本研究利用單目標與多目標粒子群演算法探討船舶球形艏最佳化設計之問題，首先討論粒子群演算法(Particle Swarm Optimization)、模擬退火法(Simulated Annealing)與基因演算法(Genetic Algorithm)計算傳統問題的比較，並利用多目標粒子群方法中的MOPSO-CD方法，結合船用計算流體動力學及船體運動學評估設計船體所需考量的適應值(fitness)，其包含：總阻力係數(Total Resistance Coefficient)、縱搖、起伏等船形表現指標，並利用NURBS理論的曲面微擾法(Surface Perturbation Method)隨機產生球艏外形，轉換檔案後供耐海性與商用計算流體力學軟體SHIPFLOW進行計算，最後比較單目標與多目標演算法對球艏形狀改變之影響，以及選用不同目標函數對結果之影響。
本研究係以MATLAB 2010a為程式架構主體撰寫粒子群演算法，輔以FORTRAN程式進行NURBS理論計算並傳回MATLAB程式中，利用已知船形之資料，修正原始船形以計算出多目標最佳化的柏拉圖解集。
本研究經多方探討後，結果建議設計船舶球艏時，耐海性問題宜同時將縱搖與起伏列入目標函數計算，多目標粒子群方法計算之球形艏能同時改善船舶球艏阻力與耐海性之問題，提升船舶設計問題之效率，並使設計之船形能有效增加船速，或降低馬力以達到節能減碳的目的。

The main purpose to this research is to use the single objective particle swarm optimization (PSO) and multiobjective PSO (MOPSO) to implement the optimization for bulbous bow on a monohull. The content of our research includes discussion of the comparison to the optimization algorithm for PSO, simulated annealing (SA) and genetic algorithm (GA) with the traditional optimization problems; using MOPSO-CD which belongs to the method of multiobjective PSO to achieve the goal of bow optimization with the theory of ship hydrodynamics and ship motion theory to evaluate the fitness, which includes the total resistance coefficient, pitch and heave.
Based on the theory of NURBS, we developed the surface perturbation method to implement PSO algorithm and transfer the format of file for the commercial computational fluid dynamic software SHIPFLOW to calculate fitness. We compare the deformation of the results in single, two and three objective functions, and indicated the importance of carefully choosing objective function.
In the end, we suggest when applying the multiobjective optimized stragety to optimize the bulbous bow, we should also take the heave and pitch motion into account. Our results show that the modified bulbous bow for the hull could improve the performance of the heave, pitch motion and total resistance and then decrease fuel consumption.

1. Carlo R. Raquel, Prospero C. Naval, Jr., “ An effective Use of Crowding Distance in Multiobjective Particle Swarm Optimization,” Proceedings of the 2005 Conference on Genetic and Evolutionary Computation,2005 , pp.257-264, Washington D.C., U.S.A., June 2005, ACM Press, New York
2. Carlos A. Coello Coello, Gregorio Toscano Pulido, and Maximino Salazar Lechuga, “Handling Multiple Objectives With Particle Swarm Optimization,” IEEE Transactions on Evolutionary Computation, Vol.8, No.3, June 2004
3. Carlos Alberto Gonzalez Pico, “Dynamic Scheduling of Computer Tasks Using Genetic Algorithms,” Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 829-833, June 26~July 2, 1994
4. Carlos M. Fonseca and Peter J. Fleming, “Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization,” Fifth Int Conf. Genetic Algorithms, San Mateo, CA, 1993, pp. 416-23
5. Cheng-Huang, Cheng-Chia Chiang, and Shean-Kwang Chou, “An Inverse Geometry Design Problem in Optimizing Hull Surface.” Journal of Ship Research, Vol.42, No.2, June 1998, pp. 79-85
6. Cordier, S, et al., “Application of OpenFOAM® To Hull Form Optimisation AT STX France,” RINA
7. Dirk Büche, Nicol N. Schraudolph, and Petros Koumoutsakos, “Accelerating Evolutionary Algorithms With Gaussian Process Fitness Function Models,” IEEE Transactions on Systems, Man and Cybernetics—PART C: Applications and Reviews, Vol. 35, No. 2, May 2005
