Discrete Optimization under Interactions and Uncertainty

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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.