利用粒子群演算法與圖形處理器尋找最佳拉丁超立方設計

Optimizing Latin Hypercube Designs by Particle Swarm with GPU Acceleration

謝岱霓(Dai-Ni Hsieh)

指導教授 ： 王偉仲

國立臺灣大學/理學院/數學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.00127

摘要

無資料

關鍵字

拉丁超立方設計 ； 粒子群演算法 ； 圖形處理器

並列摘要

Due to the expensive cost of many computer and physical experiments, it is important to carefully choose a small number of experimental points uniformly spreading out the experimental domain in order to obtain most information from these few runs. Although space-filling Latin hypercube designs (LHDs) are popu- lar ones that meet the need, LHDs need to be optimized to have the space-filling property. As the number of design points or variables becomes large, the to- tal number of LHDs grows exponentially. The huge number of feasible points makes this a difficult discrete optimization problem. In order to search the opti- mal LHDs efficiently, we propose a population based algorithm which is adapted from the standard particle swarm optimization (PSO) and customized for LHD. Moreover, we accelerate the adapted PSO for LHD (LaPSO) via graphic process- ing unit (GPU). According to the examined cases, the proposed LaPSO is more stable compared to other two methods and capable of improving some known results.

並列關鍵字

Latin hypercube design (LHD) ； particle swarm optimization (PSO) ； graphic processing unit (GPU)

參考文獻

[1] Max D. Morris and Toby J. Mitchell. Exploratory designs for computational experiments. Journal of Statistical Planning and Inference, 43(3):381 – 402, 1995.

[2] Kenny Q. Ye, William Li, and Agus Sudjianto. Algorithmic construction of optimal symmetric Latin hypercube designs. Journal of Statistical Planning and Inference, 90(1):145 – 159, 2000.

[3] Ruichen Jin, Wei Chen, and Agus Sudjianto. An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference, 134(1):268 – 287, 2005.

[4] A. Grosso, A.R.M.J.U. Jamali, and M. Locatelli. Finding maximin Latin hypercube designs by Iterated Local Search heuristics. European Journal of Operational Research, 197(2):541 – 547, 2009.

[5] Stuart J. Bates, Johann Sienz, and Vassili V. Toropov. Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm. AIAA 2004-2011, pages 1–7.