建議

1. 本研究之數值微分方法，在某些特殊問題(如新山壩滲漏問題)下也有可 能不適用，於該狀況下，或可以多層次之搜尋法取代(以 PSF-HS 修改 1 版將搜尋範圍縮小後，以此範圍當作新的搜尋範圍在以 PSF-HS 修改 1 版搜尋，重複此步驟至滿足設定之收斂準則)。

2. PSF-HS 結合 PS-HS 之方法，其中最佳 PS 之考量，原本為採用當前和 弦記憶中最佳解，未來或可考慮以偵測其叢集性之方式，選出幾組最佳 候選和弦來選取取代原本之方式。

3. PSF-HS 修改 2 版中，由於調音為定值，因此所能改善之結果有限，可 令待搜尋之結果接近收斂時，再開始數值微分之梯度法運算。

4. 本研究以 PSF-HS 結合 PS-HS 之改良效果佳，後續研究演算法之改良可 嘗試再混和不同啟發式演算法之優點，以改善既有演算法之缺點。

5. 於新山壩滲漏問題中，微分方法尚無法有效改善搜尋結果，推測原因為 問題形態為不連續問題，如未能適當選定各變數之變異量以估算導數

（偏微分），可能高估或低估微分方法中之調音值。因此在數值微分前 可先考慮參數搜尋範圍大小之影響，設法設計估算導數之策略。

6. 本研究僅針對壩體滲漏問題與邊坡穩定問題做應用，後續研究可考慮改 良此法應用於各種大地工程最佳化問題，譬如：最低成本考量，最佳配 置、最少挖填方、地工結構之安全診斷、….等等。

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參考文獻

1. Abbaspour, K. C., Schulin, R. and van Genuchten M. Th., “Estimating unsaturated soil hydraulic parameters using ant colony optimization”

Advances in Water Resources, vol. 24, pp. 827-841, 2001.

2. Abido, M. A., “Robust design of multimachine power system stabilizers using simulated annealing” IEEE Transactions on Energy Conversion, vol. 15, no. 3, pp. 297-304, 2000.

3. Alexandre, E., Cuadra, L. and Gil, R., “Sound classification in hearing aids by the harmony search algorithm” Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 173-188, 2009.

4. Ayvaz, M. T., “Identification of groundwater parameter structure using harmony search algorithm” Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 129-140, 2009.

5. Bell, J. E. and McMullen, P. R., “Ant colony optimization techniques for the vehicle routing problem” Advanced Engineering Informatics, vol. 18, pp. 41-48, 2004.

6. Camp, C. V., Pezeshk, S. and Cao, G., “Optimized design of two-dimensional structures using a genetic algorithm” Journal of Structural Engineering, vol. 124, no. 5, pp. 551-559, 1998.

7. Ceylan, H. and Ceylan, H., “Harmony search algorithm for transport energy demand modeling” Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 163-172, 2009.

8. Chang, W. A. and Ramakrishna, R. S., “A genetic algorithm for shortest path routing problem and the sizing of populations” IEEE Transactions on Evolutionary Computation, vol. 6, no. 6, pp. 566-579, 2002.

9. Cheng, Y. M. et al., “Partical swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slop stability analysis” Computers and Geotechnics, vol. 34, pp. 92-103, 2007.

10. Cheng, Y. M., Li, L. and Chi, S. C., “Performance studies on six heuristic global optimization methods in the location of critical slip surface”

Computers and Geotechnics, vol. 34, pp. 462-484, 2007.

11. Cheng, Y. M., “Modified harmony methods for slope stability problems”

Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol.

96

191, pp. 141-162, 2009.

12. Chiang, C. L., “Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels” IEEE Transactions on Power Systems, vol. 20, no. 4, pp. 1690-1699, 2005.

13. Dell'Amico, M. and Trubian, M., “Applying tabu-search to the job-shop scheduling problem” Annals of Operations Research, vol. 41, pp.

231-252, 1993.

14. Fesanghary, M., “Harmony search applications in mechanical, chemical and electrical engineering” Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 71-86, 2009.

15. Gao, X. Z., Wang, X. and Ovaska, S. J., “ Harmony search methods for Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 113-127, 2009.

17. Geem, Z. W., “Particle-swarm harmony search for water network design”,Engineering Optimization, vol. 41, no. 4, pp. 297-311,2009

18. Geem, Z. W., “State of the art in the structure of harmony search algorithm” Geem, Z. W. : Recent Advances in Harmony Search Algorithm, SCI, vol. 270, pp. 1-10, 2010.

