Discrete Optimization under Interactions and Uncertainty

该研究计划的目的是开发新的工具和方法来解决离散优化问题中的相互作用和不确定性。 决策中的交互被定义为与决策相对应的解决方案成本/收益受到其他决策影响（即非加性效应）的情况，并且是决策之间的依赖性或大规模随机数据中的相关性的结果。在建模方面，挑战在于开发集成多个因素的模型，例如可靠性、成本/收入以及数据中的相互作用和不确定性。在方法论方面，挑战在于开发能够处理模型的规模、不确定性和非线性的大规模优化技术。 使用随机和相关数据进行路由优化：当在存在大规模随机数据的情况下做出决策时，通常会更多地关注易于查看的统计数据（例如平均值），而不是潜在的复杂相关性。在数据存在显着相关性的情况下，这使得研究与现实之间存在很大差距。本研究方向的目标是研究不同类型的不确定和相关数据参数下公共交通和送货上门服务的路径优化。这包括开发基于过去的观察和决策者对风险的态度构建不确定性集的方法，以及设计易于处理的优化算法来处理这些数据驱动模型中的交互。具有交互作用的枢纽网络设计：具有单一分配的枢纽位置的经典模型过于简单化。最突出的缺点是线性化运输成本、确定性数据以及没有关于枢纽规模和类型的结构选择。而且，在轴辐式结构的包裹投递中，很多问题都是为分配到每个枢纽的车辆建立本地巡回赛，然后由这些车辆负责取件和投递任务。在这些问题中，路由之间是否存在交互是一个关键问题，需要明确考虑。此外，枢纽选址问题属于战略决策的范畴，有关网络的确切信息通常是不确定的。该方向的目标是以适当的方式解决上述挑战，一方面捕获现实世界的问题，另一方面在计算上易于处理。特别是，拟议的研究计划将研究具有非线性结构的大规模优化模型的新技术，这需要对潜在问题有更深入的了解。

The aim of this research program is to develop new tools and methodologies to address interactions and uncertainty in discrete optimization problems. Interactions in decision-making are defined as situations where the solution cost/benefit corresponding to a decision is affected (i.e., non-additive effects) by other decisions and are either the result of dependency between decisions or correlation in large-scale stochastic data. On the modeling side, the challenge is in developing models that integrate a plurality of factors such as reliability, costs/revenue, as well as the interactions and uncertainties in data. On the methodological side, the challenge is in developing large scale optimization techniques that can handle the scale, the uncertainty, and the nonlinearity of the models. Routing optimization with stochastic and correlated data: When decisions are made in the presence of large-scale stochastic data, it is common to pay more attention to the easy-to-see statistics (e.g., mean) instead of the underlying complex correlations. This puts a large gap between the research and reality in situations where significant correlations exist in data. The objective of this research direction is to study routing optimization in public transport and home delivery services under different types of uncertain and correlated data parameters. This includes developing methodologies to construct uncertainty sets based on past observations and the decision maker's attitude towards risk as well as designing tractable optimization algorithms to handle interactions in these data driven models. Hub network design with interactions: The classical models for hub location with single assignment suffer from oversimplification. The most prominent shortcomings are linearized transport costs, deterministic data and no structural choice about the size and kind of hub. Moreover, in many problems in parcel delivery with hub-and-spoke structure, local tours are established for the vehicles assigned to each hub, which are then responsible for the pickup and delivery tasks. In these problems, the presence of interaction between route is a critical issue and it needs to be considered explicitly. Furthermore, hub location problems belong to the category of strategic decisions and the exact information about the network is usually uncertain. The objective of this direction is to address the aforementioned challenges in a proper way such that it captures the real-world concerns, on the one hand, and be computationally tractable, on the other hand. In particular, the proposed research program will investigate new techniques for large scale optimization models with nonlinear structure which would require a deeper understanding of the underlying problems.