![Re-sampling Search (RS)
Multi-start single-solution structure with a high performance
Requires only 3 memory slots:
Xe (elite): global best solution
Xt (trial): trial solution
Xs (solution): obtained by
perturbing Xt
Stop criterion:
n
i=1
ρ[i]
bi −ai
2
< ε
where (bi − ai ) is the width of the
decision space D along the ith
dimension.
parameters setting:
Initial exploratory radius ρ = 40%
of the width of the decision space
Precision threshold ε = 10−6](https://image.slidesharecdn.com/rs-170417153552/85/A-seriously-simple-memetic-approach-with-a-high-performance-11-320.jpg)
![Graphical results
Function f14 from CEC2010 in 1000 dimensions
0 1e+6 2e+6 3e+6 4e+6 5e+6
10
8
10
9
10
10
10
11
10
12
Fitness function call
Fitnessvalue[Logarithmicscale]
RS
CLPSO
JADE
3SOME
MDE pBX
CCPSO2
MACh](https://image.slidesharecdn.com/rs-170417153552/85/A-seriously-simple-memetic-approach-with-a-high-performance-16-320.jpg)
A seriously simple memetic approach with a high performance
- 1. Re-sampling Search: A Seriously Simple Memetic Approach with a High Performance Fabio Caraffini, Ferrante Neri, Mario Gongora and Benjamin N. Passow De Montfort University United Kingdom 17.04.2013 (SSCI2013, Singapore)
- 2. Outline Background Ockham’s Razor in Memetic Computing Re-sampling Search (RS) Numerical/Graphical Results Conclusions and Future Developments
- 3. Background Memetic Computing (MC): structured set of heterogeneous components for solving problems Ockham’s Razor in MC: simple algorithms can display a performance which is as good as that of complex algorithms 1 1 G. Iacca, F. Neri, E. Mininno, Y.S. Ong, M.H. Lim, Ockham’s Razor in Memetic Computing: Three Stage Optimal Memetic Exploration, Information Sciences, Elsevier, Volume 188, pages 17-43, April 2012
- 4. Ockham’s Razor in MC: why simplicity? Algorithmic Design Issues A simple structure is easier to control and allows us to understand the actual importance of certain operators Complex structures often employ redundant operators which are hard to identify and whose coordination logic is not clear The increase of the algorithmic complexity is not always worth the improvement of the performances
- 5. Ockham’s Razor in MC: why simplicity? Engineering Applications Issues Complex structures: Usually require many fitness evaluations Are computationally expensive (high algorithmic overhead) Make extensive use of hardware resources (large memory footprint)
- 6. Re-sampling Search (RS) Multi-start single-solution structure with high performances Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt The local searcher’s performance highly depends on the starting point, even with uni-modal functions
- 7. Re-sampling Search (RS) Multi-start single-solution structure with high performances Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt
- 8. Re-sampling Search (RS) Multi-start single-solution structure with high performances Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt
- 9. Re-sampling Search (RS) Multi-start single-solution structure with a high performance Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt
- 10. Re-sampling Search (RS) Multi-start single-solution structure with a high performance Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt
- 11. Re-sampling Search (RS) Multi-start single-solution structure with a high performance Requires only 3 memory slots: Xe (elite): global best solution Xt (trial): trial solution Xs (solution): obtained by perturbing Xt Stop criterion: n i=1 ρ[i] bi −ai 2 < ε where (bi − ai ) is the width of the decision space D along the ith dimension. parameters setting: Initial exploratory radius ρ = 40% of the width of the decision space Precision threshold ε = 10−6
- 12. Numerical Results We considered a set of 76 problems: The CEC2005 benchmark in 30 dimensions (25 test problems) The BBOB2010 benchmark in 100 dimensions (24 test problems) The CEC2008 benchmark in 1000 dimensions (7 test problems) The CEC2010 benchmark in 1000 dimensions (20 test problems) We compared RS against 7 complex algorithms by performing the average value and the standard deviation over 100 runs, the Wilcoxon Rank-Sum test and the Holm-Bonferroni procedure.
- 13. Numerical results Table : Components and memory requirement of the algorithms under consideration Algorithm Features Memory slots CLPSO PSO structure 2 × Np modified velocity rule JADE DE structure Np+archive samples from distribution archive MA-CMA-Chains GA structure Np 1 + n2 covariance matrix driven search for multiple individuals MA-SSW-Chains GA structure Np (1 + n) Solis-Wets Local Search CCPSO2 PSO structure 2 × Np variable decomposition MDE-pBX DE structure Np+neighborhood multiple mutation strategies self adaptive parameters 3SOME single-solution structure 3 3 sequential operators trial and error coordination RS single-solution structure 3 2 operators
- 14. Numerical Results Table : Holm-Bonferroni test on the Fitness, reference algrithm = RS (Rank = 4.72e+00 ) j Optimizer Rank zj pj δ/j Hypothesis 1 CCPSO2 4.55e+00 -5.64e-01 2.87e-01 5.00e-02 Accepted 2 3SOME 4.24e+00 -1.60e+00 5.43e-02 2.50e-02 Accepted 3 MACh 4.13e+00 -1.95e+00 2.55e-02 1.67e-02 Accepted 4 MDE-pBX 3.82e+00 -2.99e+00 1.39e-03 1.25e-02 Rejected 5 CLPSO 3.43e+00 -4.25e+00 1.07e-05 1.00e-02 Rejected 6 JADE 3.09e+00 -5.38e+00 3.81e-08 8.33e-03 Rejected
- 15. Graphical results Function f5 from BBOB2010 in 100 dimensions 0 1e+5 2e+5 3e+5 4e+5 5e+5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Fitness function call Fitnessvalue RS CLPSO JADE 3SOME MDE pBX CCPSO2 MACh
- 16. Graphical results Function f14 from CEC2010 in 1000 dimensions 0 1e+6 2e+6 3e+6 4e+6 5e+6 10 8 10 9 10 10 10 11 10 12 Fitness function call Fitnessvalue[Logarithmicscale] RS CLPSO JADE 3SOME MDE pBX CCPSO2 MACh
- 17. Graphical results Average computational complexity (overhead VS dimensionality)
- 18. Conclusions and Future Developments We proposed an extremely simple Memetic Computing approach, competitive with the state-of-the-art optimization algorithms RS involves a minimal memory footprint and modest computational overhead RS is meant to be used on-board of embedded systems. Future work will involve robotic applications. At the moment we are trying to use this logic to tune the PID regulator of the heading control system of an indoor helicopter
- 19. Thank you for your attention! Any questions?