Tools and techniques for optimization

M. Bardhyl MIFTARI will publicly defend his thesis entitled "Tools and techniques for optimization".

Summary

Mathematical programming offers a robust framework for modelling and optimising complex systems involving multiple interconnected components—ranging from industrial production chains to energy networks. Optimising such systems requires determining the best sequence of actions to reach a defined objective from an initial state.
This thesis focuses on linear programming, a subclass of mathematical programming that efficiently handles large-scale problems. Specifically, it addresses two key stages of the optimisation workflow: modelling and sensitivity analysis.
We first introduce GBOML (Graph-Based Optimisation Modelling Language), a novel modelling language that captures system structure through hierarchical hypergraphs. Designed for clarity, modularity, and reuse, GBOML uses the encoded structure to facilitate model formulation, build faster instances and sometimes even accelerate the solving process itself.
We then explore how to assess the impact of uncertainty—particularly in constraint coefficients, a less-studied area. We propose two new methods:

• A bounding approach that delivers strong guarantees on the objective function under constraint changes.
• A warm-starting technique to speed up re-optimisation when adjustments occur.

We also discuss how these contributions advance the state of the art in both modelling and analysis, and open up new directions for research in mathematical programming.

Practical information

Defence will take place on Thursday June 19th at 14:30, to all at amphitheatre Mania Pavella of Institute Montefiore (Bât. B28, au Sart Tilman) or via le FSA PhD Channel.