A Multiobjectivised Memetic Algorithm for the Frequency Assignment Problem

This work presents a set of approaches used to deal with the Frequency Assignment Problem (FAP), which is one of the key issues in the design of Global System for Mobile Communications (GSM) networks. The used formulation of the FAP is focused on aspects which are relevant for real-world GSM networks. The best up to date frequency plans for the considered version of the FAP had been obtained by using parallel memetic algorithms. However, such approaches suffer from premature convergence with some real world instances. Multiobjectivisation is a technique which transforms a mono-objective optimisation problem into a multi-objective one with the aim of avoiding stagnation. A Multiobjectivised Memetic Algorithm, based on the well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) together with its required operators, is presented in this paper. Several multiobjectivised schemes, based on the addition of an artificial objective, are analysed. They have been combined with a novel crossover operator. Computational results obtained for two different real-world instances of the FAP demonstrate the validity of the proposed model. The new model provides benefits in terms of solution quality, and in terms of time saving. The previously known best frequency plans for both tested real-world networks have been improved.