Solving Frequency Assignment Problems with Constraint Programming

The topic of this diploma thesis is the solving of a Frequency Assignment Problem (FAP) in GSM radio networks by means of Constraint Programming. The task of frequency planning is the assignment of frequencies to base stations w.r.t. various constraints such that interference, which may have a substantial impact on the quality of the received signals, is avoided as far as possible. Constraint Programming is employed since currently applied heuristics aimed at interference minimization often fail for problems where it is problematic to obtain any feasible assignment. First, the focus is on feasibility problems only. Having determined valid solutions, it is also tried to explicitly minimize total interference. After the introduction of the underlying mathematical model, it is shown that the discussed version of FAP is strongly NP-hard. An overview on the theory of Constraint Programming and a proof that Constraint Satisfaction Problems are strongly NP-complete are provided as well. ILOG OPL Studio is employed for solving FAP, where the “Optimization Programming Language” (OPL) allows to state mathematical models using an own modeling language. It is investigated to what extent the additional elements of this language compared to Mixed Integer Programming really enable to express more conditions in OPL models than in Mixed Integer Programs. In this work, various OPL models for FAP feasibility problems are presented. Different modeling alternatives are analyzed and compared with each other. By means of OPL feasibility models, it is possible to obtain valid assignments for large instances as well as for instances which are difficult to solve. As the quality of the determined solutions is often not satisfactory, approaches on explicitly minimizing total interference are introduced. A minimization framework by means of OPL is developed, a construction heuristic is applied, and OPL feasibility models are combined with an improvement heuristics. Furthermore, the results for all these minimization techniques are compared with each other.