Using Self-Organized Criticality for Adjusting the Parameters of a Particle Swarm
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This document summarizes a research paper that proposes using a Bak-Sneppen model to self-adaptively control three parameters (ω, c, ρ) of particle swarm optimization (PSO). The BS-PSO method was tested on benchmark optimization problems and showed competitive performance compared to other PSO variants without requiring hand-tuning of parameters. Future work is suggested to test the method in dynamic environments, investigate scalability, and further study the critical state behavior of the Bak-Sneppen model.
![[1] BK-inspired Extremal Optimization, Boettcher and
Percus, 2003
[2] Sandpile in Evolutionary Algorithms, Krink et al., 2000-
2001
[3] SOC in PSO, Løvbjerg and Krink, 2004
[4] BK model in Evolutionary Algorithms – Self-Organized
Random Immigrants GA (SORIGA), Tinós and Yang, 2008
[5] Sand Pile Mutation for Genetic Algorithms, Fernandes et
al., 2008-2012
8
ECTA 2012, Barcelona, Spain](https://image.slidesharecdn.com/psoecta2012-121003093659-phpapp01/85/Using-Self-Organized-Criticality-for-Adjusting-the-Parameters-of-a-Particle-Swarm-8-320.jpg)
![X i(t) = ρ Xi(t-1)+Xi(t-1)+Vi(t)
Vi(t) = ω Vi(t-1)+c1r1(pi-xi(t-1))+c2r2(pg-xi(t-1))
ω = 1-bs_fitness(i)
c1 =c2=1+bs_fitness(i)
ρ =random [0, 1-bs_fitness(i)]
ECTA 2012, Barcelona, Spain 11](https://image.slidesharecdn.com/psoecta2012-121003093659-phpapp01/85/Using-Self-Organized-Criticality-for-Adjusting-the-Parameters-of-a-Particle-Swarm-11-320.jpg)
Using Self-Organized Criticality for Adjusting the Parameters of a Particle Swarm
- 1. Carlos M. Fernandes1,2 J.J. Merelo1 Agostinho C. Rosa2 1Departmentof computers architecture and technology, University of Granada, Spain 2 LaSEEB-ISR-IST, Technical Univ. of Lisbon (IST), Portugal
- 2. Why? Exploration Exploitation 2 ECTA 2012, Barcelona, Spain
- 3. SOC Deterministic: parameter values change according to Adaptive: variation depends deterministic rules indirectly on the problem and search stage Self- adaptive: values evolve together with the solutions to the problem Hand-tuning 3 ECTA 2012, Barcelona, Spain
- 4. Bio-inspired: bird flock and fish school. Cultural and social interaction: cognitive, social and random factors. 4 ECTA 2012, Barcelona, Spain
- 5. X i – position of particle i (vector) V i – velocity of particle i (vector) X i(t) =Xρ Xi(t-1)+Xi(t-1)+Vi(t) i(t-1)+Vi(t) Vi(t) = Vω Vi(t-1)+c1 r1(pi-xi(t-1))+c2 r2(pg-xi(t-1)) i(t-1)+c1 r1(pi-xi(t-1))+c2 r2(pg-xi(t-1)) c 5
- 6. SOC: a state of criticality formed by self-organization in a long transient period at the border of order and chaos. The Sandpile Model ECTA 2012, Barcelona, Spain 6
- 7. Power-laws 7 ECTA 2012, Barcelona, Spain
