Self-Balancing Multimemetic Algorithms in Dynamic Scale-Free Networks
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The document discusses the implementation of self-balancing multimemetic algorithms (MMAs) in dynamic scale-free networks, highlighting the challenges posed by unstable computational environments. It explores techniques such as dynamic rewiring and local decision-making to enhance fault tolerance and maintain performance despite node churn. Experimental results indicate that these strategies improve resilience and performance in variable computational landscapes.
![Introduction Model Description Experimental Analysis Conclusions
Network Topology
Algorithm 1: Barabási-Albert Model
function BA-Model (↓ m, n : N) : Network
m0 ← min(n, m);
net ← CreateClique(m0);
δ[1 . . . m0] ← m0;
for i ← m0 + 1 to n do
net ← AddNode(net);
for j ← 1 to m do
k ← Pick(δ) // Sampling w/o replacement ∝ δ
δ[k] ← δ[k] + 1;
net ← AddLink(net, i, k);
end
δ[i] ← m;
end
return net
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Self-Balancing Multimemetic Algorithms in Dynamic Scale-Free Networks
- 1. Evostar 2015 - The Leading European Event on Bio-Inspired Computation Self-Balancing Multimemetic Algorithms in Dynamic Scale-Free Networks Rafael Nogueras Carlos Cotta Departamento de Lenguajes y Ciencias de la Computación Universidad de Málaga, Spain EvoCOMPLEX 2015, Copenhagen, 8-10 April 2015 Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 1 / 18
- 2. Introduction Model Description Experimental Analysis Conclusions Parallel Computing & EAs Use of parallel and distributed models of EAs (GAs, MAs, MMAs, etc.) to improve solution quality and reduce computational times. The island model spatially organizes populations into partially isolated panmictic demes. island1 island2 island3 island4 migrants Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 2 / 18
- 3. Introduction Model Description Experimental Analysis Conclusions Emergent Paralell Environments Two emergent computational environments are offering new opportunities to EAs: I P2P networks: Equally privileged computing nodes carry out a distributed computation without need for central coordination. I Desktop Grids: Distributed networks of heterogeneous systems which typically contribute computing cycles while they are inactive (volunteer computing platforms). Churn The combined effect of multiple computing nodes leaving and entering the system along time. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 3 / 18
- 4. Introduction Model Description Experimental Analysis Conclusions Scope The connection topology of computing nodes is often fixed: Goal Study EAs running on unstable computational environments with dynamic scale-free topology: I Use of dynamic rewiring policies. I Impact on performance and interplay with other fault-tolerance techniques. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 4 / 18
- 5. Introduction Model Description Experimental Analysis Conclusions Network Topology Scale-free networks are commonly observed in many natural phenomena. They are characterized by a power-law distribution in node degrees. This kind of networks is often the result of processes driven by preferential attachment. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 10 0 10 1 10 −2 10 −1 10 0 10 1 α=−1.9346 degree P(degree) Cumulative distribution function Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 5 / 18
- 6. Introduction Model Description Experimental Analysis Conclusions Network Topology Algorithm 1: Barabási-Albert Model function BA-Model (↓ m, n : N) : Network m0 ← min(n, m); net ← CreateClique(m0); δ[1 . . . m0] ← m0; for i ← m0 + 1 to n do net ← AddNode(net); for j ← 1 to m do k ← Pick(δ) // Sampling w/o replacement ∝ δ δ[k] ← δ[k] + 1; net ← AddLink(net, i, k); end δ[i] ← m; end return net Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 6 / 18
- 7. Introduction Model Description Experimental Analysis Conclusions Instability Algorithms must be executed on platforms with multiple computing elements (processors)... ...but distributed platforms are prone to errors. 0 100 200 300 400 500 600 700 800 900 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time survival probability k=1 k=2 k=5 k=10 k=20 We assume node availability follows a Weibull distributiona: p(t1 | t0) = e − h t1 β η − t0 β ηi If the scale parameter η 1 the hazard rate increases with time. a J Grid Comput, doi: 10.1007/s10723-014-9315-6, 2015 Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 7 / 18
- 8. Introduction Model Description Experimental Analysis Conclusions Coping with Instability Computing in an unstable environment requires fault-tolerance. Classical approaches are redundancy or checkpointing. Note that: I These strategies require access to external safe storage and possibly some central monitoring. I As nodes go up and down, overall population size will fluctuate. An alternative strategy is used1: I No central command required: decision making and information exchange is done locally among neighboring islands. I Qualitative exchange of information among islands. 1 Comput Appl Math, doi: 10.1016/j.cam.2015.03.047 Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 8 / 18
