EURO Doctoral Dissertation Award 2025 - Finalists

The Four finalists of the 2025 EURO Doctoral Dissertation Award are:

Hannah Bakker, Karlsruhe Institute of Technology

On the Interplay Between Data and Decisions in Discrete Location Problems

The Capacitated Facility Location Problem (CFLP) is a core problem in location science and has been studied from various angles. Yet, key questions remain: Why does the runtime of state-of-the-art MIP solvers differ drastically between seemingly similar problem instances? Why does modeling temporal dynamics in a multi-period setting significantly improve the objective in some cases but is negligible in others? When the model and algorithm are fixed, such differences must stem from the problem data.
We propose a novel methodology that characterizes instances by analyzing the degree of interdependence among facility location decisions in well-performing (optimal or near-optimal) solutions. By distinguishing between instances with mostly independent facilities and those with strong interdependencies, we can anticipate and explain differences in algorithm performance and the impact of modeling extensions. It further allows us to partition candidates and customers into regions with high internal interdependence, offering new insights for algorithm design.
Our approach combines the use of state-of-the-art MIP solvers on simplified (relaxed or restricted) problem versions with efficient analytics tools. The results demonstrate how advances in computational power not only expand solvability but also open up new perspectives on long-studied problems like the CFLP.

Jesús Camacho, Miguel Hernández University of Elche

Semilocal Lipschitz Stability in Linear Optimization

In the realm of mathematical programming, particularly optimization, the concept of stability has gained significant importance. When faced with a choice between a perfectly optimal solution that is highly sensitive to small changes in the problem parameters and a slightly suboptimal solution that remains reliable under such variations, practitioners often prefer the latter. This is because real-world problems are often subject to uncertainties and approximations.
This work delves into the quantitative stability of solutions to linear optimization problems, a field with theoretical roots dating back to the 1950s. We explore how the set of feasible solutions and the set of optimal solutions change when the parameters defining the problem are altered. Understanding these changes is crucial for assessing the reliability and robustness of our optimization models.
We investigate different ways to measure this stability, categorized by the extent of the parameter and solution variations considered. Local stability measures focus on how solutions behave under small changes in the parameters around a specific nominal problem and solution. Semilocal measures examine the variation of the entire solution set when the parameters undergo small perturbations. Finally, global stability measures are concerned with the behavior of solutions across all possible parameter values. These different types of stability can be quantified using associated sharp Lipschitz constants, often referred to as moduli.
Our analysis covers various aspects of linear optimization problem stability under different types of perturbations. A significant portion is dedicated to perturbations of the right-hand side (RHS) of the constraints, as well as perturbations of the objective function. For these scenarios, we derive formulas for different stability moduli, often expressed as the maximum of finitely many local stability measures.
We also address the more complex case where the left-hand side coefficients of the constraints are subject to change. This is approached using the framework of the "radius theorem," which seeks to determine the smallest perturbation that would cause a certain desirable property (related to stability) to fail.
Furthermore, this work explores the connection between monotone operator theory and feasibility problems. By leveraging concepts from convex analysis and monotone operators, we provide new perspectives on analyzing and solving feasibility problems, including finding the smallest perturbation to an inconsistent system to make it feasible. This includes developing procedures to estimate and calculate the distance to feasibility for inconsistent convex inequality systems.
In summary, this work provides a comprehensive analysis of the stability of linear optimization problems under various types of perturbations. It offers tools and insights for quantifying this stability through different moduli and explores novel approaches to feasibility problems using concepts from variational analysis and monotone operator theory. The results aim to bridge the gap between theoretical analysis and practical considerations in optimization, enabling a better understanding and management of the sensitivity of optimization solutions to problem variations.

Pierluigi Mansueto, University of Florence

Pareto Front Reconstruction of Multi-Objective Optimization Problems

The thesis is concerned with multi-objective optimization (MOO) problems under various constraint types. In particular, we consider the unconstrained, the box constrained, the general convex constrained and the cardinality constrained settings. As a mathematical tool, MOO has received much attention over the years, being suitable both in operation research applications and in many real-world problems where contrasting goals have to be taken into account. In the dissertation, a general overview of the main MOO concepts is given, focusing on the notions typically employed in the gradient-based MOO approaches. In particular, we present a general formulation for the search direction problem and a general framework for single-point methodologies, i.e., approaches designed to generate a single solution to the problem at hand. The features of each of the two concepts are discussed and analyzed; finally, we show how they can be reduced to well-known schemes from the MOO literature. Then, we propose novel gradient-based methodologies aimed to reconstruct the Pareto front for the considered problem classes. In some of the mentioned settings it is the first attempt to define this type of approaches generating multiple solutions rather than one, while in the others the topic has been almost unexplored yet. However, in the MOO context, returning an approximation of the Pareto front rather than a single solution can be much more useful for the final user, so as they can choose among multiple tradeoffs of the objectives the one that is the most suitable for themselves. For each methodology, detailed descriptions of the algorithmic scheme and characteristic features are reported; moreover, each methodology is theoretically analyzed and its convergence properties are stated and proved. Finally, the proposed methods are numerically tested with wide benchmarks of test problems, comparing each of them with state-of-the-art approaches from the MOO literature. The results show the efficiency and the effectiveness of the proposals w.r.t. the competitors in diverse experimental settings.

Yasmine Beck, ESSEC Business School

Mixed-Integer Optimization Techniques for Robust Bilevel Problems with Here-and-Now Followers

In bilevel optimization, some variables of an optimization problem have to be an optimal solution to another nested optimization problem. This structure makes bilevel optimization a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. However, due to their nature of combining two different decision-makers in one model, bilevel problems are inherently hard to solve. Further challenges arise if problems under uncertainty are considered.
In this talk, we address different types of uncertainty in bilevel optimization using techniques from robust optimization. In particular, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to single-level optimization since not only the problem data but also the (observation of the) decisions of the two players can be uncertain. To address data uncertainty in mixed-integer linear bilevel problems, we present exact branch-and-cut approaches with cuts tailored to the important class of monotone interdiction problems, which frequently arise in critical infrastructure defense and counterterrorism. Given their overall hardness, we also propose heuristics for these problems that do not require problem-specific tailoring. Finally, we study the problem of determining optimal tolls in a traffic network in which the network users hedge against uncertain travel costs in a robust way.