We consider the optimal computing budget allocation problem to select the nondominated systems on finite sets under a stochastic multi-objective ranking and selection setting. This problem has been addressed in the settings of correct selection guarantee when all the systems have normally distributed objectives with no correlation within and between solutions. We revisit this problem from a large deviation perspective and present a mathematically robust formulation that maximizes the lower bound of the rate function of the probability of false selection ( $P(\text{FS})$) defined as the probability of not identifying the true Pareto set. The proposed formulation allows general distributions and explicitly characterizes the sampling correlations across performance measures. Three budget allocation strategies are proposed. One of the approaches is guaranteed to attain the global optimum of the lower bound of the rate function but has high computational cost. Therefore, a heuristic to approximate the global optimal strategy is proposed to save computational resources. Finally, for the case of normally distributed objectives, a computationally efficient procedure is proposed, which adopts an iterative algorithm to find the optimal budget allocation. Numerical experiments illustrate the significant improvements of the proposed strategies over others in the existing literature in terms of the rate function of $P(\text{FS})$.

中文翻译：

---

选择非支配系统的最优计算预算分配——大偏差视角

我们考虑最优计算预算分配问题，以在随机多目标排序和选择设置下选择有限集上的非支配系统。当所有系统具有正态分布目标且在解决方案内和解决方案之间没有相关性时，该问题已在正确选择保证的设置中得到解决。我们从大偏差的角度重新审视这个问题，并提出了一个数学上稳健的公式，该公式最大化错误选择概率（$P（\text{FS}）$）的比率函数的下界，定义为无法识别的概率真帕累托集。提议的公式允许一般分布并明确表征跨性能度量的采样相关性。提出了三种预算分配策略。其中一种方法可以保证获得速率函数下界的全局最优，但计算成本很高。因此，提出了一种近似全局最优策略的启发式算法以节省计算资源。最后，对于正态分布目标的情况，提出了一种计算效率高的程序，该程序采用迭代算法来寻找最佳预算分配。数值实验表明，在 $P(\text{FS})$ 的速率函数方面，所提出的策略比现有文献中的其他策略有显着改进。对于正态分布目标的情况，提出了一种计算效率高的程序，该程序采用迭代算法来寻找最佳预算分配。数值实验表明，在 $P(\text{FS})$ 的速率函数方面，所提出的策略比现有文献中的其他策略有显着改进。对于正态分布目标的情况，提出了一种计算效率高的程序，该程序采用迭代算法来寻找最佳预算分配。数值实验表明，在 $P(\text{FS})$ 的速率函数方面，所提出的策略比现有文献中的其他策略有显着改进。