Algorithmic approaches for efficient enumeration of candidate p-cycles and capacitated p-cycle network design

We develop and test an algorithmic approach for providing p-cycle survivable transport network designs. The basic approach is to first identify a set of primary p-cycles, then to search for improvements on those cycles through various operations to create a final set of cycles of high individual and collective efficiency, before finally placing one p-cycle at a time, iteratively, until all working capacity of the network is protected. We compare the solution quality of the algorithm to optimal designs obtained with ILP methods. The primary advantage of this algorithmic approach is that it entirely avoids the step of enumerating all cycles, which is a preliminary step in both ILP and heuristic solution methods based on preselection. This method proceeds initially with no more than S "primary" p-cycles, and in the worst case will enumerate no more than S²-N other candidate cycles during its execution, where S is the number of spans in the network and N is the number of nodes. We also find that the set of candidate cycles developed by the algorithm can themselves be used as a quite small but highly effective set of eligible cycles in an ILP design model.