Alain Hertz

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.

A new heuristic method for the flow shop sequencing problem

Abstract A new heuristic method is presented for solving the m -machine, n -job flow shop scheduling problem. This method, named spirit , is composed of two phases: the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques. The results of the heuristic are compared with those from other well-known methods.

New insertion and postoptimization procedures for the traveling salesman problem

This paper describes a new insertion procedure and a new post- optimization routine for the traveling salesman problem. The combination of the two methods results in an efficient algorithm (GENIUS) which outperforms known alternative heuristics in terms of solution quality and computing time. (A)

New Heuristics for the Vehicle Routing Problem

This chapter reviews some of the best metaheuristics proposed in recent years for the Vehicle Routing Problem. These are based on local search, on population search and on learning mechanisms. Comparative computational results are provided on a set of 34 benchmark instances.

A Tabu Search Heuristic for the Capacitated Arc Routing Problem

The Capacitated Arc Routing Problem arises in several contexts where streets or roads must be traversed for maintenance purposes or for the delivery of services. A tabu search is proposed for this difficult problem. On benchmark instances, it outperforms all known heuristics and often produces a proven optimum.

Tabu search for large scale timetabling problems

Tabu search techniques are adapted to timetabling problems. The objective is to reduce the number of conflicts due to courses taking place simultaneously but involving common students or teachers, or requiring the same classroom. In addition to these classical constraints we also take into account the grouping of students (courses taken by a large number of students have to be repeated several times during the week), compactness and precedence requirements and geographical constraints.

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.

A survey of local search methods for graph coloring

Tabucol is a tabu search algorithm that tries to determine whether the vertices of a given graph can be colored with a fixed number k of colors such that no edge has both endpoints with the same color. This algorithm was proposed in 1987, one year after Fred Glovers article that launched tabu search. While more performing local search algorithms have now been proposed, Tabucol remains very popular and is often chosen as a subroutine in hybrid algorithms that combine a local search with a population based method. In order to explain this unfailing success, we make a thorough survey of local search techniques for graph coloring problems, and we point out the main differences between all these techniques.

Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.