19. Geem, Z. W. et al., “Parameter-setting-free harmony search algorithm” , Computer Methods in Applied Mechanics and Engineering, vol. 217, pp.

3881-3889, 2010.

20. Gendreau, M., Hertz, A. and Laporte, G., “A tabu search heuristic for the vehicle routing problem” Management Science, vol. 40, no. 10, pp.

1276-1290, 1994.

21. Gendreau, M., “Parallel tabu search for real-time vehicle routing and dispatching” Transportation Science, vol. 33, no. 4, pp. 381-390, 1999.

22. Ingram, G. and Zhang, T., “Overview of applications and developments in the harmony search algorithm” Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp. 15-37, 2009.

23. Kariuki, B. M. et al., “The application of a genetic algorithm for solving crystal structures from powder diffraction data” Chemical Physics Letters, vol. 280, pp. 189-195, 1997.

97

24. Kahatadeniya, K. S. et al., “Determination of the critical failure surface for slope stability analysis using ant colony optimization” Engineering Geology, vol. 108, pp. 133-141, 2009

25. Lee, K. S. and Geem, Z. W., “A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice”

Computer Methods in Applied Mechanics and Engineering, vol. 194, pp.

3902-3933, 2005.

26. Mahdavi, M., Fesanghary, M. and Damangir, E., “An improved harmony search algorithm for solving optimization problems” Applied Mathematics and Computation, vol. 188, pp. 1567-1579, 2007.

27. Mahdavi, M., “Solving NP-complete problems by harmony search”

Geem, Z. W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol.

191, pp. 53-70, 2009.

28. Maier, H. R. et al., “Ant colony optimization for design of water distribution systems” Journal of Water Resources Planning and Management, vol. 129, no. 3, pp. 200-209, 2003.

29. Mukhopadhyay, A. et al., “Population-variance and explorative power of harmony search: An analysis” in Proc. 2nd MATEIT—Organized at C, vol. 37, New Delhi, India, pp. 775-781, 2008.

30. Nakano, R. and Yamada, T., “Conventional genetic algorithm for job shop problems” Proc. 4th Int. Conf. on Geneting Algorithms, pp. 474-479, San Diego, CA, 1999.

31. Park, J. B. et al., “A particle swarm optimization for economic dispatch with nonsmooth cost functions” IEEE Transactions on Power Systems, vol. 20, no. 1, pp. 34-42, 2005.

32. Panchal, A., “Harmony search in therapeutic medical physics” Geem, Z.

W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp.

189-203, 2009.

33. Rajendran, C. and Ziegler, H., “Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs”

European Journal of Operational Research, vol. 155, pp. 426-438, 2004.

34. Reklaitis, G. V., Ravindran, A. and Ragsdell, K. M., “Engineering Optimization：Methods and Applications”, vol. 1, 2

35. Svergun, D. I., “Restoring low resolution structure of biological macromolecules from solution scattering using simulated annealing”

Biophysical Journal, vol. 76, pp. 2879-2886, 1999.

98

36. Van Laarhoven, P. J. M., Aarts, E. H. L. and Lenstra, J. K., “Job shop scheduling by simulated annealing” Operations Research, vol. 40, no. 1, pp. 113-125, 1992.

37. Wachowiak, M. P. et al., “An approach to multimodal biomedical image registration utilizing particle swarm optimization” IEEE Transactions on Evolutionary Computation, vol. 8, no. 3, pp. 289-301, 2004.

38. Wang, C. M. and Huang, Y. F., “Self-adaptive harmony search algorithm for optimization” Expert Systems with Applications, vol. 37, pp.

2826-2837, 2010.

39. Xu, H. et al., “Harmony search optimization algorithm: Application to a reconfigurable mobile robot prototype” Geem, Z. W. : Recent Advances in Harmony Search Algorithm, SCI, vol. 270, pp. 11-22, 2010.

40. Yang, X. S., “Harmony search as a metaheuristc algorithm” Geem, Z.

W.(Ed.) : Music-Inspired Harmony Search Algorithm, SCI, vol. 191, pp.

1-14, 2009.

41. Yang, X.S., Engineering Optimization: An Introduction with Metaheuristic Applications. Wiley, Chichester (2010)

42. 莊勝雄譯，「工程最佳化—方法與應用」，國立編譯館，台北，民國