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Optimizing genetic algorithm strategies for evolving networks

Optimizing genetic algorithm strategies for evolving networks. Matthew Berryman. Pleiotropy. Single agent performing multiple tasks. Example 1: single protein such as p53 involved in several regulatory pathways. Example 2: single server performing multiple tasks such as email, web server.

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Optimizing genetic algorithm strategies for evolving networks

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  1. Optimizing genetic algorithm strategies for evolving networks Matthew Berryman

  2. Pleiotropy • Single agent performing multiple tasks. • Example 1: single protein such as p53 involved in several regulatory pathways. • Example 2: single server performing multiple tasks such as email, web server.

  3. Redundancy • Multiple agents performing same task. • Example 1: some level of redundancy between bicoid and nanos/caudual in anterior-posterior axis formation in Drosophila. • Example 2: load-sharing web servers.

  4. Tradeoffs and combinations • Redundancy: high robustness, high cost. • Pleiotropy: low robustness, low cost. • Combine both pleiotropy and redundancy to get an optimal combination of high redundancy and low cost.

  5. Network parameters • Set of clients, C, and set of servers, S. • Positions of clients and servers set at random but with minimum spacing. • Each client assigned a traffic value • Each server has a fixed amount of traffic it can serve, Ts. • Utilization (ideally between 0.75 and 0.85)

  6. Measuring redundancy and pleiotropy • Each client i has out degree Oi = number of links out of client • Each server j has in degree Ij = number of links into server • Redundancy • Pleiotropy

  7. Fitness function • F=R/P • R = reliability, P = cost • Minimize P, maximize R => maximize F

  8. Origin of the species • Mutations: • add links, remove links from set of edges, • add servers, remove servers from set S. • Crossover (mating): • for two networks with sets of nodes (clients and servers), Naand Nb, and edges, and form a new network • Selection: only the fittest (5) reproduce. • Population size is kept constant at 15 (rank selection)

  9. Let’s watch some sex

  10. Previous results - stuck in a rut

  11. ResultsLink failure probability = 0.001%

  12. ResultsLink failure probability = 10%

  13. Results: convergence times Varying population size Varying link failure probability

  14. Conclusions and future directions • Crossover operator allows the GA to converge much faster than mutation alone. • Cost function improved by using Dijsktra’s algorithm: optimizing towards minimum cost for a given reliability. • More work needed to analyze the convergence time -- use a simple network with known results, get rid of link failures and server replacement. • Multi-objective evolutionary algorithms (multiple fitness functions

  15. Dijkstra’s algorithm • Given an adjacency matrix, A, we compute the distance matrix D in (min,+) matrix multiplications.

  16. Alternative approach • Instead of clients, have a set of edge routers (eg DSL router for a business), connecting a set of data streams di to a server.

  17. Alternative approach: in pictures • Instead of clients, have a set of edge routers (eg DSL router for a business), connecting a set of data streams di to a server.

  18. Alternative fitness function • F=R/P • R = reliability, P = cost • Minimize P, maximize R => maximize F

  19. Results: alternative cost function

  20. Results: alternative cost function

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