Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks,
operators highly overestimate the traffic volume during network planning. In this paper we consider
telecommunication network design under traffic uncertainty, adapting the robust optimization approach
of Bertsimas and Sim [21]. We present three different mathematical formulations for this problem, provide valid inequalities,
study the computational implications, and evaluate the realized robustness.
To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every
network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they
completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge.
For realistic networks and live traffic measurements we compare the formulations and report on the
speed up by the valid inequalities. We study the “price of robustness” and evaluate the approach by
analyzing the real network load. The results show that the robust optimization approach has the potential
to support network planners better than present methods.
In this paper, we investigate the recoverable robust knapsack problem,
where the uncertainty of the item weights follows the approach of Bertsimas and
Sim. In contrast to the robust approach, a limited recovery action is allowed,
i.e., up to k items may be removed when the actual weights are known. This problem
is motivated by the assignment of traffic nodes to antennas in wireless network
planning. Starting from an exponential min-max optimization model, we derive an
integer linear programming formulation of quadratic size. In a preliminary computational
study, we evaluate the gain of recovery using realistic planning data.
The knapsack problem is one of the basic problems in combinatorial optimization. In real-world applications it is often part of a more complex problem. Examples are machine capacities in production planning or bandwidth restrictions in telecommunication network design. Due to unpredictable future settings or erroneous data, parameters of such a subproblem are subject to uncertainties.
In high risk situations a robust approach should be chosen to deal with these uncertainties.
Unfortunately, classical robust optimization outputs solutions with little profit by prohibiting any adaption of the solution when the actual realization of the uncertain parameters is known.
This ignores the fact that in most settings minor changes to a previously determined solution are possible. To overcome these drawbacks we allow a limited recovery of a previously fixed item set as soon as the data are known by deleting at most k items and adding up to l new items.
We consider the complexity status of this recoverable robust knapsack problem and extend the classical concept of cover inequalities to obtain stronger polyhedral descriptions. Finally, we present two extensive computational studies to investigate the influence of parameters k and l to the objective and evaluate the effectiveness of our new class of valid inequalities.