Season 3

Multi-stage mixed-integer robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision making under uncertainty. In this talk, I will propose solution methods for  two-stage and multi-stage versions of such problems. For the first, we will construct piecewise constant decision rules by adaptively partitioning the uncertainty set. The partitions of this set are iteratively updated by separating so-called critical scenarios. We discuss how to identify such critical scenarios based on the branch-and-bound procedure for solving the current corresponding static problem. For multi-stage robust mixed-integer programs, we will consider a finite adaptability scheme, which allows us to decompose the multi-stage problem into a large number of much simpler two-stage problems. We discuss how these two-stage problems can be solved both exactly and approximately, and we report numerical results for route planning and location-transportation problems.

Ward Romeijnders is a full professor within the Department of Operations at the University of Groningen. His research is focused on developing exact and approximate solution methods for integer optimization problems under uncertainty. This class of problems can be used to support decision making under uncertainty for a wide range of applications in, e.g., energy, healthcare, logistics, and finance. Ward publishes his research in journals such as Operations Research, Mathematical Programming, SIAM Journal on Optimization, European Journal of Operational Research, and INFORMS Journal on Computing, and he is Associate Editor of Mathematical Methods of Operations Research. He has received several research grants from the Netherlands Organisation for Scientific Research, the latest one for a project called "Discrete Decision Making under Uncertainty".

We present two machine learning methods to learn uncertainty sets in decision-making problems affected by uncertain data.  In the first part, we introduce mean robust optimization (MRO), a framework that constructs data-driven uncertainty sets based on clustered data rather than on observed data points directly. By varying the number of clusters, MRO balances computational complexity and conservatism, and effectively bridges robust and Wasserstein distributionally robust optimization.  In the second part, we present LRO, a method to automatically learn the shape and size of the uncertainty sets in robust optimization.  LRO optimizes the performance across a family of parametric problems, while guaranteeing a target probability of constraint satisfaction.  It relies on a stochastic augmented Lagrangian method that differentiates the solutions of robust optimization problems with respect to the parameters of the uncertainty set. Our approach is very flexible, and it can learn a wide variety of uncertainty sets commonly used in practice.  We illustrate the benefits of our two machine learning methods on several numerical examples, obtaining significant reductions in computational complexity and conservatism, while preserving out-of-sample constraint satisfaction guarantees.

Bartolomeo Stellato is an Assistant Professor in the Department of Operations Research and Financial Engineering at Princeton University. Previously, he was a Postdoctoral Associate at the MIT Sloan School of Management and Operations Research Center. He received a DPhil (PhD) in Engineering Science from the University of Oxford, a MSc in Robotics, Systems and Control from ETH Zurich, and a BSc in Automation Engineering from Politecnico di Milano. He is the developer of OSQP, a widely used solver in mathematical optimization. Bartolomeo Stellato's awards include the NSF CAREER Award, the Princeton SEAS Howard B. Wentz Jr. Faculty Award, the Franco Strazzabosco Young Investigator Award from ISSNAF, the Princeton SEAS Innovation Award in Data Science, the Best Paper Award in Mathematical Programming Computation, and the First Place Prize Paper Award in IEEE Transactions on Power Electronics. His research focuses on data-driven computational tools for mathematical optimization, machine learning, and optimal control.

We study network design problems for nonlinear and nonconvex flow models under demand uncertainties. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, demand scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all demand uncertainties, if and only if a finite number of worst-case demand scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future demand fluctuations.

Johannes Thürauf is a postdoctoral researcher at Trier University since 11/2021. He studied Mathematics at the Friedrich-Alexander Universität (FAU) Erlangen-Nürnberg and received his M.Sc. degree in 2017. Afterward, he worked as a PhD student at the FAU Erlangen-Nürnberg and got his PhD at the end of 2021. His main research interests include robust and bilevel optimization (under uncertainty), for example with applications to networks. In particular, he is interested in the interplay of robust and bilevel optimization.

We address a continuous-time continuous-space stochastic optimal control problem where the controller lacks exact knowledge of the underlying diffusion process. Instead, the controller relies on a finite set of historical disturbance trajectories. To tackle this challenge, we propose a novel approach called Distributionally Robust Path Integral control (DRPI). This method utilizes distributionally robust optimization (DRO) to make the resulting policy robust against the unknown diffusion process. Notably, the DRPI scheme bears resemblance to risk-sensitive control, allowing us to leverage the path integral control (PIC) framework as an efficient solution method. We establish theoretical performance guarantees for the DRPI scheme, which facilitates the determination of an appropriate risk parameter for the risk-sensitive control. Through extensive validation, we demonstrate the effectiveness of our approach and its superiority over risk-neutral and risk-averse PIC policies in scenarios where the true diffusion process is unknown.

Grani A. Hanasusanto is an Associate Professor of Industrial & Enterprise Systems Engineering at the University of Illinois Urbana-Champaign (UIUC). Before joining UIUC, he was an Assistant Professor at The University of Texas at Austin and a Postdoctoral Scholar at the College of Management of Technology at École Polytechnique Fédérale de Lausanne. He holds a Ph.D. in Operations Research from Imperial College London and an MSc in Financial Engineering from the National University of Singapore. His research focuses on developing tractable solution schemes for decision-making problems under uncertainty, with applications spanning operations management, energy systems, finance, data analytics, and machine learning. He is a recipient of the NSF CAREER award and the INFORMS Diversity, Equity, and Inclusion (DEI) Ambassadors Program award. He currently serves as a committee member of the INFORMS Diversity Community and an Associate Editor for Operations Research.