8. Donald C. Wyatt and Peter A. Chang, “Development and Assessment of a Total Resistance Optimized Bow for the AE 36,” Marine Technology, Vol.31, No.2, April 1994, pp. 149-160
9. E. Zitler and L. Thiele, “Multiobjective optimization using evolutionary algoriths : A comparative case study,” Parallel Problem Solving From Nature, Germany, pp.292-301, 1998
10. E. Zitler, M. Laumanns, L. Thiele, “SPEA2: Improving the strength Pareto evolutionary algorithms,” Technical Report TIK-103, Computer Engineering and Network Laboratory(TIK), May 2001
11. E. Zitzler, K. Deb, and L. Thiele, “Comparison of multiobjective evolutionary algorithms: Empircal results,” Evol. Comput, V8, N2, pp.173-195, 2000
12. Eberhart, R. C. and Shi, Y., “Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization,” Proceedings of the 2000 Congress on Evolutionary Computation, Vol. 1, pp.84-88, 2000
13. Emilio F. Campana, Daniel Peri, Yusuke Tahara, Frederick Stern, “Shape optimization in ship hydrodynamics using computational fluid dynamics.” Computational Methods Application Engineering, Vol.196, 2006
14. Emilio F. Campana, Giovanni Fasano, Daniele Peri and Antonio Pinto, “Particle Swarm Optimization: Efficient Globally Convergent Modifications,” III European Conference on Computational Mechanics, 5-8 June, 2006
15. F. Y. Cheng, and X. S. Li, “Generalized Center Method For Multiobjective Engineering Optimization,” Engineering Optimization, Vol. 31, pp. 641-661, 1999
16. Fourie, P. C., and Groenwold A. A., “The Particle Swarm Optimization Algorithm in Size and Shape Optimization,” Structural and Mutidisciplinary Opitimization, Vol. 23, No. 4, pp.259-267, 2002
17. Gies, D., Rahmat-Samii, Y., “Reconfigurable array design using parallel particle swarm optimization,” IEEE AP-S Symposium Digests, pp. 177-180, June 22-27, 2003
18. Hess, J. L. and Smith, A. M. O., “Calculation of Nonlifting Potential Flow About Arbritrary Three-Dimensional Bodies,” Journal of Ship Research, Vol. 8, No. 2, pp.22-44, 1964
19. Hu, X., and Eberhart, R. C., “Adaptive Particle Swarm Optimization: Detection and Response to Dynamic System,” Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1666-1670, 2002
20. J. D. Knowles and D. W. Corne, “Approximating the nondominated front using the Pareto archived evolution strategy,” Evol. Comput., Vol.8, pp. 149-172, 2000
21. J.D. Schaffer, “Some experiments in machine learning using vector evaluated genetic algorithm,” Ph. D. thesis, Vanderbilt University, Nashville, TN, 1984
22. Jacomine Grobler, “Particle Swarm Optimization and Differential Evolution for Multi-Objective Multiple Machine Scheduling,” Master of the Faculty of Engineering, thesis, , University of Pretoria, Sept. 2008
23. Josh B. Doyle and Roy J. Hartfield, “Aerodynamic Optimization for Freight Trucks Using Genetic Algortihm and CFD,” 46th AIAA Aerospace Science Meeting and Exhibit, Jan 7-10, 2008
24. K. Deb, Amrit Pratap, Sameer Agarwal and T. Meyarivan, “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, Vol.6, No. 2, April 2002
