Solving the Location Areas Problem with Strength Pareto Evolutionary Algorithm Víctor BerrocalPlaza, Miguel A. VegaRodríguez, Juan M. SánchezPérez, Juan A. GómezPulido Dept. Technologies of Computers & Communications University of Extremadura Cáceres, Spain {vicberpla, mavega, sanperez, jangomez}@unex.es —In the last few years, the management systems which control the mobile location are becoming more important due to the increase in the number of mobile users. From among the location management techniques, the use of Location Areas is an important strategy which defines the location management task as an optimization problem with two conflicting costs that must be minimized: subscriber location update and paging. In this work, we resort to a multi!objective evolutionary algorithm, Strength Pareto Evolutionary Algorithm 2 (SPEA2), to obtain quasi!optimal solutions of this optimization problem. Furthermore, we compare our results with those obtained by mono!objective algorithms of other authors because, at present, there is not any previous work that tackles the problem with a multi!objective approach. Results show the advantages of solving the Location Areas scheme by using a multi!objective approach.           !  " I. INTRODUCTION In the last decade, there has been a huge increment in the number of mobile subscribers because the new services provided by mobile networks (voice, data, videoconference, etc.) are very attractive to consumers. These services must be served regardless of the user position in the network and the moment at which they are requested. Hence, the control and management tasks are crucial in these networks. This paper focuses on one of the most important management tasks associated with the Public Land Mobile Networks (PLMN), the user location management. These networks divide the whole coverage area according to a two levels scheme. The first level divides the coverage area into regions and assigns all available radioelectric resources to these regions. And the second level divides each region into several smaller areas (also known as cells) among which the radioelectric resources are distributed. Therefore, the resource reuse is the technique applied in PLMN to provide service to a high number of mobile subscribers. Furthermore, each cell is served by a Base Station (or BS, the network entity which provides access to the user terminal) and may be of different size to adapt to the traffic density (high traffic densities require small cells whereas large cells are used with low traffic densities). The location management problem consists of two parts: subscriber location update (when a subscriber notifies the network a change of its associated cell) and location inquiry (or paging, performed by the network for locating the subscriber when it has an incoming call) [1]. Ideally, the network should know the cell associated with each subscriber at anytime, but this technique requires a high number of location update messages, so it is frequent the use of other strategies, e.g. the Location Areas (LA) scheme. The LA scheme defines the location management as an optimization problem with two conflicting objectives that must be minimized: subscriber location update and paging. In order to solve this problem, we resort to a multiobjective evolutionary algorithm that treats each goal separately, Strength Pareto Evolutionary Algorithm 2 (SPEA2), since it is one of the most popular algorithms in the multiobjective optimization field. At present, there is not any previous work that tackles the LA problem with a multiobjective approach. Therefore, we have compared our results with those obtained by mono objective algorithms of other authors, e.g. Genetic Algorithms (GAs) [13], Simulated Annealing (SA) [4], Hopfield Neural Networks (HNNs) [56], or Differential Evolution (DE) [7]. Furthermore, we have calculated indicators related to the multi objective optimization field. The paper is organized as follows. Section II defines the LA management problem. Section III shows our implementation of SPEA2 to solve this problem. Results and comparisons with other authors are discussed in Section IV. Finally, the conclusions and future work are presented in Section V. II. LOCATION AREAS SCHEME The Location Areas (LA) scheme is a strategy which is used in PLMN to manage the subscriber location update and tracking. Using this strategy, cells are grouped into nondisjoint areas such that the network only updates the subscriber location when s/he moves from a location area to another, see Fig. 1. Thus, the location update cost is reduced at expense of complicating the paging procedure, since the subscriber must be searched in the whole location area (all its cells). The LA management problem may be formulated as a multiobjective optimization problem because it handles two