Solving Two Network Design Problems by Mixed Integer Programming and Hybrid Optimization Methods

This thesis considers two NP-hard combinatorial optimization problems (COPs) from the domain of network design. Network design problems (NDPs) arise in a multitude of real world applications such as the design of telecommunication networks. The NDPs addressed in this thesis are suitable to model certain real-world scenarios occurring in the extension of communication networks on the last mile. Nowadays, telecommunication companies need to upgrade and extend existing networks due to the rising bandwidth requirements of customers. Customers are, however, not usually willing to pay significantly more than for existing lower bandwidth connections. Thus good algorithms for finding cost-efficient network layouts are crucial. The bmax-Survivable Network Design Problem (bmax-SNDP), which allows for modeling fiber-to-the-home scenarios, aims to efficiently extend an existing network to supply new customers. Here, two sets of customers are given. Standard customers which are denoted as type-1 or C1 customers need to be connected by simple routes, while type-2 (or C2) customers need a more reliable connection. For the latter, connectivity needs to be ensured even when a single link or routing node fails, i.e. pairs of node-disjoint paths are required. Furthermore, these redundancy requirements are occasionally relaxed by allowing a connection via a final non-redundant branch line that does not exceed a certain length bmax. In this thesis, two different variants with respect to the objective of bmax-SNDP are considered. In the operative planning task (OPT) a cheapest network feasibly connecting all given customers needs to be identified, while in the strategic simulation task (SST) return-on-investments are additionally considered. Here, the objective is to identify a most profitable solution supplying only a subset of all customers.