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 , web server.

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.

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.

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, T s. Utilization (ideally between 0.75 and 0.85)

Measuring redundancy and pleiotropy Each client i has out degree O i = number of links out of client Each server j has in degree I j = number of links into server Redundancy Pleiotropy

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

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), N a and N b, and edges, and form a new network Selection: only the fittest (5) reproduce. Population size is kept constant at 15 (rank selection)

Let’s watch some sex

Previous results - stuck in a rut

Results Link failure probability = 0.001%

Results Link failure probability = 10%

Results: convergence times Varying population size Varying link failure probability

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

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

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

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 d i to a server.

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

Results: alternative cost function