1. The 2st Chinese Workshop on Evolutionary Computation and Learning
Utilizing Population Distribution Information in Evolutionary Algorithms
Yong Wang
Associate Professor, PhD Supervisor
School of Information Science and Engineering,
Central South University

2. Evolutionary Algorithms (EAs)
Outline of My Talk
Evolutionary Algorithms (EAs)
DE with Single Population Distribution Information
DE with Cumulative Population Distribution Information
Conclusion 2

3. Evolutionary Algorithms (EAs)
Outline of My Talk
Evolutionary Algorithms (EAs)
DE with Single Population Distribution Information
DE with Cumulative Population Distribution Information
Conclusion 3

4. The Framework of EAs the first individual the second individual
Population
the NPth individual
Selection x y
f(x,y)
Replacement/
Selection
Parent Set
Crossover +
Mutation
New Solutions 4

5. The Main Paradigms of EAs
Genetic algorithm (GA)
Evolution strategy (ES)
Evolutionary programming (EP)
Ant colony optimization (ACO)
Estimation of Distribution Algorithm (EDA)
Particle swarm optimization (PSO)
Differential evolution (DE) …
the most popular paradigms in the current studies 5

6. Differential Evolution (1/3)
DE includes three main operators, i.e., mutation operator, crossover operator, and selection operator.
R. Storn and K. Price. Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces, Berkeley, CA, Tech. Rep. TR , 1995.
K. Price, R. Storn, and J. Lampinen. Differential Evolution—A Practical Approach to Global Optimization. Berlin, Germany: Springer-Verlag, 2005. 6

7. Differential Evolution (2/3)
The framework of DE
the target vectors
Remark: mutation + crossover = trial vector generation strategy 7

8. Differential Evolution (3/3)
mutation
DE/rand/1bin
crossover
the triangle denotes the trial vector 8

9. Particle Swarm Optimization (1/3)
The movement equation of the classic PSO
velocity update equation
position update equation
cognition part
social part
Remark: in PSO, each variable is updated independently
J. Kennedy and R. C. Eberhart. Particle swarm optimization. in Proc. IEEE Int. Conf. Neural Networks, 1995, pp 9

10. Particle Swarm Optimization (2/3)
The principle of the movement equation
the global version 10

11. Particle Swarm Optimization (3/3)
The framework of PSO 11

12. Why are EAs effective? Exploration Exploitation Diversity Convergence12

13. CMA-ES (1/3)
N. Hansen and A. Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evolutionary computation, vol. 9, no. 2, pp , 2001. 13

14. CMA-ES (2/3)
contour
An Example 14

15. CMA-ES (3/3)
Rank-μ-Update 15

16. The shortcoming of CMA-ES
Remark: CMA-ES is very likely to converge into a larger basin of attraction! 16

17. Evolutionary Algorithms (EAs)
Outline of My Talk
Evolutionary Algorithms (EAs)
DE with Single Population Distribution Information
DE with Cumulative Population Distribution Information
Conclusion 17

18. Motivation
The commonly used crossover operators of DE are dependent mainly on the coordinate system
Y. Wang, H.-X. Li, T. Huang, and L Li. Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Applied Soft Computing, vol. 18, pp , (CoBiDE) 18

19. CoBiDE (1/3)
Utilizing single population distribution information in DE 19

20. CoBiDE (2/3)
The first issue: Which individuals should be chosen for computing the covariance matrix
The second issue: How to determine the probability that the crossover is implemented in the Eigen coordinate system 20

21. CoBiDE (3/3) The third issue: the variance will decease significantly21

22. Evolutionary Algorithms (EAs)
Outline of My Talk
Evolutionary Algorithms (EAs)
DE with Single Population Distribution Information
DE with Cumulative Population Distribution Information
Conclusion 22

23. Motivation
Single population fails to contain enough information to reliably estimate the covariance matrix.
Moreover, some extra parameters have been introduced.
Y. Wang, H.-X. Li, T. Huang, and L Li. Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Applied Soft Computing, vol. 18, pp , 2014.
S. Guo and C. Yang. Enhancing differential evolution utilizing Eigenvector-based crossover operator. IEEE Trans. Evol. Comput., vol. 19, no. 1, pp , 2015. 23

24. CPI-DE (1/3)
We make use of the cumulative distribution information of the population to establish an appropriate coordinate system for DE’s crossover
The algorithmic framework
Y. Wang, Z.-Z. Liu, H.-X. Li, and G. G. Yen. Utilizing cumulative population distribution information in differential evolution. Submitted, (CPI-DE) 24

25. CPI-DE (2/3) Rank-NP-Update of the Covariance Matrix in DE
Rank-μ-Update in CMA-ES
cumulative population
distribution information 25

26. CPI-DE (3/3)
Crossover in the Eigen Coordination System 26

27. Evolutionary Algorithms (EAs)
Outline of My Talk
Evolutionary Algorithms (EAs)
DE with Single Population Distribution Information
DE with Cumulative Population Distribution Information
Conclusion 27

28. Conclusion
EAs are population-based optimization algorithms; however, population distribution information has not yet been widely utilized in the EA community, which makes EA inefficient.
Population distribution information is an effective tool to enhance the performance of EAs.
Cumulative population distribution information can provide a more reasonable estimator to the covariance matrix than single population distribution information.
Our idea can also be applied to other EA paradigms, such as PSO. 28

29. Thank you very much
for your attention!