25. K.E. Parsopoulos and M. N. Vrahatis, “Multiobjective Optimization Using Parallel Vector Evaluated Particle Swarm Optimization,” Proceedings of the IASTED International Conference on Artifical Intelligence and Application(AIA), ACTA Press, Vol.2, pp. 823-828, 2004
26. K.E. Parsopoulos and M. N. Vrahatis, “Particle Swarm Optimization Method in Multiobjective Problems,” Proceeding of the ACM 2002 Symposium on Applied Computing, pp. 603-607, 2002
27. Kennedy, J., Eberhart, R, “Particle Swarm Optimization.” IEEE, 1995
28. Kim, C.H.,Chou, F. S. and Tien D., “Motions and Hydrodynamic Load of a Ship Advancing in Oblique Waves,” Transactions of the Society of Navel Architects and Marine Engineers,1980, Vol.88, pp. 225-256
29. Kirkpatrick S., Gelatt C. D., Vecchi M. P., “Optimization by Simulated Annealing,” Science 220(4598): 671-680, 1983
30. Lam Thu Bui, “Multi-Objective Optimization in Computational Intelligence : Theory and Practice,” Springer, 2008
31. Laura and Mihai Oltean,”What Else is the Evolution of PSO Telling Us? ,” Journal of Artificial Evolutiona and Application, Nov. 2007
32. Margarita Reyes-Sierra and Carlos A. Coello Coello, “Multi-Objective Particle Swarm Optimizers : A Survey of the State-of-the-Art, ”International Journal of Computational Intelligence Research, Vol.2, No.3, 2006, pp.287-308
33. Michael Emmerich, Kyriakos Giannakoglou, Boris Naujoks, “Single- and Multi- objective Evolutionary Optimization Assisted by Gaussian Random Field Metamodels,” IEEE Transactions on Evolutionary Computation, Vol. 10, pp. 421-439, Aug. 2006
34. Nanbo Jin Rahmat-Samii, Y., “Advance in Particle Swarm Optimization for Antenna Designs: Real-Number, Binary, Single-Objective and Multiobjective Implementations,” IEEE Transactions on Antennas and Propagation, pp. 556-567, March 2007
35. Omar Al Jadaan, Lakishimi Rajamani, C.R.Rao, “Non-dominated ranked Genetic Algorithm for solving multi-objective optimization : NRGA.”Journal of Theoretical and Applied Information Technology, 2008
36. Passaro A. and Starita A.,”Particle Swarm Optimization for Multimodal Functions : A Clustering Approach,”Journal of Artificial Evolution and Application, Feb. 2008
37. Perfomance, Propulsion 1978 ITTC Performance Prediction Method, International Towing Tank Conference, ITTC, 1999
38. Peri D. and Emilio F. Campana, “Multidisciplinary Design Optimization of a Naval Surface Combatant,” Journal of Ship Research, Vol. 47, No.1, March 2003, pp.1-12
39. Peri D., Michele Rossetti and Emilio F. Campana, “Design Optimization of Ship Hulls via CFD Techniques.” Journal of Ship Research, Vol. 45, No.2, June 2001, pp. 140-149
40. Piegl, L. and Tiller, W.,”The NURBS book,” Springer, 1997
41. Pinto A., Peri D., E.F. Campana, “Multiobjective Optimization of a Containership using Deterministic Particle Swarm Optimization.” Journal of Ship Research, Vol.51, 2007
42. Praveen C., R. Duvigneau, “Low cost PSO metamodels and inexact pre-evaluation: Application to aerodynamic shape design,” Comput. Methods Appl. Mech. Engrg. 198(2009)
43. Praveen Kumar Tripipathi, Sanghamitra Banyopadhyay and Sankar Kumar Pal, “Multi-Objective Particle Swarm Optimization with time variant inertia and acceleration coefficients,” Information Sceience, 2007
