, vol. 112, pp. 296-305, 2017.
[29] M. Ziaee, "A heuristic algorithm for the distributed and flexible job-shop scheduling problem," The Journal of Supercomputing, vol. 67, no. 1, pp. 69-83, 2014.
[30] W. Xiuli and L. Xiajing, "An improved differential evolution algorithm for solving a distributed flexible job shop scheduling problem," in 2018 IEEE 14th International Conference on Automation Science and Engineering (CASE), 2018: IEEE, pp. 968-973.
[31] L. Meng, C. Zhang, Y. Ren, B. Zhang, and C. Lv, "Mixed-integer linear programming and constraint programming formulations for solving distributed flexible job shop scheduling problem," Computers & Industrial Engineering, vol. 142, p. 106347, 2020.
[32] F. T. Chan, S. H. Chung, and P. Chan, "An adaptive genetic algorithm with dominated genes for distributed scheduling problems," Expert Systems with Applications, vol. 29, no. 2, pp. 364-371, 2005.
[33] P.-H. Lu, M.-C. Wu, H. Tan, Y.-H. Peng, and C.-F. Chen, "A genetic algorithm embedded with a concise chromosome representation for distributed and flexible job-shop scheduling problems," Journal of Intelligent Manufacturing, vol. 29, no. 1, pp. 19-34, 2018.
[34] H.-C. Chang and T.-K. Liu, "Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms," Journal of Intelligent Manufacturing, vol. 28, no. 8, pp. 1973-1986, 2017.
[35] M.-C. Wu, C.-S. Lin, C.-H. Lin, and C.-F. Chen, "Effects of different chromosome representations in developing genetic algorithms to solve DFJS scheduling problems," Computers & Operations Research, vol. 80, pp. 101-112, 2017.
[36] J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, 1992.
[37] D. E. Goldberg and R. Lingle, "Alleles, loci, and the traveling salesman problem," in Proceedings of an international conference on genetic algorithms and their applications, 1985, vol. 154: Carnegie-Mellon University Pittsburgh, PA, pp. 154-159.
[38] S. Katoch, S. S. Chauhan, and V. Kumar, "A review on genetic algorithm: past, present, and future," Multimedia Tools and Applications, pp. 1-36, 2020.
[39] D. Datta, A. R. Amaral, and J. R. Figueira, "Single row facility layout problem using a permutation-based genetic algorithm," European Journal of Operational Research, vol. 213, no. 2, pp. 388-394, 2011.
[40] J. M. Palomo-Romero, L. Salas-Morera, and L. García-Hernández, "An island model genetic algorithm for unequal area facility layout problems," Expert Systems with Applications, vol. 68, pp. 151-162, 2017.
[41] R. Zhang, S. Ong, and A. Y. Nee, "A simulation-based genetic algorithm approach for remanufacturing process planning and scheduling," Applied Soft Computing, vol. 37, pp. 521-532, 2015.
[42] R. K. Arakaki and F. L. Usberti, "Hybrid genetic algorithm for the open capacitated arc routing problem," Computers & Operations Research, vol. 90, pp. 221-231, 2018.
[43] A. Hiassat, A. Diabat, and I. Rahwan, "A genetic algorithm approach for location-inventory-routing problem with perishable products," Journal of manufacturing systems, vol. 42, pp. 93-103, 2017.
[44] W.-C. Hong, Y. Dong, L.-Y. Chen, and S.-Y. Wei, "SVR with hybrid chaotic genetic algorithms for tourism demand forecasting," Applied Soft Computing, vol. 11, no. 2, pp. 1881-1890, 2011.
[45] F. Yu and X. Xu, "A short-term load forecasting model of natural gas based on optimized genetic algorithm and improved BP neural network," Applied Energy, vol. 134, pp. 102-113, 2014.
[46] H. Soleimani, K. Govindan, H. Saghafi, and H. Jafari, "Fuzzy multi-objective sustainable and green closed-loop supply chain network design," Computers & industrial engineering, vol. 109, pp. 191-203, 2017.
[47] A. Khan et al., "Color image segmentation using genetic algorithm with aggregation-based clustering validity index (CVI)," Signal, Image and Video Processing, vol. 13, no. 5, pp. 833-841, 2019.
[48] J. L. de Paiva, C. F. Toledo, and H. Pedrini, "An approach based on hybrid genetic algorithm applied to image denoising problem," Applied Soft Computing, vol. 46, pp. 778-791, 2016.
