A multi-exchange heuristic for formation of balanced disjoint rings
Sasi Kumar, Sarath K
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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.