Corinne Lucet

K-Terminal Network Reliability Measures With Binary Decision Diagrams

We present a network decomposition method using binary decision diagrams (BDD), a state-of-the-art data structure to encode, and manipulate Boolean functions, for computing the reliability of networks such as computer, communication, or power networks. We consider the K-terminal reliability measure R_K, which is defined as the probability that a subset K of nodes can communicate with each other, taking into account the possible failures of the network links. We present an exact algorithm for computing the if-terminal reliability of a network with perfect vertices in O(m^.F_max ^.2^Fmax.B_Fmax), where B_Fmax is the Bell number of the maximum boundary set of vertices F_max, and m is the number of network links. Several examples, and experiments show the effectiveness of this approach.

An exact method for graph coloring

We are interested in the graph coloring problem. We propose an exact method based on a linear-decomposition of the graph. The complexity of this method is exponential according to the linearwidth of the entry graph, but linear according to its number of vertices. We present some experiments performed on literature instances, among which COLOR02 library instances. Our method is useful to solve more quickly than other exact algorithms instances with small linearwidth, such as mug graphs. Moreover, our algorithms are the first to our knowledge to solve the COLOR02 instance 4-Inser_3 with an exact method.

Lower Bounds for the Minimal Sum Coloring Problem

In this paper we present our study of the minimum sum coloring problem (MSCP). We propose a general lower bound for MSCP based on extraction of specific partial graphs. Also, we propose a lower bound using some decomposition into cliques. The experimental results show that our approach improves the results for most literature instances.

A Memetic Algorithm for staff scheduling problem in airport security service

Abstract The staff scheduling problem is widely studied in Operational Research. Various surveys are available in the literature dealing with this problem which concerns various objectives and various constraints. In this article, we present a staff scheduling problem in airport security service. First, a modeling of the problem, and a representation of solutions are shown. The problem is solved in three steps, days-off scheduling, shift scheduling, and staff assignment. We focus on the last step, by providing a Memetic Algorithm (MA) which merged an Evolutionary Algorithm and Local Search techniques. We propose a chromosome encoding, a crossover operator and a combined neighborhood function, specially dedicated to this staff assignment problem. Besides providing better solutions than software currently used, this algorithm provides up to 50% of improvement from initial feasible solutions.

Tabu Search to Plan Schedules in a Multiskill Customer Contact Center

We have studied a realistic case of scheduling problem in a customer contact center, dealing with multiskill agents. Our model combines the last two steps of the standard approach by determining shifts and by assigning them to agents at the same time (scheduling and rostering). Moreover, we have considered realistic vacations, according to legal constraints and preferences of agents. We have envisioned entire weeks of work, with variable meal times and meal durations, without overtime. In this paper, we define the problem and describe a Tabu search based solution

Pre-processing and Linear-Decomposition Algorithm to Solve the k-Colorability Problem

We are interested in the graph coloring problem. We studied the effectiveness of some pre-processings that are specific to the k-colorability problem and that promise to reduce the size or the difficulty of the instances. We propose to apply on the reduced graph an exact method based on a linear-decomposition of the graph. We present some experiments performed on literature instances, among which DIMACS library instances.

Staff scheduling in airport security service

Abstract The staff scheduling problem is widely studied in Operational Research. Various surveys are available in the literature dealing with this problem which concerns various objectives and various constraints. In this article, we present a staff scheduling problem in airport security service. The problem is solved in three steps, days-off scheduling, shift scheduling, and staff assignment. We focus on the last step, by providing two algorithms, a greedy algorithm and a global assignment algorithm which provides an initial solution. This solution is then improved by an iterative time out destruction/construction algorithm which alternates between partial destruction and reconstruction steps. Besides providing better solutions than software currently used, this algorithm enables to deal with new further constraints.

Minimum sum coloring problem: Upper bounds for the chromatic strength

Abstract The minimum sum coloring problem ( M S C P ) is a vertex coloring problem in which a weight is associated with each color. Its aim is to find a coloring of the vertices of a graph G with the minimum sum of the weights of the used colors. The M S C P has important applications in the fields such as scheduling and VLSI design. The minimum number of colors among all optimal solutions of the M S C P for G is called the chromatic strength of G and is denoted by s ( G ) . A tight upper bound of s ( G ) allows to significantly reduce the search space when solving the M S C P . In this paper, we propose and empirically evaluate two new upper bounds of s ( G ) for general graphs, U B A and U B S , based on an abstraction of all possible colorings of G formulated as an ordered set of decreasing positive integer sequences. The experimental results on the standard benchmarks DIMACS and COLOR show that U B A is competitive, and that U B S is significantly tighter than those previously proposed in the literature for 70 graphs out of 74 and, in particular, reaches optimality for 8 graphs. Moreover, both U B A and U B S can be applied to the more general optimum cost chromatic partition ( O C C P ) problem.