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

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

3.  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.

5.  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 5 5 5 5 5 5 5 5 5 5 J. Rexford et al., http://www.cs.princeton.edu/courses/archive/spr06/cos461/http://www.cs.princeton.edu/courses/archive/spr06/cos461/

6.  How to set the weights?  Inversely proportional to link capacity?  Proportional to propagation delay?  Network-wide optimization based on traffic? 5 5 5 5 5 5 5 5 5 5 J. Rexford et al., http://www.cs.princeton.edu/courses/archive/spr06/cos461/http://www.cs.princeton.edu/courses/archive/spr06/cos461/

7.  Empirical way:  Network administrator experience  Trial and error  error-prone, not scalable 5 5 5 5 5 5 5 5 5 5 J. Rexford et al., http://www.cs.princeton.edu/courses/archive/spr06/cos461/http://www.cs.princeton.edu/courses/archive/spr06/cos461/

8. 5 5 5 5 10 5 5 5 5 5 5 congestion 20

10.  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

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

12.  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

13.  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

14.  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

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

17. Total Budget = 1500 300 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

18.  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

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

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

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

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

23.  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

24. PTAS NS-2 simulator Aggregated Througput Change link weights

25. 6% 15% 33%

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

27. Thank you…