Bilal Gonen, Murat Yuksel, Sushil Louis University of Nevada, Reno

 Motivation & Problem definition: Intra- domain traffic engineering  Black-box problem and search algorithms.  PTAS: A hybrid search algorithm  Experimental results  Future work

 Online configuration of large-scale systems such as networks require parameter optimization (e.g. setting link weights) to be done within a limited amount of time.  This time limit is even more pressing when configuration is needed as a recovery response to a failure (link failures) in the system.

 Routers flood information to learn topology  Determine “next hop” to reach other routers…  Compute shortest paths based on link weights  Link weights configured by network operator J. Rexford et al.,

 How to set the weights?  Inversely proportional to link capacity?  Proportional to propagation delay?  Network-wide optimization based on traffic? J. Rexford et al.,

 Empirical way:  Network administrator experience  Trial and error  error-prone, not scalable J. Rexford et al.,

congestion 20

 Which algorithm is better?  NFL Theorem(Wolpert, 1997): No matter what perform metric is used, the average performance of any search algorithm will be the same over all possible problems.  General-purpose universal algorithm is impossible

 Exploration: global phase, examine overall features, supply effectiveness  Exploitation: local phase, examine microscopic features, supply efficiency

 Exploration techniques:  Random sampling  Random walk  Genetic Algorithm  Exploitation techniques:  Downhill simplex  Hillclimbing  Simulated Annealing  Hybrid  Recursive Random Search (RRS), T. Ye et al. ToN 2009

 Exploration techniques:  Random sampling  Random walk  Genetic Algorithm  Exploitation techniques:  Downhill simplex  Hillclimbing  Simulated Annealing  Hybrid  Recursive Random Search (RRS), T. Ye et al. ToN 2009

 An algorithm may be good at one class of problems, but its performance will suffer in the other problems  Key Question: How to design an evolutionary hybrid search algorithm?  search for the best search  Roulette wheel: Punish the bad algorithms and reward the good ones  trans-algorithmic  Transfer the best-so-far among the algorithms

 The best known strategy to select among slot machines for investment!  Viewing each algorithm as a slot machine!

Total Budget = Round budget = 300 Algorithm-1 Round-1 budget=100 Algorithm-2Algorithm-3 budget=100 Winner Algorithm-1 Round-2 budget=110 Algorithm-2Algorithm-3 budget=98 budget=92 Winner Algorithm-1 Round-3 budget=106 Algorithm-2Algorithm-3 budget=90 budget=104 Winner Algorithm-1 Round-4 budget=120 Algorithm-2Algorithm-3 budget=92 budget=88 Winner Algorithm-1 Round-5 budget=110 Algorithm-2Algorithm-3 budget=102 budget=88 Winner

 We used several benchmark objective functions to model the black-box system:  Square Sum function  Rastrigin function  Griewangk’s Function  Axis parallel hyper-ellipsoid function  Rotated hyper-ellipsoid function  Ackley’s Path function.  PTAS outperforms all the other three algorithms for most of the objective functions

Square Sum function: f1(x)=sum(x(i)^2), i=1:n

Griewangk's function f(x)=sum(x(i)^2/4000)-prod(cos(x(i)/sqrt(i)))+1, i=1:n

PTAS’ benefits are more pronounced when objective function changes SquareSum -> Rastrigin -> SquareSum

PTAS’ benefits are more pronounced when objective function changes Griewangks -> Rastrigin -> Griewangks

 Simulation Setup:  Ns-2  Exodus topology from Rocketfuel  # of flows: 90  # of nodes: 22  # of links: 37  Confidence interval: 80% (We repeated the optimization process 30 times to gain confidence.)  Optimization objective: minimize the overall packet drop rate. Thus, maximize aggregate network throughput

PTAS NS-2 simulator Aggregated Througput Change link weights

6% 15% 33%

 PTAS framework is applicable to the various network configuration problems, e.g.:  Random Early Detection (RED) queue management algorithm  BGP inter-domain traffic engineering

Thank you…