Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications
by Lakhmi C. Jain; N.M. Martin
CRC Press, CRC Press LLC
ISBN: 0849398045   Pub Date: 11/01/98
  

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4. Optimization Problem - Case Study: Availability–Cost Optimization of All-Optical Network

The problem to be described is an example of genetic algorithm application in telecommunication network optimization. Note that this type of optimization problem could be solved by other methods as well, for example, simulated annealing and taboo search. Many of the design problems in telecommunications could be treated as optimization problems that include some kind of searching among the set of potential solutions. The choice of the method for solving the problem depends mostly on the problem complexity. In all cases, where the problem space is too big and analytical methods are not applicable, some sort of heuristic search for pseudo-optimal solution could be applied. For example, if one should find some kind of optimal network topology, among the set of n = 10 nodes, the number of possible links connecting predefined nodes is n(n-1)/2 = 45. Assuming that every candidate link could be present or not in the solution to be evaluated, the total number of topologies is 245 = 3.5 1013. If an enumeration method is used, assuming evaluation for one solution takes 1 ms, the solution will be reached in 1115 years.

4.1 Problem Statement

This section deals with the issues involved in generating an optimum topology of a European core all-optical network — a case study within the framework of the European Commission project COST 239 “Ultra-high Capacity Optical Transmission Networks” [12]. The objective of the optimization is the minimization of network unavailability and cost, while satisfying the traffic requirements among the major European cities, meeting current technological limitations in the optical domain, and the defined routing rules.

The problem could be defined in another way, too: how to minimize the network cost while keeping unavailability within the prescribed requirements, if possible. The goal is not only to have as minimum unavailability as possible, despite the high costs of the network, but to achieve a low-cost topology that fulfills the availability requirements, if any. In order to find an optimum topology for n nodes’ network, one should consider Ns = 2k, k = n(n-1)/2 different solutions (topologies). Even for a small number of nodes (in the case study the network comprises 11 nodes and has the set of 3.6 1016 different topologies) only a quasi-optimal solution could be obtained.

The case study consists of 11 nodes representing the core part of European all-optical network with total number of 20 nodes (Figure 13).


Figure 13  Case study: Core part of European all-optical network.

Every topology should fulfill symmetric traffic requirements (capacities) expressed by required bit rates, and take into account road distances between nodes (Table 1).

Table 1 Bit rate requirements and road distances
    Bit rates (Gbit/s)
    0 1 2 3 4 5 6 7 8 9 10
    Par Mil Zur Pra Vie Ber Ams Lux Bru Lon Cop
Road distances × 103 (km) 0 Par - 12.5 15 2.5 5 27.5 12.5. 2.5 15 25 2.5
1 Mil 0.82 - 15 2.5 7.5 22.5 5 2.5 5 7.5 2.5
2 Zur 0.60 0.29 - 2.5 7.5 27.5 7.5 2.5 7.5 7.5 2.5
3 Pra 1.00 0.87 0.62 - 2.5 5 2.5 2.5 2.5 2.5 2.5
4 Vie 1.20 0.82 0.80 0.32 - 22.5 2.5 2.5 2.5 5 2.5
5 Ber 1.09 1.01 0.90 0.34 0.66 - 20 5 15 20 7.5
 6 Ams 0.51 1.14 0.85 0.91 1.16 0.66 - 2.5 10 12.5 2.5
7 Lux 0.34 0.71 0.38 0.73 0.93 0.75 0.39 - 2.5 2.5 2.5
8 Bru 0.30 0.93 0.60 0.91 1.12 0.78 0.21 0.22 - 10 2.5
9 Lon 0.45 1.22 1.00 1.31 1.51 1.17 0.55 0.60 0.39 - 2.5
10 Cop 1.24 1.52 1.20 0.74 1.04 0.39 0.76 0.95 0.92 1.31 -


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