使用Tsallis隨機變數產生器於演化規劃的突變操作

Using the Tsallis Random Number Generator as the Mutator in Evolutionary Programming

賴宜和(Yi-Her Lai) ； 鄧志堅(Jyh-Jeng Deng)

《科學與工程技術期刊》 6卷2期 (2010/06) Pp. 71-84

https://doi.org/10.7117/JSET.201006.0071

摘要

演化規劃通常使用高斯突變(Gussian mutation)在非等向自我適應機制，稱爲傳統演化規劃(classical evolutionary programming, CEP)。近年來已經有許多學者提出不同的突變操作用於演化規劃的非等向自我適應機制，如Yao 提出以柯西突變的自我適應機制，稱爲快速演化規劃(fast evolutionary programming, FEP)；Iwamatsu 利用Tsallis突變應用於演化規劃稱爲廣域演化規劃(generalized evolutionary programming, GEP)。Iwamatsu所使用的Tsallis分佈的隨機變數變動的範圍比柯西分佈變動的範圍還大，預期應比快速演化規劃效果來的更好，然而Iwamatsu使用固定的尺度參數(scale parameter)σ爲1，並且他使用的隨機變數產生器是Tsallis 與Stariolo所提供的概估性的隨機變數產生器。因此廣域演化規劃的效果並沒有相當顯著並且結論有些誤導。針對這兩個缺點，我們將使用共同的尺度參數σ=√2並且用由Deng所提出精確的Tsallis隨機變數產生器產生Tsallis突變強度來改善。在處理Iwamatsu所解的5個問題中，我們實驗結果指出當問題只有一個區域最佳解或許多區域最佳解時，q=2.5時的GEP比CEP優越，但當問題具有少許最佳解時則反之。我們並且將上述的兩點修正應用於其他一個區域最佳解問題，並且分析不同維度的時候，目標值的收斂情形。

關鍵字

廣域演化規劃 ； 尺度參數 ； Tsallis隨機變數產生器

並列摘要

Generalized evolutionary programming (GEP), commonly called classical evolutionary Programming (CEP), usually uses Gaussian mutation in non-isotropic self-adaptation. In recent years several researchers have used different mutation operators, such as the Cauchy mutator (by Yao) in fast evolutionary programming (FEP) and the Tsallis mutator (by Iwamatsu) in the generalized evolutionary strategy (GEP). Since the random walking distance in the Tsallis variate is much larger than that in Cauchy, Tsallis will thus render better performance in searching for a global optimum. However, Iwamatsu used a scale parameter σ of 1 and an approximate Tsallis variate generator proposed by Tsallis and Stariolo, the application of which leads to a biased conclusion. To correct this bias, a common scale parameter σ of √2 was used in the present research, along with the exact random generator of the Tsallis distribution proposed by Deng, to investigate the performance of various adjusted q parameters. As a result of investigating five examples from Iwamatsu’s report, it was concluded that, when q=2.5, the performance in reaching the global minimum is significantly superior to that obtained with the CEP for many multi-mode and single-mode problems but, nevertheless, inferior for a few multi-mode problems. This conclusion is slightly different from Iwamatsu's only for single-mode problems, where he claimed that CEP is better.

並列關鍵字

generalized evolutionary programming ； scale parameter ； Tsallis variate generator