Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling
Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling
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DOI：
10.1287/ijoc.1050.0141
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
M. Fu;Jianqiang Hu;Chun-Hung Chen;X. Xiong
中科院分区：
文献类型：
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作者：
M. Fu;Jianqiang Hu;Chun-Hung Chen;X. Xiong
我们考虑有效分配仿真复制的问题，以便在存在相关性的情况下对系统性能进行采样的情况下最大化选择最佳设计的概率。在两种设计的情况下，我们能够准确地推导出最优分配，并发现在存在正相关的情况下，除非一种设计的方差明显大于另一种设计的方差，否则模拟重复的次数应该相同。在扩展到一般数量的竞争设计时，获得了渐近最优分配的近似值。当相关性消失时，该近似值与先前在极限条件下导出的独立情况一致，并且也与两种设计的精确解一致。此外，就设计之间的相关性和相对方差的关系而言，结果规定的分配似乎符合直觉，再次表明，对于足够高的正相关性来说，平等分配是最佳的。提出了一种基于近似的分配算法，并在几个数值例子上进行了测试。
We consider the problem of efficiently allocating simulation replications in order to maximize the probability of selecting the best design under the scenario in which system performances are sampled in the presence of correlation. In the case of two designs, we are able to derive the optimal allocation exactly, and find that in the presence of positive correlation, unless the variance of one design is significantly larger than that of the other, the number of simulation replications should be identical. In extending to a general number of competing designs, an approximation for the asymptotically optimal allocation is obtained. The approximation coincides with the independent case derived previously in the limit as the correlation vanishes and also agrees with the two-design exact solution. Furthermore, the allocations prescribed by the results seem to match intuition, in terms of the relationship to correlations and relative variances between designs, again suggesting that equal allocation is optimal for sufficiently high positive correlation. An allocation algorithm based on the approximation is proposed and tested on several numerical examples.