SCORE Allocations for Bi-objective Ranking and Selection
SCORE Allocations for Bi-objective Ranking and Selection
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DOI：
10.1145/3158666
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发表时间：
2018-01
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通讯作者：
Guy Feldman;S. R. Hunter
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作者：
Guy Feldman;S. R. Hunter
双目标排名和选择（R8S）问题是多目标模拟优化问题的一种特殊情况，其中仅通过依赖的蒙特卡洛估计量，决策空间或系统数量有限，并且每个系统都知道两个相互矛盾的目标。可以在某种程度上进行采样。对双目标R8S问题的解决方案是一组具有非主导目标向量的系统，称为帕累托系统集。我们利用双目标问题的特殊结构来表征渐近的最佳模拟预算分配，这解释了目标与平衡与两种类型的错误分类错误相关的概率之间的依赖性。像大多数R8文献一样，我们的重点是模拟观测值双变量正常的情况。假设正态性，我们使用一定的渐近限制来得出使用速率估计器（得分）采样框架进行优化的易于实现的采样标准，该框架近似于最佳分配并说明目标之间的相关性。也许令人惊讶的是，限制分数分配专门控制划分划分的事件，其中非pareto系统被错误地估计为帕累托。我们还为实施提供了一种迭代算法。我们在最终的得分框架上的数值经验表明，对于拥有多达一万个系统的问题，它是快速准确的。
The bi-objective ranking and selection (R8S) problem is a special case of the multi-objective simulation optimization problem in which two conflicting objectives are known only through dependent Monte Carlo estimators, the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the bi-objective R8S problem is a set of systems with non-dominated objective vectors, called the set of Pareto systems. We exploit the special structure of the bi-objective problem to characterize the asymptotically optimal simulation budget allocation, which accounts for dependence between the objectives and balances the probabilities associated with two types of misclassification error. Like much of the R8S literature, our focus is on the case in which the simulation observations are bivariate normal. Assuming normality, we then use a certain asymptotic limit to derive an easily-implementable Sampling Criteria for Optimization using Rate Estimators (SCORE) sampling framework that approximates the optimal allocation and accounts for correlation between the objectives. Perhaps surprisingly, the limiting SCORE allocation exclusively controls for misclassification-by-inclusion events, in which non-Pareto systems are falsely estimated as Pareto. We also provide an iterative algorithm for implementation. Our numerical experience with the resulting SCORE framework indicates that it is fast and accurate for problems having up to ten thousand systems.