Solving the Frequency Assignment Problem with Polarization by Local Search and Tabu Philippe Galinier †‡, Michel Gendreau †¶, Patrick Soriano †§ and Serge Bisaillon † †Centre de recherche sur les transports, Universit´ e de Montr´ eal, C.P. 6128, succursale Centre-ville, Montr´ eal, Qu´ ebec, Canada H3C 3J7 ‡D´ epartement de g´ enie informatique, ´ Ecole Polytechnique de Montr´ eal, C.P. 6079, succursale Centre-ville, Montr´ eal, Qu´ ebec, Canada H3C 3A7 ‡D´ epartement d’informatique et recherche op´ erationnelle, Universit´ e de Montr´ eal, C.P. 6128, succursale Centre-ville, Montr´ eal, Qu´ ebec, Canada H3C 3J7 §Service de m´ ethodes quantitatives, ´ Ecole des Hautes ´ Etudes Commerciales, 3000, chemin de la Cˆ ote-Sainte-Catherine, Montr´ eal, Qu´ ebec, Canada H3T 2A7 1 Introduction Wireless communication networks have undergone a dramatic expansion over the past two decades. Given the continuing fast growth in demand for wireless services, Frequency Assign- ment Problems (FAP) play a key role in the planning of such networks [12]. Several variants of FAP have been studied over the past ten years. A common feature of these problems is the pres- ence of distance or spacing constraints imposed on pairs of frequencies in order to avoid (or at least reduce) interferences between geographically close communication equipments. Problems arising in radio-mobile networks (i.e. cellular telephone networks, personal communications systems) generally comprise only distance constraints while problems arising in radio-link net- works have other additional constraints. Their formal expression is therefore more complex. In 1993, the CELAR (the French “Centre d’ ´ Electronique de l’Armement”) built a series of sim- plified versions of Radio Link Frequency Assignment Problems (RLFAP) based on data taken from a real network [3]. The Frequency Assignment Problem with Polarization (FAPP) that we study here is an extension of this latter problem. It was the topic of the 2001 International Challenge organized by the French operations research society ROADEF in collaboration with CELAR (see [4, 9] for more details). Strictly speaking, the FAPP no longer is a frequency as- signment problem since polarities in addition to frequencies need to be assigned, which makes the expression of the distance constraints (also referred to as electro-magnetic constraints) more complex. 1