Dominique de Werra

A user's guide to tabu search

We describe the main features of tabu search, emphasizing a perspective for guiding a user to understand basic implementation principles for solving combinatorial or nonlinear problems. We also identify recent developments and extensions that have contributed to increasing the efficiency of the method. One of the useful aspects of tabu search is the ability to adapt a rudimentary prototype implementation to encompass additional model elements, such as new types of constraints and objective functions. Similarly, the method itself can be evolved to varying levels of sophistication. We provide several examples of discrete optimization problems to illustrate the strategic concerns of tabu search, and to show how they may be exploited in various contexts. Our presentation is motivated by the emergence of an extensive literature of computational results, which demonstrates that a well-tuned implementation makes it possible to obtain solutions of high quality for difficult problems, yielding outcomes in some settings that have not been matched by other known techniques.

Using tabu search techniques for graph coloring

Tabu search techniques are used for moving step by step towards the minimum value of a function. A tabu list of forbidden movements is updated during the iterations to avoid cycling and being trapped in local minima. Such techniques are adapted to graph coloring problems. We show that they provide almost optimal colorings of graphs having up to 1000 nodes and their efficiency is shown to be significantly superior to the famous simulated annealing.ZusammenfassungTabu-Methoden werden benützt, um schrittweise den minimalen Wert einer Funktion zu erreichen. Eine sogenannte Tabuliste von verbotenen Schritten wird während des Prozesses nachgeführt, so daß man im Algorithmus keine Zyklen hat und nicht in lokalen Minima gefangen wird. Solche Methoden werden auf Graphenfärbung angepaßt. Wir zeigen, daß man mit dieser Technik fast optimale Färbungen für Graphen mit bis zu 1000 Knoten erhält. Die Effizienz dieser Methoden ist viel besser als diejenige der berühmten „Simulated Annealing” Algorithmen.

An introduction to timetabling

Abstract A huge variety of timetabling models have been described in the OR literature; they range from the weekly timetable of a school to the scheduling of courses or exams in a university. Graphs and networks have proven to be useful in the formulation and solution of such problems. Various models will be described with an emphasis on graph theoretical models.

Some experiments with simulated annealing for coloring graphs

Abstract Methods of thermodynamical simulation have been used for several famous combinatorial optimization problems. For graph coloring (i.e. partition of the node set into as few independent sets as possible) we describe a method of simulation. Such an approach is combined with other techniques for graph coloring. Experiments on random graphs show evidence that this combination gives better results than anyone of the original non-combined methods.

Tabu search: a tutorial and an application to neural networks

SummaryTabu Search is a general heuristic procedure for global optimization. Based on simple ideas it has been extremely efficient in getting almost optimal solutions for many types of difficult combinatorial optimization problems.The principles of Tabu Search are discribed and illustrations are given. An example of problem type where the use of Tabu Search has drastically cut down the computational effort is presented; it consists of the learning process of an associative memory represented by a neural network.ZusammenfassungTabu Search ist eine heuristische Methode, die für globale Optimierung mit viel Erfolg in verschiedenen Umständen angewandt wurde.Die Grundideen der Methode werden erklärt und mit Beispielen illustriert. Eine Anwendung an ein Lernprozess im Gebiet der Neuronen Netzwerke wird beschrieben.Tabu Search is a general heuristic procedure for global optimization. Based on simple ideas it has been extremely efficient in getting almost optimal solutions for many types of difficult combinatorial optimization problems. The principles of Tabu Search are discribed and illustrations are given. An example of problem type where the use of Tabu Search has drastically cut down the computational effort is presented; it consists of the learning process of an associative memory represented by a neural network.

Four classes of perfectly orderable graphs

A graph is called “perfectly orderable” if its vertices can be ordered in such a way that, for each induced subgraph F, a certain “greedy” coloring heuristic delivers an optimal coloring of F. No polynomial-time algorithm to recognize these graphs is known. We present four classes of perfectly orderable graphs: Welsh–Powell perfect graphs, Matula perfect graphs, graphs of Dilworth number at most three, and unions of two threshold graphs. Graphs in each of the first three classes are recognizable in a polynomial time. In every graph that belongs to one of the first two classes, we can find a largest clique and an optimal coloring in a linear time.

The tabu search metaheuristic: How we used it

A general description of tabu search is given and various applications to optimization problems are presented. Some guidelines for applying the tabu metaheuristic are exhibited.

Scheduling in Sports

The purpose of this paper is to present the problem of scheduling the games of a hockey or football league. It is shown how a graph theoretical model may be used and how some constraints related to the alternating pattern of home-games and away-games can be handled. Finally some other requirements occurring in practice are also discussed and introduced into the model.

Some models of graphs for scheduling sports competitions

Abstract Graph-theoretical models are given for constructing the season schedule of a sports league; we consider in particular the problem of having an alternation of home-games and away-games which is as regular as possible, and we characterize schedules with a minimum number of breaks in the alternations. Some related graph-theoretical properties are discussed and a solvable case with preassignments of home-games and away-games is presented.

Stabulus: a technique for finding stable sets in large graphs with tabu search

Numerical experiments with tabu search have been carried out for constructing independent sets in large graphs. We present some variations on the independent set problem and discuss the results obtained by the tabu search technique.As for graph coloring, this method seems to be a very efficient heuristic procedure.ZusammenfassungNumerische Experimente mit der sogenannten Tabu-Search-Methode wurden durchgeführt, um unabhängige Knotenmengen in Graphen zu finden (eine KnotenmengeS ist dann unabhängig, wenn keine Kante beide Endknoten inS hat).Einige Variationen über dieses Problem werden betrachtet (eine gewichtete Version wird beschrieben) und wir geben Resultate an, die zeigen, daß die Tabu-Methode für die Bestimmung unabhängiger Knotenmengen so effizient wie für die Graphenfärbung ist.