Invited Speakers

• CEVHER Volkan (EPFL, Suisse)

• DE SANTIS Marianna (Université de Florence, Italie)

• SUROWIEC Thomas (Simula Research Laboratory, Norvège)

• VAN HENTENRYCK Pascal (Georgia Tech., Etats-Unis)

Marianna De Santis

University of Florence

Exact approaches for multi-objective binary quadratic optimizations

Multi-objective mixed-integer nonlinear programming (MOMINLP) provides a powerful framework for modeling complex real-world decision problems. Practical applications often involve multiple, conflicting objectives and require binary or general integer variables to capture logical constraints or discrete decisions. Solving MOMINLP problems entails identifying the set of efficient solutions - i.e., solutions where no objective can be improved without deteriorating at least one other.

An efficient integer assignment refers to a fixing of the integer variables such that there exists at least one efficient solution for the corresponding continuous subproblem. In many cases, correctly solving MOMINLPs requires exploring a large number of such assignments - potentially all integer-feasible ones - rendering full enumeration unavoidable. This significantly complicates the solution process compared to the single-objective case and poses substantial challenges for algorithm development.

In this talk, we review essential tools recently proposed for developing branch-and-bound methods for multi-objective mixed-integer nonlinear optimization, and we explore approaches specifically tailored to problems with quadratic objective functions. Building on the well-established technique of quadratic convex reformulation - originally developed for single-objective binary quadratic programs - we extend this methodology to the multi-objective setting. We propose a branch-and-bound algorithm where lower bound sets are obtained from appropriately defined convex quadratic subproblems. Computational experiments on multiobjective k-item Quadratic Knapsack and multiobjective Max-Cut instances demonstrate the effectiveness of our approach.

Pascal Van Hentenryck

Georgia Tech., États-Unis

“Learning to Optimize”

In many industry settings, the same optimization problem is solved repeatedly for instances taken from a distribution that can be learned or forecasted. Indeed, such parametric optimization problems are ubiquitous in applications over complex infrastructures such as electrical power grids, supply chains, manufacturing, and transportation networks. The scale and complexity of these applications have grown significantly in recent years, challenging traditional optimization approaches. This talk studies how to speed up these parametric optimization problems to meet real-time constraints present in many applications. covering concepts such as primal and dual optimization proxies, learning to optimize, contextual optimization, and decision-focused learning. The methodologies are highlighted on industrial problems in grid optimization, end-to-end supply chains, logistics, and transporation systems.