A decomposition algorithm for the ring spur assignment problem

Abstract

This paper describes the ring spur assignment problem (RSAP), a new problem arising in the design of next generation networks. The RSAP complements the sonet ring assignment problem (SRAP). We describe the RSAP, positioning it in relation to problems previously addressed in the literature. We decompose the problem into two IP problems and describe a branch-and-cut decomposition heuristic algorithm suitable for solving problem instances in a reasonable time. We present promising computational results.

A branch‐and‐cut algorithm for the ring spur assignment problem

“…Because we wish to foster high resilience by having locations assigned to rings where possible, we assign a sufficiently high weight, b , to links that are spurs. We use a similar approach to Carroll and McGarraghy [5] to quantify a penalty weighting value in terms of other network parameters sufficient to ensure the creation of ring solutions if they exist. For simplicity, we set the coefficient of each arc ( i , j )∈ A , to be b c i j in our objective function, that is, the cost of using a spur edge is the network cost of that edge, c i j , multiplied by the penalty weighting value of b for the network.…”

Program Optimisation with Dependency Injection

“…The cost is the sum of costs of the edges used, with a penalty per spur. The RSAP was described by Carroll and McGarraghy [9], and integer programming (IP) formulations were given. However for some test problems, the IP method is excessively slow.…”

“…Lower costs are better. Table 1 shows results achieved on the problem instances used in previous work [9,10]. The IP results are known to be optimal [9] except where marked *.…”

“…Table 1 shows results achieved on the problem instances used in previous work [9,10]. The IP results are known to be optimal [9] except where marked *. For PODI and the GA, these are the best (lowest cost) results out of 30 runs, with population 1000 and 100 generations, tournament size 10, crossover probability 0.9, mutation probability 0.05, and elitism of 10 individuals.…”

Hierarchical Survivable Network Design Problems

“…There are few studies that consider the design of two level networks with survivability requirements in both levels. The majority of such studies are on designing ring/ring networks (Thomadsen and Stidsen [19], Carroll and Mc Garraghy [3]), and most of the approaches proposed are heuristic approaches (Shi and Fonseca [17], Balakrishnan et al [1]). The contribution of the present paper is to propose formulations and exact solution methods for the two level survivable network design problem where both rings and 2-edge connected networks are used to ensure survivability.…”