DC 12 – Advances on optimisation under uncertainty

Project Title: Advances on optimisation under uncertainty
Doctoral Candidate: N.N.
Host Institution: University of Bologna
Supervisors: Enrico Malaguti, Christoph Buchheim

Objectives: We will consider optimisation problems under uncertainty. Classical approaches are stochastic optimisation and robust optimisation. While the former produces mathematical models of very large size, which may limit its practical applicability, the latter may be overconservative, producing low-quality solutions. Our objective is to introduce mathematical formulations and computational approaches for handling uncertainty, without strictly following the classical paradigms. We will investigate the following 3 approaches: 1) bulk optimisation, which is typically used when the problem asks to select a subset of items with some property. Here, instead of producing one or more solutions, one looks for a superset of items that includes a feasible solution for each possible realisation of uncertainty; 2) adaptability, which finds applications in contexts where the decisions have to be taken at different times; e.g., in 2-stage optimisation some decisions are taken immediately, and other decisions can be postponed, after that uncertainty materializes. In k-adaptability, the first stage consists in computing a set of k solutions (where k is a parameter), whereas the second stage consists in selecting one of these solutions; 3) chance-constrained optimisation, which consists in relaxing some hard constraints and requiring them to be satisfied with a given (large) probability. This paradigm avoids overconservative solutions and produces models that can be solved efficiently in practice.

Expected Results: Some of the aforementioned frameworks lack computational methodologies for effectively approaching specific cases involving integer variables and/or nonlinear objective functions and constraints. We expect to contribute to filling this gap. In addition, we are interested in hybridizing those paradigms, e.g., considering (k-)Adaptability with chance-constraints.

Planned secondment: 6 months at TUDO (C. Buchheim) during the 2nd year for studying complexity of uncertain optimisation problems; 3 months at Schenker (I. Hedtke) at the beginning of the 3rd year to evaluate applicability of robust optimisation to the practical transportation and logistics context.

Degree awarding institution: University of Bologna

Note: The DC will be hired by the University of Bologna under a “Research  Appointment” in accordance with Italian regulations. This requires that the candidate must have obtained their Master’s degree  no more than six years prior to November 2026.