44. Rania Hassan, Babak Cohanim, Olivier de Weck and Gerhard Venter, “A comparison of particles swarm optimization and the genetic algorithm,” Proceedings of the First AIAA Multidisciplinary Design Optimization Specialist Conference, pp. 18-21, 2005
45. Roshdy Georges S. Barsoum, “Interdisciplinary computational mechanics—some computational problems in naval ship design.” International Journal for Numerical Methods In Engineering, Vol. 47, April 2000
46. S. L. Ho, Shiyou Yang, Guangzheng Ni, Edward W. C. Lo and H.C. Wong, “A Particle Swarm Optimization-Based Method for Multiobjective Design Optimizations,” IEEE Transactions on Magnetics, Vol.41, No.5, May 2005
47. Shi, Y., and Eberhart, R. C., “Parameter Selection in Particle Swarm Optimizzation,” V. W. Porto, N. Saravanan, D. Waagen, and A. E. Eiben (eds), Lecture Notes in Computer Science, 1447, Evolutionary Programming VII, Springer, Berlin, pp.591-600, 1998
48. Shi, Y., and Eberhart, R. C., ”A Modified Particle Swarm Optimizer,” Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 69-73,1998
49. Srinivas M. and Patnaik L.M., “Adaptive probabilities of crossover and mutation in genetic algorithms,” IEEE Transactions on System, Man and Cybernetics, Vol. 24, no.4, pp.656-667, 1994
50. Stefano Cagnoni, “Particle Swarms: The Second Decade,” Hindawi, 2008
51. T. W. Lowe, M. I. G. Bloor and M. J. Wilson, “The Automatic Functional Design of Hull Surface Geometry.” Journal of Ship Research, Vol. 38, No.4, pp.319-328, Dec. 1994
52. Ting and Chuan Kang, “On the mean convergence time of multiparent genetic algorithms without selection,” Advance in Artificial Life, pp.403-412, 2005
53. Xiaodong Li, “ A Non-dominated Sorting Particle Swarm Optimization for Multiobjective Optimization,” Genetic and Evolutionary Computation, GECCO 2003, Proceedings, Part I, Springer, Lecture Notes in Computer Science, Vol. 2723, 2003, pp.37-48
54. Xueyi Li, Hong Jiang, Song Cheng and Xiaochun Wang, “An efficient surface-surface intersection algorithm based on geometry characteristics,” Computer & Graphics, 2004, 28, pp.527~537
55. Y. Tahara, F. Stern and Y. Himeno, “Computational Fluid Dynamics—Based Optimization of a Surface Combatant.” Journal of Ship Research, Vol.28, No.4, Dec. 2004, pp.273-287
56. Y. Tahara, Himeno, Y., “An Application of Computation Fluid Dynamics to Tanker Hull Form Optimization Problem,” Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka Prefecture University and Osaka University, Japan 1998
57. 余岱璟，”多目標最佳化解集合在不確定因素下之分析及預測”，國立成功大學機械工程研究所，碩士論文(2007)
58. 吳宜親，”波浪中三體船非線性力之三維解”，國立成功大學造船暨船舶機電工程研究所，碩士論文(2007)
59. 卓永堂，”球形船艏對船舶運動與阻力之影響評估”， 國立成功大學造船暨船舶機電工程研究所，碩士論文(2003)
60. 周家宏，”最佳化船型預測之研究”，國立成功大學造船暨船舶機電工程研究所，碩士論文(2002)
61. 林敬堯，”停車場立體多目標使用最佳化之研究-以泰山停(三)立體停車場為例”，國立中央大學土木工程研究所，碩士論文(2010)
62. 林翰屏，”以小板法求解航行船舶之輻射問題”，國立成功大學造船暨船舶機電工程研究所，碩士論文(1997)
63. 柯仁凱，”工具機單元結構中補強肋之最佳化設計”，國立中興大學機械工程學系研究所，碩士論文(2010)
64. 胡登凱，”波浪中三體船之穩態及非穩態之流體動力解析”，國立成功大學造船暨船舶機電工程研究所，碩士論文(2007)
65. 莊玟珊，”PSO-SA混合搜尋法與其他結構最佳化”，國立中央大學土木工程研究所，碩士論文(2007)
66. 陳柏汎，”反算設計法於最適化船形預測之研究”，國立成功大學造船暨船舶機電工程研究所，博士論文(2003)
67. 辜文元，”多目標直交粒子群最佳化演算法”，逢甲大學資訊工程學系研究所，碩士論文(2005)
68. 楊淳云，”應用模糊與賽局理論多目標優化法於曾文水庫集水區管理之研究”，崑山科技大學環境工程研究所，碩士論文(2009)
69. 廖培元，”波浪中船體運動三維解”，國立成功大學造船暨船舶機電工程研究所，碩士論文(1998)
70. 銀徽，”以超啟發式法則進行鋼筋混凝土結構最佳化設計”，國立台灣科技大學營建工程系，碩士論文(2009)
71. 鄭嘉賢，”瞬時波形中船體水下網格建立技術之研發”，國立成功大學造船暨船舶機電工程研究所，碩士論文(2011)