A Randomized Cost Smoothing Approach for Optical Network Design

In designing infocommunications networks the cost of optical ports and links grows in discrete steps as the capacity is being increased. This cost function is referred to as "step function" or "staged capacity cost". If a sequential algorithm is used to design the networks it often results in sub-optimal solution due to the so called "long path problem", where the weighted shortest path algorithms rather choose very long paths where such links are chosen where no additional capacity step (and therefore no additional cost step) has to be made. In this paper we propose and compare methods that perform randomised smoothing of these staged capacity cost functions to allow decomposition of the network design problem to a sequence of weighted shortest path searches, that is the mostly used approach. The problem can be interpreted as an Unsplittable Multi-Commodity Flow Problem with staged capacity costs.