In this talk, we focus on static robust optimization problems where the uncertainty set can be controlled through the actions of the decision maker known as decision-dependent uncertainty. Particularly, we consider an uncertainty reduction paradigm where the decision-maker can reduce upper bounds of uncertain parameters as a result of some proactive actions. This paradigm was recently proposed in the literature and the resulting problems were shown to be NP-Hard.  In this talk, we pay particular attention to the special case of robust combinatorial optimization problems, and show that they are also NP-Hard under the uncertainty reduction paradigm. Despite this discouraging result, we show that under some additional assumptions polynomial-time algorithms can be devised to solve robust combinatorial optimization problems with uncertainty reduction. We additionally provide insights into possible MILP reformulations in the general case and illustrate the practical relevance of our results on the shortest path instances from the literature.

Ayse N. Arslan is a junior researcher at Inria Center of Bordeaux. Her research interests lie at the intersection of mixed-integer programming and optimization under uncertainty with a particular focus on stochastic and robust optimization and their applications. Some of her recent work includes decomposition algorithms for solving two-stage robust optimization problems and primal and dual decision rules for approximating multi-stage robust optimization problems.

In this talk, we will present our new inexact column-and-constraint generation (i-C&CG) method for solving challenging two-stage robust and distributionally robust optimization problems. In our i-C&CG method, the master problems only need to be solved to a prescribed relative optimality gap or time limit, which may be the only tractable option when solving large-scale and/or challenging problems in practice. We equip i-C&CG with a backtracking routine that controls the trade-off between bound improvement and inexactness. Importantly, this routine allows us to derive theoretical finite convergence guarantees for our i-C&CG method, demonstrating that it converges to the exact optimal solution under some parameter settings. Numerical experiments on a scheduling problem and a facility location problem demonstrate the computational advantages of our i-C&CG method over a state-of-the-art C&CG method.

Dr. Karmel S. Shehadeh is an Assistant Professor in the Department of Industrial and Systems Engineering at Lehigh University. Before joining Lehigh, she was a presidential and dean postdoctoral fellow at Heinz College of Information Systems and Public Policy at Carnegie Mellon University. She holds a doctoral degree in Industrial and Operations Engineering from the University of Michigan, a master's degree in Systems Science and Industrial Engineering from Binghamton University, and a bachelor's in Biomedical Engineering from Jordan University of Science and Technology. Her research interests revolve around stochastic and robust optimization with applications to healthcare operations and analytics, facility location, transportation systems, and fair decision-making. Professional recognition of her work includes an INFORMS Minority Issues Forum Paper Award (winner), Junior Faculty Interest Group Paper Prize (finalist), Service Science Best Cluster Paper Award (finalist), and Lehigh's Alfred Noble Robinson Faculty Award.

In combinatorial optimization problems under budget uncertainty the solution space is deterministic, but the objective is uncertain. By the seminal work of Bertsimas & Sim (2003, 2004), such problems can be solved in various ways: by separating constraints bounding the objective, by a compact reformulation, or by solving n+1 deterministic problems of the same type. Although the complexity of the problem does not increase in theory, in many cases the performance deteriorates significantly. 

In this talk, we show two ways to enhance the computation times of the compact reformulation: (i) recycling valid inequalities known for the deterministic problem yielding surprisingly strong valid inequalities for the robust problem and (ii) a tailored branch and bound algorithm performing a tree search on one of the dual variables. This is joint work with Timo Gersing and Christina Büsing.

Arie M.C.A. Koster is since 2009 a Professor of Mathematics at RWTH Aachen University. Before, he received his PhD from Maastricht University and worked at Zuse Institute Berlin and University of Warwick. His research interests include integer linear programming, polyhedral combinatorics, robust optimization, algorithmic graph theory, and network optimization. He has published over 100 research papers and is on the editorial board of Annals of Operations Research, INFORMS Journal on Computing, and Networks.

We study inventory control with volume flexibility: A firm can replenish using period-dependent base capacity at regular sourcing costs and access additional supply at a premium. The optimal replenishment policy is characterized by two period-dependent base-stock levels but determining their values is not trivial, especially for nonstationary and correlated demand. We propose the Lookahead Peak-Shaving policy that anticipates and peak shaves orders from future peak-demand periods to the current period, thereby matching capacity and demand. Peak shaving anticipates future order peaks and partially shifts them forward. This contrasts with conventional smoothing, which recovers the inventory deficit resulting from demand peaks by increasing later orders. Our contribution is threefold. First, we use a novel iterative approach to prove the robust optimality of the Lookahead Peak-Shaving policy. Second, we provide explicit expressions of the period-dependent base-stock levels and analyze the amount of peak shaving. Finally, we demonstrate how our policy outperforms other heuristics in stochastic systems. Most cost savings occur when demand is nonstationary and negatively correlated, and base capacities fluctuate around the mean demand. Our insights apply to several practical settings, including production systems with overtime, sourcing from multiple capacitated suppliers, or transportation planning with a spot market. Applying our model to data from a manufacturer reduces inventory and sourcing costs by 6.7%, compared to the manufacturer's policy without peak shaving.

This is a joint work with Joren Gijsbrechts, Robert N. Boute, Jan A. Van Mieghem.

Christina Imdahl is Assistant Professor of Machine Learning in Operations Management at the OPAC group of Eindhoven University of Technology (TU/e). Christina's research is focuses on decision-making in operations management. She develops models that are motivated by operational practice and explores how we can leverage data to make better decisions. In her research, she combines the use of stochastic and robust optimization with empirical analyses to gain insights into performance.