Chaos on Evolutionary Computing
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Usage of Chaos theory in Evolutionary Algorithms and review some applied sample on EAs.
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Chaos on Evolutionary Computing
- 1. CHAOS FOR EP Mehdi Saman Booy Evolutionary Processing 1
- 2. CONTENTS β’ Chaos Theory β’ When chaos met evolutionary β’ Applications β’ Experiment results β’ Conclusion 2
- 3. CHAOS THEORY Examples Chaos Theory 3
- 4. EXAMPLE 1 β’ Edward Lorenz creates a system to predict weather β’ extensive array of complex formulas β’ Never repeat a sequence β’ It was really like real weather β’ One day Edward wants to cheat β¦ β’ He wants to run prediction from a certain point β’ The results were wonderful!! 4 Chaos Theory
- 5. EXAMPLE 1 (CONTβD) 5 Chaos Theory
- 6. ANOTHER EXAMPLE 6 Chaos Theory Linguistic map X0=0.01 X0=0.01000001
- 7. CHAOS THEORY β’ A state of complete disorder and confusion [dictionary] β’ Phenomenon that has deterministic underlying rules behind irregular appearance [Science] Order in disorder Deterministic randomness β’ Future is completely determined by past β’ a very small change can lead a different result (batterfly effect) 7 Chaos Theory
- 8. WHEN CHAOS MET EVOLUTIONARY EA Features Chaotic System Features Chaos in Evolutionary Chaotic maps 8
- 9. EA FEATURES β’ Evolutionary algorithms are very sensitive to β’ initial population β’ Initial parameters β’ Random populations has no certain distribution So has no appropriate distribution β’ So Different execution of algorithm -> different results 9 When Chaos met evolutionary
- 10. CHAOTIC SYSTEM FEATURES β’ All rules of system is known β’ Rules: physical rules, systematic rules, β¦ β’ Initial values are very important β’ Nature is random and unpredictable β’ But most of them are well distributed 10 When Chaos met evolutionary
- 11. CHAOS IN EVOLUTIONARY β’ Evolutionary algorithms need a good distribution β’ Chaotic sequences have a good distribution β’ So β¦ ??? 11 When Chaos met evolutionary
- 12. CHAOTIC MAPS β’ Map = evolution function β’ Chaotic map is a discrete-time dynamical system running in chaotic sequence π π+1 = π π π βΆ 0 < π₯ π < 1, π = 0,1,2, β¦ β’ Chaotic maps exhibits some sort of chaotic behavior β’ Linguistic map π₯ π+1 = π 1 β π₯ π π₯ π 12 When Chaos met evolutionary
- 14. BAT ALGORITHM (BA) β’ based on the echolocation behavior of microbats β’ Bats fly randomly with velocity π£π at position π₯π = [π₯π1, π₯π2, β¦ , π₯ππ] β’ Loudness can change (A) β’ Radius of search β’ Control exploration β’ Frequency can change (f) β’ Frequency of pulse emission β’ Control exploitation β’ Loudness decay factor (πΌ) β’ Frequency increase factor (πΎ) β’ Random initial values for A, F, V, X 14 Applications
- 15. CHAOTIC BAT ALGORITHM (CBA) β’ Premature and/or false convergence is the most serious weakness of BA β’ Random initialization of parameters β’ We can use chaotic sequence for β’ Frequency initialization β’ Loudness initialization 15 Applications
- 16. ANT BEE COLONY (ABC) 16 Applications
