Laurent Moalic

Alexandre Gondran, Vincent Duchamp, Laurent Moalic

The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition problem with additional constraints. We improve the lower bound for 18 graphs of standard benchmark DIMACS, and prove the optimal value for 4 graphs by reaching their known upper bound.

Mehdi Katranji, Sami Kraiem, Laurent Moalic et al.

In this study, we present a machine learning approach to infer the worker and student mobility flows on daily basis from static censuses. The rapid urbanization has made the estimation of the human mobility flows a critical task for transportation and urban planners. The primary objective of this paper is to complete individuals' census data with working and studying trips, allowing its merging with other mobility data to better estimate the complete origin-destination matrices. Worker and student mobility flows are among the most weekly regular displacements and consequently generate road congestion problems. Estimating their round-trips eases the decision-making processes for local authorities. Worker and student censuses often contain home location, work places and educational institutions. We thus propose a neural network model that learns the temporal distribution of displacements from other mobility sources and tries to predict them on new censuses data. The inclusion of multi-task learning in our neural network results in a significant error rate control in comparison to single task learning.

Laurent Moalic, Alexandre Gondran

Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for \textless{}dsjc1000.9\textgreater{}, 81-colorings for \textless{}flat1000\_76\_0\textgreater{} and even 47-colorings for \textless{}dsjc500.5\textgreater{} and 82-colorings for \textless{}dsjc1000.5\textgreater{}.