Annals of Operations Research 130, 217–239, 2004  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. Solving a Network Design Problem ALAIN CHABRIER achabrier@ilog.fr ILOG Spain, Gobelas 21, 28023 Madrid, Spain EMILIE DANNA edanna@ilog.fr ILOG SA, 9 rue de Verdun, F-94253 Gentilly Cedex, France, and Laboratoire d’Informatique d’Avignon, CRNS – FRE 2487, 339, chemin des Meinajariès, Agroparc, BP 1228, F-84911 Avignon Cedex 9, France CLAUDE LE PAPE and LAURENT PERRON {clepape,lperron}@ilog.fr ILOG SA, 9 rue de Verdun, F-94253 Gentilly Cedex, France Abstract. Industrial optimization applications must be “robust” i.e., they must provide good solutions to problem instances of different size and numerical characteristics, and continue to work well when side con- straints are added. This paper presents a case study that addresses this requirement and its consequences on the applicability of different optimization techniques. An extensive benchmark suite, built on real network design data, is used to test multiple algorithms for robustness against variations in problem size, numerical characteristics, and side constraints. The experimental results illustrate the performance discrepancies that have occurred and how some have been corrected. In the end, the results suggest that we shall remain very humble when assessing the adequacy of a given algorithm for a given problem, and that a new generation of public optimization benchmark suites is needed for the academic community to attack the issue of algorithm robustness as it is encountered in industrial settings. Keywords: network design, constraint programming, mixed integer programming, branch and price, in- dustrial benchmark Introduction In the design and development of industrial optimization applications, one major con- cern is that the optimization algorithm must be robust. By “robust” we mean not only that the algorithm must provide “good” solutions to problem instances of different size and numerical characteristics, but also that the algorithm must continue to work well when constraints are added or removed. This expectation is heightened in constraint programming as its inherent flexibility is often put forward as its main advantage over other optimization techniques. Yet this requirement for robustness is rarely recognized as the top priority when the application is designed. Similarly, the benchmark problem suites that are used by the academic community generally do not reflect this requirement. In practice, it has important effects on the reinforcement of problem formulation, search management, the advantages of parallel search, the applicability of different optimiza- tion techniques including hybrid combinations, etc. This paper presents a specific case study in which such questions are addressed.