Fuzzy Optimization Problems in Wavelength Division Multiplexing (WDM) Networks Belén Melián Dpto. Estadística, I. O. y Computación. University of La Laguna - Spain mbmelian@ull.es José Luis Verdegay Dpto. de Ciencias de la Computación e Inteligencia Artificial. University of Granada - Spain verdegay@decsai.ugr.es Abstract The basic wavelength division multiplexing (WDM) routing and provisioning problem is considered in this paper. The literature is replete with prescriptive integer programming models for various versions of WDM design problems, but in no case they consider the real situation of solving them taking into account the former nature of the problem, that is, its inherent vagueness. In this paper this vagueness is assumed and handled by means of fuzzy sets based methodologies. In particular a Fuzzy Integer Linear Programming model is proposed to be used as auxiliary model for solving the former WDM provisioning and routing problem. Besides a heuristic algorithm solving it is outlined. Keywords: WDM Networks, Heuristics, Fuzzy Integer Programming. 1 Introduction Problems related to planning and routing in telecommunications networks have become a fertile ground for developing and applying optimization techniques. Several technological developments that occurred during the last decades as well as the increase in the volume of demand have triggered a new era in telecommunications where analogical technology is being substituted with digital technology. The replacement of traditional copper wires with optical transmission equipment not only increased bandwidth but also reduced operational costs. Although in theory fiber has extremely high bandwidth, since the rate at which an end user can access the network is limited by electronic speed, only speeds of a few gigabits per second can be achieved. Therefore, it is not possible to exploit the bandwidth of a single fiber due to the optical- electronic conversion. Wavelength Division Multiplexing (WDM) and the erbium-doped fiber amplifier (EDFA) are two major recent developments that overcome these limitations. However, algorithms and model formulations have usually assumed that the data for the given problems are known accurately, but this is not true in most real-world applications. This is particularly problematic for data representing future traffic demands that cannot be known with certainty. These demands can be perfectly modelled by making use of fuzzy numbers as proposed in this work. In this work, we consider and solve the Provisioning and Routing Problem in WDM networks under demand uncertainty described in the next section. Section 3 reports the fuzzy version of this problem, as well as a problem solving methodology. Last section summarizes the algorithm proposed to solve the problem and the obtained computational results. 2 Problem Description Wavelength Division Multiplexing is the transmission of multiple laser signals at different wavelengths (colors) in the same direction, at the same time and over the same strand of fiber. The optimization problem on hand deals with a set of demands to be routed through the existing optical network. Associated with each demand is an origin node, a destination node, and a size, expressed in OC-48 units. Optical fiber joining pairs of nodes is EUSFLAT - LFA 2005 720