David Schindl

Ant Local Search and its efficient adaptation to graph colouring

In this paper, we propose a new kind of ant algorithm called Ant Local Search. In most ant algorithms, the role of each ant is to build a solution in a constructive way. In contrast, we propose to consider each ant as a local search, where at each step and in concordance with all ant algorithms, each ant modifies the current solution by the use of the greedy force and the trail systems. We also propose ways to reduce the computational effort associated with each ant decision. Such a new and general ant methodology is then applied to the well-known k-colouring problem, which is NP-hard. Computational experiments give evidence that our algorithm is competitive with the best colouring methods.

P 5 -free augmenting graphs and the maximum stable set problem

The complexity status of the maximum stable set problem in the class of P5-free graphs is unknown. In this paper, we first propose a characterization of all connected P5-free augmenting graphs. We then use this characterization to detect families of subclasses of P5-free graphs where the maximum stable set problem has a polynomial time solution. These families extend several previously studied classes.

Lower bounding and tabu search procedures for the frequency assignment problem with polarization constraints

Abstract.The problem retained for the ROADEF’2001 international challenge was a Frequency Assignment Problem with polarization constraints (FAPP). This NP-hard problem was proposed by the CELAR of the French Department of Defense, within the context of the CALMA project. Twenty seven competitors took part to this contest, and we present in this paper the contribution of our team that allowed us to be selected as one of the six finalists qualified for the final round of the competition.There is typically no solution satisfying all constraints of the FAPP. For this reason, some electromagnetic compatibility constraints can be progressively relaxed, and the objective is to find a feasible solution with the lowest possible level of relaxation. We have developed a procedure that computes a lower bound on the best possible level of relaxation, as well as two tabu search algorithms for the FAPP, one for the frequency assignment, and one for the polarization assignment.

Finding augmenting chains in extensions of claw-free graphs

Finding augmenting chains is in the heart of the maximum matching problem, which is equivalent to the maximum stable set problem in the class of line graphs. Due to the celebrated result of Edmonds, augmenting chains can be found in line graphs in polynomial time. Minty and Sbihi generalized this result to claw-free graphs. In this paper we extend it to larger classes. As a particular consequence, a new polynomially solvable case for the maximum stable set problem has been detected.

Heuristics for a project management problem with incompatibility and assignment costs

Consider a project which consists of a set of jobs to be performed, assuming each job has a duration of at most one time period. We assume that the project manager provides a set of possible durations (in time periods) for the whole project. When a job is assigned to a specific time period, an assignment cost is encountered. In addition, for some pairs of jobs, an incompatibility cost is encountered if they are performed at the same time period. Both types of cost depend on the duration of the whole project, which also has to be determined. The goal is to assign a time period to each job while minimizing the costs. We propose a tabu search heuristic, as well as an adaptive memory algorithm, and compare them with other heuristics on large instances, and with an exact method on small instances. Variations of the problems are also discussed

Solution Methods for Fuel Supply of Trains

Abstract The considered problem consists in optimizing the refueling costs of a fleet of locomotives over a railway network. The goal consists in determining the number of trucks contracted for each yard (truck assignment problem) and to determine the refueling plan of each locomotive (fuel distribution problem), while minimizing the costs and satisfying constraints. A two-levels approach is proposed to tackle this NP-hard problem. Three metaheuristics (namely a descent procedure, a tabu search, and an ant local search algorithm) are proposed for the truck assignment level, and a flow model is designed for the fuel distribution level. A post-optimization procedure can be combined with the latter flow model. Six algorithms are proposed for the whole problem, and were tested on a realistic instance proposed by the Railway Applications Section of INFORMS. Competitive results were obtained. A strength of the proposed approach is its flexibility, as it can be easily adapted to non linear cases.

Learning Tabu Search for Combinatorial Optimization

In this paper, a new type of local search algorithm is proposed, called Learning Tabu Search and denoted \(\textit{LTS}\). It is assumed that any solution of the considered problem can be represented with a list of characteristics. \(\textit{LTS}\) involves a learning process relying on a trail system. The trail system is based on the idea that if some combinations of characteristics often belong to good solutions during the search process, such combinations of characteristics should be favored when generating new solutions. It will be showed that \(\textit{LTS}\) obtained promising results on a refueling problem in a railway network.

Some simple optimization techniques for self-organized public key management in mobile ad hoc networks

We consider some graph theoretical problems arising from security requirements in some communication networks. Basically one has to associate to each node of a directed graph G = (V, E) a partial subgraph of G. A solution consists hence of a collection of |V| subgraphs, subject to some packing constraints or connectivity requirements. We first describe the usual graph theoretical model and we review a known construction procedure for which we point out some basic properties. We then study in more details the case of complete graphs and show the existence of a solution with a guaranteed quality. Next, we study the performance of the construction procedure and we propose an additional construction. We attempt to characterize the cases in which either construction is preferable. In the last section, a tabu search approach is proposed and tested on a sample of numerical examples.