1. Biologically-inspired ring design in Telecommunications Tony White email: tony@sce.carleton.ca

2. Overview of Talk Description of the Genetic AlgorithmDescription of the Genetic Algorithm –operators –selection –creation of next generation Ring designRing design –problem statement and sub-problems –GA representation –results

3. Genetic Search GA P,Q,R: populations of solutions from the problem domain; initialize(P); while not finish(P) do begin Q := select(P); R := create(Q); P := merge(P, Q, R); endend Uses a population of candidate solutions; each one has a fitness valueUses a population of candidate solutions; each one has a fitness value Search based upon Genetics and dynamics of populationsSearch based upon Genetics and dynamics of populations Uses an encoding of problem parametersUses an encoding of problem parameters

4. Genetic Search: select GA P,Q,R: populations of solutions from the problem domain; initialize(P); while not finish(P) do begin Q := select(P); R := create(Q); P := merge(P, Q, R); endend Uses fitness of solutions in order to bias production of next generation of candidate solutions e.g. biased roulette wheel. 2 1.5 1.8

5. Genetic Search: create GA P,Q,R: populations of solutions from the problem domain; initialize(P); while not finish(P) do begin Q := select(P); R := create(Q); P := merge(P, Q, R); endend Use crossover and mutation operators to modify solutionsUse crossover and mutation operators to modify solutions Crossover Mutation

6. Genetic Search: merge GA P,Q,R: populations of solutions from the problem domain; initialize(P); while not finish(P) do begin Q := select(P); R := create(Q); P := merge(P, Q, R); endend Uses initial, selected and genetically-manipulated populations to create next generation of solutionsUses initial, selected and genetically-manipulated populations to create next generation of solutions For example, sort solutions according to decreasing fitness and select first n solutions.For example, sort solutions according to decreasing fitness and select first n solutions.

7. Ring Design Cost effective network design is an important aspect of telecommunications networks.Cost effective network design is an important aspect of telecommunications networks. Ring design networks provide high degree of survivability in networks.Ring design networks provide high degree of survivability in networks. Bi-directional hierarchical self healing ring (BHSHR) design is an NP complete problem.Bi-directional hierarchical self healing ring (BHSHR) design is an NP complete problem. Enumeration of all designs is impractical. Topology design using integer programming techniques takes too long.Enumeration of all designs is impractical. Topology design using integer programming techniques takes too long. Heuristic search such as GAs are required.Heuristic search such as GAs are required.

8. Network Ring Design Consists of three sub-problems:Consists of three sub-problems: –routing; –capacity assignment; –ring determination. Current approaches break the design problem into serial stagesCurrent approaches break the design problem into serial stages –locally optimal designs; –sensitivity to traffic routing very high.

9. Heuristic Approaches to Network Design Topology design: two distinct classesTopology design: two distinct classes –Start with a fully-meshed network and remove capacity by link reduction. Examples of link reduction techniques are the Branch X-change and Concave Branch elimination algorithms. –Start with an empty network and add links as traffic is routed. Ring designRing design –Route traffic using Dijkstra’s (or other) shortest path algorithm –Determine link capacities –Use a modified depth first search (DFS) algorithm to generate ring covering

10. GA representation Representation encompasses all dimensions of the design problem.Representation encompasses all dimensions of the design problem. Hybrid bit and permutation representation.Hybrid bit and permutation representation.

11. Routing representation Large networks contain exponentially increasing number of routes. Only consider k possible paths for each T ij i.e. s = ceil (log2 k) bits are required. For n nodes, sn(n-1) bits are required, e.g. n=20, k=8, 1140 bits are required. Routing Table Link Bandwidths Ring Design

12. Bandwidth representation Store index into an array of permitted bandwidths augment with zero implying no link can bias choice of bandwidth by including multiple entries for single bandwidth Routing Table Link Bandwidths Ring Design

13. Ring Covering representation Consists of two segments Permutation of nodes in the graph n permutation of edges, one for each node in the graph

14. Ring Covering Algorithm Select starting node from node permutation.Select starting node from node permutation. Select end node by using first link in link permutation for node.Select end node by using first link in link permutation for node. Use DFS to find route to node at other end of link.Use DFS to find route to node at other end of link. Repeat above until all links are covered.Repeat above until all links are covered.

15. GA Fitness Function Terms for: - cost of routing; - cost of providing bandwidth; - cost of ring; - cost of inter-ring traffic.

16. GA Fitness Function Penalty Terms Terms for: - excessive link utilization and infeasible link utilizations; - infeasible ring structures and penalties for links in multiple rings.

17. Class 2: Results

18. Class 2: Rings Rings exhibit strong COI correlation. Few edges used multiple times.

19. Class 2: Fitness Variation Rapid convergence to feasible, cost effective solution. Small number (90,000) of potential designs evaluated.

20. Greedy search Two stage process used:Two stage process used: –Initialization step Fully meshed network generated with zero bandwidth links.Fully meshed network generated with zero bandwidth links. Generate k shortest paths for all traffic, Tij.Generate k shortest paths for all traffic, Tij. –Stage 1 Route each traffic element along one of k shortest paths such that the increase in network cost due to allocating bandwidth to links is locally minimal.Route each traffic element along one of k shortest paths such that the increase in network cost due to allocating bandwidth to links is locally minimal. Compute loadings on links and remove zero bandwidth links.Compute loadings on links and remove zero bandwidth links.

21. Ring computation Stage 2Stage 2 –Depth first search used to find ring structures by ordering nodes according to Pr(i), choosing the most expensive outbound link and searching until the remote end of the link is visited. –As rings are found using DFS, node priorities are recalculated and new DFSes are initiated from the highest priority node. A ring cover is computed when no link remains uncovered.

22. GA summary GAs provide an effective mechanism for network designGAs provide an effective mechanism for network design –Feasible, cost effective networks can be designed; –a one-step design process is possible; –designs are lower cost than heuristics used for comparison; –The integration of simple local optimisation heuristics is desirable.