- 17. CHAOTIC ANT BEE COLONY (CABC) β’ CABC1 : Generate chaotic population π₯π,π = π₯π πππ + πππ,π π₯π πππ₯ β π₯π πππ : π‘βππ‘ ππ ππ πππππππ‘ππ ππ¦ π πβπππ‘ππ πππ β’ CABC2 : if fitness of a food source donβt improved by πππππ‘ 2 trial β’ source is abandoned by itβs employed bee β’ Scouts of this employee start chaotic search for πππππ‘ 2 trial β’ CABC3 : CABC1 + CABC2 17 Applications Chaotic initialization of population Chaotic search
- 18. PSO β’ Particles doing optimization with respect to its local best and global best position π£π π‘+1 = π€π£π π‘ + π1 ππ ππππ π‘ β π₯π + π2(ππ ππππ π‘ β π₯π) β’ w : balance between exploration and exploitation β’ A good choice for w β’ change linearly from 0.9 to 0.4 18 Applications
- 19. PSO AIWF β’ An adaptive solution for tuning w is Adaptive Inertia Weight Factor π€ = π€ πππ + π€ πππ β π€ πππ₯ π β π πππ πππ£π β π πππ βΆ π β€ πππ£π π€ πππ₯ βΆ π>πππ£π β’ f is the value of objective function β’ If π β€ πππ£π value of w change : exploration β’ else value of w set to max : exploitation 19 Applications
- 20. PSO CLS β’ Chaotic Local Search β’ linguistic map ππ₯π π+1 = 4ππ₯π π 1 β ππ₯π π , π = 1,2, β¦ β’ Algorithm β’ ππ₯π 0 = π₯ π 0 βπ₯ πππ,π π₯ πππ₯,πβπ₯ πππ,π , i = 1,2, β¦ β’ Determine ππ₯π π+1 with linguistic map β’ π₯π π+1 = π₯ πππ,π + ππ₯π π+1 (π₯ πππ₯,π β π₯ πππ,π): convert chaotic to decision variables β’ Evaluate new solution 20 Applications
- 21. CPSO (CHAOTIC PSO) β’ Use both: β’ AIWF for exploration β’ CLS for exploitation β’ Same as standard PSO but β’ Reserve top N/5 particles β’ Use CLS to find and update best particles β’ Decrease the search space β’ Generate 4N/5 new particles and add to population 21 Applications
- 23. CBA 23 Experiment Results β’ Schewegel function
- 24. CBA 24 Experiment Results β’ Rosenbrock function
- 26. CONCLUSION β’ Chaos is a complicated theory ο β’ EAs suffer premature and false convergence β’ Chaotic sequences have a good and amazing distribution β’ Chaos helps to avoid local optima and easily escape from sub- optimal solution β’ Chaotic EAs have faster convergence 26 Chaotic Evolutionary Algorithms
- 27. REFERENCES β’ Afrabandpey, H.; Ghaffari, M.; Mirzaei, A.; Safayani, M., "A novel Bat Algorithm based on chaos for optimization tasks," Intelligent Systems (ICIS), 2014 Iranian Conference on , vol., no., pp.1,6, 4-6 Feb. 2014 β’ Bilal Alatas, Chaotic bee colony algorithms for global numerical optimization, Expert Systems with Applications, Volume 37, Issue 8, August 2010 β’ Hefny, H.A.; Azab, S.S., "Chaotic particle swarm optimization," Informatics and Systems (INFOS), 2010 The 7th International Conference on , vol., no., pp.1,8, 28-30 March 2010 β’ Bo Liu, Ling Wang, Yi-Hui Jin, Fang Tang, De-Xian Huang, Improved particle swarm optimization combined with chaos, Chaos, Solitons & Fractals, Volume 25, Issue 5, September 2005 β’ And a lots of sites, videos, blogs and β¦ for chaos concept 27
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- 29. BACKUP SLIDES 29
- 30. CHAOTIC MAPS β’ Logistic map π₯ π+1 = ππ₯ π 1 β π₯ π β’ Gauss map π₯ π+1 = 0 βΆ π₯ = 0 1 π₯ π βΆ π₯ β (0,1) β’ Sinusoidal map π₯ π+1 = sin(ππ₯ π) 30
- 31. EXPERIMENT FUNCTIONS β’ Rosenbrock function β’ Schewegel function 31