• 沒有找到結果。

本論文提出以MOEA/D 為基礎結合區域搜尋的演算法,並針對演算法各階段

進行實驗分析,在MOEA/D 方面對效能影響最大者為取代機制,我們發現使用學

者提出的DU 取代機制搭配 Tchebycheff 方法效果最好;而區域搜尋能讓效能大幅

提升;我們也針對於區域搜尋的各階段進行實驗分析,發現適應性控制的效果並

不顯著,這部分為我們將來深入研究的目標。除此之外,在族群初始化階段加入

策略解對於效能也有明顯提升。最後我們將演算法與已知最佳解進行效能比較;

實驗結果顯示我們的演算法在中、大型測資效能表現良好。

未來可能的研究方向,可以加入新的擾動機制,讓個體脫離區域最佳解;除

此之外尚可研究針對具有問題背景知識(domain knowledge)的搜尋方式進行適

應式控制。在選擇機制方面可以排除重複的個體,增加族群多樣性。另一方面,

可以將MOEA/D-LS 用於求解不同目標,如最大延遲時間等。

56

參考文獻

[1] E. Zitzler, M. Laumanns, and L. Thiele, "SPEA2: Improving the strength Pareto evolutionary algorithm," Eidgenössische Technische Hochschule Zürich (ETH), Institut für Technische Informatik und Kommunikationsnetze (TIK) Zürich, Switzerland, 2001.

[2] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, 2002.

[3] E. Zitzler and S. Künzli, "Indicator-based selection in multiobjective search,"

in Parallel Problem Solving from Nature-PPSN VIII, 2004, pp. 832-842:

Springer.

[4] N. Beume, B. Naujoks, and M. Emmerich, "SMS-EMOA: Multiobjective selection based on dominated hypervolume," European Journal of Operational Research, vol. 181, no. 3, pp. 1653-1669, 2007.

[5] Q. Zhang and H. Li, "MOEA/D: A multiobjective evolutionary algorithm based on decomposition," IEEE Transactions on Evolutionary Computation, vol. 11, no. 6, pp. 712-731, 2007.

[6] G. Minella, R. Ruiz, and M. Ciavotta, "A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem," INFORMS Journal on Computing, vol. 20, no. 3, pp. 451-471, 2008.

[7] M. M. Yenisey and B. Yagmahan, "Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends,"

Omega, vol. 45, pp. 119-135, 2014.

[8] S.-W. Lin and K.-C. Ying, "Minimizing makespan and total flowtime in permutation flowshops by a bi-objective multi-start simulated-annealing algorithm," Computers & Operations Research, vol. 40, no. 6, pp. 1625-1647, 2013.

[9] T.-C. Chiang, H.-C. Cheng, and L.-C. Fu, "NNMA: An effective memetic algorithm for solving multiobjective permutation flow shop scheduling problems," Expert Systems with Applications, vol. 38, no. 5, pp. 5986-5999, 2011.

[10] T. K. Varadharajan and C. Rajendran, "A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs," European Journal of Operational Research, vol. 167, no. 3, pp. 772-795, 2005.

57

[11] M. Nawaz, E. E. Enscore, and I. Ham, "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, vol. 11, no. 1, pp.

91-95, 1983.

[12] C. Rajendran, "Heuristic algorithm for scheduling in a flowshop to minimize total flowtime," International Journal of Production Economics, vol. 29, no. 1, pp. 65-73, 1993.

[13] J. E. C. Arroyo and A. A. de Souza Pereira, "A GRASP heuristic for the multi-objective permutation flowshop scheduling problem," The International Journal of Advanced Manufacturing Technology, vol. 55, no. 5-8, pp. 741-753, 2010.

[14] V. A. Armentano and J. E. C. Arroyo, "An application of a multi-objective tabu search algorithm to a bicriteria flowshop problem," Journal of Heuristics, vol.

10, no. 5, pp. 463-481, 2004.

