A decomposition approach for the Frequency Assignment Problem

The Frequency Assignment Problem (FAP) is an important optimization problem that arises in operational cellular wireless networks. Solution techniques based on meta-heuristic algorithms have been shown to be successful for some test problems but they have not been usually demonstrated on large scale problems that occur in practice. This thesis applies a problem decomposition approach in order to solve FAP in stances with standard meta-heuristics. Three different formulations of the problem are considered in order of difficulty: Minimum Span (MS-FAP), Fixed Spectrum (MS-FAP), and Minimum Interference FAP (MI-FAP). We propose a decomposed assignment technique which aims to divide the initial problem into a number of subproblems and then solves them either independently or in sequence respecting the constraints between them. Finally, partial subproblem solutions are recomposed into a solution of the original problem. Standard implementations of meta-heuristics may require considerable run times to produce good quality results whenever a problem is very large or complex. Our results, obtained by applying the decomposed approach to a Simulated Annealing and a Genetic Algorithm with two different assignment representations (direct and order-based), show that the decomposed assignment approach proposed can improve their outcomes, both in terms of solution quality and runtime. A number of partitioning methods are presented and compared for each FAP, such as clique detection partitioning based on sequential orderings and novel applications of existing graph partitioning and clustering methods adapted for this problem