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

Abstract

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. IndexTermsp-cycles, optical mesh network design, algorithmic and heuristic design, restoration and protection. 0-7803-81 18-1/03/$17.00 0 2003 IEEE

Multi-criteria p-cycle network design

“…To evaluate our solution in terms of redundancy and number of p-cycle structures, we compare its performance to the heuristics CIDA and SLA introduced in [3], [8]. We also compare our algorithm to the exact solution given by an ILP formulation [1].…”

“…In the first approach, after the working paths are routed (e.g. using shortest paths) the optimal set of p-cycles is calculated using available capacity [1], [2], [3], [4], [5]. In the second approach, the routing of the working paths and the p-cycles are computed simultaneously optimizing the total capacity [6], [7], [10].…”

“…The second sub-class (pure heuristic) tries to find a good solution without using ILP formulation. The objective of this kind of solutions is to reduce the time required to compute an efficient set of p-cycles that protects the network [3], [5].…”

An Algorithm for Unrestored Flow Optimization in Survivable Networks Based on p-Cycles

“…It is quite simple and never generates more cycles than number of spans in network. In [7,11] there have been described several different algorithms providing rules for transformations from simple p-cycles to complex ones. Among them, three have been chosen as the most promising: SP-Add (Span Add), Expand and Grow, described in [7].…”

“…In both cases a "good" p-cycles are expected from the generation algorithm. The problem of generation cycle components is nontrivial and has been studied among others in [5,6,7,8,9,10].…”