混合批次振動和諧演算法與循環座標下降法用於數學最佳化問題

A hybrid search by integrating batch vibration harmony search and cyclic coordinate decent for numerical optimization problems

杜建輝(Jian-Huei Du)

指導教授 ： 詹君治

健行科技大學/電資學院/資訊工程系碩士班/碩士(2014年)

https://doi.org/10.6824/UCH.2014.00025

摘要

本論文發展一個批次振動和諧演算法(Batch Vibration Harmony Search, BVHS)並與循環座標下降法(Cyclic Coordinate Descent, CCD)結合，先由批次振動和諧演算法負責探索工作尋找最佳解所在的子搜尋區域，再由循環座標下降法挖掘高精確度的最佳解。批次振動和諧演算法被設計成只負責探索工作，因此每當和諧記憶體內儲存的解答彼此靠近時需以隨機方式更換和諧記憶體。為了瞭解BVHS-CCD的搜尋效能，論文中使用十個經典測試函數測試並與IHS、GHS、EHS三種知名和諧演算法做比較。比較結果顯示，BVHS-CCD比IHS-CCD、GHS-CCD與EHS-CCD有更佳的空間搜尋能力。除此之外，BVHS-CCD具有辨識問題變數間關係的能力，在解一個數學最佳化問題前可先用不同寬鬆和諧記憶體振動條件的BVHS-CCD做小計算量測試，若振動條件寬鬆者所對應的搜尋結果較嚴格者佳代表問題變數間的關係偏向相依，否則代表問題變數間的關係偏向獨立。

關鍵字

批次 ； 振動 ； 和諧演算法 ； 循環座標下降法

並列摘要

A hybrid search by integrating batch vibration harmony search and cyclic coordinate decent has been developed for numerical optimization problems in this thesis. The difference between the proposed harmony search and the other harmony searches is that the proposed harmony search uses a vibration mechanism to avoid premature convergence problems. In doing so, the batch vibration harmony search always explores the search space. To understand the performances of the proposed harmony search, ten classic testing functions are adopted for test. Moreover, the batch vibration harmony search is compared with three popular harmony searches, including IHS, GHS, and EHS. The comparing results indicate that the batch vibration harmony search shows the best search performance. Additionally, the proposed harmony search can identify whether the variables of an optimization problem are dependent or independent.

並列關鍵字

batch ； vibration ； harmony search ； cyclic coordinate descent

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