We propose a new solution to the problem of positioning base station transmitters of a mobile phone network and assigning frequencies to the transmitters, both in an optimal way. Since an exact solution cannot be expected to run in polynomial time for all interesting versions of this problem (they are all NP-hard), our algorithm follows a heuristic approach based on the evolutionary paradigm. For this evolution to be efficient, that is at the same time goal-oriented and sufficiently random, problem specific knowledge is embedded in the operators. The problem requires both the minimization of the cost and of the channel interference. We examine and compare two standard multiobjective techniques and a new algorithm, the steady state evolutionary algorithm with Pareto tournaments (stEAPT). One major finding of the empirical investigation is a strong influence of the choice of the multiobjective selection method on the utility of the problem-specific recombination leading to a significant difference in the solution quality. The engineering and architecture of large cellular networks is a highly complicated task with substantial impact on the quality-ofservice perceived by users, the cost incurred by the network providers, and environmental effects such as radio smog. Because so many different aspects are involved, the respective optimization problems are a proper object for multiobjective optimization and may serve as real-world benchmarks for multiobjective methods. For all cellular network systems one major design step is selecting the locations for the base station transmitters (BST Location problem) and setting up optimal configurations such that coverage of the desired area with strong enough radio signals is high and deployment costs are low. For Frequency Division/Time Division Multiple Access (FD/TDMA) systems a second design step is to allocate frequency channels to the cells. For GSM (Global System for Mobile Communications) systems, a fixed frequency spectrum is available. This spectrum is divided into a fixed number of channels. For a good quality-of-service, network providers should allocate to each cell enough channels to satisfy all simultaneous demands (calls). The channels should be assigned to the cells in such a way that interference with channels of neighbor cells or inside the same cell is low. This problem is called in the literature the fixed spectrum frequency channel assignment problem (FS-FAP). BST-Location (BST-L) and the FAP problem are known to be NP-hard: The Minimum Set Cover problem can be reduced in polynomial time to the BST-L problem, and the FAP problem contains the Vertex Coloring Problem as a special case. For both problems, BST-L and FAP, several [13] . For the BST Location problem which considers also interferences, one interesting practical approach was presented in [24] . The most recent result is by Galota et. al. [10] , showing a polynomial time approximation scheme for one version of the BST-L problem. Also for a weighted coloring version of the FAP an optimization algorithm was presented recently [29] that works for the special case of series-parallel graphs. Two separate optimization steps, BST-L followed by FAP, must be viewed critically-a solution of BST-L restricts the space of possible overall solutions considerably and might delimit the outcome of the FAP optimization. Usually an iterated two-phase procedure is chosen to approach a sufficient solution. However, it is usually difficult to feed back the results of the second phase into an optimization of the first phase again. This paper shows that with today's increased availability of computing power it has become practically feasible to address the cellular network design problems (BST-L and FS-FAP) with an integrated approach that considers the whole problem in a single optimization phase. Since the two separate optimization steps do influence each other for practical problem instances, we expect better overall results when they are integrated into a single design step although the search space is enlarged drastically. To our knowledge, there were only very few papers that addressed the integrated problem (e.g. [14] ), and none of them pursues an evolutionary approach. We are interested in exploring the potential that evolutionary algorithms have to offer.
In REF , the steady-state EA with Pareto tournaments (stEAPT) approach is introduced as a new MO technique that considers frequency assignment and channel interference for BS placement.
Evolutionary Multiobjective Optimization for Base Station Transmitter Placement with Frequency Assignment
IC-AI
Computer Science Mathematics