Coloration de graphes et attribution d'activités dans des quarts de travail

Revue de littérature -- Organisation de la thèse -- Lower bounds and a tabu search algorithm for the minimum deficiency problem -- On a reduction of the interval coloring problem to a series of bandwidth coloring problems -- About equivalent interval colorings of weighted graphs -- Une approche de programmation en nombres entiers pour la résolution d'un problème d'horaire -- Discussion générale et conclusion

Two genetic algorithms for the bandwidth multicoloring problem

In this paper the Bandwidth Multicoloring Problem (BMCP) and the Bandwidth Coloring Problem (BCP) are considered. The problems are solved by two genetic algorithms (GAs) which use the integer encoding and standard genetic operators adapted to the problems. In both proposed implementations, all individuals are feasible by default, so search is directed into the promising regions. The first proposed method named GA1 is a constructive metaheuristic that construct solution, while the second named GA2 is an improving metaheuristic used to improve an existing solution. Genetic algorithms are tested on the publicly-available GEOM instances from the literature. Proposed GA1 has achieved a much better solution than the calculated upper bound for a given problem, and GA2 has significantly improved the solutions obtained by GA1. The obtained results are also compared with the results of the existing methods for solving BCP and BMCP

Optimization in Telecommunication Networks

Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;

The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives precise analyses of the problem with respect to pathwidth