Theme Combinatorial optimization

Presentation

This theme involves modelling and research into efficient algorithms for various optimisation problems arising from operations research and applied mathematics. The application context is very broad, ranging from continuous to discrete, from deterministic to stochastic, from graphs to algorithmic complexity.
 The nature of the optimisation problems studied is :

    Combinatorial: finding the smallest or largest element from a finite set of elements. Variables take integer values.

    Continuous: find the smallest or largest point in a non-countable infinite set. Variables can take real values.

Combinatorial optimisation problems are studied using several approaches depending on their difficulty and structure:

  • Polyhedral approaches: the aim is to reduce the problem to the solution of a linear programme. This task is impossible when the problem in question is NP-complete, but the determination of a relaxed linear program is easy and generally offers very useful bounds for starting the solution using branch-and-bound-and-cut algorithms. These are the best-performing exact algorithms for solving difficult combinatorial optimisation problems. This approach is also used to describe instances where an NP-complete problem becomes polynomial. This is achieved by completely describing the polytope associated with the problem by a linear program with constraints that are easy to separate (we can introduce the constraints needed for optimisation in polynomial time despite their exponential number in most cases).
  • Approximation algorithms: this involves developing polynomial algorithms in which the value of the solution found is analytically comparable to the value of the optimal solution. The measure taken is the worst-case approximation ratio between the value found and the value of the optimum. Average approximation ratio measures are also considered where this can be defined.
  • Game algorithms: This involves combining mathematics, economics and computer science to manage situations where individual interests conflict with the common welfare. The application of algorithms is recent: the aim is to find the right strategies to ensure stability in exchanges between individuals and in the sharing of common resources. Game algorithms emphasise the complexity of calculating these equilibria and rely on performance-guaranteed bounds and approximations to respond to models whose exact solutions are unrealistic or unknown.
  • Stochastic and robust optimisation: In many applications, the data is not known exactly. The associated uncertainty is often represented by several scenarios. These different scenarios are usually modelled by adding new variables and constraints.

The problems studied come from a variety of fields: transport networks, telecommunication networks, electricity networks, bioinformatics, sensor networks, infrastructure localisation, nuclear and automotive.

last publications

Mourad Baïou, Francisco Barahona - May 1, 2025
An algorithm for packing hypertrees
Discrete Mathematics

Minh Hieu Nguyen, Mourad Baïou, Viet Hung Nguyen - April 1, 2025
Generalized Nash Fairness Solutions for Bi-Objective Discrete Optimization: Theory and Algorithms
Discrete Applied Mathematics

Victoria Kaial, Annegret K Wagler - March 26, 2025
Minimal non-EPT graphs based on minimal non-interval graphs


Minh Hieu Nguyen, Thanh Loan Nguyen - March 11, 2025
A multi-objective optimization approach for generalized linear multiplicative programming


Hassene Aissi, Mourad Baïou, Francisco Barahona - March 1, 2025
New bounds for the number of lightest cycles in undirected graphs
Information Processing Letters

An Tran, Mourad Baiou, Rafael Colares-Borges, Hector Gatt, Thomas Guy - Feb. 26, 2025
Two Approaches for the Cubic Facility Layout Problem
ROADEF 2025

Mourad Baïou, David R.C. Hill - Jan. 23, 2025
Évolution des méthodes de calcul en théorie des jeux


Mourad Baïou, Francisco Barahona, Joao Goncalves - Dec. 29, 2024
Volume Algorithm: Training Neural Networks and Solving Difficult Linear Programs


Chi Thao Nguyen, Jean-Philippe Gayon, Viet Hung Nguyen, Anh Son Ta - Dec. 20, 2024
A heuristics for Pickup-Delivery Problem with Cooperative Robots
ICAMCS 2024 (International Conference on Applied Mathematics and Computer Science)

Aurélien Mombelli, Alain Quilliot, Mourad Baiou - Dec. 15, 2024
Multiple Heuristics with Reinforcement Learning to Solve the Safe Shortest Path Problem in a Warehouse


All publications are here