Self-sampling Strategies for Multimemetic Algorithms in Unstable Computational Environments
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This document discusses self-sampling strategies for multimemetic algorithms (MMAs) in unstable computational environments subject to churn. It proposes using probabilistic models to sample new individuals when populations need to be enlarged due to node failures. Experimental results show the bivariate model is superior for high churn, maintaining diversity and convergence better than random strategies. Future work aims to extend these self-sampling strategies to dynamic network topologies and more complex probabilistic models.
![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-sampling Strategies for MMAs Universidad de Málaga 6 / 18](https://image.slidesharecdn.com/presentiwinac-211028104054/85/Self-sampling-Strategies-for-Multimemetic-Algorithms-in-Unstable-Computational-Environments-6-320.jpg)
![Introduction Model Description Experimental Analysis Conclusions
Self-balancing
b
10 16
a
22 16 18 17
c
20 18
d
16 17
← ping
→ ping
→ ping
→ pong
← status?
→ h10, 4i
← push(6)
← pong
→ status?
← h20, 3i
→ request(2)
← push(2)
← pong
→ status?
← h16, 5i
→ push(1) b a
17 21
← ping
[timeout]
Compensate the loss of islands and balance population sizes2.
2
Comput Appl Math, doi:10.1016/j.cam.2015.03.047, 2015.
Self-sampling Strategies for MMAs Universidad de Málaga 9 / 18](https://image.slidesharecdn.com/presentiwinac-211028104054/85/Self-sampling-Strategies-for-Multimemetic-Algorithms-in-Unstable-Computational-Environments-9-320.jpg)
Self-sampling Strategies for Multimemetic Algorithms in Unstable Computational Environments
- 1. 6th International Work-Conference on the Interplay between Natural and Artificial Computation Self-sampling Strategies for Multimemetic Algorithms in Unstable Computational Environments Rafael Nogueras Carlos Cotta Departamento de Lenguajes y Ciencias de la Computación Universidad de Málaga, Spain IWINAC 2015, Elche-Elx, 1-5 June 2015 Self-sampling Strategies for MMAs 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-sampling Strategies for MMAs 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-sampling Strategies for MMAs Universidad de Málaga 3 / 18
- 4. Introduction Model Description Experimental Analysis Conclusions Scope Dynamic population sizing has been proposed to deal with the phenomenon of churn. 1. Enlarge populations to cope with loss of subpopulations. 2. Exchange individuals to balance subpopulation size. Goal Study EAs running on unstable computational environments with scale-free topology and fault-tolerance mechanisms: I Use of dynamic population sizes by means of probabilistic models. I Impact on performance and comparison with random strategies. Self-sampling Strategies for MMAs 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 feature 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-sampling Strategies for MMAs 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-sampling Strategies for MMAs 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 shape parameter η 1 the hazard rate increases with time. a J Grid Comput, doi: 10.1007/s10723-014-9315-6, 2015 Self-sampling Strategies for MMAs 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, 2015. Self-sampling Strategies for MMAs Universidad de Málaga 8 / 18
- 9. Introduction Model Description Experimental Analysis Conclusions Self-balancing b 10 16 a 22 16 18 17 c 20 18 d 16 17 ← ping → ping → ping → pong ← status? → h10, 4i ← push(6) ← pong → status? ← h20, 3i → request(2) ← push(2) ← pong → status? ← h16, 5i → push(1) b a 17 21 ← ping [timeout] Compensate the loss of islands and balance population sizes2. 2 Comput Appl Math, doi:10.1016/j.cam.2015.03.047, 2015. Self-sampling Strategies for MMAs Universidad de Málaga 9 / 18
- 10. Introduction Model Description Experimental Analysis Conclusions Self-sampling Strategies Self-balancing only captures the quantitative aspect of resizing: I New solutions are randomly constructed from scratch. I This method introduces diversity but does not keep up the momentum of the search. Improvement by using smart strategies: 1. Probabilistic model to estimate the population of each island to be enlarged. 2. New individuals are generated by sampling from previous model. 3. Diversity is still introduced since new individuals can be different. Self-sampling Strategies for MMAs Universidad de Málaga 10 / 18
- 11. Introduction Model Description Experimental Analysis Conclusions Self-sampling Strategies Model Definition I We consider two alternatives: I Univariate model (UMDA) → the joint distribution is the product of independent distributions: p(~ x = hv1, · · · , vni) = n Y j=1 p(xj = vj ) where p(xj = vj ) = 1 µ µ X i=1 δ(popij , vj ) Self-sampling Strategies for MMAs Universidad de Málaga 11 / 18
- 12. Introduction Model Description Experimental Analysis Conclusions Self-sampling Strategies Model Definition II I Bivariate model (COMIT) → relations among pairs of variables are assumed: p(~ x = hv1, · · · , vni) = p(xj1 = vj1 ) n Y i=2 p(xji = vji | xja(i) = vja(i) ) where j1 · · · jn is a permutation of the indices 1 · · · n built as follows: • j1 is the variable with the lowest entropy H(Xk ), • a(i) i is the permutation index of the variable which xji depends on. It is chosen as the variable that minimizes H(Xk | Xjs , s i). Self-sampling Strategies for MMAs Universidad de Málaga 12 / 18
- 13. 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-sampling Strategies for MMAs Universidad de Málaga 13 / 18
- 14. Introduction Model Description Experimental Analysis Conclusions Numerical Results Approximation to the Optimum Deviation from the optimum as a function of the churn rate. 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 LBQ rand LBQ umda LBQ comit 0.5 1 1.5 2 2.5 3 3.5 4 4.5 rank LBQcomit LBQ umda LBQrand noB Performance degrades with increasing churn rates but not in the same way for the different strategies. Self-sampling Strategies for MMAs Universidad de Málaga 14 / 18
- 15. Introduction Model Description Experimental Analysis Conclusions Numerical Results Evolution of Best Fitness Evolution of best fitness on the TRAP function for different churn rates. (Left) UMDA and (Right) COMIT. 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 LBQcomit is clearly superior in the most severe scenarios (k = 1 and k = 2). Self-sampling Strategies for MMAs Universidad de Málaga 15 / 18
- 16. Introduction Model Description Experimental Analysis Conclusions Numerical Results Evolution of Genetic Diversity Population entropy is an indicator of algorithmic convergence. (Left) UMDA and (Right) COMIT. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 evaluations entropy 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 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 evaluations entropy K = 1 K = 2 K = 5 K = 10 K = 20 LBQumda faces convergence problems as churn increases. Self-sampling Strategies for MMAs Universidad de Málaga 16 / 18
- 17. Introduction Model Description Experimental Analysis Conclusions Conclusions Resilience is a key feature on unstable computational environments. Self-sampling strategies based on probabilistic models to enlarge populations can improve the performance of the MMA, especially with severe churn. Bivariate model seems superior when churn is high. Future work: I extend to dynamically-rewired network topologies, I consider more complex probabilistic models (multivariate). Self-sampling Strategies for MMAs 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-sampling Strategies for MMAs Universidad de Málaga 18 / 18