[15] J. Arroyo and V. Armentano, "A partial enumeration heuristic for multi-objective flowshop scheduling problems," Journal of the Operational Research Society, vol. 55, no. 9, pp. 1000-1007, 2004.

[16] R. Ruiz and T. Stützle, "A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem," European Journal of Operational Research, vol. 177, no. 3, pp. 2033-2049, 2007.

[17] H. R. Lourenço, O. C. Martin, and T. Stützle, Iterated Local Search. Springer, 2003.

[18] J. M. Framinan and R. Leisten, "A multi-objective iterated greedy search for flowshop scheduling with makespan and flowtime criteria," OR Spectrum, vol.

30, no. 4, pp. 787-804, 2007.

[19] J. M. Framinan and R. Leisten, "An efficient constructive heuristic for flowtime minimisation in permutation flow shops," Omega, vol. 31, no. 4, pp.

311-317, 2003.

[20] G. Minella, R. Ruiz, and M. Ciavotta, "Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems," Computers &

Operations Research, vol. 38, no. 11, pp. 1521-1533, 2011.

[21] L. Paquete, M. Chiarandini, and T. Stützle, "Pareto local optimum sets in the biobjective traveling salesman problem: An experimental study," in Metaheuristics for Multiobjective Optimisation: Springer, 2004, pp. 177-199.

[22] J. Dubois-Lacoste, M. López-Ibáñez, and T. Stützle, "A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems," Computers &

Operations Research, vol. 38, no. 8, pp. 1219-1236, 2011.

[23] J. Dubois-Lacoste, M. López-Ibáñez, and T. Stützle, "Adaptive “anytime”

two-phase local search," in Learning and Intelligent Optimization: Springer,

58

2010, pp. 52-67.

[24] L. Paquete and T. Stützle, "A two-phase local search for the biobjective traveling salesman problem," in Evolutionary Multi-Criterion Optimization, 2003, pp. 479-493: Springer.

[25] H. Ishibuchi and T. Murata, "A multi-objective genetic local search algorithm and its application to flowshop scheduling," IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 28, no. 3, pp.

392-403, 1998.

[26] T. Murata and H. Ishibuchi, "MOGA: multi-objective genetic algorithms," in IEEE International Conference on Evolutionary Computation, 1995, vol. 1, pp.

289-294.

[27] H. Ishibuchi, T. Yoshida, and T. Murata, "Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling," IEEE Transactions on Evolutionary Computation, vol. 7, no. 2, pp.

204-223, 2003.

[28] P.-C. Chang, J.-C. Hsieh, and S.-G. Lin, "The development of gradual-priority weighting approach for the multi-objective flowshop scheduling problem,"

International Journal of Production Economics, vol. 79, no. 3, pp. 171-183, 2002.

[29] P. Chang, S. Chen, and C. Liu, "Sub-population genetic algorithm with mining gene structures for multiobjective flowshop scheduling problems," Expert Systems with Applications, vol. 33, no. 3, pp. 762-771, 2007.

[30] P. Chang, S. Chen, and K. Lin, "Two‐phase sub population genetic algorithm for parallel machine-scheduling problem," Expert Systems with Applications, vol. 29, no. 3, pp. 705-712, 2005.

[31] C. Rajendran and H. Ziegler, "A multi-objective ant-colony algorithm for permutation flowshop scheduling to minimize the makespan and total flowtime of jobs," in Computational Intelligence in Flow Shop and Job Shop Scheduling, vol. 230, U. Chakraborty, Ed. (Studies in Computational Intelligence: Springer Berlin Heidelberg, 2009, pp. 53-99.

[32] P. C. Chang, S. H. Chen, Q. Zhang, and J. L. Lin, "MOEA/D for flowshop scheduling problems," in IEEE Congress on Evolutionary Computation, 2008.

CEC 2008. (IEEE World Congress on Computational Intelligence). 2008, pp.

1433-1438.

[33] A. Alhindi and Q. Zhang, "MOEA/D with Tabu Search for multiobjective permutation flow shop scheduling problems," in IEEE Congress on Evolutionary Computation (CEC), 2014, 2014, pp. 1155-1164.

