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光华讲坛—【鲁棒与随机优化系列讲座(一)】The Dao of Robustness

发布时间:2021-04-07

主题【鲁棒与随机优化系列讲座(一)】The Dao of Robustness

主讲人新加坡国立大学 Melvyn Sim教授

主持人工商管理学院 寇纲教授

时间2021年4月8日(周四)14:00-15:30

直播平台及会议ID腾讯会议 会议ID:856 207 699(密码:123456)

主办单位:工商管理学院 科研处


主讲人简介:

Dr. Melvyn Sim is Professor and Provost's Chair at the Department of Analytics & Operations, NUS Business school. His research interests fall broadly under the categories of decision making and optimization under uncertainty with applications ranging from finance, supply chain management, healthcare to engineered systems. He is one of the active proponents of robust optimization and has given invited talks in this field at international conferences. Dr. Sim serves as a Department Editor of Manufacturing & Service Operations Management, and as an Associate Editor for Operations Research, Management Science, Mathematical Programming Computations and INFORMS Journal on Optimization.

Melvyn Sim,新加坡国立大学商学院分析与运营系教授兼系主任,主要研究方向是不确定性下的决策和优化,及其在金融、供应链管理、医疗、工程系统等领域的应用,是鲁棒优化的重要推动者之一,并受邀在该领域的国际会议上发表演讲。现担任《Manufacturing & Service Operations Management》期刊的区域主编,及《Operations Research》、《Management Science》、《Mathematical Programming Computations》和《INFORMS Journal on Optimization》期刊的副主编。


内容提要:

We present a general framework for data-driven optimization called robustness optimization that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution deviates from the empirical distribution. Unlike robust optimization approaches, the decision maker does not have to size the ambiguity set, but specifies an acceptable target, or loss of optimality compared to the empirical optimization model, as a trade off for the model’s ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robustness optimization, termed as the fragility measure, and present its representation theorem. Focusing on Wasserstein distance measure with l1-norm, we present tractable robustness optimization models for risk-based linear optimization, combinatorial optimization, and linear optimization problems with recourse. Serendipitously, the insights to the approximation also provide a recipe for approximating solutions for hard stochastic optimization problems without relatively complete recourse. We perform numerical studies on a portfolio optimization problem and a network lot-sizing problem. We show that the solutions to the robustness optimization models are more effective in improving the out-of-sample performance evaluated on a variety of metrics, hence alleviating the Optimizer’s Curse.

本研究提出一种数据驱动的一般优化框架——鲁棒性优化,即使在实际概率分布偏离经验分布的情况下,该框架仍支持考虑风险的目标函数能在可接受范围内找到最好的解决方案。与鲁棒优化方法不同,决策者不必给定模糊集的大小,而是指定一个可接受的目标,或指定与经验优化模型相比的最优性损失值,以作为模型对承受更大不确定性能力的补偿。同时公理化与鲁棒性优化相关的决策准则,即脆弱性测度,并给出它的表示定理,针对l1范数的Wasserstein距离,提出基于风险的线性优化、组合优化和带补偿的线性优化问题的鲁棒性优化模型,对近似理论的研究也为不具备完全补偿矩阵的随机优化问题提供了近似的解决方案。此外,投资组合优化问题和网络批量计划问题的算例实验表明,鲁棒性优化模型的解决方案在提高样本性能评估的各项指标上更有效,因此能够减轻“最优解的诅咒”。



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