报告内容摘要

Despite the recent advancements in mathematical programming techniques, solving large-scale optimization problems is still a challenging task for many practical applications. For some problems where the evaluation of the objective function is subject to random noise, finding the optimal solutions is even more difficult. This talk will present two efficient sampling techniques for large-scale optimization and simulation optimization respectively.

First, a new statistical sampling and optimization framework for large-scale optimization is presented. The new method is called peak-over-threshold search (POTS). POTS uses the partitioning idea and iteratively moves to the promising subregion of the solution space for sampling. When comparing the quality of several subregion alternatives, POTS constructs a generalized Pareto distribution (GPD) to model the behavior of the extreme of each subregion. This method is shown to converge with probability one to the optimal region. Numerical examples are also presented to demonstrate the effectiveness of this new method.

Second, we consider the sample allocation problem of selecting the best simulated design from a finite set of alternatives in simulation optimization. Due to the slow convergence of performance, efficiency is a major concern when conducting simulation experiments, and as a result, the research in sample allocation has drawn more and more attention recently. In this research, we assess the quality of the selection by the expected opportunity cost, which is a wildly used measure in business, engineering, and other applications where design performance represents economic value. We characterize the optimal sample allocation rule that minimizes the expected opportunity cost and develop a corresponding sequential algorithm for the implementation purpose. Numerical experiments indicate that the resulting allocation is superior to other methods in the literature

报告人简介

Siyang Gao received the B.S. degree in Mathematics from Peking University, Beijing, China, in 2009, and the Ph.D. degree in Industrial Engineering from University of Wisconsin-Madison, Madison, WI, in 2014. Dr. Gao is an Assistant Professor with the Department of Systems Engineering and Engineering Management, City University of Hong Kong. His research is devoted to simulation optimization, large-scale optimization and radiation treatment. His work has appeared in IEEE Transactions on Automation Science and Engineering, Physics in Medicine and Biology, and etc. Dr. Gao is a member of the Institute for Operations Research and the Management Sciences (INFORMS).

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