An epsilon-constraint method for integer-ordered bi-objective simulation optimization
An epsilon-constraint method for integer-ordered bi-objective simulation optimization
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DOI：
10.1109/wsc.2017.8247961
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
K. Cooper;S. R. Hunter;K. Nagaraj
中科院分区：
文献类型：
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作者：
K. Cooper;S. R. Hunter;K. Nagaraj
考虑整数排序的双目标模拟优化的上下文，其中可行区域是整数晶格的有限子集。我们提出了一个回顾性近似（RA）框架，以识别一个局部帕累托集，该集合涉及在增加样本量时解决一系列样品path双聚目标优化问题。我们将Epsilon-constraint方法应用于每个样品path生物原则优化问题，从而解决了每种RA迭代中约束的单目标问题的序列。我们使用样条算法解决了每个受约束的单目标优化问题，从而利用基于梯度的信息。在早期的RA迭代中，当样本量很小并且标准误差相对较大时，我们仅通过使Epsilon-constraint问题的数量成为标准误差的函数来对帕累托设置的粗略表征。随着RA算法的进展，表征的粒度增加了，直到我们解决尽可能多的Epsilon-constraint问题，因为局部帕累托集的（有限）图像中的一点。我们的算法显示有希望的数值性能。
Consider the context of integer-ordered bi-objective simulation optimization, in which the feasible region is a finite subset of the integer lattice. We propose a retrospective approximation (RA) framework to identify a local Pareto set that involves solving a sequence of sample-path bi-objective optimization problems at increasing sample sizes. We apply the epsilon-constraint method to each sample-path biobjective optimization problem, thus solving a sequence of constrained single-objective problems in each RA iteration. We solve each constrained single-objective optimization problem using the SPLINE algorithm, thus exploiting gradient-based information. In early RA iterations, when sample sizes are small and standard errors are relatively large, we provide only a rough characterization of the Pareto set by making the number of epsilon-constraint problems a function of the standard error. As the RA algorithm progresses, the granularity of the characterization increases until we solve as many epsilon-constraint problems as there are points in the (finite) image of the local Pareto set. Our algorithm displays promising numerical performance.