- 8. [1] BK-inspired Extremal Optimization, Boettcher and Percus, 2003 [2] Sandpile in Evolutionary Algorithms, Krink et al., 2000- 2001 [3] SOC in PSO, Løvbjerg and Krink, 2004 [4] BK model in Evolutionary Algorithms – Self-Organized Random Immigrants GA (SORIGA), Tinós and Yang, 2008 [5] Sand Pile Mutation for Genetic Algorithms, Fernandes et al., 2008-2012 8 ECTA 2012, Barcelona, Spain
- 9. Per Bak (How Nature Works): Random numbers are arranged in a circle. At each time step, the f = 0.41 0.16 f = 0.55 lowest number, and the numbers at its two neighbours, are replaced by new random f f= 0.32 = 0.14 numbers. f = 0.91 f = 0.79 f = 0.23 f = 0.90 ECTA 2012, Barcelona, Spain 9
- 10. ECTA 2012, Barcelona, Spain 10
- 11. X i(t) = ρ Xi(t-1)+Xi(t-1)+Vi(t) Vi(t) = ω Vi(t-1)+c1r1(pi-xi(t-1))+c2r2(pg-xi(t-1)) ω = 1-bs_fitness(i) c1 =c2=1+bs_fitness(i) ρ =random [0, 1-bs_fitness(i)] ECTA 2012, Barcelona, Spain 11
- 12. ω BS model bs_fitness c PSO ρ BS species Particles 12 ECTA 2012, Barcelona, Spain
- 13. o Sphere, Rastrigin, Rosenbrock, Griewank o lbest and gbest topologies. o TVIW-PSO, RANDIW- PSO, GLbestIW-PSO and IA-PSO o Population size: n = 20 o 3000 generations 13 ECTA 2012, Barcelona, Spain
- 14. (ω, c, ρ) bs, 1.49, 0 bs, 2.0, 0 bs, bs, 0 bs, bs, 0.25 bs. bs, bs f1 3.35e+01 1.38e-15 8.30e-32 0.00e+00 0.00e+00 (1.90e+02) (3.21e-15) (3.47e-31) (0.00e+00) (0.00e+00) f2 1.67e+05 1.88e+02 8.56e+01 2.61e+01 2.60e+01 (1.17e+06) (2.53e+02) (7.98e+01) (2.66e-01) (1.58e-01) f3 2.82e+02 1.11e+02 2.02e+02 4.88e+00 3.32e+00 (4.44e+01) (2.75e+01) (4.16e+01) (7.73e+00) (7.09e+00) f4 1.63e+00 1.25e-02 1.65e-02 3.79e-03 4.51e-03 (5.93e+00) (1.26e-02) (2.24e-02) (2.29e-03) (4.00e-03) 14 ECTA 2012, Barcelona, Spain
- 15. full control PSO 1 vs. PSO 2 f1 f2 f3 f4 BS-PSO vs TVIW-PSO + + + + BS-PSO vs RANDIW-PSO + + + + BS-PSOvs GLbestIW-PSO + + + + without perturbation of position PSO 1 vs. PSO 2 f1 f2 f3 f4 BS-PSO vs TVIW-PSO + + – – BS-PSO vs RANDIW-PSO + ~ – ~ BS-PSO vs GLbestIW-PSO + + ~ + 15 ECTA 2012, Barcelona, Spain
- 16. PSO 1 vs. PSO 2 f1 f2 f3 f4 BS-PSO vs IA-PSO + + ~ + BS-PSOvs IA-PSO (bs controled ) ~ ~ + ~ 16 ECTA 2012, Barcelona, Spain
- 17. PSO 1 vs. PSO 2 f1 f2 f3 f4 BS-PSO vs TVIW-PSO + + + + BS-PSO vs RANDIW-PSO + + + + BS-PSOvs GLbestIW-PSO + + + + BS-PSO) vs IA-PSO + + ~ + 17 ECTA 2012, Barcelona, Spain
- 18. 1 0.8 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 iterations 1000 number of samples 100 10 1 0.01 0.1 1 ωi =ρi 18
- 19. o With a simple set of equations we are able to control three (four) parameters of the PSO. o The resulting algorithm is competitive with other variants of the PSO. o Full control of the PSO by BS attains good performance. o Hand-tuning is not required. 19 ECTA 2012, Barcelona, Spain
- 20. o Information (state) from PSO into the model. o Test BS-PSO on dynamic environments. o Scalability. o BS critical state: investigate the behaviour before and after the system reaches the critical state. 20 ECTA 2012, Barcelona, Spain
- 21. ECTA 2012, Barcelona, Spain 21