修正模擬退火搜尋多階質數乘餘法亂數產生器

A Modified Simulated Annealing Search for Good Multiple Recursiverandom Number Generators

唐惠欽(Hui-Chin Tang) ； 黃敏聖(Min-Sheng Huang)

《中國統計學報》 43卷4期 (2005/12) Pp. 407-421

https://doi.org/10.29973/JCSA.200512.0003

摘要

本研究探討之問題為搜尋具長週期及健全格子結構之多階質數乘餘法亂數產生器，結合禁忌搜尋之禁忌列表和基因演算法之突變法則於模擬退火法以設計一新啟發演算法，並利用田口方法設計最佳之啟發參數組合。結果顯示，修正模擬退火法搜尋縮減三階質數乘餘法之光譜值優於前後向搜尋法。

關鍵字

多階質數乘餘法 ； 亂數 ； 模擬退火法 ； 光譜檢定 ； 田口方法

並列摘要

This paper considers the problem of searching for good multiple recursive generators (MRGs) with long period and good lattice structure. We propose a new algorithm that embeds both the tabu list of tabu search and the mutation of genetic algorithm into the simulated annealing (SA) method. Taguchi method is used to find the optimal heuristic parameters in the SA such that the effectiveness of the SA can be further improved. The proposed algorithm is compared with forward/backward method, and its effectiveness is numerically confirmed by the experiments we perform on the reduced third-order MRGs.

並列關鍵字

Multiple recursive generator ； random number ； simulated annealing ； spectral test ； Taguchi method

參考文獻

Aarts, E.,Korst, J.(1989).Simulated annealing and Boltzmann machines.New York:Wiley.

Anily, S.,Federgruen, A.(1987).Simulated annealing methods with general acceptance probability.Journal of Applied Probability.24,657-667.

Bölte, A.,Thonemann, U.W.(1996).Optimizing simulated annealing schedules with genetic programming.European Journal of Operational Research.92,402-416.

Cassels, J.W.S.(1959).An introduction to the Geometry of Number.New York:Springer-Verlag.

Deng, L.Y.,Lin, D.K.J.(2000).Random number generation for the new century.American Statistician.54,145-150.