臺灣博碩士論文加值系統

差分進化演算法(Differential evolution)，是近年來正快速發展，並在許多領域上皆受到證實為一有效、快速的演化式演算法。差分演算法的優點在於結構簡單、所需設定的參數較少及程式簡單、容易實作等等，在許多情況下，其求解的能力也相當突出。
傳統差分演算法與許多演化式演算法一樣，在處理高維度複雜函數時，可能會因為陷入區域最佳解(Local Optimum)而無法跳脫。
本研究嘗試改良差分演算法，並以動態突變權重的方式產生函數，透過每一個迭代中動態產生突變權重以平衡求解精確度及跳脫區域最佳解的能力。

Differential Evolution (DE) algorithm, first published in 1995, has proven to be a powerful tool for complicated optimization problems. Its outstanding performance and accuracy makes it applicable to different research fields. However, since differential evolution belongs to the Evolutionary Algorithm, problems like dropping in local optimum may also occur in this algorithm. In order to improve the performance of differential evolution, we propose a novel algorithm, which will generate a dynamical function for changing the differential evolution parameter "mutation factor" replace traditional differential evolution algorithm use constant mutation factor. The present study is to increase the performance of this novel algorithm and to avoid dropping into local optimum.

中文摘要 I
英文摘要 II
誌謝辭 III
目錄 IV
圖目錄 V
表目錄 VI
一、 緒論 1
1.1研究背景及動機 1
1.2研究目的 1
二、 文獻探討 3
2.1 演化式計算(evolutionary computation ,EC) 3
2.2差分進化演算法 5
2.3突變權重的相關研究 12
三、 改良突變權重的差分進化演算法 13
四、 實驗設計 16
4.1 參數設定 16
4.2 實驗環境 17
4.3 評估及測試 17
五、 實驗結果 21
5.1不同維度下的比較 21
5.2平移測試 24
5.3雜訊函數測試 26
5.4與相關文獻間的比較 33
六、 結論 35
參考文獻 36


圖目錄
圖1、差分演化基本概念圖 6
圖2、差分進化演算法流程圖 7
圖3、交換運算示意圖 10
圖4、差分進化演算法示意圖 10
圖5、MFDE 演算法流程圖 14
圖6、測試函數圖型 20
圖7、不同維度下的收斂情型 23
圖8、平移函數示意圖 24
圖9、求解雜訊函數的收斂情型 32



表目錄
表1、參數設定表 16
表2、MFDE 參數設定表 17
表3、測試函數特性表 18
表4、不同維度下的實驗結果 21
表5、函數平移實驗結果 25
表6、10 維的雜訊實驗結果 28
表7、30 維的雜訊實驗結果 30
表8、比較實驗測試函數設定 33
表9、比較實驗結果 34

[1] Kennedy, J. and Eberhart, R. C. ”Particle swarm optimization,” Proceedings of IEEE International Confernce on Neural Networks, Piscataway, NJ., 1995, pp:1942-1948.
[2] S. Kirkpatrick ,C. D. Gelatt and M. P. Vecchi, Optimization by Simulated Annealing, Science, Vol 220, Number 4598, 1983, pp. 671-680.
[3] M. Dorigo, V. Maniezzo & A. Colorni, "Ant System: Optimization by a Colony of Cooperating Agents", IEEE Transactions on Systems, Man, and Cybernetics–Part B, 26 (1), 1996, pp.29–41.
[4] K. V. Price, "Differential evolution: a fast and simple numerical optimizer," Fuzzy Information Processing Society, 1996. NAFIPS. 1996 Biennial Conference of the North American, 1996, pp. 524-527.
[5] R. Storn, "On the usage of differential evolution for function optimization," Fuzzy Information Processing Society, 1996. NAFIPS. 1996 Biennial Conference of the North American, 1996, pp. 519-523.
[6] Schwefel, H, Numerical Optimization of Computer Models,Wiley, Chichester, 1981.
[7] S. Rahnamayan, H. R. Tizhoosh and M. M. A. Salama, “Opposition-Based Differential Evolution,” Evolutionary Computation, IEEE Transactions on, vol. 12, 2008, pp. 64-79.
[8] T. Bäck, D. B. Fogel, and Z. Michalewicz, Eds., Evolutionary Computation 2: Advanced Algorithms and Operators. Bristol, U.K.: Institute of Physics, 2000.
[9] Ali, M. M. and Torn, A. “Population set-based global optimization algorithms: some modications and numerical studies.” Comput. Oper. Res., vol.31, issue 10, 2004, pp. 1703-1725.
[10] Hong-Kyu Kim, Jin-Kyo Chong, Kyong-Yop Park and D. A. Lowther, "Differential Evolution Strategy for Constrained Global Optimization and Application to Practical Engineering Problems," Magnetics, IEEE Transactions on, vol. 43, 2007, pp. 1565-1568.
[11] K. V. Price, R. Storn and J. A. Lampinen, Differential Evolution: A practial Approach to Global Optimization, Birkhäuser, 2005.
[12] M. Rickert, O. Brock and A. Knoll, "Balancing exploration and exploitation in motion planning," Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, 2008, pp. 2812-2817.
[13] K. Price, “An introduction to differential evolution”, in: D.Corne, M. Dorigo, F. Glover (Eds.), New Ideas in Optimization, McGraw-Hill, London, 1999, pp. 79–108.
[14] P. Kaelo and M. M. Ali, "A numerical study of some modified differential evolution algorithms," European Journal of Operational Research, vol. 169, 2006, pp. 1176-1184.
[15] M.M. Ali, A. Törn, “Topographical differential evolution using pre-calculated differentials”, in: G. Dzemyda, V. Saltenis, A. Zilinskas (Eds.), Stochastic and Global Optimization, Kluwer Academic Publisher, London, 2002, pp. 1–17.
[16]R. Storn, “Differential evolution research – trends and open questions,” Advances
in Differential Evolution, Volume 143, Heidelberg : Springer Berlin ,2008 ,pp. 1-31.
[17] Storn, R., Price, K., “Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization vol. 11, 1997, pp. 41–359.
[18] Krink, T., Bodgan, F., Fogel, G.B., Thomson, R., “Noisy Optimization Problems - A Particular Challenge for Differential Evolution,” Proc. Sixth Congress on Evolutionary Computation (CEC-2004). IEEE Press.2004, pp. 332-339.
[19] Wenyin Gong, Zhihua Cai and Liangxiao Jiang, “Enhancing the performance of differential evolution using orthogonal design method,” Applied Mathematics and Computation, vol. 6, issue 1, 2008, pp.56-69.