Optimization Problems in Mobile Communication

In one way or another mobile phones have changed everyone’s life. Mobile communication networks made it possible to be connected and reachable even in the most remote places. A lot of research effort has been put lately in the planning and optimization of mobile networks. Network providers as well as users can only gain in efficiency and usability if the algorithmic optimization community provides them with efficient algorithmic solutions to the optimization problems raised by mobile communication networks. In this thesis, we analyze three different algorithmically interesting problems stemming from mobile telecommunication: the base station location with frequency assignment; the OVSF code assignment problem; and the joint base station scheduling problem. We propose a new solution technique to the problem of positioning base station transmitters and assigning frequencies to the transmitters. This problem stands at the core of GSM network design and optimization. Since most interesting versions of this problem are NP-hard, we follow a heuristic approach based on the evolutionary paradigm to find good solutions. We examine and compare two standard multiobjective techniques and a new algorithm, the steady state evolutionary algorithm with Pareto tournaments (stEAPT). The evolutionary algorithms used raised an interesting data structure problem. We present a fast priority queue based technique to solve the layers-of-maxima problem arising in the evolutionary computation. The layers-of-maxima problem asks to partition a set of points of size n into layers based on their non-dominatedness. A point in ddimensional space is said to dominate another point if it is not worse than the other point in all of the d dimensions. We also look at the problem of dynamically allocating OVSF codes to users in an UMTS network. The combinatorial core of the OVSF code assignment problem is to assign some nodes of a complete binary tree of height h (the code tree) to n simultaneous connections, such that no two assigned nodes (codes) are on the same root-to-leaf path. A connection that uses 2−d of the total bandwidth requires an arbitrary code at depth d in the tree. This code assignment is allowed to change over time, but we want to keep the number of code changes as small as possible. We consider the one-step code assignment problem: Given an assignment, move the minimum number