[34] F. Jin, S. Song, and C. Wu, "Structural property and meta-heuristic for the flow

59

shop scheduling problem," in Computational Intelligence in Flow Shop and Job Shop Scheduling: Springer, 2009, pp. 1-20.

[35] J. E. C. Arroyo and V. A. Armentano, "Genetic local search for multi-objective flowshop scheduling problems," European Journal of Operational Research, vol. 167, no. 3, pp. 717-738, 2005.

[36] T. Pasupathy, C. Rajendran, and R. K. Suresh, "A multi-objective genetic algorithm for scheduling in flow shops to minimize the makespan and total flow time of jobs," International Journal of Advanced Manufacturing Technology, vol. 27, no. 7-8, pp. 804-815, 2005.

[37] Yandra and H. Tamura, "A new multiobjective genetic algorithm with heterogeneous population for solving flowshop scheduling problems,"

International Journal of Computer Integrated Manufacturing, vol. 20, no. 5, pp.

465-477, 2007.

[38] H.-C. Cheng, T.-C. Chiang, and L.-C. Fu, "Multiobjective permutation flowshop scheduling by an adaptive genetic local search algorithm," in IEEE Congress on Evolutionary Computation, 2008. CEC 2008.(IEEE World Congress on Computational Intelligence). 2008, pp. 1596-1602: IEEE.

[39] D. W. Corne, N. R. Jerram, J. D. Knowles, and M. J. Oates, "PESA-II:

Region-based selection in evolutionary multiobjective optimization," in Proc.

of the Genetic and Evolutionary Computation Conference, 2001, pp. 283-290.

[40] X. Li and M. Li, "Multiobjective local search algorithm-based decomposition for multiobjective permutation flow shop scheduling problem," IEEE Transactions on Engineering Management, vol. 62, no. 4, pp. 544-557, 2015.

[41] L. Ke, Q. Zhang, and R. Battiti, "Hybridization of Decomposition and Local Search for Multiobjective Optimization," IEEE Transactions on Cybernetics, vol. 44, no. 10, pp. 1808-1820, 2014.

[42] B.-B. Li and L. Wang, "A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling," IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 37, no. 3, pp. 576-591, 2007.

[43] H. Li and Q. Zhang, "Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 13, no. 2, pp. 284-302, 2009.

[44] J. Liu and C. R. Reeves, "Constructive and composite heuristic solutions to the P//∑Ci scheduling problem," European Journal of Operational Research, vol.

132, no. 2, pp. 439-452, 7/16/ 2001.

[45] C. Rajendran and H. Ziegler, "An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs," European Journal of Operational Research, vol. 103, no. 1, pp. 129-138, 1997.

60

[46] Q.-K. Pan and R. Ruiz, "A comprehensive review and evaluation of permutation flowshop heuristics to minimize flowtime," Computers &

Operations Research, vol. 40, no. 1, pp. 117-128, 2013.

[47] H. Ishibuchi, Y. Sakane, N. Tsukamoto, and Y. Nojima, "Adaptation of scalarizing functions in MOEA/D: An adaptive scalarizing function-based multiobjective evolutionary algorithm," in Evolutionary Multi-Criterion Optimization, 2009, pp. 438-452: Springer.

[48] Z. Wang, Q. Zhang, A. Zhou, M. Gong, and L. Jiao, "Adaptive Replacement Strategies for MOEA/D," IEEE Transactions on Cybernetics, vol. 46, no. 2, pp.

474 - 486, 2015.

[49] Y. Yuan, H. Xu, B. Wang, B. Zhang, and X. Yao, "Balancing convergence and diversity in decomposition-based many-objective optimizers," IEEE Transactions on Evolutionary Computation, vol. 20, no. 2, pp. 180-198, 2015.

[50] E. Taillard, "Benchmarks for basic scheduling problems," European Journal of Operational Research, vol. 64, no. 2, pp. 278-285, 1993.

相關文件