• robust
• optimization
• network
• design
• chance
• routing

the thesis deals with important problem of planning of telecommunication
networks (and other networks which carry demand between different network nodes
requiring allocation of capacities along the network links). More specifically, the problem
is to find the network with the minimal cost which will satisfy uncertain demand. Two
descriptions of uncertainty are considered. In the first one the demand matrices belong to
a known set defined by different sets of linear constraints, this approach of robust
optimization. In the second one the demand matrices belong to a given set with some
specified probability, this problem formulation can be classified as stochastic
programming problem with probability (chance) constraints.
- In robust setting an interesting and important special case is found when the static
routing in certain sense gives no worse results as dynamic routing.
- In chance constrained case several approximate deterministic formulations are
developed and studied. These approximations are critical from the point of view of
computability because the original chance constrained formulation presents considerable
computational difficulties.
Extensive numerical experiments with different problem formulations are presented which allows to analyze meaningfully relative properties of different approximations