#### 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

Progress towards the two-thirds conjecture on locating-total dominating sets

Discrete Mathematics

Duy Dao Do, Hervé Kerivin, Philippe Lacomme, Bogdan Vulpescu - Oct. 31, 2024

Comparative study of quantum methods in the resolution of track findings instances

José Luis Figueroa González, Mourad Baiou, Alain Quilliot, Hélène Toussaint, Annegret Wagler - Oct. 1, 2024

A project and lift approach for a 2-commodity flow relocation model in a time expanded network

Discrete Applied Mathematics

Dipayan Chakraborty, Florent Foucaud, Aline Parreau, Annegret K Wagler - July 22, 2024

On three domination-based identification problems in block graphs

Fundamenta Informaticae

Thanh Loan Nguyen, Viet Hung Nguyen, Minh Hieu Nguyen, Thi Viet Thanh Vu - July 7, 2024

On the Kalai-Smorodinsky solutions for Bi-objective Spanning Tree Problem

Huy Phuc Nguyen Ha, Viet Hung Nguyen, Anh Son Ta - June 4, 2024

Solving Edge-Weighted Maximum Clique Problem with DCA Warm-Start Quantum Approximate Optimization Algorithm

Metaheuristics International Conference (MIC 2024)

Huy Phuc Nguyen Ha, Viet Hung Nguyen, Anh Son Ta - June 4, 2024

Solving Quadratic Knapsack Problem with Biased Quantum State Optimization Algorithm

Metaheuristics International Conference (MIC 2024)

Dipayan Chakraborty, Annegret Wagler - May 22, 2024

Open-Separating Dominating Codes in Graphs

International Symposium on Combinatorial Optimization

Fatiha Bendali, Alejandro Olivas Gonzales, Alain Quilliot, Hélène Toussaint - May 22, 2024

Surrogate Constraints for Synchronized Energy Production/Consumption

Fatiha Bendali, Eloise Yollande Mole Kamga, Jean Mailfert, Alain Quilliot, Hélène Toussaint - May 20, 2024

A polyhedral analysis of the synchronous management of energy production and consumption problem

Annals of Operations Research

All publications are here