建構序列式克利金模式求解全域隨機最佳化問題

Stochastic Global Optimization Using Sequential Kriging Metamodeling

盧彥含(Lu, Yan Han)

指導教授 ： 張國浩

國立清華大學/工學院/工業工程與工程管理學系/碩士(2015年)

摘要

隨機最佳化問題存在於許多領域上，舉凡財金、醫療、電子、製藥產業等，所謂的隨機問題為目標式內含著不確定性，由於不確定性的存在使得在搜尋全域性最佳解的過程中十分地困難，因此本研究目的為發展新的演算法以解決隨機最佳化問題。發展之演算法為使用全域性的搜索方式找出最佳解，其架構為建構序列性的克利金反應曲面以預測目標值，並結合了核密度估計的方式以建構最佳解所在位置之機率密度函數讓我們可以有效地搜尋到最佳解。數值實驗以及個案實證結果均顯示此方法能夠有效地解決隨機最佳化的問題。

關鍵字

隨機最佳化 ； 全域最佳化 ； 克利金模型 ； 核密度估計

並列摘要

Stochastic global optimization refers an iterative procedure in attempt to find the global optima in the parameter space when the objective function can be estimated with noise. Due to the noise inherent in the objective value, the problem is difficult to be solved, especially when the time given to solve the problem is limited, which is usually the case in practice. In this research, we propose a framework that allows the stochastic global optimization problem to be solved efficiently. The proposed framework sequentially builds a Kriging metamodel based on kernel density estimation for predicting the functional behavior of the objective function and solves for the optimal solution of the metamodel. Numerical experiments show that its efficiency is satisfactory.

並列關鍵字

Stochastic optimization ； Global optimization ； Kriging metamodeling ； Kernel density estimation

參考文獻

Anderson, E. J., & Ferris, M. C. (2001). A direct search algorithm for optimization with noisy function evaluations. SIAM Journal on Optimization, 11(3), 837-857.

Angün, E., & Kleijnen, J. (2012). An asymptotic test of optimality conditions in multiresponse simulation optimization. INFORMS Journal on Computing, 24(1), 53-65.

Ankenman, B., Nelson, B. L., & Staum, J. (2010). Stochastic kriging for simulation metamodeling. Operations Research, 58(2), 371-382.

Bansal, S. (2002). Promise and problems of simulation technology in SCM domain. Proceedings of the 2002 Winter Simulation Conference, 2, 1831-1837.

Bierens, H. J. (1987). Kernel estimators of regression functions. Advances in Econometrics: Fifth World Congress, 1, 99-144.