[49] A. Kavitha and C. Chellamuthu, "Brain tumour segmentation from MRI image using genetic algorithm with fuzzy initialisation and seeded modified region growing (GFSMRG) method," The Imaging Science Journal, vol. 64, no. 5, pp. 285-297, 2016.
[50] Y. Lee, T. Hara, H. Fujita, S. Itoh, and T. Ishigaki, "Automated detection of pulmonary nodules in helical CT images based on an improved template-matching technique," IEEE Transactions on medical imaging, vol. 20, no. 7, pp. 595-604, 2001.
[51] Y. Pachepsky and B. Acock, "Stochastic imaging of soil parameters to assess variability and uncertainty of crop yield estimates," Geoderma, vol. 85, no. 2-3, pp. 213-229, 1998.
[52] T. Scully and K. N. Brown, "Wireless LAN load-balancing with genetic algorithms," in International Conference on Innovative Techniques and Applications of Artificial Intelligence, 2008: Springer, pp. 3-16.
[53] J. He, S. Ji, M. Yan, Y. Pan, and Y. Li, "Load–balanced CDS construction in wireless sensor networks via genetic algorithm," International Journal of Sensor Networks, vol. 11, no. 3, pp. 166-178, 2012.
[54] W.-C. Yeh, "An improved simplified swarm optimization," Knowledge-Based Systems, vol. 82, pp. 60-69, 2015.
[55] W.-C. Yeh, "Orthogonal simplified swarm optimization for the series–parallel redundancy allocation problem with a mix of components," Knowledge-Based Systems, vol. 64, pp. 1-12, 2014.
[56] C.-L. Huang, "A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems," Reliability Engineering & System Safety, vol. 142, pp. 221-230, 2015.
[57] W.-C. Yeh, Y.-Z. Su, X.-Z. Gao, C.-F. Hu, J. Wang, and C.-L. Huang, "Simplified swarm optimization for bi-objection active reliability redundancy allocation problems," Applied Soft Computing, vol. 106, p. 107321, 2021.
[58] C.-M. Lai and W.-C. Yeh, "Two-stage simplified swarm optimization for the redundancy allocation problem in a multi-state bridge system," Reliability Engineering & System Safety, vol. 156, pp. 148-158, 2016.
[59] W.-C. Yeh, "A novel boundary swarm optimization method for reliability redundancy allocation problems," Reliability Engineering & System Safety, vol. 192, p. 106060, 2019.
[60] W.-C. Yeh, Y.-M. Yeh, P.-C. Chang, Y.-C. Ke, and V. Chung, "Forecasting wind power in the Mai Liao Wind Farm based on the multi-layer perceptron artificial neural network model with improved simplified swarm optimization," International Journal of Electrical Power & Energy Systems, vol. 55, pp. 741-748, 2014.
[61] W.-C. Yeh, "New parameter-free simplified swarm optimization for artificial neural network training and its application in the prediction of time series," IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 4, pp. 661-665, 2013.
[62] W.-C. Yeh, Y.-P. Lin, Y.-C. Liang, and C.-M. Lai, "Convolution Neural Network Hyperparameter Optimization Using Simplified Swarm Optimization," arXiv preprint arXiv:2103.03995, 2021.
[63] W.-C. Yeh, C.-M. Lai, and K.-C. Tseng, "Fog computing task scheduling optimization based on multi-objective simplified swarm optimization," in Journal of Physics: Conference Series, 2019, vol. 1411, no. 1: IOP Publishing, p. 012007.
[64] C.-M. Lai, "Integrating simplified swarm optimization with AHP for solving capacitated military logistic depot location problem," Applied Soft Computing, vol. 78, pp. 1-12, 2019.
[65] W.-C. Yeh, C.-M. Lai, and M.-H. Tsai, "Nurse scheduling problem using Simplified Swarm Optimization," in Journal of Physics: Conference Series, 2019, vol. 1411, no. 1: IOP Publishing, p. 012010.
[66] W.-C. Yeh, C.-M. Lai, Y.-C. Huang, T.-W. Cheng, H.-P. Huang, and Y. Jiang, "Simplified swarm optimization for task assignment problem in distributed computing system," in 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2017: IEEE, pp. 773-776.
[67] W.-C. Yeh, "Optimization of the disassembly sequencing problem on the basis of self-adaptive simplified swarm optimization," IEEE transactions on systems, man, and cybernetics-part A: systems and humans, vol. 42, no. 1, pp. 250-261, 2011.
[68] P. Lin, S. Cheng, W. Yeh, Z. Chen, and L. Wu, "Parameters extraction of solar cell models using a modified simplified swarm optimization algorithm," Solar Energy, vol. 144, pp. 594-603, 2017.