| Summary: | Telecommunication networks form an integral part of life. Avoiding failures on
these networks is always not possible. Designing network structures that survive these
failures have become important in ensuring the reliability of these network structures.
With the introduction of SONET (Synchronous Optical Network) technology, rings
have become the preferred survivable network structure. This network configuration
has a set of disjoint rings (each node being a part of single ring), and these disjoint
rings are connected via another main ring. In this research, we present a mathematical
model for the design of such disjoint rings with node number balance criterion
among the rings. When, given a set of nodes and distances between them, the Balanced
Disjoint Rings (BDR) problem is the minimum total link length clustering of
nodes into a given number of disjoint rings in such a way that there is almost the
same number of nodes in each ring. The BDR problem is a class of the standard
Traveling Salesman Problem (TSP). It is clear from this observation that the BDR
problem becomes a TSP when the number of rings required is set to one. Hence
BDR is NP-Hard, and we do not expect to obtain a polynomial time algorithm for
its solution. To overcome this problem, we developed a set of construction heuristics
(Break-MST, Distance Method, Hybrid Method, GRASP-Based Distance Method)
and improvement heuristics (Multi-Exchange, Single Move). Different combinations of construction and improvement heuristics were implemented and the quality of solution
thus obtained was compared to the standard Branch and Cut Technique. It was
found that the algorithm with GRASP-Based Distance Method as the construction
heuristic and multi-exchange - single-move combination as the improvement heuristic
performed better than other combinations. All combinations performed better in
general than the standard Branch and Cut technique in terms of solution time.
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