- 9. Introduction Model Description Experimental Analysis Conclusions Self-Balancing Node B 10 Node A 20 Node C 25 ping pong status? status(10,3) push(5) 15 15 ping pong status? status(25,2) request(5) push(5) 20 20 msc Balancing routine for node A Node B 16 Node A 40 status(16,4) push(12) 28 28 30 ping grow(7) 37 msc Resizing population upon neighbor failure Compensate the loss of islands and balance population sizes2. 2 Comput Appl Math, 10.1016/j.cam.2015.03.047, 2015. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 9 / 18
- 10. Introduction Model Description Experimental Analysis Conclusions Dynamic Rewiring When no rewiring, networks become more sparse and even disconnected: I Restricted flow of information via migration among islands. I Disrupted functioning of balancing algorithms for frequent reinitializations from scratch. Rewiring strategy proceeds as follows: I Inactive neighbors during balancing are forgotten. I When the number of active neighbors of an island is below a threshold, additional neighbors are searched. I Rewiring is performed according to the BA model. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 10 / 18
- 11. Introduction Model Description Experimental Analysis Conclusions Dynamic Rewiring Evolution of a volatile network (nι = 32, k = 10). 1 2 3 4 5 6 7 8 9 12 13 14 16 17 18 20 21 22 23 24 25 26 27 28 29 30 32 t = 100 2 3 4 5 6 8 13 16 17 18 21 22 23 25 28 29 30 t = 250 1 2 3 4 6 11 13 16 17 18 19 21 22 23 30 t = 500 1 2 3 4 5 6 7 8 9 12 13 14 16 17 18 20 21 22 23 24 25 26 27 28 29 30 32 t = 100 2 3 4 5 6 8 13 16 17 18 21 22 23 25 28 29 30 t = 250 1 2 3 4 6 11 13 16 17 18 19 21 22 23 30 t = 500 Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 11 / 18
- 12. Introduction Model Description Experimental Analysis Conclusions Benchmark and Settings Parameters for island-based model: I nι = 32 islands and µ = 16 individuals (at the beginning). I m = 2 (BA model). Node deactivation/reactivation: I shape parameter η = 1.5. I scale parameters β = −1/ log(p) for p = 1 − (knι)−1, k ∈ {1, 2, 5, 10, 20, ∞}. Problems used: I Deb’s trap function (concatenating 32 four-bit traps). I HIFF function (using 128 bits). I MMDP (using 24 six-bit blocks). 25 runs @ 50,000 evaluations are performed for each problem and algorithm. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 12 / 18
- 13. Introduction Model Description Experimental Analysis Conclusions Numerical Results Approximation to the Optimum Deviation from the optimum as a function of the churn rate. From left to right: TRAP, HIFF and MMDP. 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 90 100 1/k deviation from optimum (%) noB noB r LBQ LBQ r 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 90 100 1/k deviation from optimum (%) noB noB r LBQ LBQ r 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 90 100 1/k deviation from optimum (%) noB noB r LBQ LBQ r Performance degrades with increasing churn rates but not in the same way for the different algorithms. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 13 / 18
- 14. Introduction Model Description Experimental Analysis Conclusions Numerical Results Evolution of Best Fitness Evolution of best fitness on the TRAP function for different churn rates. From left to right: noB, LBQ and LBQr . 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 14 16 18 20 22 24 26 28 30 32 evaluations best fitness k=1 k=2 k=5 k=10 k=20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 14 16 18 20 22 24 26 28 30 32 evaluations best fitness k=1 k=2 k=5 k=10 k=20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 14 16 18 20 22 24 26 28 30 32 evaluations best fitness k=1 k=2 k=5 k=10 k=20 Rewiring increases performance for high churn rates. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 14 / 18
- 15. Introduction Model Description Experimental Analysis Conclusions Numerical Results Spectral Analysis 10 0 10 1 10 −3 10 −2 10 −1 frequency PSD 0 0.2 0.4 0.6 0.8 1 −1.8 −1.6 −1.4 −1.2 −1 −0.8 1/k spectrum slope LBQ LBQr The dynamics for increasing churn goes from Brown noise ∝ f −2 to pink noise ∝ f −1. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 15 / 18
- 16. Introduction Model Description Experimental Analysis Conclusions Numerical Results Mean Size of Islands k = 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 16 18 20 22 24 26 28 30 32 34 evaluations mean popsize LBQ LBQr k = 2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 16 18 20 22 24 26 28 30 32 evaluations mean popsize LBQ LBQr Rewiring in the presence of high churn results in decreasing island sizes. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 16 / 18
- 17. Introduction Model Description Experimental Analysis Conclusions Conclusions Performance in unstable computational environments requires churn-aware strategies. Rewiring policies keeping the global network connectivity pattern result in increased resilience and better performance. Future work: I scalability analysis and study of the influence of network parameters, I analyze other rewiring strategies, I design more complex fault-aware policies. Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 17 / 18
- 18. Introduction Model Description Experimental Analysis Conclusions Thank You! AnySelf Project Please find us in Facebook http://facebook.com/AnySelfProject and in Twitter @anyselfproject Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 18 / 18